Daily Papers

Multihop reasoning remains an elusive goal as existing multihop benchmarks are known to be largely solvable via shortcuts. Can we create a question answering (QA) dataset that, by construction, requires proper multihop reasoning? To this end, we introduce a bottom-up approach that systematically selects composable pairs of single-hop questions that are connected, i.e., where one reasoning step critically relies on information from another. This bottom-up methodology lets us explore a vast space of questions and add stringent filters as well as other mechanisms targeting connected reasoning. It provides fine-grained control over the construction process and the properties of the resulting k-hop questions. We use this methodology to create MuSiQue-Ans, a new multihop QA dataset with 25K 2-4 hop questions. Relative to existing datasets, MuSiQue-Ans is more difficult overall (3x increase in human-machine gap), and harder to cheat via disconnected reasoning (e.g., a single-hop model has a 30 point drop in F1). We further add unanswerable contrast questions to produce a more stringent dataset, MuSiQue-Full. We hope our datasets will help the NLP community develop models that perform genuine multihop reasoning.

Recent open-source large reasoning models (LRMs) exhibit strong performance on complex reasoning tasks, but their large parameter count makes them prohibitively expensive for individuals. The compression of large language models (LLMs) offers an effective solution to reduce cost of computational resources. However, systematic studies on the performance of compressed LLMs in complex reasoning tasks, especially for LRMs, are lacking. Most works on quantization and pruning focus on preserving language modeling performance, while existing distillation works do not comprehensively benchmark student models based on reasoning difficulty or compression impact on knowledge and reasoning. In this paper, we benchmark compressed DeepSeek-R1 models on four different reasoning datasets (AIME 2024, FOLIO, Temporal Sequences of BIG-Bench Hard, and MuSiQue), ranging from mathematical to multihop reasoning, using quantization, distillation, and pruning methods. We benchmark 2.51-, 1.73-, and 1.58-bit R1 models that adopt dynamic quantization. We also benchmark distilled R1 models that are based on LLaMA or Qwen and run SparseGPT on them to obtain various sparsity levels. Studying the performance and behavior of compressed LRMs, we report their performance scores and test-time compute (number of tokens spent on each question). Notably, using MuSiQue, we find that parameter count has a much greater impact on LRMs' knowledge memorization than on their reasoning capability, which can inform the choice of compression techniques. Through our empirical analysis of test-time compute, we find that shorter model outputs generally achieve better performance than longer ones across several benchmarks for both R1 and its compressed variants, highlighting the need for more concise reasoning chains.

The Superficial Alignment Hypothesis posits that almost all of a language model's abilities and knowledge are learned during pre-training, while post-training is about giving a model the right style and format. We re-examine these claims by empirically studying the scaling behavior of post-training with increasing finetuning examples and evaluating them using objective task-specific standardized benchmarks. Through experiments with the Llama-3, Mistral, and Llama-2 model families of multiple sizes, we observe that, similar to the pre-training scaling laws, post-training task performance scales as a power law against the number of finetuning examples. This power law relationship holds across a broad array of capabilities, including mathematical reasoning, coding, instruction following, and multihop-reasoning. In addition, for tasks like math and multihop reasoning, we observe that a handful of examples merely align the model stylistically but do not saturate performance on the benchmarks. Model performance is instead correlated with its reasoning ability and it improves significantly with more examples, illustrating the need for holistic evaluation programs leveraging objective benchmarks in addition to measurement of alignment to human preferences. We also observe that language models are not necessarily limited to using knowledge learned during pre-training. With appropriate post-training, a model's ability to integrate new knowledge greatly improves on downstream tasks like multihop question-answering. Taken together, these results shed new light on the Superficial Alignment Hypothesis, suggesting that it is, at best, an over-simplification.

We present a new resource for the NLP community, namely a large (3.5M+ sentence) knowledge base of *generic statements*, e.g., "Trees remove carbon dioxide from the atmosphere", collected from multiple corpora. This is the first large resource to contain *naturally occurring* generic sentences, as opposed to extracted or crowdsourced triples, and thus is rich in high-quality, general, semantically complete statements. All GenericsKB sentences are annotated with their topical term, surrounding context (sentences), and a (learned) confidence. We also release GenericsKB-Best (1M+ sentences), containing the best-quality generics in GenericsKB augmented with selected, synthesized generics from WordNet and ConceptNet. In tests on two existing datasets requiring multihop reasoning (OBQA and QASC), we find using GenericsKB can result in higher scores and better explanations than using a much larger corpus. This demonstrates that GenericsKB can be a useful resource for NLP applications, as well as providing data for linguistic studies of generics and their semantics. GenericsKB is available at https://allenai.org/data/genericskb.

Large language models (LLMs) have demonstrated remarkable capabilities in a wide range of tasks, yet their application to specialized domains remains challenging due to the need for deep expertise. Retrieval-augmented generation (RAG) has emerged as a promising solution to customize LLMs for professional fields by seamlessly integrating external knowledge bases, enabling real-time access to domain-specific expertise during inference. Despite its potential, traditional RAG systems, based on flat text retrieval, face three critical challenges: (i) complex query understanding in professional contexts, (ii) difficulties in knowledge integration across distributed sources, and (iii) system efficiency bottlenecks at scale. This survey presents a systematic analysis of Graph-based Retrieval-Augmented Generation (GraphRAG), a new paradigm that revolutionizes domain-specific LLM applications. GraphRAG addresses traditional RAG limitations through three key innovations: (i) graph-structured knowledge representation that explicitly captures entity relationships and domain hierarchies, (ii) efficient graph-based retrieval techniques that enable context-preserving knowledge retrieval with multihop reasoning ability, and (iii) structure-aware knowledge integration algorithms that leverage retrieved knowledge for accurate and logical coherent generation of LLMs. In this survey, we systematically analyze the technical foundations of GraphRAG and examine current implementations across various professional domains, identifying key technical challenges and promising research directions. All the related resources of GraphRAG, including research papers, open-source data, and projects, are collected for the community in blue{https://github.com/DEEP-PolyU/Awesome-GraphRAG}.

Entities and events are crucial to natural language reasoning and common in procedural texts. Existing work has focused either exclusively on entity state tracking (e.g., whether a pan is hot) or on event reasoning (e.g., whether one would burn themselves by touching the pan), while these two tasks are often causally related. We propose CREPE, the first benchmark on causal reasoning of event plausibility and entity states. We show that most language models, including GPT-3, perform close to chance at .35 F1, lagging far behind human at .87 F1. We boost model performance to .59 F1 by creatively representing events as programming languages while prompting language models pretrained on code. By injecting the causal relations between entities and events as intermediate reasoning steps in our representation, we further boost the performance to .67 F1. Our findings indicate not only the challenge that CREPE brings for language models, but also the efficacy of code-like prompting combined with chain-of-thought prompting for multihop event reasoning.

Multimodal multihop question answering is a complex task that requires reasoning over multiple sources of information, such as images and text, to answer questions. While there has been significant progress in visual question answering, the multihop setting remains unexplored due to the lack of high-quality datasets. Current methods focus on single-hop question answering or a single modality, which makes them unsuitable for real-world scenarios such as analyzing multimodal educational materials, summarizing lengthy academic articles, or interpreting scientific studies that combine charts, images, and text. To address this gap, we propose a novel methodology, introducing the first framework for creating a high-quality dataset that enables training models for multimodal multihop question answering. Our approach consists of a 5-stage pipeline that involves acquiring relevant multimodal documents from Wikipedia, synthetically generating high-level questions and answers, and validating them through rigorous criteria to ensure quality data. We evaluate our methodology by training models on our synthesized dataset and testing on two benchmarks, our results demonstrate that, with an equal sample size, models trained on our synthesized data outperform those trained on human-collected data by 1.9 in exact match (EM) on average. We believe our data synthesis method will serve as a strong foundation for training and evaluating multimodal multihop question answering models.

Multi-hop reasoning (i.e., reasoning across two or more documents) is a key ingredient for NLP models that leverage large corpora to exhibit broad knowledge. To retrieve evidence passages, multi-hop models must contend with a fast-growing search space across the hops, represent complex queries that combine multiple information needs, and resolve ambiguity about the best order in which to hop between training passages. We tackle these problems via Baleen, a system that improves the accuracy of multi-hop retrieval while learning robustly from weak training signals in the many-hop setting. To tame the search space, we propose condensed retrieval, a pipeline that summarizes the retrieved passages after each hop into a single compact context. To model complex queries, we introduce a focused late interaction retriever that allows different parts of the same query representation to match disparate relevant passages. Lastly, to infer the hopping dependencies among unordered training passages, we devise latent hop ordering, a weak-supervision strategy in which the trained retriever itself selects the sequence of hops. We evaluate Baleen on retrieval for two-hop question answering and many-hop claim verification, establishing state-of-the-art performance.

Retrieval-augmented generation (RAG) augments large language models (LLM) by retrieving relevant knowledge, showing promising potential in mitigating LLM hallucinations and enhancing response quality, thereby facilitating the great adoption of LLMs in practice. However, we find that existing RAG systems are inadequate in answering multi-hop queries, which require retrieving and reasoning over multiple pieces of supporting evidence. Furthermore, to our knowledge, no existing RAG benchmarking dataset focuses on multi-hop queries. In this paper, we develop a novel dataset, MultiHop-RAG, which consists of a knowledge base, a large collection of multi-hop queries, their ground-truth answers, and the associated supporting evidence. We detail the procedure of building the dataset, utilizing an English news article dataset as the underlying RAG knowledge base. We demonstrate the benchmarking utility of MultiHop-RAG in two experiments. The first experiment compares different embedding models for retrieving evidence for multi-hop queries. In the second experiment, we examine the capabilities of various state-of-the-art LLMs, including GPT-4, PaLM, and Llama2-70B, in reasoning and answering multi-hop queries given the evidence. Both experiments reveal that existing RAG methods perform unsatisfactorily in retrieving and answering multi-hop queries. We hope MultiHop-RAG will be a valuable resource for the community in developing effective RAG systems, thereby facilitating greater adoption of LLMs in practice. The MultiHop-RAG and implemented RAG system is publicly available at https://github.com/yixuantt/MultiHop-RAG/.

Autonomous embodied agents live on an Internet of multimedia websites. Can they hop around multimodal websites to complete complex user tasks? Existing benchmarks fail to assess them in a realistic, evolving environment for their embodiment across websites. To answer this question, we present MMInA, a multihop and multimodal benchmark to evaluate the embodied agents for compositional Internet tasks, with several appealing properties: 1) Evolving real-world multimodal websites. Our benchmark uniquely operates on evolving real-world websites, ensuring a high degree of realism and applicability to natural user tasks. Our data includes 1,050 human-written tasks covering various domains such as shopping and travel, with each task requiring the agent to autonomously extract multimodal information from web pages as observations; 2) Multihop web browsing. Our dataset features naturally compositional tasks that require information from or actions on multiple websites to solve, to assess long-range reasoning capabilities on web tasks; 3) Holistic evaluation. We propose a novel protocol for evaluating an agent's progress in completing multihop tasks. We experiment with both standalone (multimodal) language models and heuristic-based web agents. Extensive experiments demonstrate that while long-chain multihop web tasks are easy for humans, they remain challenging for state-of-the-art web agents. We identify that agents are more likely to fail on the early hops when solving tasks of more hops, which results in lower task success rates. To address this issue, we propose a simple memory augmentation approach replaying past action trajectories to reflect. Our method significantly improved both the single-hop and multihop web browsing abilities of agents. See our code and data at https://mmina.cliangyu.com

State-of-the-art Large Language Models (LLMs) are accredited with an increasing number of different capabilities, ranging from reading comprehension, over advanced mathematical and reasoning skills to possessing scientific knowledge. In this paper we focus on their multi-hop reasoning capability: the ability to identify and integrate information from multiple textual sources. Given the concerns with the presence of simplifying cues in existing multi-hop reasoning benchmarks, which allow models to circumvent the reasoning requirement, we set out to investigate, whether LLMs are prone to exploiting such simplifying cues. We find evidence that they indeed circumvent the requirement to perform multi-hop reasoning, but they do so in more subtle ways than what was reported about their fine-tuned pre-trained language model (PLM) predecessors. Motivated by this finding, we propose a challenging multi-hop reasoning benchmark, by generating seemingly plausible multi-hop reasoning chains, which ultimately lead to incorrect answers. We evaluate multiple open and proprietary state-of-the-art LLMs, and find that their performance to perform multi-hop reasoning is affected, as indicated by up to 45% relative decrease in F1 score when presented with such seemingly plausible alternatives. We conduct a deeper analysis and find evidence that while LLMs tend to ignore misleading lexical cues, misleading reasoning paths indeed present a significant challenge.

Most existing multi-hop datasets are extractive answer datasets, where the answers to the questions can be extracted directly from the provided context. This often leads models to use heuristics or shortcuts instead of performing true multi-hop reasoning. In this paper, we propose a new multi-hop dataset, MoreHopQA, which shifts from extractive to generative answers. Our dataset is created by utilizing three existing multi-hop datasets: HotpotQA, 2WikiMultihopQA, and MuSiQue. Instead of relying solely on factual reasoning, we enhance the existing multi-hop questions by adding another layer of questioning that involves one, two, or all three of the following types of reasoning: commonsense, arithmetic, and symbolic. Our dataset is created through a semi-automated process, resulting in a dataset with 1,118 samples that have undergone human verification. We then use our dataset to evaluate five different large language models: Mistral 7B, Gemma 7B, Llama 3 (8B and 70B), and GPT-4. We also design various cases to analyze the reasoning steps in the question-answering process. Our results show that models perform well on initial multi-hop questions but struggle with our extended questions, indicating that our dataset is more challenging than previous ones. Our analysis of question decomposition reveals that although models can correctly answer questions, only a portion - 38.7% for GPT-4 and 33.4% for Llama3-70B - achieve perfect reasoning, where all corresponding sub-questions are answered correctly. Evaluation code and data are available at https://github.com/Alab-NII/morehopqa

Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms operate only on classical, triple-based graphs, whereas modern KGs often employ a hyper-relational modeling paradigm. In this paradigm, typed edges may have several key-value pairs known as qualifiers that provide fine-grained context for facts. In queries, this context modifies the meaning of relations, and usually reduces the answer set. Hyper-relational queries are often observed in real-world KG applications, and existing approaches for approximate query answering cannot make use of qualifier pairs. In this work, we bridge this gap and extend the multi-hop reasoning problem to hyper-relational KGs allowing to tackle this new type of complex queries. Building upon recent advancements in Graph Neural Networks and query embedding techniques, we study how to embed and answer hyper-relational conjunctive queries. Besides that, we propose a method to answer such queries and demonstrate in our experiments that qualifiers improve query answering on a diverse set of query patterns.

The problem of Question Answering (QA) has attracted significant research interest for long. Its relevance to language understanding and knowledge retrieval tasks, along with the simple setting makes the task of QA crucial for strong AI systems. Recent success on simple QA tasks has shifted the focus to more complex settings. Among these, Multi-Hop QA (MHQA) is one of the most researched tasks over the recent years. The ability to answer multi-hop questions and perform multi step reasoning can significantly improve the utility of NLP systems. Consequently, the field has seen a sudden surge with high quality datasets, models and evaluation strategies. The notion of `multiple hops' is somewhat abstract which results in a large variety of tasks that require multi-hop reasoning. This implies that different datasets and models differ significantly which makes the field challenging to generalize and survey. This work aims to provide a general and formal definition of MHQA task, and organize and summarize existing MHQA frameworks. We also outline the best methods to create MHQA datasets. The paper provides a systematic and thorough introduction as well as the structuring of the existing attempts to this highly interesting, yet quite challenging task.

Augmenting pretrained language models with retrievers to select the supporting documents has shown promise in effectively solving common NLP problems, including language modeling and question answering, in an interpretable way. In this paper, we first study the strengths and weaknesses of different retriever-augmented language models (REALM, kNN-LM, FiD coupled with DPR, and ATLAS and Flan-T5 coupled with Contriever) in reasoning over the retrieved statements in different tasks. We show how the retrieve-then-read models' limitations in reasoning are rooted both in the retriever module as well as the language model. Our experimental results demonstrate that the similarity metric used by the retrievers is generally insufficient for reasoning tasks. Additionally, we show that the language models in retriever-augmented models do not take the complicated relations between the statements into account, which leads to poor reasoning performance even when using the larger models. Moreover, we analyze the reasoning performance of large language models using multihop retrieval but we only observe minor improvements. Overall, this shows great room for further research in this area.

