kishizaki-sci commited on
Commit
6263f7d
Β·
verified Β·
1 Parent(s): ddba123

Upload llama4_inference.ipynb

Browse files
Files changed (1) hide show
  1. llama4_inference.ipynb +385 -22
llama4_inference.ipynb CHANGED
@@ -52,7 +52,7 @@
52
  "metadata": {},
53
  "outputs": [],
54
  "source": [
55
- "quant_path = '/workspace/hf_cache/Llama-4-Scout-17B-16E-Instruct-AWQ'"
56
  ]
57
  },
58
  {
@@ -61,24 +61,65 @@
61
  "id": "c13b72e4-f6cd-4642-a110-040844127541",
62
  "metadata": {},
63
  "outputs": [
 
 
 
 
 
 
 
 
 
 
 
 
 
 
64
  {
65
  "name": "stderr",
66
  "output_type": "stream",
67
  "text": [
68
- "/workspace/llama4-awq/AutoAWQ/awq/models/llama4.py:313: UserWarning: Multimodal input has not been implemented in Llama4AWQForConditionalGeneration yet.\n",
69
- " warnings.warn(\"Multimodal input has not been implemented in Llama4AWQForConditionalGeneration yet.\", UserWarning)\n",
70
- "You have set `use_cache` to `False`, but cache_implementation is set to hybrid. cache_implementation will have no effect.\n"
71
  ]
72
  },
73
  {
74
  "data": {
75
  "application/vnd.jupyter.widget-view+json": {
76
- "model_id": "15b41a3c3e154516b93b4f2b90e976fb",
77
  "version_major": 2,
78
  "version_minor": 0
79
  },
80
  "text/plain": [
81
- "Replacing MoE Block...: 0%| | 0/48 [00:00<?, ?it/s]"
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
82
  ]
83
  },
84
  "metadata": {},
@@ -87,12 +128,306 @@
87
  {
88
  "data": {
89
  "application/vnd.jupyter.widget-view+json": {
90
- "model_id": "38fe24c9ae5549a7a7c674292b0e4f95",
91
  "version_major": 2,
92
  "version_minor": 0
93
  },
94
  "text/plain": [
95
- "Replacing layers...: 0%| | 0/48 [00:00<?, ?it/s]"
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
96
  ]
97
  },
98
  "metadata": {},
@@ -102,7 +437,29 @@
102
  "name": "stderr",
103
  "output_type": "stream",
104
  "text": [
105
- "/workspace/llama4-awq/AutoAWQ/awq/models/base.py:540: UserWarning: Skipping fusing modules because AWQ extension is not installed.No module named 'awq_ext'\n",
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
106
  " warnings.warn(\"Skipping fusing modules because AWQ extension is not installed.\" + msg)\n"
107
  ]
108
  },
@@ -110,8 +467,8 @@
110
  "name": "stdout",
111
  "output_type": "stream",
112
  "text": [
113
- "CPU times: user 1h 36min 24s, sys: 24min 59s, total: 2h 1min 23s\n",
114
- "Wall time: 30min 59s\n"
115
  ]
116
  }
117
  ],
@@ -131,7 +488,7 @@
131
  "name": "stdout",
132
  "output_type": "stream",
133
  "text": [
134
- "Sat Apr 19 17:03:15 2025 \n",
135
  "+-----------------------------------------------------------------------------------------+\n",
136
  "| NVIDIA-SMI 565.57.01 Driver Version: 565.57.01 CUDA Version: 12.7 |\n",
137
  "|-----------------------------------------+------------------------+----------------------+\n",
@@ -139,8 +496,8 @@
139
  "| Fan Temp Perf Pwr:Usage/Cap | Memory-Usage | GPU-Util Compute M. |\n",
140
  "| | | MIG M. |\n",
141
  "|=========================================+========================+======================|\n",
142
- "| 0 NVIDIA A100-SXM4-80GB On | 00000000:B7:00.0 Off | 0 |\n",
143
- "| N/A 25C P0 75W / 400W | 60415MiB / 81920MiB | 0% Default |\n",
144
  "| | | Disabled |\n",
145
  "+-----------------------------------------+------------------------+----------------------+\n",
146
  " \n",
@@ -200,8 +557,8 @@
200
  "name": "stdout",
201
  "output_type": "stream",
202
  "text": [
203
- "CPU times: user 5min 36s, sys: 5min 9s, total: 10min 45s\n",
204
- "Wall time: 10min 45s\n"
205
  ]
206
  }
207
  ],
@@ -237,15 +594,21 @@
237
  "\n",
238
  "where $\\Gamma^i_{jk}$ are the Christoffel symbols of the second kind, which define the connection.\n",
239
  "\n",
240
- "In general relativity, the Levi-Civita connection is a fundamental concept, and it is assumed to be torsion-free. This connection is used to define the covariant derivative of tensors, which is essential for describing the curvature of spacetime.\n",
 
