Shalyt/ASyMOB-Algebraic_Symbolic_Mathematical_Operations_Benchmark

ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark

This dataset is associated with the paper "ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark".

Abstract

Large language models (LLMs) are rapidly approaching the level of proficiency in university-level symbolic mathematics required for applications in advanced science and technology. However, existing benchmarks fall short in assessing the core skills of LLMs in symbolic mathematics—such as integration, limits, differential equations, and algebraic simplification.

To address this gap, we introduce ASyMOB (pronounced Asimov, in tribute to the renowned author), a novel assessment framework focused exclusively on symbolic manipulation, featuring 17,092 unique math challenges, organized by similarity and complexity. ASyMOB enables analysis of LLM failure root-causes and generalization capabilities by comparing performance in problems that differ by simple numerical or symbolic "perturbations".

Evaluated LLMs exhibit substantial degradation in performance for all perturbation types (up to -70.3%), suggesting reliance on memorized patterns rather than deeper understanding of symbolic math, even among models achieving high baseline accuracy. Comparing LLM performance to computer algebra systems (CAS, e.g. SymPy), we identify examples where CAS fail while LLMs succeed, as well as problems solved only when combining both approaches. Models capable of integrated code execution yielded higher accuracy compared to their performance without code, particularly stabilizing weaker models (up to +33.1% for certain perturbation types).

Notably, the most advanced models (o4-mini, Gemini 2.5 Flash) demonstrate not only high symbolic math proficiency (scoring 96.8% and 97.6% on the unperturbed set), but also remarkable robustness against perturbations, (-21.7% and -21.2% vs. average -50.4% for the other models). This may indicate a recent "phase transition" in the generalization capabilities of frontier LLMs. It remains to be seen whether the path forward lies in deeper integration with more sophisticated external tools, or in developing models so capable that symbolic math systems like CAS become unnecessary.

ASyMOB Dataset Generation

See the ASyMOB code repository for the data generation code and seed CSV.

ASyMOB_Generation.py generates a diverse set of mathematical question variants from a seed CSV file. It leverages the SymPy library for symbolic mathematics to create various perturbations of original questions, including symbolic, numeric, and equivalence-based transformations. The generated questions are then saved to a JSON file.

Usage

1. Prepare your seed data: Ensure you have a CSV file named Seed_and_Max_Symbolic_Perturbations.csv in the same directory as the script. This CSV should contain the seed mathematical questions, their maximal symbolic perturbations, and answers as SymPy expressions.

   The expected fields in Seed_and_Max_Symbolic_Perturbations.csv are:

   • Challenge: The mathematical question in LaTeX format, including assumptions regarding variables or other mathematical details.
   • Answer in LaTeX (optional): The answer to the question, represented as a LaTeX string.
   • Answer in Sympy: The answer to the question, represented as a SymPy expression string.
   • Variation: "Original" or "Symbolic".
   • Source: Identifies the origin of the question.

2. Run the script:

   python ASyMOB_Generation.py
   

3. Output: The script will generate a JSON file named Full_ASyMOB_Dataset.json in the same directory. This file will contain all the original seed and symbolic questions along with their newly generated symbolic, numeric, and equivalence-based variants.

   The fields in Full_ASyMOB_Dataset.json are:

   • Index: Sequential ID.
   • Challenge: The mathematical question in LaTeX format, including assumptions regarding variables or other mathematical details.
   • Answer in Sympy: The answer to the question, represented as a SymPy expression string.
   • Variation: e.g., Equivalence-All-Hard, Numeric-One-3, etc.
   • Source: Same as the seed question from which this variation originated.

Customization

• Seed_and_Max_Symbolic_Perturbations.csv: Modify this CSV to add new seed questions or adjust existing ones.
• symnoise_char_list, symnoise_sym_list: Adjust the lists of symbolic characters and their SymPy representations if your questions use different symbols for perturbation (ASyMOB uses 'A', 'B', 'F', 'G', 'H' by default).
• equivalent_forms_easy, equivalent_forms_hard: Add or modify the equivalent forms to introduce different types of mathematical equivalences.
• noise_digits and reps_num: In generate_NA2S, you can change noise_digits to control the range of random numbers used for numeric perturbations and reps_num to control the number of repetitions for each item.

Citation

If you use ASyMOB in your research, please cite the paper:

@misc{ASyMOB,
      title={ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark}, 
      author={Michael Shalyt and Rotem Elimelech and Ido Kaminer},
      year={2025},
      eprint={2505.23851},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2505.23851}, 
}