In this paper, we introduce Writing in the Margins (WiM), a new inference pattern for Large Language Models designed to optimize the handling of long input sequences in retrieval-oriented tasks. This approach leverages the chunked prefill of the key-value cache to perform segment-wise inference, which enables efficient processing of extensive contexts along with the generation and classification of intermediate information ("margins") that guide the model towards specific tasks. This method increases computational overhead marginally while significantly enhancing the performance of off-the-shelf models without the need for fine-tuning. Specifically, we observe that WiM provides an average enhancement of 7.5% in accuracy for reasoning skills (HotpotQA, MultiHop-RAG) and more than a 30.0% increase in the F1-score for aggregation tasks (CWE). Additionally, we show how the proposed pattern fits into an interactive retrieval design that provides end-users with ongoing updates about the progress of context processing, and pinpoints the integration of relevant information into the final response. We release our implementation of WiM using Hugging Face Transformers library at https://github.com/writer/writing-in-the-margins.

We propose a novel Chain Guided Retriever-reader ({\tt CGR}) framework to model the reasoning chain for multi-hop Science Question Answering. Our framework is capable of performing explainable reasoning without the need of any corpus-specific annotations, such as the ground-truth reasoning chain, or human-annotated entity mentions. Specifically, we first generate reasoning chains from a semantic graph constructed by Abstract Meaning Representation of retrieved evidence facts. A Chain-aware loss, concerning both local and global chain information, is also designed to enable the generated chains to serve as distant supervision signals for training the retriever, where reinforcement learning is also adopted to maximize the utility of the reasoning chains. Our framework allows the retriever to capture step-by-step clues of the entire reasoning process, which is not only shown to be effective on two challenging multi-hop Science QA tasks, namely OpenBookQA and ARC-Challenge, but also favors explainability.

Multi-modal large language models have seen rapid advancement alongside large language models. However, while language models can effectively leverage chain-of-thought prompting for zero or few-shot learning, similar prompting strategies are less effective for multi-modal LLMs due to modality gaps and task complexity. To address this challenge, we explore two prompting approaches: a dual-query method that separates multi-modal input analysis and answer generation into two prompting steps, and an ensemble prompting method that combines multiple prompt variations to arrive at the final answer. Although these approaches enhance the model's reasoning capabilities without fine-tuning, they introduce significant inference overhead. Therefore, building on top of these two prompting techniques, we propose a self-distillation framework such that the model can improve itself without any annotated data. Our self-distillation framework learns representation intervention modules from the reasoning traces collected from ensembled dual-query prompts, in the form of hidden representations. The lightweight intervention modules operate in parallel with the frozen original model, which makes it possible to maintain computational efficiency while significantly improving model capability. We evaluate our method on five widely-used VQA benchmarks, demonstrating its effectiveness in performing multi-hop reasoning for complex tasks.

Multi-hop QA (MHQA) involves step-by-step reasoning to answer complex questions and find multiple relevant supporting facts. However, Existing large language models'(LLMs) reasoning ability in multi-hop question answering remains exploration, which is inadequate in answering multi-hop questions. Moreover, it is unclear whether LLMs follow a desired reasoning chain to reach the right final answer. In this paper, we propose a generative question decomposition method (GenDec) from the perspective of explainable QA by generating independent and complete sub-questions based on incorporating additional extracted evidence for enhancing LLMs' reasoning ability in RAG. To demonstrate the impact, generalization, and robustness of Gendec, we conduct two experiments, the first is combining GenDec with small QA systems on paragraph retrieval and QA tasks. We secondly examine the reasoning capabilities of various state-of-the-art LLMs including GPT-4 and GPT-3.5 combined with GenDec. We experiment on the HotpotQA, 2WikihopMultiHopQA, MuSiQue, and PokeMQA datasets.

Answering multi-hop reasoning questions requires retrieving and synthesizing information from diverse sources. Large Language Models (LLMs) struggle to perform such reasoning consistently. Here we propose an approach to pinpoint and rectify multi-hop reasoning failures through targeted memory injections on LLM attention heads. First, we analyze the per-layer activations of GPT-2 models in response to single and multi-hop prompts. We then propose a mechanism that allows users to inject pertinent prompt-specific information, which we refer to as "memories," at critical LLM locations during inference. By thus enabling the LLM to incorporate additional relevant information during inference, we enhance the quality of multi-hop prompt completions. We show empirically that a simple, efficient, and targeted memory injection into a key attention layer can often increase the probability of the desired next token in multi-hop tasks, by up to 424%.

Despite readily memorizing world knowledge about entities, pre-trained language models (LMs) struggle to compose together two or more facts to perform multi-hop reasoning in question-answering tasks. In this work, we propose techniques that improve upon this limitation by relying on random walks over structured knowledge graphs. Specifically, we use soft prompts to guide LMs to chain together their encoded knowledge by learning to map multi-hop questions to random walk paths that lead to the answer. Applying our methods on two T5 LMs shows substantial improvements over standard tuning approaches in answering questions that require 2-hop reasoning.

In this study, we introduced a new benchmark consisting of a curated dataset and a defined evaluation process to assess the compositional reasoning capabilities of large language models within the chemistry domain. We designed and validated a fully automated pipeline, verified by subject matter experts, to facilitate this task. Our approach integrates OpenAI reasoning models with named entity recognition (NER) systems to extract chemical entities from recent literature, which are then augmented with external knowledge bases to form a comprehensive knowledge graph. By generating multi-hop questions across these graphs, we assess LLM performance in both context-augmented and non-context augmented settings. Our experiments reveal that even state-of-the-art models face significant challenges in multi-hop compositional reasoning. The results reflect the importance of augmenting LLMs with document retrieval, which can have a substantial impact on improving their performance. However, even perfect retrieval accuracy with full context does not eliminate reasoning errors, underscoring the complexity of compositional reasoning. This work not only benchmarks and highlights the limitations of current LLMs but also presents a novel data generation pipeline capable of producing challenging reasoning datasets across various domains. Overall, this research advances our understanding of reasoning in computational linguistics.

Transformers have achieved great success in numerous NLP tasks but continue to exhibit notable gaps in multi-step factual reasoning, especially when real-world knowledge is sparse. Recent advances in grokking have demonstrated that neural networks can transition from memorizing to perfectly generalizing once they detect underlying logical patterns - yet these studies have primarily used small, synthetic tasks. In this paper, for the first time, we extend grokking to real-world factual data and address the challenge of dataset sparsity by augmenting existing knowledge graphs with carefully designed synthetic data to raise the ratio phi_r of inferred facts to atomic facts above the threshold required for grokking. Surprisingly, we find that even factually incorrect synthetic data can strengthen emergent reasoning circuits rather than degrade accuracy, as it forces the model to rely on relational structure rather than memorization. When evaluated on multi-hop reasoning benchmarks, our approach achieves up to 95-100% accuracy on 2WikiMultiHopQA - substantially improving over strong baselines and matching or exceeding current state-of-the-art results. We further provide an in-depth analysis of how increasing phi_r drives the formation of generalizing circuits inside Transformers. Our findings suggest that grokking-based data augmentation can unlock implicit multi-hop reasoning capabilities, opening the door to more robust and interpretable factual reasoning in large-scale language models.

We study whether Large Language Models (LLMs) latently perform multi-hop reasoning with complex prompts such as "The mother of the singer of 'Superstition' is". We look for evidence of a latent reasoning pathway where an LLM (1) latently identifies "the singer of 'Superstition'" as Stevie Wonder, the bridge entity, and (2) uses its knowledge of Stevie Wonder's mother to complete the prompt. We analyze these two hops individually and consider their co-occurrence as indicative of latent multi-hop reasoning. For the first hop, we test if changing the prompt to indirectly mention the bridge entity instead of any other entity increases the LLM's internal recall of the bridge entity. For the second hop, we test if increasing this recall causes the LLM to better utilize what it knows about the bridge entity. We find strong evidence of latent multi-hop reasoning for the prompts of certain relation types, with the reasoning pathway used in more than 80% of the prompts. However, the utilization is highly contextual, varying across different types of prompts. Also, on average, the evidence for the second hop and the full multi-hop traversal is rather moderate and only substantial for the first hop. Moreover, we find a clear scaling trend with increasing model size for the first hop of reasoning but not for the second hop. Our experimental findings suggest potential challenges and opportunities for future development and applications of LLMs.

Large audio-language models (LALMs) extend the large language models with multimodal understanding in speech, audio, etc. While their performances on speech and audio-processing tasks are extensively studied, their reasoning abilities remain underexplored. Particularly, their multi-hop reasoning, the ability to recall and integrate multiple facts, lacks systematic evaluation. Existing benchmarks focus on general speech and audio-processing tasks, conversational abilities, and fairness but overlook this aspect. To bridge this gap, we introduce SAKURA, a benchmark assessing LALMs' multi-hop reasoning based on speech and audio information. Results show that LALMs struggle to integrate speech/audio representations for multi-hop reasoning, even when they extract the relevant information correctly, highlighting a fundamental challenge in multimodal reasoning. Our findings expose a critical limitation in LALMs, offering insights and resources for future research.

We investigate how large language models perform latent multi-hop reasoning in prompts like "Wolfgang Amadeus Mozart's mother's spouse is". To analyze this process, we introduce logit flow, an interpretability method that traces how logits propagate across layers and positions toward the final prediction. Using logit flow, we identify four distinct stages in single-hop knowledge prediction: (A) entity subject enrichment, (B) entity attribute extraction, (C) relation subject enrichment, and (D) relation attribute extraction. Extending this analysis to multi-hop reasoning, we find that failures often stem from the relation attribute extraction stage, where conflicting logits reduce prediction accuracy. To address this, we propose back attention, a novel mechanism that enables lower layers to leverage higher-layer hidden states from different positions during attention computation. With back attention, a 1-layer transformer achieves the performance of a 2-layer transformer. Applied to four LLMs, back attention improves accuracy on five reasoning datasets, demonstrating its effectiveness in enhancing latent multi-hop reasoning ability.

We evaluate how well Large Language Models (LLMs) latently recall and compose facts to answer multi-hop queries like "In the year Scarlett Johansson was born, the Summer Olympics were hosted in the country of". One major challenge in evaluating this ability is that LLMs may have developed shortcuts by encounters of the head entity "Scarlett Johansson" and the answer entity "United States" in the same training sequences or merely guess the answer based on frequency-based priors. To prevent shortcuts, we exclude test queries where the head and answer entities co-appear in pretraining corpora. Through careful selection of relations and facts and systematic removal of cases where models might guess answers or exploit partial matches, we construct an evaluation dataset SOCRATES (ShOrtCut-fRee lATent rEaSoning). We observe that LLMs demonstrate promising latent multi-hop reasoning abilities without exploiting shortcuts, but only for certain types of queries. For queries requiring latent recall of countries as the intermediate answer, the best models achieve 80% latent composability, but this drops to just 5% for the recall of years. Comparisons with Chain-of-Thought composability highlight a significant gap between the ability of models to reason latently versus explicitly. Analysis reveals that latent representations of the intermediate answer are constructed more often in queries with higher latent composability, and shows the emergence of latent multi-hop reasoning during pretraining.

This paper introduces an innovative approach to analyzing and improving multi-hop reasoning in AI systems by drawing inspiration from Hamiltonian mechanics. We propose a novel framework that maps reasoning chains in embedding spaces to Hamiltonian systems, allowing us to leverage powerful analytical tools from classical physics. Our method defines a Hamiltonian function that balances the progression of reasoning (kinetic energy) against the relevance to the question at hand (potential energy). Using this framework, we analyze a large dataset of reasoning chains from a multi-hop question-answering task, revealing intriguing patterns that distinguish valid from invalid reasoning. We show that valid reasoning chains have lower Hamiltonian energy and move in ways that make the best trade-off between getting more information and answering the right question. Furthermore, we demonstrate the application of this framework to steer the creation of more efficient reasoning algorithms within AI systems. Our results not only provide new insights into the nature of valid reasoning but also open up exciting possibilities for physics-inspired approaches to understanding and improving artificial intelligence.

With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose significant challenges to state-of-the-art models. Drawing inspiration from the beam search algorithm, we propose PathFinder, a tree-search-based reasoning path generation approach. It enhances diverse branching and multi-hop reasoning through the integration of dynamic decoding, enabled by varying sampling methods and parameters. Using constrained reasoning, PathFinder integrates novel quality constraints, pruning, and exploration methods to enhance the efficiency and the quality of generation. Moreover, it includes scoring and ranking features to improve candidate selection. Our approach outperforms competitive baselines on three complex arithmetic and commonsense reasoning tasks by 6% on average. Our model generalizes well to longer, unseen reasoning chains, reflecting similar complexities to beam search with large branching factors.

Large language models (LLMs) have demonstrated strong reasoning capabilities. Nevertheless, they still suffer from factual errors when tackling knowledge-intensive tasks. Retrieval-augmented reasoning represents a promising approach. However, significant challenges still persist, including inaccurate and insufficient retrieval for complex questions, as well as difficulty in integrating multi-source knowledge. To address this, we propose Beam Aggregation Reasoning, BeamAggR, a reasoning framework for knowledge-intensive multi-hop QA. BeamAggR explores and prioritizes promising answers at each hop of question. Concretely, we parse the complex questions into trees, which include atom and composite questions, followed by bottom-up reasoning. For atomic questions, the LLM conducts reasoning on multi-source knowledge to get answer candidates. For composite questions, the LLM combines beam candidates, explores multiple reasoning paths through probabilistic aggregation, and prioritizes the most promising trajectory. Extensive experiments on four open-domain multi-hop reasoning datasets show that our method significantly outperforms SOTA methods by 8.5%. Furthermore, our analysis reveals that BeamAggR elicits better knowledge collaboration and answer aggregation.

Modern systems for multi-hop question answering (QA) typically break questions into a sequence of reasoning steps, termed chain-of-thought (CoT), before arriving at a final answer. Often, multiple chains are sampled and aggregated through a voting mechanism over the final answers, but the intermediate steps themselves are discarded. While such approaches improve performance, they do not consider the relations between intermediate steps across chains and do not provide a unified explanation for the predicted answer. We introduce Multi-Chain Reasoning (MCR), an approach which prompts large language models to meta-reason over multiple chains of thought, rather than aggregating their answers. MCR examines different reasoning chains, mixes information between them and selects the most relevant facts in generating an explanation and predicting the answer. MCR outperforms strong baselines on 7 multi-hop QA datasets. Moreover, our analysis reveals that MCR explanations exhibit high quality, enabling humans to verify its answers.

The advancement of large language models (LLMs) has significantly broadened the scope of applications in natural language processing, with multi-modal LLMs extending these capabilities to integrate and interpret visual data. However, existing benchmarks for visual language models (VLMs) predominantly focus on single-image inputs, neglecting the crucial aspect of multi-image understanding. In this paper, we introduce a Multi-Image Relational Benchmark MIRB, designed to evaluate VLMs' ability to compare, analyze, and reason across multiple images. Our benchmark encompasses four categories: perception, visual world knowledge, reasoning, and multi-hop reasoning. Through a comprehensive evaluation of a wide range of open-source and closed-source models, we demonstrate that while open-source VLMs were shown to approach the performance of GPT-4V in single-image tasks, a significant performance gap remains in multi-image reasoning tasks. Our findings also reveal that even the state-of-the-art GPT-4V model struggles with our benchmark, underscoring the need for further research and development in this area. We believe our contribution of MIRB could serve as a testbed for developing the next-generation multi-modal models.

Multi-hop question answering (MHQA) requires a model to retrieve and integrate information from multiple passages to answer a complex question. Recent systems leverage the power of large language models and integrate evidence retrieval with reasoning prompts (e.g., chain-of-thought reasoning) for the MHQA task. However, the complexities in the question types (bridge v.s. comparison questions) and the reasoning types (sequential v.s. parallel reasonings) require more novel and fine-grained prompting methods to enhance the performance of MHQA under the zero-shot setting. In this paper, we propose STOC-TOT, a stochastic tree-of-thought reasoning prompting method with constrained decoding for MHQA and conduct a detailed comparison with other reasoning prompts on different question types and reasoning types. Specifically, we construct a tree-like reasoning structure by prompting the model to break down the original question into smaller sub-questions to form different reasoning paths. In addition, we prompt the model to provide a probability estimation for each reasoning path at each reasoning step. At answer time, we conduct constrained decoding on the model to generate more grounded answers and reduce hallucination. Experiments comparing STOC-TOT with two MHQA datasets and five large language models showed that our framework outperforms other reasoning prompts by a significant margin.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

Multi-hop query answering over a Knowledge Graph (KG) involves traversing one or more hops from the start node to answer a query. Path-based and logic-based methods are state-of-the-art for multi-hop question answering. The former is used in link prediction tasks. The latter is for answering complex logical queries. The logical multi-hop querying technique embeds the KG and queries in the same embedding space. The existing work incorporates First Order Logic (FOL) operators, such as conjunction (wedge), disjunction (vee), and negation (neg), in queries. Though current models have most of the building blocks to execute the FOL queries, they cannot use the dense information of multi-modal entities in the case of Multi-Modal Knowledge Graphs (MMKGs). We propose RConE, an embedding method to capture the multi-modal information needed to answer a query. The model first shortlists candidate (multi-modal) entities containing the answer. It then finds the solution (sub-entities) within those entities. Several existing works tackle path-based question-answering in MMKGs. However, to our knowledge, we are the first to introduce logical constructs in querying MMKGs and to answer queries that involve sub-entities of multi-modal entities as the answer. Extensive evaluation of four publicly available MMKGs indicates that RConE outperforms the current state-of-the-art.