 
 
 
 
 
 
241
  "\n",
242
- "The assumption of a torsion-free connection has important implications:\n",
 
243
  "\n",
244
- "1. **Geodesic equation**: The geodesic equation, which describes the shortest path in curved spacetime, is derived from the Levi-Civita connection. A torsion-free connection ensures that geodesics are symmetric, meaning that they have no \"twist\" or \"turn\".\n",
245
- "2. **Riemannian geometry**: The Levi-Civita connection is a fundamental ingredient in Riemannian geometry, which is the mathematical framework for describing curved spacetime in general relativity.\n",
246
- "3. **Einstein's field equations**: The Einstein field equations, which relate the curvature of spacetime to the distribution of mass and energy, rely on the Levi-Civita connection.\n",
247
  "\n",
248
- "In summary, a torsion-free connection in general relativity means that the connection used to describe the curvature of spacetime has zero torsion, which is a fundamental assumption in Riemannian geometry and leads to the Levi-Civita connection. This assumption is crucial for the mathematical formulation of general relativity, including the geodesic equation and Einstein's field equations.<|eot|>\n"
249
  ]
250
  }
251
  ],
 
52
  "metadata": {},
53
  "outputs": [],
54
  "source": [
55
+ "quant_path = 'kishizaki-sci/Llama-4-Scout-17B-16E-Instruct-AWQ'"
56
  ]
57
  },
58
  {
 
61
  "id": "c13b72e4-f6cd-4642-a110-040844127541",
62
  "metadata": {},
63
  "outputs": [
64
+ {
65
+ "data": {
66
+ "application/vnd.jupyter.widget-view+json": {
67
+ "model_id": "4f6c7b795fb24940b752dded2f51dea0",
68
+ "version_major": 2,
69
+ "version_minor": 0
70
+ },
71
+ "text/plain": [
72
+ "config.json: 0%| | 0.00/3.55k [00:00<?, ?B/s]"
73
+ ]
74
+ },
75
+ "metadata": {},
76
+ "output_type": "display_data"
77
+ },
78
  {
79
  "name": "stderr",
80
  "output_type": "stream",
81
  "text": [
82
+ "/workspace/AutoAWQ/awq/models/llama4.py:312: UserWarning: Multimodal input has not been implemented in Llama4AWQForConditionalGeneration yet.\n",
83
+ " warnings.warn(\"Multimodal input has not been implemented in Llama4AWQForConditionalGeneration yet.\", UserWarning)\n"
 
