Papers › Solving Quantitative Reasoning Problems with Language Models
Solving Quantitative Reasoning Problems with Language Models
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
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| 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
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