Enabling Large Language Models (LLMs) to handle a wider range of complex tasks (e.g., coding, math) has drawn great attention from many researchers. As LLMs continue to evolve, merely increasing the number of model parameters yields diminishing performance improvements and heavy computational costs. Recently, OpenAI's o1 model has shown that inference strategies (i.e., Test-time Compute methods) can also significantly enhance the reasoning capabilities of LLMs. However, the mechanisms behind these methods are still unexplored. In our work, to investigate the reasoning patterns of o1, we compare o1 with existing Test-time Compute methods (BoN, Step-wise BoN, Agent Workflow, and Self-Refine) by using OpenAI's GPT-4o as a backbone on general reasoning benchmarks in three domains (i.e., math, coding, commonsense reasoning). Specifically, first, our experiments show that the o1 model has achieved the best performance on most datasets. Second, as for the methods of searching diverse responses (e.g., BoN), we find the reward models' capability and the search space both limit the upper boundary of these methods. Third, as for the methods that break the problem into many sub-problems, the Agent Workflow has achieved better performance than Step-wise BoN due to the domain-specific system prompt for planning better reasoning processes. Fourth, it is worth mentioning that we have summarized six reasoning patterns of o1, and provided a detailed analysis on several reasoning benchmarks.

Recent advances in reasoning models have demonstrated significant improvements in accuracy, particularly for complex tasks such as mathematical reasoning, by employing detailed and comprehensive reasoning processes. However, generating these lengthy reasoning sequences is computationally expensive and time-consuming. To address this inefficiency, we leverage the inherent parallelizability of certain tasks to accelerate the reasoning process. Specifically, when multiple parallel reasoning branches exist, we decode multiple tokens per step using a specialized attention mask, processing them within a single sequence, avoiding additional memory usage. Experimental results show that our method achieves over 100% speedup in decoding time while maintaining the answer quality.

Recent research developing neural network architectures with external memory have often used the benchmark bAbI question and answering dataset which provides a challenging number of tasks requiring reasoning. Here we employed a classic associative inference task from the memory-based reasoning neuroscience literature in order to more carefully probe the reasoning capacity of existing memory-augmented architectures. This task is thought to capture the essence of reasoning -- the appreciation of distant relationships among elements distributed across multiple facts or memories. Surprisingly, we found that current architectures struggle to reason over long distance associations. Similar results were obtained on a more complex task involving finding the shortest path between nodes in a path. We therefore developed MEMO, an architecture endowed with the capacity to reason over longer distances. This was accomplished with the addition of two novel components. First, it introduces a separation between memories (facts) stored in external memory and the items that comprise these facts in external memory. Second, it makes use of an adaptive retrieval mechanism, allowing a variable number of "memory hops" before the answer is produced. MEMO is capable of solving our novel reasoning tasks, as well as match state of the art results in bAbI.

Current multimodal benchmarks often conflate reasoning with domain-specific knowledge, making it difficult to isolate and evaluate general reasoning abilities in non-expert settings. To address this, we introduce VisualPuzzles, a benchmark that targets visual reasoning while deliberately minimizing reliance on specialized knowledge. VisualPuzzles consists of diverse questions spanning five categories: algorithmic, analogical, deductive, inductive, and spatial reasoning. One major source of our questions is manually translated logical reasoning questions from the Chinese Civil Service Examination. Experiments show that VisualPuzzles requires significantly less intensive domain-specific knowledge and more complex reasoning compared to benchmarks like MMMU, enabling us to better evaluate genuine multimodal reasoning. Evaluations show that state-of-the-art multimodal large language models consistently lag behind human performance on VisualPuzzles, and that strong performance on knowledge-intensive benchmarks does not necessarily translate to success on reasoning-focused, knowledge-light tasks. Additionally, reasoning enhancements such as scaling up inference compute (with "thinking" modes) yield inconsistent gains across models and task types, and we observe no clear correlation between model size and performance. We also found that models exhibit different reasoning and answering patterns on VisualPuzzles compared to benchmarks with heavier emphasis on knowledge. VisualPuzzles offers a clearer lens through which to evaluate reasoning capabilities beyond factual recall and domain knowledge.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Composing knowledge from multiple pieces of texts is a key challenge in multi-hop question answering. We present a multi-hop reasoning dataset, Question Answering via Sentence Composition(QASC), that requires retrieving facts from a large corpus and composing them to answer a multiple-choice question. QASC is the first dataset to offer two desirable properties: (a) the facts to be composed are annotated in a large corpus, and (b) the decomposition into these facts is not evident from the question itself. The latter makes retrieval challenging as the system must introduce new concepts or relations in order to discover potential decompositions. Further, the reasoning model must then learn to identify valid compositions of these retrieved facts using common-sense reasoning. To help address these challenges, we provide annotation for supporting facts as well as their composition. Guided by these annotations, we present a two-step approach to mitigate the retrieval challenges. We use other multiple-choice datasets as additional training data to strengthen the reasoning model. Our proposed approach improves over current state-of-the-art language models by 11% (absolute). The reasoning and retrieval problems, however, remain unsolved as this model still lags by 20% behind human performance.

Multi-hop Question Answering (QA) requires the machine to answer complex questions by finding scattering clues and reasoning from multiple documents. Graph Network (GN) and Question Decomposition (QD) are two common approaches at present. The former uses the "black-box" reasoning process to capture the potential relationship between entities and sentences, thus achieving good performance. At the same time, the latter provides a clear reasoning logical route by decomposing multi-hop questions into simple single-hop sub-questions. In this paper, we propose a novel method to complete multi-hop QA from the perspective of Question Generation (QG). Specifically, we carefully design an end-to-end QG module on the basis of a classical QA module, which could help the model understand the context by asking inherently logical sub-questions, thus inheriting interpretability from the QD-based method and showing superior performance. Experiments on the HotpotQA dataset demonstrate that the effectiveness of our proposed QG module, human evaluation further clarifies its interpretability quantitatively, and thorough analysis shows that the QG module could generate better sub-questions than QD methods in terms of fluency, consistency, and diversity.

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to particular domains. This has enabled the creation of powerful and adaptive routing-based "Model MoErging" methods with the goal of using expert modules to create an aggregate system with improved performance or generalization. However, existing MoErging methods often prioritize generalization to unseen tasks at the expense of performance on held-in tasks, which limits its practical applicability in real-world deployment scenarios. We observe that current token-level routing mechanisms neglect the global semantic context of the input task. This token-wise independence hinders effective expert selection for held-in tasks, as routing decisions fail to incorporate the semantic properties of the task. To address this, we propose, Global and Local Instruction Driven Expert Router (GLIDER) that integrates a multi-scale routing mechanism, encompassing a semantic global router and a learned local router. The global router leverages LLM's advanced reasoning capabilities for semantic-related contexts to enhance expert selection. Given the input query and LLM, the router generates semantic task instructions that guide the retrieval of the most relevant experts across all layers. This global guidance is complemented by a local router that facilitates token-level routing decisions within each module, enabling finer control and enhanced performance on unseen tasks. Our experiments using T5-based models for T0 and FLAN tasks demonstrate that GLIDER achieves substantially improved held-in performance while maintaining strong generalization on held-out tasks. We also perform ablations experiments to dive deeper into the components of GLIDER. Our experiments highlight the importance of our multi-scale routing that leverages LLM-driven semantic reasoning for MoErging methods.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing the reasoning ability of foundation models and has garnered significant attention. However, the reasoning process of CoT is linear, step-by-step, similar to personal logical reasoning, suitable for solving general and slightly complicated problems. On the contrary, the thinking pattern of an expert owns two prominent characteristics that cannot be handled appropriately in CoT, i.e., high-order multi-hop reasoning and multimodal comparative judgement. Therefore, the core motivation of this paper is transcending CoT to construct a reasoning paradigm that can think like an expert. The hyperedge of a hypergraph could connect various vertices, making it naturally suitable for modelling high-order relationships. Inspired by this, this paper innovatively proposes a multimodal Hypergraph-of-Thought (HoT) reasoning paradigm, which enables the foundation models to possess the expert-level ability of high-order multi-hop reasoning and multimodal comparative judgement. Specifically, a textual hypergraph-of-thought is constructed utilizing triple as the primary thought to model higher-order relationships, and a hyperedge-of-thought is generated through multi-hop walking paths to achieve multi-hop inference. Furthermore, we devise a visual hypergraph-of-thought to interact with the textual hypergraph-of-thought via Cross-modal Co-Attention Graph Learning for multimodal comparative verification. Experimentations on the ScienceQA benchmark demonstrate the proposed HoT-based T5 outperforms CoT-based GPT3.5 and chatGPT, which is on par with CoT-based GPT4 with a lower model size.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Recent work on neural algorithmic reasoning has investigated the reasoning capabilities of neural networks, effectively demonstrating they can learn to execute classical algorithms on unseen data coming from the train distribution. However, the performance of existing neural reasoners significantly degrades on out-of-distribution (OOD) test data, where inputs have larger sizes. In this work, we make an important observation: there are many different inputs for which an algorithm will perform certain intermediate computations identically. This insight allows us to develop data augmentation procedures that, given an algorithm's intermediate trajectory, produce inputs for which the target algorithm would have exactly the same next trajectory step. Then, we employ a causal framework to design a corresponding self-supervised objective, and we prove that it improves the OOD generalisation capabilities of the reasoner. We evaluate our method on the CLRS algorithmic reasoning benchmark, where we show up to 3times improvements on the OOD test data.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Recent studies on transformer-based language models show that they can answer questions by reasoning over knowledge provided as part of the context (i.e., in-context reasoning). However, since the available knowledge is often not filtered for a particular question, in-context reasoning can be sensitive to distractor facts, additional content that is irrelevant to a question but that may be relevant for a different question (i.e., not necessarily random noise). In these situations, the model fails to distinguish the knowledge that is necessary to answer the question, leading to spurious reasoning and degraded performance. This reasoning failure contrasts with the model's apparent ability to distinguish its contextual knowledge from all the knowledge it has memorized during pre-training. Following this observation, we propose teaching the model to reason more robustly by folding the provided contextual knowledge into the model's parameters before presenting it with a question. Our method, RECKONING, is a bi-level learning algorithm that teaches language models to reason by updating their parametric knowledge through back-propagation, allowing them to then answer questions using the updated parameters. During training, the inner loop rapidly adapts a copy of the model weights to encode contextual knowledge into its parameters. In the outer loop, the model learns to use the updated weights to reproduce and answer reasoning questions about the memorized knowledge. Our experiments on two multi-hop reasoning datasets show that RECKONING's performance improves over the in-context reasoning baseline (by up to 4.5%). We also find that compared to in-context reasoning, RECKONING generalizes better to longer reasoning chains unseen during training, is more robust to distractors in the context, and is more computationally efficient when multiple questions are asked about the same knowledge.

Deep iterative chain-of-thought (CoT) reasoning enables LLMs to tackle complex tasks by progressively activating relevant pre-trained knowledge. However, it faces challenges in ensuring continual improvement and determining a stopping criterion. In this paper, we investigate whether the relevant knowledge that contributes directly to solving the given question can be activated from the initial reasoning path, thus circumventing the need for iterative refinement. Our experiments reveal that increasing the diversity of initial reasoning paths can achieve comparable or superior performance, a concept we term breadth reasoning. However, existing breadth reasoning approaches, such as self-consistency, offer limited diversity. To address this limitation, we propose a simple yet effective method that enhances reasoning breadth by integrating contextual exploration with reduced sampling randomness. Extensive experiments demonstrate that our approach significantly outperforms deep iterative reasoning. Our code is provided in https://github.com/zongqianwu/breadth.

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. However, effectively extending these capabilities into multimodal contexts-where models must integrate both visual and textual inputs-continues to be a significant challenge. Multimodal reasoning introduces complexities, such as handling conflicting information across modalities, which require models to adopt advanced interpretative strategies. Addressing these challenges involves not only sophisticated algorithms but also robust methodologies for evaluating reasoning accuracy and coherence. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs. Through a thorough and up-to-date comparison, we clearly formulate core reasoning challenges and opportunities, highlighting practical methods for post-training optimization and test-time inference. Our work provides valuable insights and guidance, bridging theoretical frameworks and practical implementations, and sets clear directions for future research.

Large multimodal models extend the impressive capabilities of large language models by integrating multimodal understanding abilities. However, it is not clear how they can emulate the general intelligence and reasoning ability of humans. As recognizing patterns and abstracting concepts are key to general intelligence, we introduce PuzzleVQA, a collection of puzzles based on abstract patterns. With this dataset, we evaluate large multimodal models with abstract patterns based on fundamental concepts, including colors, numbers, sizes, and shapes. Through our experiments on state-of-the-art large multimodal models, we find that they are not able to generalize well to simple abstract patterns. Notably, even GPT-4V cannot solve more than half of the puzzles. To diagnose the reasoning challenges in large multimodal models, we progressively guide the models with our ground truth reasoning explanations for visual perception, inductive reasoning, and deductive reasoning. Our systematic analysis finds that the main bottlenecks of GPT-4V are weaker visual perception and inductive reasoning abilities. Through this work, we hope to shed light on the limitations of large multimodal models and how they can better emulate human cognitive processes in the future (Our data and code will be released publicly at https://github.com/declare-lab/LLM-PuzzleTest).

Retrieval-augmented generation (RAG) offers an effective approach for addressing question answering (QA) tasks. However, the imperfections of the retrievers in RAG models often result in the retrieval of irrelevant information, which could introduce noises and degrade the performance, especially when handling multi-hop questions that require multiple steps of reasoning. To enhance the multi-hop reasoning ability of RAG models, we propose TRACE. TRACE constructs knowledge-grounded reasoning chains, which are a series of logically connected knowledge triples, to identify and integrate supporting evidence from the retrieved documents for answering questions. Specifically, TRACE employs a KG Generator to create a knowledge graph (KG) from the retrieved documents, and then uses an Autoregressive Reasoning Chain Constructor to build reasoning chains. Experimental results on three multi-hop QA datasets show that TRACE achieves an average performance improvement of up to 14.03% compared to using all the retrieved documents. Moreover, the results indicate that using reasoning chains as context, rather than the entire documents, is often sufficient to correctly answer questions.

Commonsense question answering (QA) research requires machines to answer questions based on commonsense knowledge. However, this research requires expensive labor costs to annotate data as the basis of research, and models that rely on fine-tuning paradigms only apply to specific tasks, rather than learn a general commonsense reasoning ability. As a more robust method, zero-shot commonsense question answering shows a good prospect. The current zero-shot framework tries to convert triples in commonsense knowledge graphs (KGs) into QA-form samples as the pre-trained data source to incorporate commonsense knowledge into the model. However, this method ignores the multi-hop relationship in the KG, which is also an important central problem in commonsense reasoning. In this paper, we propose a novel multi-hop commonsense knowledge injection framework. Specifically, it explores multi-hop reasoning paradigm in KGs that conform to linguistic logic, and we further propose two multi-hop QA generation methods based on KGs. Then, we utilize contrastive learning to pre-train the model with the synthetic QA dataset to inject multi-hop commonsense knowledge. Extensive experiments on five commonsense question answering benchmarks demonstrate that our framework achieves state-of-art performance.