84
  ]
85
  },
86
  {
87
  "data": {
88
  "application/vnd.jupyter.widget-view+json": {
89
+ "model_id": "02743a30540244bbb4c05585becc4cc8",
90
  "version_major": 2,
91
  "version_minor": 0
92
  },
93
  "text/plain": [
94
+ "Fetching 25 files: 0%| | 0/25 [00:00<?, ?it/s]"
95
+ ]
96
+ },
97
+ "metadata": {},
98
+ "output_type": "display_data"
99
+ },
100
+ {
101
+ "data": {
102
+ "application/vnd.jupyter.widget-view+json": {
103
+ "model_id": "3200dd87c1df4ad2a0d1ce0a300f094c",
104
+ "version_major": 2,
105
+ "version_minor": 0
106
+ },
107
+ "text/plain": [
108
+ "llama4_inference.ipynb: 0%| | 0.00/10.5k [00:00<?, ?B/s]"
109
+ ]
110
+ },
111
+ "metadata": {},
112
+ "output_type": "display_data"
113
+ },
114
+ {
115
+ "data": {
116
+ "application/vnd.jupyter.widget-view+json": {
117
+ "model_id": "b132c3a11c024af78dd8fd4d30b579cc",
118
+ "version_major": 2,
119
+ "version_minor": 0
120
+ },
121
+ "text/plain": [
122
+ "generation_config.json: 0%| | 0.00/239 [00:00<?, ?B/s]"
123
  ]
124
  },
125
  "metadata": {},
 
