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--- |
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license: llama2 |
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datasets: |
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- EleutherAI/proof-pile-2 |
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language: |
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- en |
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tags: |
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- math |
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- reasoning |
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--- |
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<img src="llemma.jpg" width="400"> |
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[Zhangir Azerbayev](https://zhangir-azerbayev.github.io/), [Hailey Schoelkopf](https://github.com/haileyschoelkopf), [Keiran Paster](https://keirp.com), [Marco Dos Santos](https://github.com/dsantosmarco), [Stephen McAleer](https://www.andrew.cmu.edu/user/smcaleer/), [Albert Q. Jiang](https://albertqjiang.github.io/), [Jia Deng](https://www.cs.princeton.edu/~jiadeng/), [Stella Biderman](https://www.stellabiderman.com/), [Sean Welleck](https://wellecks.com/) |
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[Github ](https://github.com/EleutherAI/math-lm) | [ArXiv](#) |
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**Llemma 34B** is a language model for mathematics. It was initialized with [Code Llama 34B](https://github.com/facebookresearch/codellama) weights, and trained on the [Proof-Pile-2](https://huggingface.co/datasets/EleutherAI/proof-pile-2) for 50B tokens. |
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This model also comes in a 7B parameter version: [Llemma 7B](https://huggingface.co/EleutherAI/llemma_7b). |
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## Evaluations |
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Llemma models are particularly strong at chain-of-thought mathematical reasoning and using computational tools for mathematics, such as Python and formal theorem provers. |
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### Chain-of-thought Math |
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On chain-of-thought mathematics tasks, Llemma models outperform Llama-2, Code Llama, and when controlled for model size, outperform Minerva. |
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| Model | Size | GSM8k | [OCW](https://openreview.net/forum?id=IFXTZERXdM7) | MMLU-STEM | [SAT](https://huggingface.co/datasets/mcaleste/sat_multiple_choice_math_may_23) | MATH | |
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|------------|------|--------|-------|-----------|-------|-------| |
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| Llama 2 | 7B | 11.8% | 3.7% | 29.9% | 25% | 3.2% | |
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| Code Llama | 7B | 10.5% | 4.4% | 25.1% | 9.4% | 4.4% | |
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| LLEMMA | 7B | 36.4% | 7.7% | 37.7% | 53.1% | 17.2% | |
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| Minerva | 8B | 16.2% | 7.7% | 35.6% | - | 14.1% | |
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|------------|------|--------|-------|-----------|-------|-------| |
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| Code Llama | 34B | 29.6% | 7.0% | 40.5% | 40.6% | 11.9% | |
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| LLEMMA | 34B | 51.5% | 11.8% | 49.0% | 71.9% | 24.1% | |
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|------------|------|--------|-------|-----------|-------|-------| |
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| Minerva | 62B | 52.4% | 12.0% | 53.9% | - | 27.6% | |
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| Minerva | 540B | 58.8% | 17.6% | 63.9% | - | 33.6% | |
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Further performance can be extracted by using majority voting: |
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| Model | Size | GSM8k maj@100 | OCW maj@100 | MMLU-STEM maj@16 | SAT maj@16 | MATH maj@256 | |
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|---------|------|-------------|-----------|-----------------|-----------|------------| |
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| LLEMMA | 7B | 54.0% | 14.3% | 49.9% | 78.1% | 32.0% | |
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| Minerva | 8B | 28.4% | 12.5% | 43.4% | - | 25.4% | |
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|---------|------|-------------|-----------|-----------------|-----------|------------| |
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| LLEMMA | 34B | 69.3% | 18.4% | 59.7% | 81.3% | 41.0% | |
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|---------|------|-------------|-----------|-----------------|-----------|------------| |
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| Minerva | 62B | 68.5% | 23.5% | 63.5% | - | 43.4% | |
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| Minerva | 540B | 78.5% | 30.8% | 75.0% | - | 50.3% | |
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### Tool Use and Theorem Proving |
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In addition to chain-of-thought reasoning, Llemma has strong capabilities in computational mathematics tasks. For tool use and formal theorem proving evaluations, see [our paper](#). |
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