We study the interpretability issue of task-oriented dialogue systems in this paper. Previously, most neural-based task-oriented dialogue systems employ an implicit reasoning strategy that makes the model predictions uninterpretable to humans. To obtain a transparent reasoning process, we introduce neuro-symbolic to perform explicit reasoning that justifies model decisions by reasoning chains. Since deriving reasoning chains requires multi-hop reasoning for task-oriented dialogues, existing neuro-symbolic approaches would induce error propagation due to the one-phase design. To overcome this, we propose a two-phase approach that consists of a hypothesis generator and a reasoner. We first obtain multiple hypotheses, i.e., potential operations to perform the desired task, through the hypothesis generator. Each hypothesis is then verified by the reasoner, and the valid one is selected to conduct the final prediction. The whole system is trained by exploiting raw textual dialogues without using any reasoning chain annotations. Experimental studies on two public benchmark datasets demonstrate that the proposed approach not only achieves better results, but also introduces an interpretable decision process.

Recent advances in large language models have demonstrated remarkable reasoning capabilities through Chain of Thought (CoT) prompting, but often at the cost of excessive verbosity in their intermediate outputs, which increases computational overhead. We introduce Sketch-of-Thought (SoT), a novel prompting framework that combines cognitive-inspired reasoning paradigms with linguistic constraints to minimize token usage while preserving reasoning accuracy. SoT is designed as a flexible framework that can incorporate any custom reasoning paradigms based on cognitive science, and we instantiate it with three such paradigms - Conceptual Chaining, Chunked Symbolism, and Expert Lexicons - each tailored to different reasoning tasks and selected dynamically via a lightweight routing model. Through comprehensive evaluation across 15 reasoning datasets with multiple languages and multimodal scenarios, we demonstrate that SoT achieves token reductions of 76% with negligible accuracy impact. In certain domains like mathematical and multi-hop reasoning, it even improves accuracy while using significantly fewer tokens. Our code is publicly available: https://www.github.com/SimonAytes/SoT.

While sentiment analysis systems try to determine the sentiment polarities of given targets based on the key opinion expressions in input texts, in implicit sentiment analysis (ISA) the opinion cues come in an implicit and obscure manner. Thus detecting implicit sentiment requires the common-sense and multi-hop reasoning ability to infer the latent intent of opinion. Inspired by the recent chain-of-thought (CoT) idea, in this work we introduce a Three-hop Reasoning (THOR) CoT framework to mimic the human-like reasoning process for ISA. We design a three-step prompting principle for THOR to step-by-step induce the implicit aspect, opinion, and finally the sentiment polarity. Our THOR+Flan-T5 (11B) pushes the state-of-the-art (SoTA) by over 6% F1 on supervised setup. More strikingly, THOR+GPT3 (175B) boosts the SoTA by over 50% F1 on zero-shot setting. Our code is open at https://github.com/scofield7419/THOR-ISA.

Large Multimodal Models (LMMs) have achieved strong performance across a range of vision and language tasks. However, their spatial reasoning capabilities are under-investigated. In this paper, we construct a novel VQA dataset, Spatial-MM, to comprehensively study LMMs' spatial understanding and reasoning capabilities. Our analyses on object-relationship and multi-hop reasoning reveal several important findings. Firstly, bounding boxes and scene graphs, even synthetic ones, can significantly enhance LMMs' spatial reasoning. Secondly, LMMs struggle more with questions posed from the human perspective than the camera perspective about the image. Thirdly, chain of thought (CoT) prompting does not improve model performance on complex multi-hop questions involving spatial relations. % Moreover, spatial reasoning steps are much less accurate than non-spatial ones across MLLMs. Lastly, our perturbation analysis on GQA-spatial reveals that LMMs are much stronger at basic object detection than complex spatial reasoning. We believe our benchmark dataset and in-depth analyses can spark further research on LMMs spatial reasoning. Spatial-MM benchmark is available at: https://github.com/FatemehShiri/Spatial-MM

The releases of OpenAI's o1 and o3 mark a significant paradigm shift in Large Language Models towards advanced reasoning capabilities. Notably, o3 outperformed humans in novel problem-solving and skill acquisition on the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI). However, this benchmark is limited to symbolic patterns, whereas humans often perceive and reason about multimodal scenarios involving both vision and language data. Thus, there is an urgent need to investigate advanced reasoning capabilities in multimodal tasks. To this end, we track the evolution of the GPT-[n] and o-[n] series models on challenging multimodal puzzles, requiring fine-grained visual perception with abstract or algorithmic reasoning. The superior performance of o1 comes at nearly 750 times the computational cost of GPT-4o, raising concerns about its efficiency. Our results reveal a clear upward trend in reasoning capabilities across model iterations, with notable performance jumps across GPT-series models and subsequently to o1. Nonetheless, we observe that the o1 model still struggles with simple multimodal puzzles requiring abstract reasoning. Furthermore, its performance in algorithmic puzzles remains poor. We plan to continuously track new models in the series and update our results in this paper accordingly. All resources used in this evaluation are openly available https://github.com/declare-lab/LLM-PuzzleTest.

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

Large language models have demonstrated impressive reasoning capabilities but are inherently limited by their knowledge reservoir. Retrieval-augmented reasoning mitigates this limitation by allowing LLMs to query external resources, but existing methods often retrieve irrelevant or noisy information, hindering accurate reasoning. In this paper, we propose AutoRefine, a reinforcement learning post-training framework that adopts a new ``search-and-refine-during-think'' paradigm. AutoRefine introduces explicit knowledge refinement steps between successive search calls, enabling the model to iteratively filter, distill, and organize evidence before generating an answer. Furthermore, we incorporate tailored retrieval-specific rewards alongside answer correctness rewards using group relative policy optimization. Experiments on single-hop and multi-hop QA benchmarks demonstrate that AutoRefine significantly outperforms existing approaches, particularly in complex, multi-hop reasoning scenarios. Detailed analysis shows that AutoRefine issues frequent, higher-quality searches and synthesizes evidence effectively.

A key limitation in current datasets for multi-hop reasoning is that the required steps for answering the question are mentioned in it explicitly. In this work, we introduce StrategyQA, a question answering (QA) benchmark where the required reasoning steps are implicit in the question, and should be inferred using a strategy. A fundamental challenge in this setup is how to elicit such creative questions from crowdsourcing workers, while covering a broad range of potential strategies. We propose a data collection procedure that combines term-based priming to inspire annotators, careful control over the annotator population, and adversarial filtering for eliminating reasoning shortcuts. Moreover, we annotate each question with (1) a decomposition into reasoning steps for answering it, and (2) Wikipedia paragraphs that contain the answers to each step. Overall, StrategyQA includes 2,780 examples, each consisting of a strategy question, its decomposition, and evidence paragraphs. Analysis shows that questions in StrategyQA are short, topic-diverse, and cover a wide range of strategies. Empirically, we show that humans perform well (87%) on this task, while our best baseline reaches an accuracy of sim66%.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named OmegaPRM for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train a Process Reward Model (PRM). Utilizing this fully automated process supervision alongside the weighted self-consistency algorithm, we have enhanced the instruction tuned Gemini Pro model's math reasoning performance, achieving a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from the 51\% base model performance. Additionally, the entire process operates without any human intervention, making our method both financially and computationally cost-effective compared to existing methods.

Recent advancements in long-context modeling have enhanced language models (LMs) for complex tasks across multiple NLP applications. Despite this progress, we find that these models struggle with multi-hop reasoning and exhibit decreased performance in the presence of noisy contexts. In this paper, we introduce Reasoning with Attributions, a novel approach that prompts LMs to supply attributions for each assertion during their reasoning. We validate our approach through experiments on three multi-hop datasets, employing both proprietary and open-source models, and demonstrate its efficacy and resilience. Furthermore, we explore methods to augment reasoning capabilities via fine-tuning and offer an attribution-annotated dataset and a specialized training strategy. Our fine-tuned model achieves competitive performance on multi-hop reasoning benchmarks, closely paralleling proprietary LMs such as ChatGPT and Claude-instant.

Fact verification aims to automatically probe the veracity of a claim based on several pieces of evidence. Existing works are always engaging in the accuracy improvement, let alone the explainability, a critical capability of fact verification system. Constructing an explainable fact verification system in a complex multi-hop scenario is consistently impeded by the absence of a relevant high-quality dataset. Previous dataset either suffer from excessive simplification or fail to incorporate essential considerations for explainability. To address this, we present EX-FEVER, a pioneering dataset for multi-hop explainable fact verification. With over 60,000 claims involving 2-hop and 3-hop reasoning, each is created by summarizing and modifying information from hyperlinked Wikipedia documents. Each instance is accompanied by a veracity label and an explanation that outlines the reasoning path supporting the veracity classification. Additionally, we demonstrate a novel baseline system on our EX-FEVER dataset, showcasing document retrieval, explanation generation, and claim verification and observe that existing fact verification models trained on previous datasets struggle to perform well on our dataset. Furthermore, we highlight the potential of utilizing Large Language Models in the fact verification task. We hope our dataset could make a significant contribution by providing ample opportunities to explore the integration of natural language explanations in the domain of fact verification.

Relation Extraction (RE) has been extended to cross-document scenarios because many relations are not simply described in a single document. This inevitably brings the challenge of efficient open-space evidence retrieval to support the inference of cross-document relations, along with the challenge of multi-hop reasoning on top of entities and evidence scattered in an open set of documents. To combat these challenges, we propose MR.COD (Multi-hop evidence retrieval for Cross-document relation extraction), which is a multi-hop evidence retrieval method based on evidence path mining and ranking. We explore multiple variants of retrievers to show evidence retrieval is essential in cross-document RE. We also propose a contextual dense retriever for this setting. Experiments on CodRED show that evidence retrieval with MR.COD effectively acquires crossdocument evidence and boosts end-to-end RE performance in both closed and open settings.

Large Language Models (LLMs) have shown impressive capabilities in transforming natural language questions about relational databases into SQL queries. Despite recent improvements, small LLMs struggle to handle questions involving multiple tables and complex SQL patterns under a Zero-Shot Learning (ZSL) setting. Supervised Fine-Tuning (SFT) partially compensate the knowledge deficits in pretrained models but falls short while dealing with queries involving multi-hop reasoning. To bridge this gap, different LLM training strategies to reinforce reasoning capabilities have been proposed, ranging from leveraging a thinking process within ZSL, including reasoning traces in SFT, or adopt Reinforcement Learning (RL) strategies. However, the influence of reasoning on Text2SQL performance is still largely unexplored. This paper investigates to what extent LLM reasoning capabilities influence their Text2SQL performance on four benchmark datasets. To this end, it considers the following LLM settings: (1) ZSL, including general-purpose reasoning or not; (2) SFT, with and without task-specific reasoning traces; (3) RL, leveraging execution accuracy as primary reward function; (4) SFT+RL, i.e, a two-stage approach that combines SFT and RL. The results show that general-purpose reasoning under ZSL proves to be ineffective in tackling complex Text2SQL cases. Small LLMs benefit from SFT with reasoning much more than larger ones, bridging the gap of their (weaker) model pretraining. RL is generally beneficial across all tested models and datasets, particularly when SQL queries involve multi-hop reasoning and multiple tables. Small LLMs with SFT+RL excel on most complex datasets thanks to a strategic balance between generality of the reasoning process and optimization of the execution accuracy. Thanks to RL, the7B Qwen-Coder-2.5 model performs on par with 100+ Billion ones on the Bird dataset.

When answering a question, humans utilize the information available across different modalities to synthesize a consistent and complete chain of thought (CoT). This process is normally a black box in the case of deep learning models like large-scale language models. Recently, science question benchmarks have been used to diagnose the multi-hop reasoning ability and interpretability of an AI system. However, existing datasets fail to provide annotations for the answers, or are restricted to the textual-only modality, small scales, and limited domain diversity. To this end, we present Science Question Answering (ScienceQA), a new benchmark that consists of ~21k multimodal multiple choice questions with a diverse set of science topics and annotations of their answers with corresponding lectures and explanations. We further design language models to learn to generate lectures and explanations as the chain of thought (CoT) to mimic the multi-hop reasoning process when answering ScienceQA questions. ScienceQA demonstrates the utility of CoT in language models, as CoT improves the question answering performance by 1.20% in few-shot GPT-3 and 3.99% in fine-tuned UnifiedQA. We also explore the upper bound for models to leverage explanations by feeding those in the input; we observe that it improves the few-shot performance of GPT-3 by 18.96%. Our analysis further shows that language models, similar to humans, benefit from explanations to learn from fewer data and achieve the same performance with just 40% of the data. The data and code are available at https://scienceqa.github.io.

Artificial intelligence (AI) has made remarkable progress across various domains, with large language models like ChatGPT gaining substantial attention for their human-like text-generation capabilities. Despite these achievements, spatial reasoning remains a significant challenge for these models. Benchmarks like StepGame evaluate AI spatial reasoning, where ChatGPT has shown unsatisfactory performance. However, the presence of template errors in the benchmark has an impact on the evaluation results. Thus there is potential for ChatGPT to perform better if these template errors are addressed, leading to more accurate assessments of its spatial reasoning capabilities. In this study, we refine the StepGame benchmark, providing a more accurate dataset for model evaluation. We analyze GPT's spatial reasoning performance on the rectified benchmark, identifying proficiency in mapping natural language text to spatial relations but limitations in multi-hop reasoning. We provide a flawless solution to the benchmark by combining template-to-relation mapping with logic-based reasoning. This combination demonstrates proficiency in performing qualitative reasoning on StepGame without encountering any errors. We then address the limitations of GPT models in spatial reasoning. We deploy Chain-of-thought and Tree-of-thoughts prompting strategies, offering insights into GPT's ``cognitive process", and achieving remarkable improvements in accuracy. Our investigation not only sheds light on model deficiencies but also proposes enhancements, contributing to the advancement of AI with more robust spatial reasoning capabilities.

Mixture-of-Experts (MoE) architectures within Large Reasoning Models (LRMs) have achieved impressive reasoning capabilities by selectively activating experts to facilitate structured cognitive processes. Despite notable advances, existing reasoning models often suffer from cognitive inefficiencies like overthinking and underthinking. To address these limitations, we introduce a novel inference-time steering methodology called Reinforcing Cognitive Experts (RICE), designed to improve reasoning performance without additional training or complex heuristics. Leveraging normalized Pointwise Mutual Information (nPMI), we systematically identify specialized experts, termed ''cognitive experts'' that orchestrate meta-level reasoning operations characterized by tokens like ''<think>''. Empirical evaluations with leading MoE-based LRMs (DeepSeek-R1 and Qwen3-235B) on rigorous quantitative and scientific reasoning benchmarks demonstrate noticeable and consistent improvements in reasoning accuracy, cognitive efficiency, and cross-domain generalization. Crucially, our lightweight approach substantially outperforms prevalent reasoning-steering techniques, such as prompt design and decoding constraints, while preserving the model's general instruction-following skills. These results highlight reinforcing cognitive experts as a promising, practical, and interpretable direction to enhance cognitive efficiency within advanced reasoning models.

Multi-hop Question Answering (MHQA) adds layers of complexity to question answering, making it more challenging. When Language Models (LMs) are prompted with multiple search results, they are tasked not only with retrieving relevant information but also employing multi-hop reasoning across the information sources. Although LMs perform well on traditional question-answering tasks, the causal mask can hinder their capacity to reason across complex contexts. In this paper, we explore how LMs respond to multi-hop questions by permuting search results (retrieved documents) under various configurations. Our study reveals interesting findings as follows: 1) Encoder-decoder models, such as the ones in the Flan-T5 family, generally outperform causal decoder-only LMs in MHQA tasks, despite being significantly smaller in size; 2) altering the order of gold documents reveals distinct trends in both Flan T5 models and fine-tuned decoder-only models, with optimal performance observed when the document order aligns with the reasoning chain order; 3) enhancing causal decoder-only models with bi-directional attention by modifying the causal mask can effectively boost their end performance. In addition to the above, we conduct a thorough investigation of the distribution of LM attention weights in the context of MHQA. Our experiments reveal that attention weights tend to peak at higher values when the resulting answer is correct. We leverage this finding to heuristically improve LMs' performance on this task. Our code is publicly available at https://github.com/hwy9855/MultiHopQA-Reasoning.

We present Step-Back Prompting, a simple prompting technique that enables LLMs to do abstractions to derive high-level concepts and first principles from instances containing specific details. Using the concepts and principles to guide the reasoning steps, LLMs significantly improve their abilities in following a correct reasoning path towards the solution. We conduct experiments of Step-Back Prompting with PaLM-2L models and observe substantial performance gains on a wide range of challenging reasoning-intensive tasks including STEM, Knowledge QA, and Multi-Hop Reasoning. For instance, Step-Back Prompting improves PaLM-2L performance on MMLU Physics and Chemistry by 7% and 11%, TimeQA by 27%, and MuSiQue by 7%.