128
  {
129
  "data": {
130
  "application/vnd.jupyter.widget-view+json": {
131
+ "model_id": "1f505cb27bc04c92b48ca9e27202cb4b",
132
  "version_major": 2,
133
  "version_minor": 0
134
  },
135
  "text/plain": [
136
+ ".gitattributes: 0%| | 0.00/1.57k [00:00<?, ?B/s]"
137
+ ]
138
+ },
139
+ "metadata": {},
140
+ "output_type": "display_data"
141
+ },
142
+ {
143
+ "data": {
144
+ "application/vnd.jupyter.widget-view+json": {
145
+ "model_id": "43b1b86a0c304e56b1870d08598b374f",
146
+ "version_major": 2,
147
+ "version_minor": 0
148
+ },
149
+ "text/plain": [
150
+ "model-00002-of-00013.safetensors: 0%| | 0.00/4.98G [00:00<?, ?B/s]"
151
+ ]
152
+ },
153
+ "metadata": {},
154
+ "output_type": "display_data"
155
+ },
156
+ {
157
+ "data": {
158
+ "application/vnd.jupyter.widget-view+json": {
159
+ "model_id": "7babbb9a6b154f509c88a56b4fee3d0e",
160
+ "version_major": 2,
161
+ "version_minor": 0
162
+ },
163
+ "text/plain": [
164
+ "README.md: 0%| | 0.00/138 [00:00<?, ?B/s]"
165
+ ]
166
+ },
167
+ "metadata": {},
168
+ "output_type": "display_data"
169
+ },
170
+ {
171
+ "data": {
172
+ "application/vnd.jupyter.widget-view+json": {
173
+ "model_id": "405cd2691a844317b6570eb80c622d24",
174
+ "version_major": 2,
175
+ "version_minor": 0
176
+ },
177
+ "text/plain": [
178
+ "model-00001-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
179
+ ]
180
+ },
181
+ "metadata": {},
182
+ "output_type": "display_data"
183
+ },
184
+ {
185
+ "data": {
186
+ "application/vnd.jupyter.widget-view+json": {
187
+ "model_id": "e979f0b6efbe40baa318dccb57bffe24",
188
+ "version_major": 2,
189
+ "version_minor": 0
190
+ },
191
+ "text/plain": [
192
+ "model-00004-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
193
+ ]
194
+ },
195
+ "metadata": {},
196
+ "output_type": "display_data"
197
+ },
198
+ {
199
+ "data": {
200
+ "application/vnd.jupyter.widget-view+json": {
201
+ "model_id": "efccd71f8aa2492bad03ebadbbef596d",
202
+ "version_major": 2,
203
+ "version_minor": 0
204
+ },
205
+ "text/plain": [
206
+ "model-00005-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
207
+ ]
208
+ },
209
+ "metadata": {},
210
+ "output_type": "display_data"
211
+ },
212
+ {
213
+ "data": {
214
+ "application/vnd.jupyter.widget-view+json": {
215
+ "model_id": "a3028a64430744beb181ace86753bee6",
216
+ "version_major": 2,
217
+ "version_minor": 0
218
+ },
219
+ "text/plain": [
220
+ "chat_template.json: 0%| | 0.00/5.18k [00:00<?, ?B/s]"
221
+ ]
222
+ },
223
+ "metadata": {},
224
+ "output_type": "display_data"
225
+ },
226
+ {
227
+ "data": {
228
+ "application/vnd.jupyter.widget-view+json": {
229
+ "model_id": "448ff54d8a6642e685474d3bc49de09b",
230
+ "version_major": 2,
231
+ "version_minor": 0
232
+ },
233
+ "text/plain": [
234
+ "model-00003-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
235
+ ]
236
+ },
237
+ "metadata": {},
238
+ "output_type": "display_data"
239
+ },
240
+ {
241
+ "data": {
242
+ "application/vnd.jupyter.widget-view+json": {
243
+ "model_id": "63cb05c948ef476c98df712735133fa7",
244
+ "version_major": 2,
245
+ "version_minor": 0
246
+ },
247
+ "text/plain": [
248
+ "model-00006-of-00013.safetensors: 0%| | 0.00/4.98G [00:00<?, ?B/s]"
249
+ ]
250
+ },
251
+ "metadata": {},
252
+ "output_type": "display_data"
253
+ },
254
+ {
255
+ "data": {
256
+ "application/vnd.jupyter.widget-view+json": {
257
+ "model_id": "1afb22e38b7c46c0ab496bd67c949402",
258
+ "version_major": 2,
259
+ "version_minor": 0
260
+ },
261
+ "text/plain": [
262
+ "model-00007-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
263
+ ]
264
+ },
265
+ "metadata": {},
266
+ "output_type": "display_data"
267
+ },
268
+ {
269
+ "data": {
270
+ "application/vnd.jupyter.widget-view+json": {
271
+ "model_id": "ded5ae0f710a4124b00cb0b061383962",
272
+ "version_major": 2,
273
+ "version_minor": 0
274
+ },
275
+ "text/plain": [
276
+ "model-00008-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
277
+ ]
278
+ },
279
+ "metadata": {},
280
+ "output_type": "display_data"
281
+ },
282
+ {
283
+ "data": {
284
+ "application/vnd.jupyter.widget-view+json": {
285
+ "model_id": "0db9d375464c415ebb33fc0b268a9950",
286
+ "version_major": 2,
287
+ "version_minor": 0
288
+ },
289
+ "text/plain": [
290
+ "model-00009-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
291
+ ]
292
+ },
293
+ "metadata": {},
294
+ "output_type": "display_data"
295
+ },
296
+ {
297
+ "data": {
298
+ "application/vnd.jupyter.widget-view+json": {
299
+ "model_id": "e49ff7276a7b493cb5ab7dc222e9d3ec",
300
+ "version_major": 2,
301
+ "version_minor": 0
302
+ },
303
+ "text/plain": [
304
+ "model-00010-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
305
+ ]
306
+ },
307
+ "metadata": {},
308
+ "output_type": "display_data"
309
+ },
310
+ {
311
+ "data": {
312
+ "application/vnd.jupyter.widget-view+json": {
313
+ "model_id": "cbb0557242c546708bfb5ba4c7789499",
314
+ "version_major": 2,
315
+ "version_minor": 0
316
+ },
317
+ "text/plain": [
318
+ "model-00011-of-00013.safetensors: 0%| | 0.00/4.98G [00:00<?, ?B/s]"
319
+ ]
320
+ },
321
+ "metadata": {},
322
+ "output_type": "display_data"
323
+ },
324
+ {
325
+ "data": {
326
+ "application/vnd.jupyter.widget-view+json": {
327
+ "model_id": "2c603da8fcc34e0584963099695e7142",
328
+ "version_major": 2,
329
+ "version_minor": 0
330
+ },
331
+ "text/plain": [
332
+ "model-00012-of-00013.safetensors: 0%| | 0.00/5.00G [00:00<?, ?B/s]"
333
+ ]
334
+ },
335
+ "metadata": {},
336
+ "output_type": "display_data"
337
+ },
338
+ {
339
+ "data": {
340
+ "application/vnd.jupyter.widget-view+json": {
341
+ "model_id": "645fee17e47d44e1b7fb51865a00fc73",
342
+ "version_major": 2,
343
+ "version_minor": 0
344
+ },
345
+ "text/plain": [
346
+ "model-00013-of-00013.safetensors: 0%| | 0.00/2.79G [00:00<?, ?B/s]"
347
+ ]
348
+ },
349
+ "metadata": {},
350
+ "output_type": "display_data"
351
+ },
352
+ {
353
+ "data": {
354
+ "application/vnd.jupyter.widget-view+json": {
355
+ "model_id": "a022c5cb1f174ac5bd9fad91cda9352a",
356
+ "version_major": 2,
357
+ "version_minor": 0
358
+ },
359
+ "text/plain": [
360
+ "model.safetensors.index.json: 0%| | 0.00/1.13M [00:00<?, ?B/s]"
361
+ ]
362
+ },
363
+ "metadata": {},
364
+ "output_type": "display_data"
365
+ },
366
+ {
367
+ "data": {
368
+ "application/vnd.jupyter.widget-view+json": {
369
+ "model_id": "f68405f7857d4db1b40b264f25175f43",
370
+ "version_major": 2,
371
+ "version_minor": 0
372
+ },
373
+ "text/plain": [
374
+ "preprocessor_config.json: 0%| | 0.00/636 [00:00<?, ?B/s]"
375
+ ]
376
+ },
377
+ "metadata": {},
378
+ "output_type": "display_data"
379
+ },
380
+ {
381
+ "data": {
382
+ "application/vnd.jupyter.widget-view+json": {
383
+ "model_id": "81bc3a84390f4c388f1012044d4ce6ec",
384
+ "version_major": 2,
385
+ "version_minor": 0
386
+ },
387
+ "text/plain": [
388
+ "processor_config.json: 0%| | 0.00/128 [00:00<?, ?B/s]"
389
+ ]
390
+ },
391
+ "metadata": {},
392
+ "output_type": "display_data"
393
+ },
394
+ {
395
+ "data": {
396
+ "application/vnd.jupyter.widget-view+json": {
397
+ "model_id": "842746981e6e478aae858d3daf844460",
398
+ "version_major": 2,
399
+ "version_minor": 0
400
+ },
401
+ "text/plain": [
402
+ "special_tokens_map.json: 0%| | 0.00/448 [00:00<?, ?B/s]"
403
+ ]
404
+ },
405
+ "metadata": {},
406
+ "output_type": "display_data"
407
+ },
408
+ {
409
+ "data": {
410
+ "application/vnd.jupyter.widget-view+json": {
411
+ "model_id": "067b4e51f41840cdb7305972f1aa0dc6",
412
+ "version_major": 2,
413
+ "version_minor": 0
414
+ },
415
+ "text/plain": [
416
+ "tokenizer.json: 0%| | 0.00/27.9M [00:00<?, ?B/s]"
417
+ ]
418
+ },
419
+ "metadata": {},
420
+ "output_type": "display_data"
421
+ },
422
+ {
423
+ "data": {
424
+ "application/vnd.jupyter.widget-view+json": {
425
+ "model_id": "5ceb2f619f9f4513bc307c5846fae2e5",
426
+ "version_major": 2,
427
+ "version_minor": 0
428
+ },
429
+ "text/plain": [
430
+ "tokenizer_config.json: 0%| | 0.00/237k [00:00<?, ?B/s]"
431
  ]
432
  },
433
  "metadata": {},
 
