Papers › Solving Quantitative Reasoning Problems with Language Models

Solving Quantitative Reasoning Problems with Language Models

29 Jun 2022arXiv:2206.14858archive 2025-07-28

Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Solo, Yuhuai Wu, Behnam Neyshabur, Guy Gur-Ari, Vedant Misra

Language models have achieved remarkable performance on a wide range of tasks that require natural language understanding. Nevertheless, state-of-the-art models have generally struggled with tasks that require quantitative reasoning, such as solving mathematics, science, and engineering problems at the college level. To help close this gap, we introduce Minerva, a large language model pretrained on general natural language data and further trained on technical content. The model achieves state-of-the-art performance on technical benchmarks without the use of external tools. We also evaluate our model on over two hundred undergraduate-level problems in physics, biology, chemistry, economics, and other sciences that require quantitative reasoning, and find that the model can correctly answer nearly a third of them.

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Code

gair-nlp/abel mentioned on GitHubpytorch report

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Tasks

Arithmetic ReasoningLanguage ModelingLanguage ModellingLarge Language ModelMath Word Problem SolvingMulti-task Language UnderstandingNatural Language Understanding

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Arithmetic Reasoning GSM8K Minerva 62B (maj5@100) Accuracy 89 #26 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 62B (maj5@100) Parameters (Billion) 62 #26 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 540B (CoT) Accuracy 78.5 #77 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 540B (CoT) Parameters (Billion) 540 #77 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 62B (maj1@100) Accuracy 68.5 #105 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 62B (maj1@100) Parameters (Billion) 62 #105 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 8B (maj5@100) Accuracy 56.8 #122 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 8B (maj5@100) Parameters (Billion) 8 #122 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K PaLM 540B (8-shot) Accuracy 56.5 #124 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K PaLM 540B (8-shot) Parameters (Billion) 540 #124 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 62B (8-shot) Accuracy 52.4 #130 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 62B (8-shot) Parameters (Billion) 62 #130 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K PaLM 62B (8-shot) Accuracy 33.0 #145 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K PaLM 62B (8-shot) Parameters (Billion) 62 #145 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 8B-maj1@k (8-shot) Accuracy 28.4 #148 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 8B-maj1@k (8-shot) Parameters (Billion) 8 #148 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 8B (8-shot) Accuracy 16.2 #157 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Minerva 8B (8-shot) Parameters (Billion) 8 #157 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K PaLM 8B (8-shot) Accuracy 4.1 #163 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K PaLM 8B (8-shot) Parameters (Billion) 8 #163 of 164 Archive leaderboard report
Math Word Problem Solving MATH Minerva 62B (maj5@256) Accuracy 64.9 #21 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 62B (maj5@256) Parameters (Billions) 62 #21 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 540B (maj1@k, k=64) Accuracy 50.3 #48 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 8B (maj5@256) Accuracy 47.6 #57 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 8B (maj5@256) Parameters (Billions) 8 #57 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 62B (maj1@k, k=64) Accuracy 43.4 #73 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 62B (maj1@k, k=64) Parameters (Billions) 62 #73 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 540B Accuracy 33.6 #82 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 540B Parameters (Billions) 540 #82 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 62B (4-shot) Accuracy 27.6 #94 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 62B (4-shot) Parameters (Billions) 62 #94 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 8B (maj1@k, k=64) Accuracy 25.4 #97 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 8B (maj1@k, k=64) Parameters (Billions) 8 #97 of 135 Archive leaderboard report
Math Word Problem Solving MATH davinci-002 175B Accuracy 19.1 #105 of 135 Archive leaderboard report
Math Word Problem Solving MATH davinci-002 175B Parameters (Billions) 175 #105 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 8B Accuracy 14.1 #109 of 135 Archive leaderboard report
Math Word Problem Solving MATH Minerva 8B Parameters (Billions) 8 #109 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 540B Accuracy 8.8 #117 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 540B Parameters (Billions) 540 #117 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 8B (fine-tuned) Accuracy 5.6 #126 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 8B (fine-tuned) Parameters (Billions) 8 #126 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 62B Accuracy 4.4 #130 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 62B Parameters (Billions) 62 #130 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 8B Accuracy 1.5 #135 of 135 Archive leaderboard report
Math Word Problem Solving MATH PaLM 8B Parameters (Billions) 8 #135 of 135 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

1-bit AdamAdam

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