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Decomposition-based multi-hop retrieval methods rely on many autoregressive steps to break down complex queries, which breaks end-to-end differentiability and is computationally expensive. Decomposition-free methods tackle this, but current decomposition-free approaches struggle with longer multi-hop problems and generalization to out-of-distribution data. To address these challenges, we introduce GRITHopper-7B, a novel multi-hop dense retrieval model that achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks. GRITHopper combines generative and representational instruction tuning by integrating causal language modeling with dense retrieval training. Through controlled studies, we find that incorporating additional context after the retrieval process, referred to as post-retrieval language modeling, enhances dense retrieval performance. By including elements such as final answers during training, the model learns to better contextualize and retrieve relevant information. GRITHopper-7B offers a robust, scalable, and generalizable solution for multi-hop dense retrieval, and we release it to the community for future research and applications requiring multi-hop reasoning and retrieval capabilities.

Theory-of-Mind (ToM), the ability to infer others' perceptions and mental states, is fundamental to human interaction but remains a challenging task for Large Language Models (LLMs). While existing ToM reasoning methods show promise with reasoning via perceptual perspective-taking, they often rely excessively on LLMs, reducing their efficiency and limiting their applicability to high-order ToM reasoning, which requires multi-hop reasoning about characters' beliefs. To address these issues, we present EnigmaToM, a novel neuro-symbolic framework that enhances ToM reasoning by integrating a Neural Knowledge Base of entity states (Enigma) for (1) a psychology-inspired iterative masking mechanism that facilitates accurate perspective-taking and (2) knowledge injection that elicits key entity information. Enigma generates structured representations of entity states, which construct spatial scene graphs -- leveraging spatial information as an inductive bias -- for belief tracking of various ToM orders and enhancing events with fine-grained entity state details. Experimental results on multiple benchmarks, including ToMi, HiToM, and FANToM, show that EnigmaToM significantly improves ToM reasoning across LLMs of varying sizes, particularly excelling in high-order reasoning scenarios.

Multimodal Large Language Models (MLLMs) have demonstrated impressive abilities across various tasks, including visual question answering and chart comprehension, yet existing benchmarks for chart-related tasks fall short in capturing the complexity of real-world multi-chart scenarios. Current benchmarks primarily focus on single-chart tasks, neglecting the multi-hop reasoning required to extract and integrate information from multiple charts, which is essential in practical applications. To fill this gap, we introduce MultiChartQA, a benchmark that evaluates MLLMs' capabilities in four key areas: direct question answering, parallel question answering, comparative reasoning, and sequential reasoning. Our evaluation of a wide range of MLLMs reveals significant performance gaps compared to humans. These results highlight the challenges in multi-chart comprehension and the potential of MultiChartQA to drive advancements in this field. Our code and data are available at https://github.com/Zivenzhu/Multi-chart-QA

This paper addresses the problem of generating questions from a given context and an answer, specifically focusing on questions that require multi-hop reasoning across an extended context. Previous studies have suggested that key phrase selection is essential for question generation (QG), yet it is still challenging to connect such disjointed phrases into meaningful questions, particularly for long context. To mitigate this issue, we propose MultiFactor, a novel QG framework based on multi-level content planning. Specifically, MultiFactor includes two components: FA-model, which simultaneously selects key phrases and generates full answers, and Q-model which takes the generated full answer as an additional input to generate questions. Here, full answer generation is introduced to connect the short answer with the selected key phrases, thus forming an answer-aware summary to facilitate QG. Both FA-model and Q-model are formalized as simple-yet-effective Phrase-Enhanced Transformers, our joint model for phrase selection and text generation. Experimental results show that our method outperforms strong baselines on two popular QG datasets. Our code is available at https://github.com/zeaver/MultiFactor.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their performance is highly dependent on the prompting strategy and model scale. While reinforcement learning and fine-tuning have been deployed to boost reasoning, these approaches incur substantial computational and data overhead. In this work, we introduce Adaptive Graph of Thoughts (AGoT), a dynamic, graph-based inference framework that enhances LLM reasoning solely at test time. Rather than relying on fixed-step methods like Chain of Thought (CoT) or Tree of Thoughts (ToT), AGoT recursively decomposes complex queries into structured subproblems, forming an dynamic directed acyclic graph (DAG) of interdependent reasoning steps. By selectively expanding only those subproblems that require further analysis, AGoT unifies the strengths of chain, tree, and graph paradigms into a cohesive framework that allocates computation where it is most needed. We validate our approach on diverse benchmarks spanning multi-hop retrieval, scientific reasoning, and mathematical problem-solving, achieving up to 46.2% improvement on scientific reasoning tasks (GPQA) - comparable to gains achieved through computationally intensive reinforcement learning approaches and outperforming state-of-the-art iterative approaches. These results suggest that dynamic decomposition and structured recursion offer a scalable, cost-effective alternative to post-training modifications, paving the way for more robust, general-purpose reasoning in LLMs.

Prior research on training grounded factuality classification models to detect hallucinations in large language models (LLMs) has relied on public natural language inference (NLI) data and synthetic data. However, conventional NLI datasets are not well-suited for document-level reasoning, which is critical for detecting LLM hallucinations. Recent approaches to document-level synthetic data generation involve iteratively removing sentences from documents and annotating factuality using LLM-based prompts. While effective, this method is computationally expensive for long documents and limited by the LLM's capabilities. In this work, we analyze the differences between existing synthetic training data used in state-of-the-art models and real LLM output claims. Based on our findings, we propose a novel approach for synthetic data generation, CG2C, that leverages multi-hop reasoning on context graphs extracted from documents. Our fact checker model, FactCG, demonstrates improved performance with more connected reasoning, using the same backbone models. Experiments show it even outperforms GPT-4-o on the LLM-Aggrefact benchmark with much smaller model size.

In this paper, we aim to improve the reasoning ability of large language models (LLMs) over knowledge graphs (KGs) to answer complex questions. Inspired by existing methods that design the interaction strategy between LLMs and KG, we propose an autonomous LLM-based agent framework, called KG-Agent, which enables a small LLM to actively make decisions until finishing the reasoning process over KGs. In KG-Agent, we integrate the LLM, multifunctional toolbox, KG-based executor, and knowledge memory, and develop an iteration mechanism that autonomously selects the tool then updates the memory for reasoning over KG. To guarantee the effectiveness, we leverage program language to formulate the multi-hop reasoning process over the KG, and synthesize a code-based instruction dataset to fine-tune the base LLM. Extensive experiments demonstrate that only using 10K samples for tuning LLaMA-7B can outperform state-of-the-art methods using larger LLMs or more data, on both in-domain and out-domain datasets. Our code and data will be publicly released.

While question answering over knowledge bases (KBQA) has shown progress in addressing factoid questions, KBQA with numerical reasoning remains relatively unexplored. In this paper, we focus on the complex numerical reasoning in KBQA and propose a new task, NR-KBQA, which necessitates the ability to perform both multi-hop reasoning and numerical reasoning. We design a logic form in Python format called PyQL to represent the reasoning process of numerical reasoning questions. To facilitate the development of NR-KBQA, we present a large dataset called MarkQA, which is automatically constructed from a small set of seeds. Each question in MarkQA is equipped with its corresponding SPARQL query, alongside the step-by-step reasoning process in the QDMR format and PyQL program. Experimental results of some state-of-the-art QA methods on the MarkQA show that complex numerical reasoning in KBQA faces great challenges.

Although large language models (LLMs) have achieved excellent performance in a variety of evaluation benchmarks, they still struggle in complex reasoning tasks which require specific knowledge and multi-hop reasoning. To improve the reasoning abilities, we propose ChatCoT, a tool-augmented chain-of-thought reasoning framework for chat-based LLMs. In ChatCoT, we model the chain-of-thought~(CoT) reasoning as multi-turn conversations, to utilize tools in a more natural way through chatting. At each turn, LLMs can either interact with tools or perform the reasoning. Our approach can effectively leverage the multi-turn conversation ability of chat-based LLMs, and integrate the thought chain following and tools manipulation in a unified way. Specially, we initialize the early turns of the conversation by the tools, tasks and reasoning format, and propose an iterative tool-augmented reasoning step to perform step-by-step tool-augmented reasoning. The experiment results on two complex reasoning datasets (MATH and HotpotQA) have shown the effectiveness of ChatCoT on complex reasoning tasks, achieving a 6.8\% relative improvement over the state-of-the-art baseline. Our code and data are available at: https://github.com/RUCAIBOX/ChatCoT.

Transformers have become the gold standard for many natural language processing tasks and, in particular, for multi-hop question answering (MHQA). This task includes processing a long document and reasoning over the multiple parts of it. The landscape of MHQA approaches can be classified into two primary categories. The first group focuses on extracting supporting evidence, thereby constraining the QA model's context to predicted facts. Conversely, the second group relies on the attention mechanism of the long input encoding model to facilitate multi-hop reasoning. However, attention-based token representations lack explicit global contextual information to connect reasoning steps. To address these issues, we propose GEMFormer, a two-stage method that first collects relevant information over the entire document to the memory and then combines it with local context to solve the task. Our experimental results show that fine-tuning a pre-trained model with memory-augmented input, including the most certain global elements, improves the model's performance on three MHQA datasets compared to the baseline. We also found that the global explicit memory contains information from supporting facts required for the correct answer.

Large Language Models with chain-of-thought prompting, such as OpenAI-o1, have shown impressive capabilities in natural language inference tasks. However, Multi-hop Question Answering (MHQA) remains challenging for many existing models due to issues like hallucination, error propagation, and limited context length. To address these challenges and enhance LLMs' performance on MHQA, we propose the Self-Guiding prompting Finite State Machine (SG-FSM), designed to strengthen multi-hop reasoning abilities. Unlike traditional chain-of-thought methods, SG-FSM tackles MHQA by iteratively breaking down complex questions into sub-questions, correcting itself to improve accuracy. It processes one sub-question at a time, dynamically deciding the next step based on the current context and results, functioning much like an automaton. Experiments across various benchmarks demonstrate the effectiveness of our approach, outperforming strong baselines on challenging datasets such as Musique. SG-FSM reduces hallucination, enabling recovery of the correct final answer despite intermediate errors. It also improves adherence to specified output formats, simplifying evaluation significantly.

Large Language Models (LLMs) have advanced Verilog code generation significantly, yet face challenges in data quality, reasoning capabilities, and computational efficiency. This paper presents ReasoningV, a novel model employing a hybrid reasoning strategy that integrates trained intrinsic capabilities with dynamic inference adaptation for Verilog code generation. Our framework introduces three complementary innovations: (1) ReasoningV-5K, a high-quality dataset of 5,000 functionally verified instances with reasoning paths created through multi-dimensional filtering of PyraNet samples; (2) a two-stage training approach combining parameter-efficient fine-tuning for foundational knowledge with full-parameter optimization for enhanced reasoning; and (3) an adaptive reasoning mechanism that dynamically adjusts reasoning depth based on problem complexity, reducing token consumption by up to 75\% while preserving performance. Experimental results demonstrate ReasoningV's effectiveness with a pass@1 accuracy of 57.8\% on VerilogEval-human, achieving performance competitive with leading commercial models like Gemini-2.0-flash (59.5\%) and exceeding the previous best open-source model by 10.4 percentage points. ReasoningV offers a more reliable and accessible pathway for advancing AI-driven hardware design automation, with our model, data, and code available at https://github.com/BUAA-CLab/ReasoningV.

Large language models (LLMs) with memory are computationally universal. However, mainstream LLMs are not taking full advantage of memory, and the designs are heavily influenced by biological brains. Due to their approximate nature and proneness to the accumulation of errors, conventional neural memory mechanisms cannot support LLMs to simulate complex reasoning. In this paper, we seek inspiration from modern computer architectures to augment LLMs with symbolic memory for complex multi-hop reasoning. Such a symbolic memory framework is instantiated as an LLM and a set of SQL databases, where the LLM generates SQL instructions to manipulate the SQL databases. We validate the effectiveness of the proposed memory framework on a synthetic dataset requiring complex reasoning. The project website is available at https://chatdatabase.github.io/ .

We introduce Phi-4-reasoning, a 14-billion parameter reasoning model that achieves strong performance on complex reasoning tasks. Trained via supervised fine-tuning of Phi-4 on carefully curated set of "teachable" prompts-selected for the right level of complexity and diversity-and reasoning demonstrations generated using o3-mini, Phi-4-reasoning generates detailed reasoning chains that effectively leverage inference-time compute. We further develop Phi-4-reasoning-plus, a variant enhanced through a short phase of outcome-based reinforcement learning that offers higher performance by generating longer reasoning traces. Across a wide range of reasoning tasks, both models outperform significantly larger open-weight models such as DeepSeek-R1-Distill-Llama-70B model and approach the performance levels of full DeepSeek-R1 model. Our comprehensive evaluations span benchmarks in math and scientific reasoning, coding, algorithmic problem solving, planning, and spatial understanding. Interestingly, we observe a non-trivial transfer of improvements to general-purpose benchmarks as well. In this report, we provide insights into our training data, our training methodologies, and our evaluations. We show that the benefit of careful data curation for supervised fine-tuning (SFT) extends to reasoning language models, and can be further amplified by reinforcement learning (RL). Finally, our evaluation points to opportunities for improving how we assess the performance and robustness of reasoning models.

Recent advances in Multi-Modal Large Language Models (MLLMs) have enabled unified processing of language, vision, and structured inputs, opening the door to complex tasks such as logical deduction, spatial reasoning, and scientific analysis. Despite their promise, the reasoning capabilities of MLLMs, particularly those augmented with intermediate thinking traces (MLLMs-T), remain poorly understood and lack standardized evaluation benchmarks. Existing work focuses primarily on perception or final answer correctness, offering limited insight into how models reason or fail across modalities. To address this gap, we introduce the MMMR, a new benchmark designed to rigorously evaluate multi-modal reasoning with explicit thinking. The MMMR comprises 1) a high-difficulty dataset of 1,083 questions spanning six diverse reasoning types with symbolic depth and multi-hop demands and 2) a modular Reasoning Trace Evaluation Pipeline (RTEP) for assessing reasoning quality beyond accuracy through metrics like relevance, consistency, and structured error annotations. Empirical results show that MLLMs-T overall outperform non-thinking counterparts, but even top models like Claude-3.7-Sonnet and Gemini-2.5 Pro suffer from reasoning pathologies such as inconsistency and overthinking. This benchmark reveals persistent gaps between accuracy and reasoning quality and provides an actionable evaluation pipeline for future model development. Overall, the MMMR offers a scalable foundation for evaluating, comparing, and improving the next generation of multi-modal reasoning systems.

Human-like chatbots necessitate the use of commonsense reasoning in order to effectively comprehend and respond to implicit information present within conversations. Achieving such coherence and informativeness in responses, however, is a non-trivial task. Even for large language models (LLMs), the task of identifying and aggregating key evidence within a single hop presents a substantial challenge. This complexity arises because such evidence is scattered across multiple turns in a conversation, thus necessitating integration over multiple hops. Hence, our focus is to facilitate such multi-hop reasoning over a dialogue context, namely dialogue chain-of-thought (CoT) reasoning. To this end, we propose a knowledge distillation framework that leverages LLMs as unreliable teachers and selectively distills consistent and helpful rationales via alignment filters. We further present DOCTOR, a DialOgue Chain-of-ThOught Reasoner that provides reliable CoT rationales for response generation. We conduct extensive experiments to show that enhancing dialogue agents with high-quality rationales from DOCTOR significantly improves the quality of their responses.

With the continuous advancement of large language models (LLMs), it is essential to create new benchmarks to effectively evaluate their expanding capabilities and identify areas for improvement. This work focuses on multi-image reasoning, an emerging capability in state-of-the-art LLMs. We introduce ReMI, a dataset designed to assess LLMs' ability to Reason with Multiple Images. This dataset encompasses a diverse range of tasks, spanning various reasoning domains such as math, physics, logic, code, table/chart understanding, and spatial and temporal reasoning. It also covers a broad spectrum of characteristics found in multi-image reasoning scenarios. We have benchmarked several cutting-edge LLMs using ReMI and found a substantial gap between their performance and human-level proficiency. This highlights the challenges in multi-image reasoning and the need for further research. Our analysis also reveals the strengths and weaknesses of different models, shedding light on the types of reasoning that are currently attainable and areas where future models require improvement. To foster further research in this area, we are releasing ReMI publicly: https://huggingface.co/datasets/mehrankazemi/ReMI.