437
  "name": "stderr",
438
  "output_type": "stream",
439
  "text": [
440
+ "You have set `use_cache` to `False`, but cache_implementation is set to hybrid. cache_implementation will have no effect.\n"
441
+ ]
442
+ },
443
+ {
444
+ "data": {
445
+ "application/vnd.jupyter.widget-view+json": {
446
+ "model_id": "db4fddb7315c464ea87c8ad507f9a651",
447
+ "version_major": 2,
448
+ "version_minor": 0
449
+ },
450
+ "text/plain": [
451
+ "Replacing MoE Block...: 0%| | 0/48 [00:00<?, ?it/s]"
452
+ ]
453
+ },
454
+ "metadata": {},
455
+ "output_type": "display_data"
456
+ },
457
+ {
458
+ "name": "stderr",
459
+ "output_type": "stream",
460
+ "text": [
461
+ "Replacing layers...: 100%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ| 48/48 [00:07<00:00, 6.18it/s]\n",
462
+ "/workspace/AutoAWQ/awq/models/base.py:539: UserWarning: Skipping fusing modules because AWQ extension is not installed.No module named 'awq_ext'\n",
463
  " warnings.warn(\"Skipping fusing modules because AWQ extension is not installed.\" + msg)\n"
464
  ]
465
  },
 
