File size: 4,154 Bytes
e8473e1 acc26c5 e8473e1 74cd0a5 f99619d 74cd0a5 21a6f14 74cd0a5 660c780 74cd0a5 f99619d b2ce480 f99619d 74cd0a5 f99619d 74cd0a5 f99619d 74cd0a5 84c323e 74cd0a5 f99619d 21a6f14 f99619d acc26c5 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 |
---
license: llama2
datasets:
- EleutherAI/proof-pile-2
- open-web-math/open-web-math
language:
- en
tags:
- math
- reasoning
---
<img src="llemma.png" width="400">
[ArXiv](http://arxiv.org/abs/2310.10631) | [Models](https://huggingface.co/EleutherAI/llemma_34b) | [Data](https://huggingface.co/datasets/EleutherAI/proof-pile-2) | [Code](https://github.com/EleutherAI/math-lm) | [Blog](https://blog.eleuther.ai/llemma/) | [Sample Explorer](https://llemma-demo.github.io/)
[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/)
**Llemma 7B** is a language model for mathematics. It was initialized with [Code Llama 7B](https://github.com/facebookresearch/codellama) weights, and trained on the [Proof-Pile-2](https://huggingface.co/datasets/EleutherAI/proof-pile-2) for 200B tokens.
This model also comes in a 34B parameter version: [Llemma 34B](https://huggingface.co/EleutherAI/llemma_34b).
## Evaluations
Llemma models are particularly strong at chain-of-thought mathematical reasoning and using computational tools for mathematics, such as Python and formal theorem provers.
### Chain-of-thought Math
On chain-of-thought mathematics tasks, Llemma models outperform Llama-2, Code Llama, and when controlled for model size, outperform Minerva.
| 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 |
|------------|------|--------|-------|-----------|-------|-------|
| Llama 2 | 7B | 11.8% | 3.7% | 29.9% | 25% | 3.2% |
| Code Llama | 7B | 10.5% | 4.4% | 25.1% | 9.4% | 4.5% |
| LLEMMA | 7B | **36.4%** | **7.7%** | **37.7%** | **53.1%** | **18.0%** |
| Minerva | 8B | 16.2% | **7.7%** | 35.6% | - | 14.1% |
|------------|------|--------|-------|-----------|-------|-------|
| Code Llama | 34B | 29.6% | 7.0% | 40.5% | 40.6% | 12.2% |
| LLEMMA | 34B | **51.5%** | **11.8%** | **49.0%** | **71.9%** | **25.0%** |
|------------|------|--------|-------|-----------|-------|-------|
| Minerva | 62B | 52.4% | 12.0% | 53.9% | - | 27.6% |
| Minerva | 540B | 58.8% | 17.6% | 63.9% | - | 33.6% |
Further performance can be extracted by using majority voting:
| Model | Size | GSM8k maj@100 | OCW maj@100 | MMLU-STEM maj@16 | SAT maj@16 | MATH maj@256 |
|---------|------|-------------|-----------|-----------------|-----------|------------|
| LLEMMA | 7B | 54.0% | 14.3% | 49.9% | 78.1% | **33.5** |
| Minerva | 8B | 28.4% | 12.5% | 43.4% | - | 25.4% |
|---------|------|-------------|-----------|-----------------|-----------|------------|
| LLEMMA | 34B | 69.3% | 18.4% | 59.7% | 81.3% | **43.1%** |
|---------|------|-------------|-----------|-----------------|-----------|------------|
| Minerva | 62B | 68.5% | 23.5% | 63.5% | - | 43.4% |
| Minerva | 540B | 78.5% | 30.8% | 75.0% | - | 50.3% |
### Tool Use and Theorem Proving
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](http://arxiv.org/abs/2310.10631).
### Citation
```
@misc{azerbayev2023llemma,
title={Llemma: An Open Language Model For Mathematics},
author={Zhangir Azerbayev and Hailey Schoelkopf and Keiran Paster and Marco Dos Santos and Stephen McAleer and Albert Q. Jiang and Jia Deng and Stella Biderman and Sean Welleck},
year={2023},
eprint={2310.10631},
archivePrefix={arXiv},
primaryClass={cs.CL}
}
``` |