Reasoning stands as a cornerstone of intelligence, enabling the synthesis of existing knowledge to solve complex problems. Despite remarkable progress, existing reasoning benchmarks often fail to rigorously evaluate the nuanced reasoning capabilities required for complex, real-world problemsolving, particularly in multi-disciplinary and multimodal contexts. In this paper, we introduce a graduate-level, multi-disciplinary, EnglishChinese benchmark, dubbed as Reasoning Bench (R-Bench), for assessing the reasoning capability of both language and multimodal models. RBench spans 1,094 questions across 108 subjects for language model evaluation and 665 questions across 83 subjects for multimodal model testing in both English and Chinese. These questions are meticulously curated to ensure rigorous difficulty calibration, subject balance, and crosslinguistic alignment, enabling the assessment to be an Olympiad-level multi-disciplinary benchmark. We evaluate widely used models, including OpenAI o1, GPT-4o, DeepSeek-R1, etc. Experimental results indicate that advanced models perform poorly on complex reasoning, especially multimodal reasoning. Even the top-performing model OpenAI o1 achieves only 53.2% accuracy on our multimodal evaluation. Data and code are made publicly available at here.

Multimodal reasoning is a challenging task that requires models to reason across multiple modalities to answer questions. Existing approaches have made progress by incorporating language and visual modalities into a two-stage reasoning framework, separating rationale generation from answer inference. However, these approaches often fall short due to the inadequate quality of the generated rationales. In this work, we delve into the importance of rationales in model reasoning. We observe that when rationales are completely accurate, the model's accuracy significantly improves, highlighting the need for high-quality rationale generation. Motivated by this, we propose MC-CoT, a self-consistency training strategy that generates multiple rationales and answers, subsequently selecting the most accurate through a voting process. This approach not only enhances the quality of generated rationales but also leads to more accurate and robust answers. Through extensive experiments, we demonstrate that our approach significantly improves model performance across various benchmarks. Remarkably, we show that even smaller base models, when equipped with our proposed approach, can achieve results comparable to those of larger models, illustrating the potential of our approach in harnessing the power of rationales for improved multimodal reasoning. The code is available at https://github.com/chengtan9907/mc-cot.

Existing benchmarks for frontier models often test specialized, ``PhD-level'' knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark based on the NPR Sunday Puzzle Challenge that requires only general knowledge. Our benchmark is challenging for both humans and models, however correct solutions are easy to verify, and models' mistakes are easy to spot. Our work reveals capability gaps that are not evident in existing benchmarks: OpenAI o1 significantly outperforms other reasoning models that are on par on benchmarks that test specialized knowledge. Furthermore, our analysis of reasoning outputs uncovers new kinds of failures. DeepSeek R1, for instance, often concedes with ``I give up'' before providing an answer that it knows is wrong. R1 can also be remarkably ``uncertain'' in its output and in rare cases, it does not ``finish thinking,'' which suggests the need for an inference-time technique to ``wrap up'' before the context window limit is reached. We also quantify the effectiveness of reasoning longer with R1 and Gemini Thinking to identify the point beyond which more reasoning is unlikely to improve accuracy on our benchmark.

Recent advancements in large language models (LLMs) have demonstrated their impressive abilities in various reasoning and decision-making tasks. However, the quality and coherence of the reasoning process can still benefit from enhanced introspection and self-reflection. In this paper, we introduce Multiplex CoT (Chain of Thought), a method that enables LLMs to simulate a form of self-review while reasoning, by initiating double Chain of Thought (CoT) thinking. Multiplex CoT leverages the power of iterative reasoning, where the model generates an initial chain of thought and subsequently critiques and refines this reasoning with a second round of thought generation. This recursive approach allows for more coherent, logical, and robust answers, improving the overall decision-making process. We demonstrate how this method can be effectively implemented using simple prompt engineering in existing LLM architectures, achieving an effect similar to that of the Learning-Refinement Model (LRM) without the need for additional training. Additionally, we present a practical guide for implementing the method in Google Colab, enabling easy integration into real-world applications.

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

Reasoning is a fundamental capability for solving complex multi-step problems, particularly in visual contexts where sequential step-wise understanding is essential. Existing approaches lack a comprehensive framework for evaluating visual reasoning and do not emphasize step-wise problem-solving. To this end, we propose a comprehensive framework for advancing step-by-step visual reasoning in large language models (LMMs) through three key contributions. First, we introduce a visual reasoning benchmark specifically designed to evaluate multi-step reasoning tasks. The benchmark presents a diverse set of challenges with eight different categories ranging from complex visual perception to scientific reasoning with over 4k reasoning steps in total, enabling robust evaluation of LLMs' abilities to perform accurate and interpretable visual reasoning across multiple steps. Second, we propose a novel metric that assesses visual reasoning quality at the granularity of individual steps, emphasizing both correctness and logical coherence. The proposed metric offers deeper insights into reasoning performance compared to traditional end-task accuracy metrics. Third, we present a new multimodal visual reasoning model, named LlamaV-o1, trained using a multi-step curriculum learning approach, where tasks are progressively organized to facilitate incremental skill acquisition and problem-solving. The proposed LlamaV-o1 is designed for multi-step reasoning and learns step-by-step through a structured training paradigm. Extensive experiments show that our LlamaV-o1 outperforms existing open-source models and performs favorably against close-source proprietary models. Compared to the recent Llava-CoT, our LlamaV-o1 achieves an average score of 67.3 with an absolute gain of 3.8\% across six benchmarks while being 5 times faster during inference scaling. Our benchmark, model, and code are publicly available.

Reasoning lies at the heart of intelligence, shaping the ability to make decisions, draw conclusions, and generalize across domains. In artificial intelligence, as systems increasingly operate in open, uncertain, and multimodal environments, reasoning becomes essential for enabling robust and adaptive behavior. Large Multimodal Reasoning Models (LMRMs) have emerged as a promising paradigm, integrating modalities such as text, images, audio, and video to support complex reasoning capabilities and aiming to achieve comprehensive perception, precise understanding, and deep reasoning. As research advances, multimodal reasoning has rapidly evolved from modular, perception-driven pipelines to unified, language-centric frameworks that offer more coherent cross-modal understanding. While instruction tuning and reinforcement learning have improved model reasoning, significant challenges remain in omni-modal generalization, reasoning depth, and agentic behavior. To address these issues, we present a comprehensive and structured survey of multimodal reasoning research, organized around a four-stage developmental roadmap that reflects the field's shifting design philosophies and emerging capabilities. First, we review early efforts based on task-specific modules, where reasoning was implicitly embedded across stages of representation, alignment, and fusion. Next, we examine recent approaches that unify reasoning into multimodal LLMs, with advances such as Multimodal Chain-of-Thought (MCoT) and multimodal reinforcement learning enabling richer and more structured reasoning chains. Finally, drawing on empirical insights from challenging benchmarks and experimental cases of OpenAI O3 and O4-mini, we discuss the conceptual direction of native large multimodal reasoning models (N-LMRMs), which aim to support scalable, agentic, and adaptive reasoning and planning in complex, real-world environments.

Large Language Models (LLMs) have shown potential in reasoning over structured environments, e.g., knowledge graph and table. Such tasks typically require multi-hop reasoning, i.e., match natural language utterance with instances in the environment. Previous methods leverage LLMs to incrementally build a reasoning path, where the LLMs either invoke tools or pick up schemas by step-by-step interacting with the environment. We propose Reasoning-Path-Editing (Readi), a novel framework where LLMs can efficiently and faithfully reason over structured environments. In Readi, LLMs initially generate a reasoning path given a query, and edit the path only when necessary. We instantiate the path on structured environments and provide feedback to edit the path if anything goes wrong. Experimental results on three KGQA and two TableQA datasets show the effectiveness of Readi, significantly surpassing previous LLM-based methods (by 9.1% Hit@1 on WebQSP, 12.4% on MQA-3H and 9.5% on WTQ), comparable with state-of-the-art fine-tuned methods (67% on CWQ and 74.7% on WebQSP) and substantially boosting the vanilla LLMs (by 14.9% on CWQ). Our code will be available on https://aka.ms/readi.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

Large language models (LLMs) can improve their accuracy on various tasks through iteratively refining and revising their output based on feedback. We observe that these revisions can introduce errors, in which case it is better to roll back to a previous result. Further, revisions are typically homogeneous: they use the same reasoning method that produced the initial answer, which may not correct errors. To enable exploration in this space, we present SCREWS, a modular framework for reasoning with revisions. It is comprised of three main modules: Sampling, Conditional Resampling, and Selection, each consisting of sub-modules that can be hand-selected per task. We show that SCREWS not only unifies several previous approaches under a common framework, but also reveals several novel strategies for identifying improved reasoning chains. We evaluate our framework with state-of-the-art LLMs (ChatGPT and GPT-4) on a diverse set of reasoning tasks and uncover useful new reasoning strategies for each: arithmetic word problems, multi-hop question answering, and code debugging. Heterogeneous revision strategies prove to be important, as does selection between original and revised candidates.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the MCoTInstruct dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

Multi-step spatial reasoning entails understanding and reasoning about spatial relationships across multiple sequential steps, which is crucial for tackling complex real-world applications, such as robotic manipulation, autonomous navigation, and automated assembly. To assess how well current Multimodal Large Language Models (MLLMs) have acquired this fundamental capability, we introduce LEGO-Puzzles, a scalable benchmark designed to evaluate both spatial understanding and sequential reasoning in MLLMs through LEGO-based tasks. LEGO-Puzzles consists of 1,100 carefully curated visual question-answering (VQA) samples spanning 11 distinct tasks, ranging from basic spatial understanding to complex multi-step reasoning. Based on LEGO-Puzzles, we conduct a comprehensive evaluation of state-of-the-art MLLMs and uncover significant limitations in their spatial reasoning capabilities: even the most powerful MLLMs can answer only about half of the test cases, whereas human participants achieve over 90\% accuracy. In addition to VQA tasks, we evaluate MLLMs' abilities to generate LEGO images following assembly illustrations. Our experiments show that only Gemini-2.0-Flash and GPT-4o exhibit a limited ability to follow these instructions, while other MLLMs either replicate the input image or generate completely irrelevant outputs. Overall, LEGO-Puzzles exposes critical deficiencies in existing MLLMs' spatial understanding and sequential reasoning capabilities, and underscores the need for further advancements in multimodal spatial reasoning.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely out of reach for open models. To address this gap, we examine the potential of Generative Flow Networks as a fine-tuning method for LLMs to unlock advanced reasoning capabilities. In this paper, we present a proof of concept in the domain of formal reasoning, specifically in the Neural Theorem Proving (NTP) setting, where proofs specified in a formal language such as Lean can be deterministically and objectively verified. Unlike classical reward-maximization reinforcement learning, which frequently over-exploits high-reward actions and fails to effectively explore the state space, GFlowNets have emerged as a promising approach for sampling compositional objects, improving generalization, and enabling models to maintain diverse hypotheses. Our early results demonstrate GFlowNet fine-tuning's potential for enhancing model performance in a search setting, which is especially relevant given the paradigm shift towards inference time compute scaling and "thinking slowly."

Modern Question Answering (QA) and Reasoning approaches based on Large Language Models (LLMs) commonly use prompting techniques, such as Chain-of-Thought (CoT), assuming the resulting generation will have a more granular exploration and reasoning over the question space and scope. However, such methods struggle with generating outputs that are faithful to the intermediate chain of reasoning produced by the model. On the other end of the spectrum, neuro-symbolic methods such as Faithful CoT (F-CoT) propose to combine LLMs with external symbolic solvers. While such approaches boast a high degree of faithfulness, they usually require a model trained for code generation and struggle with tasks that are ambiguous or hard to formalise strictly. We introduce Faithful Logic-Aided Reasoning and Exploration (\ours), a novel interpretable approach for traversing the problem space using task decompositions. We use the LLM to plan a solution, soft-formalise the query into facts and predicates using a logic programming code and simulate that code execution using an exhaustive multi-hop search over the defined space. Our method allows us to compute the faithfulness of the reasoning process w.r.t. the generated code and analyse the steps of the multi-hop search without relying on external solvers. Our methods achieve SOTA results on 7 out of 9 diverse reasoning benchmarks. We also show that model faithfulness positively correlates with overall performance and further demonstrate that {\ours} allows pinpointing the decisive factors sufficient for and leading to the correct answer with optimal reasoning during the multi-hop search.

We demonstrate LLM agent specification gaming by instructing models to win against a chess engine. We find reasoning models like o1 preview and DeepSeek-R1 will often hack the benchmark by default, while language models like GPT-4o and Claude 3.5 Sonnet need to be told that normal play won't work to hack. We improve upon prior work like (Hubinger et al., 2024; Meinke et al., 2024; Weij et al., 2024) by using realistic task prompts and avoiding excess nudging. Our results suggest reasoning models may resort to hacking to solve difficult problems, as observed in OpenAI (2024)'s o1 Docker escape during cyber capabilities testing.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Recent advancements in building domain-specific large language models (LLMs) have shown remarkable success, especially in tasks requiring reasoning abilities like logical inference over complex relationships and multi-step problem solving. However, creating a powerful all-in-one LLM remains challenging due to the need for proprietary data and vast computational resources. As a resource-friendly alternative, we explore the potential of merging multiple expert models into a single LLM. Existing studies on model merging mainly focus on generalist LLMs instead of domain experts, or the LLMs under the same architecture and size. In this work, we propose an unconstrained model merging framework that accommodates both homogeneous and heterogeneous model architectures with a focus on reasoning tasks. A fine-grained layer-wise weight merging strategy is designed for homogeneous models merging, while heterogeneous model merging is built upon the probabilistic distribution knowledge derived from instruction-response fine-tuning data. Across 7 benchmarks and 9 reasoning-optimized LLMs, we reveal key findings that combinatorial reasoning emerges from merging which surpasses simple additive effects. We propose that unconstrained model merging could serve as a foundation for decentralized LLMs, marking a notable progression from the existing centralized LLM framework. This evolution could enhance wider participation and stimulate additional advancement in the field of artificial intelligence, effectively addressing the constraints posed by centralized models.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

Multi-agent systems (MAS) built on large language models (LLMs) offer a promising path toward solving complex, real-world tasks that single-agent systems often struggle to manage. While recent advancements in test-time scaling (TTS) have significantly improved single-agent performance on challenging reasoning tasks, how to effectively scale collaboration and reasoning in MAS remains an open question. In this work, we introduce an adaptive multi-agent framework designed to enhance collaborative reasoning through both model-level training and system-level coordination. We construct M500, a high-quality dataset containing 500 multi-agent collaborative reasoning traces, and fine-tune Qwen2.5-32B-Instruct on this dataset to produce M1-32B, a model optimized for multi-agent collaboration. To further enable adaptive reasoning, we propose a novel CEO agent that dynamically manages the discussion process, guiding agent collaboration and adjusting reasoning depth for more effective problem-solving. Evaluated in an open-source MAS across a range of tasks-including general understanding, mathematical reasoning, and coding-our system significantly outperforms strong baselines. For instance, M1-32B achieves 12% improvement on GPQA-Diamond, 41% on AIME2024, and 10% on MBPP-Sanitized, matching the performance of state-of-the-art models like DeepSeek-R1 on some tasks. These results highlight the importance of both learned collaboration and adaptive coordination in scaling multi-agent reasoning. Code is available at https://github.com/jincan333/MAS-TTS

We introduce S1-Bench, a novel benchmark designed to evaluate Large Reasoning Models' (LRMs) performance on simple tasks that favor intuitive system 1 thinking rather than deliberative system 2 reasoning. While LRMs have achieved significant breakthroughs in complex reasoning tasks through explicit chains of thought, their reliance on deep analytical thinking may limit their system 1 thinking capabilities. Moreover, a lack of benchmark currently exists to evaluate LRMs' performance in tasks that require such capabilities. To fill this gap, S1-Bench presents a set of simple, diverse, and naturally clear questions across multiple domains and languages, specifically designed to assess LRMs' performance in such tasks. Our comprehensive evaluation of 22 LRMs reveals significant lower efficiency tendencies, with outputs averaging 15.5 times longer than those of traditional small LLMs. Additionally, LRMs often identify correct answers early but continue unnecessary deliberation, with some models even producing numerous errors. These findings highlight the rigid reasoning patterns of current LRMs and underscore the substantial development needed to achieve balanced dual-system thinking capabilities that can adapt appropriately to task complexity.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Large language models (LLMs) have exhibited impressive performance in language comprehension and various reasoning tasks. However, their abilities in spatial reasoning, a crucial aspect of human cognition, remain relatively unexplored. Human possess a remarkable ability to create mental images of unseen objects and actions through a process known as the Mind's Eye, enabling the imagination of the unseen world. Inspired by this cognitive capacity, we propose Visualization-of-Thought (VoT) prompting. VoT aims to elicit spatial reasoning of LLMs by visualizing their reasoning traces, thereby guiding subsequent reasoning steps. We employed VoT for multi-hop spatial reasoning tasks, including natural language navigation, visual navigation, and visual tiling in 2D grid worlds. Experimental results demonstrated that VoT significantly enhances the spatial reasoning abilities of LLMs. Notably, VoT outperformed existing multimodal large language models (MLLMs) in these tasks. While VoT works surprisingly well on LLMs, the ability to generate mental images to facilitate spatial reasoning resembles the mind's eye process, suggesting its potential viability in MLLMs.