467
  "name": "stdout",
468
  "output_type": "stream",
469
  "text": [
470
+ "CPU times: user 1h 44min 26s, sys: 26min 26s, total: 2h 10min 53s\n",
471
+ "Wall time: 28min 55s\n"
472
  ]
473
  }
474
  ],
 
488
  "name": "stdout",
489
  "output_type": "stream",
490
  "text": [
491
+ "Sat Apr 19 22:53:42 2025 \n",
492
  "+-----------------------------------------------------------------------------------------+\n",
493
  "| NVIDIA-SMI 565.57.01 Driver Version: 565.57.01 CUDA Version: 12.7 |\n",
494
  "|-----------------------------------------+------------------------+----------------------+\n",
 
496
  "| Fan Temp Perf Pwr:Usage/Cap | Memory-Usage | GPU-Util Compute M. |\n",
497
  "| | | MIG M. |\n",
498
  "|=========================================+========================+======================|\n",
499
+ "| 0 NVIDIA A100-SXM4-80GB On | 00000000:87:00.0 Off | 0 |\n",
500
+ "| N/A 30C P0 71W / 400W | 60415MiB / 81920MiB | 0% Default |\n",
501
  "| | | Disabled |\n",
502
  "+-----------------------------------------+------------------------+----------------------+\n",
503
  " \n",
 
557
  "name": "stdout",
558
  "output_type": "stream",
559
  "text": [
560
+ "CPU times: user 4min 28s, sys: 3min 39s, total: 8min 7s\n",
561
+ "Wall time: 8min 8s\n"
562
  ]
563
  }
564
  ],
 
594
  "\n",
595
  "where $\\Gamma^i_{jk}$ are the Christoffel symbols of the second kind, which define the connection.\n",
596
  "\n",
597
+ "In general relativity, the Levi-Civita connection is a fundamental example of a torsion-free connection. It's the unique connection that is:\n",
598
+ "\n",
599
+ "1. **Metric-compatible**: it preserves the metric tensor under parallel transport.\n",
600
+ "2. **Torsion-free**: it has zero torsion.\n",
601
+ "\n",
602
+ "The Levi-Civita connection is used to define the covariant derivative, which is essential for describing the curvature of spacetime.\n",
603
+ "\n",
604
+ "The assumption of a torsion-free connection is crucial in general relativity, as it allows us to:\n",
605
  "\n",
606
+ "1. **Define a unique covariant derivative**: which is necessary for formulating the Einstein field equations.\n",
607
+ "2. **Ensure geodesic equation**: which describes the shortest path in curved spacetime, is well-defined.\n",
608
  "\n",
609
+ "However, it's worth noting that there are some alternative theories, such as Einstein-Cartan theory, which consider torsion as a fundamental aspect of spacetime geometry.\n",
 
 
610
  "\n",
611
+ "I hope this explanation helps! Do you have any follow-up questions?<|eot|>\n"
612
  ]
613
  }
614
  ],