This survey paper proposes a clearer view of natural language reasoning in the field of Natural Language Processing (NLP), both conceptually and practically. Conceptually, we provide a distinct definition for natural language reasoning in NLP, based on both philosophy and NLP scenarios, discuss what types of tasks require reasoning, and introduce a taxonomy of reasoning. Practically, we conduct a comprehensive literature review on natural language reasoning in NLP, mainly covering classical logical reasoning, natural language inference, multi-hop question answering, and commonsense reasoning. The paper also identifies and views backward reasoning, a powerful paradigm for multi-step reasoning, and introduces defeasible reasoning as one of the most important future directions in natural language reasoning research. We focus on single-modality unstructured natural language text, excluding neuro-symbolic techniques and mathematical reasoning.

Recent advances in large language models (LLMs) have demonstrated the power of reasoning through self-generated chains of thought. Multiple reasoning agents can collaborate to raise joint reasoning quality above individual outcomes. However, such agents typically interact in a turn-based manner, trading increased latency for improved quality. In this paper, we propose Group Think--a single LLM that acts as multiple concurrent reasoning agents, or thinkers. With shared visibility into each other's partial generation progress, Group Think introduces a new concurrent-reasoning paradigm in which multiple reasoning trajectories adapt dynamically to one another at the token level. For example, a reasoning thread may shift its generation mid-sentence upon detecting that another thread is better positioned to continue. This fine-grained, token-level collaboration enables Group Think to reduce redundant reasoning and improve quality while achieving significantly lower latency. Moreover, its concurrent nature allows for efficient utilization of idle computational resources, making it especially suitable for edge inference, where very small batch size often underutilizes local~GPUs. We give a simple and generalizable modification that enables any existing LLM to perform Group Think on a local GPU. We also present an evaluation strategy to benchmark reasoning latency and empirically demonstrate latency improvements using open-source LLMs that were not explicitly trained for Group Think. We hope this work paves the way for future LLMs to exhibit more sophisticated and more efficient collaborative behavior for higher quality generation.

Despite significant achievements in improving the instruction-following capabilities of large language models (LLMs), the ability to process multiple potentially entangled or conflicting instructions remains a considerable challenge. Real-world scenarios often require consistency across multiple instructions over time, such as secret privacy, personal preferences, and prioritization, which demand sophisticated abilities to integrate multiple turns and carefully balance competing objectives when instructions intersect or conflict. This work presents a systematic investigation of LLMs' capabilities in handling multiple turns of instructions, covering three levels of difficulty: (1) retrieving information from instructions, (2) tracking and reasoning across turns, and (3) resolving conflicts among instructions. We construct MultiTurnInstruct with around 1.1K high-quality multi-turn conversations through the human-in-the-loop approach and result in nine capability categories, including statics and dynamics, reasoning, and multitasking. Our finding reveals an intriguing trade-off between different capabilities. While GPT models demonstrate superior memorization, they show reduced effectiveness in privacy-protection tasks requiring selective information withholding. Larger models exhibit stronger reasoning capabilities but still struggle with resolving conflicting instructions. Importantly, these performance gaps cannot be attributed solely to information loss, as models demonstrate strong BLEU scores on memorization tasks but their attention mechanisms fail to integrate multiple related instructions effectively. These findings highlight critical areas for improvement in complex real-world tasks involving multi-turn instructions.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

Recent advancements in large language models (LLMs) have demonstrated impressive chain-of-thought reasoning capabilities, with reinforcement learning (RL) playing a crucial role in this progress. While "aha moment" patterns--where models exhibit self-correction through reflection--are often attributed to emergent properties from RL, we first demonstrate that these patterns exist in multimodal LLMs (MLLMs) prior to RL training but may not necessarily correlate with improved reasoning performance. Building on these insights, we present a comprehensive study on enhancing multimodal reasoning through a two-stage approach: (1) supervised fine-tuning (SFT) as a cold start with structured chain-of-thought reasoning patterns, followed by (2) reinforcement learning via GRPO to further refine these capabilities. Our extensive experiments show that this combined approach consistently outperforms both SFT-only and RL-only methods across challenging multimodal reasoning benchmarks. The resulting models achieve state-of-the-art performance among open-source MLLMs at both 3B and 7B scales, with our 7B model showing substantial improvements over base models (e.g., 66.3 %rightarrow73.4 % on MathVista, 62.9 %rightarrow70.4 % on We-Math) and our 3B model achieving performance competitive with several 7B models. Overall, this work provides practical guidance for building advanced multimodal reasoning models. Our code is available at https://github.com/waltonfuture/RL-with-Cold-Start.

Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs) have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we define the multi-hop logical reasoning problem on TKGs. With generated three datasets, we propose the first temporal CQE named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. We utilize vector logic to compute the logic part of Temporal Feature-Logic embeddings, thus naturally modeling all First-Order Logic (FOL) operations on entity set. In addition, our framework extends vector logic on timestamp set to cope with three extra temporal operators (After, Before and Between). Experiments on numerous query patterns demonstrate the effectiveness of our method.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Despite recent advancements in large language models (LLMs), their performance on complex reasoning problems requiring multi-step thinking and combining various skills is still limited. To address this, we propose a novel framework HDFlow for complex reasoning with LLMs that combines fast and slow thinking modes in an adaptive manner. Our approach consists of two key components: 1) a new approach for slow, deliberate reasoning called Dynamic Workflow, which automatically decomposes complex problems into more manageable sub-tasks and dynamically designs a workflow to assemble specialized LLM or symbolic reasoning tools to solve sub-tasks; 2) Hybrid Thinking, a general framework that dynamically combines fast and slow thinking based on problem complexity. Finally, we propose an easy-to-scale method for automatically synthesizing a large-scale dataset of 27K challenging reasoning problems for complex reasoning and a hybrid thinking tuning method that trains smaller LLMs on this dataset to internalize the fast/slow hybrid reasoning strategies. Experiments on four reasoning benchmark datasets demonstrate that our slow thinking with dynamic workflows significantly outperforms Chain-of-Thought, and hybrid thinking achieves the highest accuracy while providing an effective balance between computational efficiency and performance. Fine-tuning using our hybrid thinking approach also significantly boosts the complex reasoning capabilities of open-source language models. The results showcase the promise of slow thinking, dynamic workflows, and hybrid thinking in expanding the frontier of complex problem-solving with LLMsCode and data will be released at \url{https://github.com/wenlinyao/HDFlow.}.

Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases--thinking and solution--with independently allocated budgets. At test time, Elastic Reasoning prioritize that completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale.

Reasoning and strategic behavior in social interactions is a hallmark of intelligence. This form of reasoning is significantly more sophisticated than isolated planning or reasoning tasks in static settings (e.g., math problem solving). In this paper, we present Strategic Planning, Interaction, and Negotiation (SPIN-Bench), a new multi-domain evaluation designed to measure the intelligence of strategic planning and social reasoning. While many existing benchmarks focus on narrow planning or single-agent reasoning, SPIN-Bench combines classical PDDL tasks, competitive board games, cooperative card games, and multi-agent negotiation scenarios in one unified framework. The framework includes both a benchmark as well as an arena to simulate and evaluate the variety of social settings to test reasoning and strategic behavior of AI agents. We formulate the benchmark SPIN-Bench by systematically varying action spaces, state complexity, and the number of interacting agents to simulate a variety of social settings where success depends on not only methodical and step-wise decision making, but also conceptual inference of other (adversarial or cooperative) participants. Our experiments reveal that while contemporary LLMs handle basic fact retrieval and short-range planning reasonably well, they encounter significant performance bottlenecks in tasks requiring deep multi-hop reasoning over large state spaces and socially adept coordination under uncertainty. We envision SPIN-Bench as a catalyst for future research on robust multi-agent planning, social reasoning, and human--AI teaming.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.

Large Reasoning Models (LRMs) have the ability to self-correct even when they make mistakes in their reasoning paths. However, our study reveals that when the reasoning process starts with a short but poor beginning, it becomes difficult for the model to recover. We refer to this phenomenon as the "Prefix Dominance Trap". Inspired by psychological findings that peer interaction can promote self-correction without negatively impacting already accurate individuals, we propose **Learning from Peers** (LeaP) to address this phenomenon. Specifically, every tokens, each reasoning path summarizes its intermediate reasoning and shares it with others through a routing mechanism, enabling paths to incorporate peer insights during inference. However, we observe that smaller models sometimes fail to follow summarization and reflection instructions effectively. To address this, we fine-tune them into our **LeaP-T** model series. Experiments on AIME 2024, AIME 2025, AIMO 2025, and GPQA Diamond show that LeaP provides substantial improvements. For instance, QwQ-32B with LeaP achieves nearly 5 absolute points higher than the baseline on average, and surpasses DeepSeek-R1-671B on three math benchmarks with an average gain of 3.3 points. Notably, our fine-tuned LeaP-T-7B matches the performance of DeepSeek-R1-Distill-Qwen-14B on AIME 2024. In-depth analysis reveals LeaP's robust error correction by timely peer insights, showing strong error tolerance and handling varied task difficulty. LeaP marks a milestone by enabling LRMs to collaborate during reasoning. Our code, datasets, and models are available at https://learning-from-peers.github.io/ .

Structure reasoning is a fundamental capability of large language models (LLMs), enabling them to reason about structured commonsense and answer multi-hop questions. However, existing benchmarks for structure reasoning mainly focus on horizontal and coordinate structures (e.g. graphs), overlooking the hierarchical relationships within them. Hierarchical structure reasoning is crucial for human cognition, particularly in memory organization and problem-solving. It also plays a key role in various real-world tasks, such as information extraction and decision-making. To address this gap, we propose HiBench, the first framework spanning from initial structure generation to final proficiency assessment, designed to benchmark the hierarchical reasoning capabilities of LLMs systematically. HiBench encompasses six representative scenarios, covering both fundamental and practical aspects, and consists of 30 tasks with varying hierarchical complexity, totaling 39,519 queries. To evaluate LLMs comprehensively, we develop five capability dimensions that depict different facets of hierarchical structure understanding. Through extensive evaluation of 20 LLMs from 10 model families, we reveal key insights into their capabilities and limitations: 1) existing LLMs show proficiency in basic hierarchical reasoning tasks; 2) they still struggle with more complex structures and implicit hierarchical representations, especially in structural modification and textual reasoning. Based on these findings, we create a small yet well-designed instruction dataset, which enhances LLMs' performance on HiBench by an average of 88.84\% (Llama-3.1-8B) and 31.38\% (Qwen2.5-7B) across all tasks. The HiBench dataset and toolkit are available here, https://github.com/jzzzzh/HiBench, to encourage evaluation.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

Human beings naturally utilize multiple reasoning modalities to learn and solve logical problems, i.e., different representational formats such as natural language, code, and symbolic logic. In contrast, most existing LLM-based approaches operate with a single reasoning modality during training, typically natural language. Although some methods explored modality selection or augmentation at inference time, the training process remains modality-blind, limiting synergy among modalities. To fill in this gap, we propose Mixture-of-Thought (MoT), a framework that enables LLMs to reason across three complementary modalities: natural language, code, and a newly introduced symbolic modality, truth-table, which systematically enumerates logical cases and partially mitigates key failure modes in natural language reasoning. MoT adopts a two-phase design: (1) self-evolving MoT training, which jointly learns from filtered, self-generated rationales across modalities; and (2) MoT inference, which fully leverages the synergy of three modalities to produce better predictions. Experiments on logical reasoning benchmarks including FOLIO and ProofWriter demonstrate that our MoT framework consistently and significantly outperforms strong LLM baselines with single-modality chain-of-thought approaches, achieving up to +11.7pp average accuracy gain. Further analyses show that our MoT framework benefits both training and inference stages; that it is particularly effective on harder logical reasoning problems; and that different modalities contribute complementary strengths, with truth-table reasoning helping to overcome key bottlenecks in natural language inference.

The ability to organically reason over and with both text and images is a pillar of human intelligence, yet the ability of Multimodal Large Language Models (MLLMs) to perform such multimodal reasoning remains under-explored. Existing benchmarks often emphasize text-dominant reasoning or rely on shallow visual cues, failing to adequately assess integrated visual and textual reasoning. We introduce EMMA (Enhanced MultiModal reAsoning), a benchmark targeting organic multimodal reasoning across mathematics, physics, chemistry, and coding. EMMA tasks demand advanced cross-modal reasoning that cannot be addressed by reasoning independently in each modality, offering an enhanced test suite for MLLMs' reasoning capabilities. Our evaluation of state-of-the-art MLLMs on EMMA reveals significant limitations in handling complex multimodal and multi-step reasoning tasks, even with advanced techniques like Chain-of-Thought prompting and test-time compute scaling underperforming. These findings underscore the need for improved multimodal architectures and training paradigms to close the gap between human and model reasoning in multimodality.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

Prompt engineering and calibration make large language models excel at reasoning tasks, including multiple choice commonsense reasoning. From a practical perspective, we investigate and evaluate these strategies on smaller language models. Through experiments on five commonsense reasoning benchmarks, we find that each strategy favors certain models, but their joint effects are mostly negative.

Multimodal reasoning, which integrates language and visual cues into problem solving and decision making, is a fundamental aspect of human intelligence and a crucial step toward artificial general intelligence. However, the evaluation of multimodal reasoning capabilities in Multimodal Large Language Models (MLLMs) remains inadequate. Most existing reasoning benchmarks are constrained by limited data size, narrow domain coverage, and unstructured knowledge distribution. To close these gaps, we introduce MDK12-Bench, a multi-disciplinary benchmark assessing the reasoning capabilities of MLLMs via real-world K-12 examinations. Spanning six disciplines (math, physics, chemistry, biology, geography, and information science), our benchmark comprises 140K reasoning instances across diverse difficulty levels from primary school to 12th grade. It features 6,827 instance-level knowledge point annotations based on a well-organized knowledge structure, detailed answer explanations, difficulty labels and cross-year partitions, providing a robust platform for comprehensive evaluation. Additionally, we present a novel dynamic evaluation framework to mitigate data contamination issues by bootstrapping question forms, question types, and image styles during evaluation. Extensive experiment on MDK12-Bench reveals the significant limitation of current MLLMs in multimodal reasoning. The findings on our benchmark provide insights into the development of the next-generation models. Our data and codes are available at https://github.com/LanceZPF/MDK12.

Language models have recently advanced into the realm of reasoning, yet it is through multimodal reasoning that we can fully unlock the potential to achieve more comprehensive, human-like cognitive capabilities. This survey provides a systematic overview of the recent multimodal reasoning approaches, categorizing them into two levels: language-centric multimodal reasoning and collaborative multimodal reasoning. The former encompasses one-pass visual perception and active visual perception, where vision primarily serves a supporting role in language reasoning. The latter involves action generation and state update within reasoning process, enabling a more dynamic interaction between modalities. Furthermore, we analyze the technical evolution of these methods, discuss their inherent challenges, and introduce key benchmark tasks and evaluation metrics for assessing multimodal reasoning performance. Finally, we provide insights into future research directions from the following two perspectives: (i) from visual-language reasoning to omnimodal reasoning and (ii) from multimodal reasoning to multimodal agents. This survey aims to provide a structured overview that will inspire further advancements in multimodal reasoning research.

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam et al. (2024); Zecevic et al. (2023); Wu et al. (2024) highlight a significant gap between their language proficiency and reasoning abilities. Reasoning in LLMs and Vision Language Models (VLMs) aims to bridge this gap by enabling these models to think and re-evaluate their actions and responses. Reasoning is an essential capability for complex problem-solving and a necessary step toward establishing trust in Artificial Intelligence (AI). This will make AI suitable for deployment in sensitive domains, such as healthcare, banking, law, defense, security etc. In recent times, with the advent of powerful reasoning models like OpenAI O1 and DeepSeek R1, reasoning endowment has become a critical research topic in LLMs. In this paper, we provide a detailed overview and comparison of existing reasoning techniques and present a systematic survey of reasoning-imbued language models. We also study current challenges and present our findings.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors. However, these benchmarks evaluate models solely based on final numerical answers, neglecting rigorous reasoning and proof generation which are essential for real-world mathematical tasks. To address this, we introduce the first comprehensive evaluation of full-solution reasoning for challenging mathematical problems. Using expert human annotators, we evaluated several state-of-the-art reasoning models on the six problems from the 2025 USAMO within hours of their release. Our results reveal that all tested models struggled significantly, achieving less than 5% on average. Through detailed analysis of reasoning traces, we identify the most common failure modes and find several unwanted artifacts arising from the optimization strategies employed during model training. Overall, our results suggest that current LLMs are inadequate for rigorous mathematical reasoning tasks, highlighting the need for substantial improvements in reasoning and proof generation capabilities.

The reasoning capabilities of LLM (Large Language Model) are widely acknowledged in recent research, inspiring studies on tool learning and autonomous agents. LLM serves as the "brain" of the agent, orchestrating multiple tools for collaborative multi-step task solving. Unlike methods invoking tools like calculators or weather APIs for straightforward tasks, multi-modal agents excel by integrating diverse AI models for complex challenges. However, current multi-modal agents neglect the significance of model selection: they primarily focus on the planning and execution phases, and will only invoke predefined task-specific models for each subtask, making the execution fragile. Meanwhile, other traditional model selection methods are either incompatible with or suboptimal for the multi-modal agent scenarios, due to ignorance of dependencies among subtasks arising by multi-step reasoning. To this end, we identify the key challenges therein and propose the M^3 framework as a plug-in with negligible runtime overhead at test-time. This framework improves model selection and bolsters the robustness of multi-modal agents in multi-step reasoning. In the absence of suitable benchmarks, we create MS-GQA, a new dataset specifically designed to investigate the model selection challenge in multi-modal agents. Our experiments reveal that our framework enables dynamic model selection, considering both user inputs and subtask dependencies, thereby robustifying the overall reasoning process. Our code and benchmark: https://github.com/LINs-lab/M3.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Reasoning capabilities have significantly improved the performance of vision-language models (VLMs) in domains such as mathematical problem-solving, coding, and visual question-answering. However, their impact on real-world applications remains unclear. This paper presents the first empirical study on the effectiveness of reasoning-enabled VLMs in mobile GUI agents, a domain that requires interpreting complex screen layouts, understanding user instructions, and executing multi-turn interactions. We evaluate two pairs of commercial models--Gemini 2.0 Flash and Claude 3.7 Sonnet--comparing their base and reasoning-enhanced versions across two static benchmarks (ScreenSpot and AndroidControl) and one interactive environment (AndroidWorld). We surprisingly find the Claude 3.7 Sonnet reasoning model achieves state-of-the-art performance on AndroidWorld. However, reasoning VLMs generally offer marginal improvements over non-reasoning models on static benchmarks and even degrade performance in some agent setups. Notably, reasoning and non-reasoning VLMs fail on different sets of tasks, suggesting that reasoning does have an impact, but its benefits and drawbacks counterbalance each other. We attribute these inconsistencies to the limitations of benchmarks and VLMs. Based on the findings, we provide insights for further enhancing mobile GUI agents in terms of benchmarks, VLMs, and their adaptability in dynamically invoking reasoning VLMs. The experimental data are publicly available at https://github.com/LlamaTouch/VLM-Reasoning-Traces.

By extending the advantage of chain-of-thought (CoT) reasoning in human-like step-by-step processes to multimodal contexts, multimodal CoT (MCoT) reasoning has recently garnered significant research attention, especially in the integration with multimodal large language models (MLLMs). Existing MCoT studies design various methodologies and innovative reasoning paradigms to address the unique challenges of image, video, speech, audio, 3D, and structured data across different modalities, achieving extensive success in applications such as robotics, healthcare, autonomous driving, and multimodal generation. However, MCoT still presents distinct challenges and opportunities that require further focus to ensure consistent thriving in this field, where, unfortunately, an up-to-date review of this domain is lacking. To bridge this gap, we present the first systematic survey of MCoT reasoning, elucidating the relevant foundational concepts and definitions. We offer a comprehensive taxonomy and an in-depth analysis of current methodologies from diverse perspectives across various application scenarios. Furthermore, we provide insights into existing challenges and future research directions, aiming to foster innovation toward multimodal AGI.

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

This paper presents a case study of coding tasks by the latest reasoning models of OpenAI, i.e. o1-preview and o1-mini, in comparison with other frontier models. The o1 models deliver SOTA results for WebApp1K, a single-task benchmark. To this end, we introduce WebApp1K-Duo, a harder benchmark doubling number of tasks and test cases. The new benchmark causes the o1 model performances to decline significantly, falling behind Claude 3.5. Moreover, they consistently fail when confronted with atypical yet correct test cases, a trap non-reasoning models occasionally avoid. We hypothesize that the performance variability is due to instruction comprehension. Specifically, the reasoning mechanism boosts performance when all expectations are captured, meanwhile exacerbates errors when key expectations are missed, potentially impacted by input lengths. As such, we argue that the coding success of reasoning models hinges on the top-notch base model and SFT to ensure meticulous adherence to instructions.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench benchmark, a dataset designed to evaluate logical coherence and real-world reasoning, we propose a multi-step prompting strategy coupled with global consistency checks to improve model accuracy and robustness. Through comparative analysis of state-of-the-art models, including Claude 3 Opus, Claude 3.5, GPT- 4o, and o1-preview, we demonstrate that iterative reasoning significantly enhances model performance, with improvements observed in both standard accuracy metrics (AVG@5) and a newly introduced metric, Extreme Averaging (EAG@5). Our results reveal model-specific strengths: Claude excels in maintaining logical consistency, while GPT-4o exhibits exploratory creativity but struggles with ambiguous prompts. By analyzing case studies and identifying gaps in spatial and temporal reasoning, we highlight areas for further refinement. The findings underscore the potential of structured reasoning frameworks to address inherent model limitations, irrespective of pretraining methodologies. This study lays the groundwork for integrating dynamic feedback mechanisms, adaptive restart strategies, and diverse evaluation metrics to advance LLM reasoning capabilities across complex and multi-domain problem spaces.

Advanced reasoning in large language models has achieved remarkable performance on challenging tasks, but the prevailing long-context reasoning paradigm faces critical limitations: quadratic computational scaling with sequence length, reasoning constrained by maximum context boundaries, and performance degradation beyond pre-training context windows. Existing approaches primarily compress reasoning chains without addressing the fundamental scaling problem. To overcome these challenges, we introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization. By interleaving short reasoning segments with concise progress summaries, our approach enables unbounded reasoning depth while maintaining bounded computational costs. This creates a characteristic sawtooth memory pattern that significantly reduces computational complexity compared to traditional approaches. Furthermore, we develop a methodology for reconstructing long-context reasoning datasets into our iterative format, transforming OpenR1-Math into 333K training instances. Experiments across multiple model architectures demonstrate that our approach reduces computational costs while improving performance, with Qwen2.5-Math-7B showing 3-13% improvements across MATH500, AIME24, and GPQA_diamond benchmarks. Our work challenges the assumed trade-off between reasoning depth and computational efficiency, providing a more scalable approach to complex reasoning without architectural modifications.

Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging benchmark aimed at evaluating the general cognitive reasoning abilities of MLLMs. PolyMATH comprises 5,000 manually collected high-quality images of cognitive textual and visual challenges across 10 distinct categories, including pattern recognition, spatial reasoning, and relative reasoning. We conducted a comprehensive, and quantitative evaluation of 15 MLLMs using four diverse prompting strategies, including Chain-of-Thought and Step-Back. The best scores achieved on PolyMATH are ~41%, ~36%, and ~27%, obtained by Claude-3.5 Sonnet, GPT-4o and Gemini-1.5 Pro respectively - highlighting the logical and visual complexity of these questions. A further fine-grained error analysis reveals that these models struggle to understand spatial relations and perform drawn-out, high-level reasoning. This is further strengthened by our ablation study estimating MLLM performance when given textual descriptions in place of diagrams. As evidenced by ~4% improvement over textual descriptions as opposed to actual images, we discover that models do not truly comprehend visual diagrams and the spatial information therein, and are thus prone to logical errors. Finally, we evaluate the OpenAI o1 models and find that their performance only matches the human baseline, highlighting the difficulty of the benchmark. The results on PolyMATH highlight the room for improvement in multi-modal reasoning and provide unique insights to guide the development of future MLLMs.

We introduce HoVer (HOppy VERification), a dataset for many-hop evidence extraction and fact verification. It challenges models to extract facts from several Wikipedia articles that are relevant to a claim and classify whether the claim is Supported or Not-Supported by the facts. In HoVer, the claims require evidence to be extracted from as many as four English Wikipedia articles and embody reasoning graphs of diverse shapes. Moreover, most of the 3/4-hop claims are written in multiple sentences, which adds to the complexity of understanding long-range dependency relations such as coreference. We show that the performance of an existing state-of-the-art semantic-matching model degrades significantly on our dataset as the number of reasoning hops increases, hence demonstrating the necessity of many-hop reasoning to achieve strong results. We hope that the introduction of this challenging dataset and the accompanying evaluation task will encourage research in many-hop fact retrieval and information verification. We make the HoVer dataset publicly available at https://hover-nlp.github.io

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

Efficiently tackling combinatorial reasoning problems, particularly the notorious NP-hard tasks, remains a significant challenge for AI research. Recent efforts have sought to enhance planning by incorporating hierarchical high-level search strategies, known as subgoal methods. While promising, their performance against traditional low-level planners is inconsistent, raising questions about their application contexts. In this study, we conduct an in-depth exploration of subgoal-planning methods for combinatorial reasoning. We identify the attributes pivotal for leveraging the advantages of high-level search: hard-to-learn value functions, complex action spaces, presence of dead ends in the environment, or using data collected from diverse experts. We propose a consistent evaluation methodology to achieve meaningful comparisons between methods and reevaluate the state-of-the-art algorithms.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

We propose a framework for robust evaluation of reasoning capabilities of language models, using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a problem compared to a snapshot of the functional variant. We have rewritten the relevant fragment of the MATH benchmark into its functional variant MATH(), with functionalization of other benchmarks to follow. When evaluating current state-of-the-art models over snapshots of MATH(), we find a reasoning gap -- the percentage difference between the static and functional accuracies. We find reasoning gaps from 58.35% to 80.31% among the state-of-the-art closed and open weights models that perform well on static benchmarks, with the caveat that the gaps are likely to be smaller with more sophisticated prompting strategies. Here we show that models which anecdotally have good reasoning performance over real-world tasks, have quantifiable lower gaps, motivating the open problem of building "gap 0" models. Code for evaluation and new evaluation datasets, three MATH() snapshots, are publicly available at https://github.com/consequentai/fneval/.

Large Language Models (LLMs) have excelled in multi-hop question-answering (M-QA) due to their advanced reasoning abilities. However, the impact of the inherent reasoning structures on LLM M-QA performance remains unclear, largely due to the absence of QA datasets that provide fine-grained reasoning structures. To address this gap, we introduce the Graph Reasoning-Structured Question Answering Dataset (GRS-QA), which includes both semantic contexts and reasoning structures for QA pairs. Unlike existing M-QA datasets, where different reasoning structures are entangled together, GRS-QA explicitly captures intricate reasoning pathways by constructing reasoning graphs, where nodes represent textual contexts and edges denote logical flows. These reasoning graphs of different structures enable a fine-grained evaluation of LLM reasoning capabilities across various reasoning structures. Our empirical analysis reveals that LLMs perform differently when handling questions with varying reasoning structures. This finding facilitates the exploration of textual structures as compared with semantics.

Reasoning has long been viewed as an emergent property of large language models (LLMs), appearing at or above a certain scale (sim100B parameters). However, recent studies challenge this assumption, showing that small language models (SLMs) can also achieve competitive reasoning performance. SLMs are increasingly favored for their efficiency and deployability. However, there is a lack of systematic study on the reasoning abilities of diverse SLMs, including those trained from scratch or derived from LLMs through quantization, pruning, and distillation. This raises a critical question: Can SLMs achieve reasoning abilities comparable to LLMs? In this work, we systematically survey, benchmark, and analyze 72 SLMs from six model families across 14 reasoning benchmarks. For reliable evaluation, we examine four evaluation methods and compare four LLM judges against human evaluations on 800 data points. We repeat all experiments three times to ensure a robust performance assessment. Additionally, we analyze the impact of different prompting strategies in small models. Beyond accuracy, we also evaluate model robustness under adversarial conditions and intermediate reasoning steps. Our findings challenge the assumption that scaling is the only way to achieve strong reasoning. Instead, we foresee a future where SLMs with strong reasoning capabilities can be developed through structured training or post-training compression. They can serve as efficient alternatives to LLMs for reasoning-intensive tasks.

While large language models demonstrate impressive performance on static benchmarks, the true potential of large language models as self-learning and reasoning agents in dynamic environments remains unclear. This study systematically evaluates the efficacy of self-reflection, heuristic mutation, and planning as prompting techniques to test the adaptive capabilities of agents. We conduct experiments with various open-source language models in dynamic environments and find that larger models generally outperform smaller ones, but that strategic prompting can close this performance gap. Second, a too-long prompt can negatively impact smaller models on basic reactive tasks, while larger models show more robust behaviour. Third, advanced prompting techniques primarily benefit smaller models on complex games, but offer less improvement for already high-performing large language models. Yet, we find that advanced reasoning methods yield highly variable outcomes: while capable of significantly improving performance when reasoning and decision-making align, they also introduce instability and can lead to big performance drops. Compared to human performance, our findings reveal little evidence of true emergent reasoning. Instead, large language model performance exhibits persistent limitations in crucial areas such as planning, reasoning, and spatial coordination, suggesting that current-generation large language models still suffer fundamental shortcomings that may not be fully overcome through self-reflective prompting alone. Reasoning is a multi-faceted task, and while reasoning methods like Chain of thought improves multi-step reasoning on math word problems, our findings using dynamic benchmarks highlight important shortcomings in general reasoning capabilities, indicating a need to move beyond static benchmarks to capture the complexity of reasoning.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

Vision-Language Models (VLMs) such as GPT-4V have recently demonstrated incredible strides on diverse vision language tasks. We dig into vision-based deductive reasoning, a more sophisticated but less explored realm, and find previously unexposed blindspots in the current SOTA VLMs. Specifically, we leverage Raven's Progressive Matrices (RPMs), to assess VLMs' abilities to perform multi-hop relational and deductive reasoning relying solely on visual clues. We perform comprehensive evaluations of several popular VLMs employing standard strategies such as in-context learning, self-consistency, and Chain-of-thoughts (CoT) on three diverse datasets, including the Mensa IQ test, IntelligenceTest, and RAVEN. The results reveal that despite the impressive capabilities of LLMs in text-based reasoning, we are still far from achieving comparable proficiency in visual deductive reasoning. We found that certain standard strategies that are effective when applied to LLMs do not seamlessly translate to the challenges presented by visual reasoning tasks. Moreover, a detailed analysis reveals that VLMs struggle to solve these tasks mainly because they are unable to perceive and comprehend multiple, confounding abstract patterns in RPM examples.

Large language models (LLMs) have shown impressive performance in various reasoning benchmarks with the emergence of Chain-of-Thought (CoT) and its derivative methods, particularly in tasks involving multi-choice questions (MCQs). However, current works all process data uniformly without considering the problem-solving difficulty, which means an excessive focus on simple questions while insufficient to intricate ones. To address this challenge, we inspired by humans using heuristic strategies to categorize tasks and handle them individually, propose to apply the Divide and Conquer to LLMs reasoning. First, we divide questions into different subsets based on the statistical confidence score (CS), then fix nearly resolved sets and conquer demanding nuanced process ones with elaborately designed methods, including Prior Knowledge based Reasoning (PKR) and Filter Choices based Reasoning (FCR), as well as their integration variants. Our experiments demonstrate that this proposed strategy significantly boosts the models' reasoning abilities across nine datasets involving arithmetic, commonsense, and logic tasks. For instance, compared to baseline, we make a striking improvement on low confidence subsets of 8.72\% for AQuA, 15.07\% for ARC Challenge and 7.71\% for RiddleSense. In addition, through extensive analysis on length of rationale and number of options, we verify that longer reasoning paths in PKR could prevent models from referring infer-harmful shortcuts, and also find that removing irrelevant choices in FCR would substantially avoid models' confusion. The code is at https://github.com/AiMijie/Divide-and-Conquer

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.