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--- |
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pipeline_tag: text-generation |
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license: other |
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language: |
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- en |
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- zh |
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tags: |
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- math |
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--- |
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# InternLM-Math |
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<div align="center"> |
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<img src="https://raw.githubusercontent.com/InternLM/InternLM/main/assets/logo.svg" width="200"/> |
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<div> </div> |
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<div align="center"> |
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<b><font size="5">InternLM-Math</font></b> |
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<sup> |
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<a href="https://internlm.intern-ai.org.cn/"> |
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<i><font size="4">HOT</font></i> |
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</a> |
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</sup> |
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<div> </div> |
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</div> |
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State-of-the-art bilingual open-sourced Math reasoning LLMs. |
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A **solver**, **prover**, **verifier**, **augmentor**. |
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[💻 Github](https://github.com/InternLM/InternLM-Math) [🤗 Demo](https://huggingface.co/spaces/internlm/internlm2-math-7b) [🤗 Checkpoints](https://huggingface.co/internlm/internlm2-math-7b) [](https://openxlab.org.cn/models/detail/OpenLMLab/InternLM2-Math-7B) [<img src="https://raw.githubusercontent.com/InternLM/InternLM-Math/main/assets/modelscope_logo.png" width="20px" /> ModelScope](https://modelscope.cn/models/Shanghai_AI_Laboratory/internlm2-math-7b/summary) |
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</div> |
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# News |
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- [2024.01.29] We add checkpoints from ModelScope. Tech report is on the way! |
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- [2024.01.26] We add checkpoints from OpenXLab, which ease Chinese users to download! |
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# Introduction |
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- **7B and 20B Chinese and English Math LMs with better than ChatGPT performances.** InternLM2-Math are continued pretrained from InternLM2-Base with ~100B high quality math-related tokens and SFT with ~2M bilingual math supervised data. We apply minhash and exact number match to decontaminate possible test set leakage. |
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- **Add Lean as a support language for math problem solving and math theorem proving.** We are exploring combining Lean 3 with InternLM-Math for verifiable math reasoning. InternLM-Math can generate Lean codes for simple math reasoning tasks like GSM8K or provide possible proof tactics based on Lean states. |
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- **Also can be viewed as a reward model, which supports the Outcome/Process/Lean Reward Model.** We supervise InternLM2-Math with various types of reward modeling data, to make InternLM2-Math can also verify chain-of-thought processes. We also add the ability to convert a chain-of-thought process into Lean 3 code. |
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- **A Math LM Augment Helper** and **Code Interpreter**. InternLM2-Math can help augment math reasoning problems and solve them using the code interpreter which makes you generate synthesis data quicker! |
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# Models |
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**InternLM2-Math-Base-7B** and **InternLM2-Math-Base-20B** are pretrained checkpoints. **InternLM2-Math-7B** and **InternLM2-Math-20B** are SFT checkpoints. |
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| Model |Model Type | Transformers(HF) |OpenXLab| ModelScope | Release Date | |
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| **InternLM2-Math-Base-7B** | Base| [🤗internlm/internlm2-math-base-7b](https://huggingface.co/internlm/internlm2-math-base-7b) |[](https://openxlab.org.cn/models/detail/OpenLMLab/InternLM2-Math-Base-7B)| [<img src="https://raw.githubusercontent.com/InternLM/InternLM-Math/main/assets/modelscope_logo.png" width="20px" /> internlm2-math-base-7b](https://modelscope.cn/models/Shanghai_AI_Laboratory/internlm2-math-base-7b/summary)| 2024-01-23| |
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| **InternLM2-Math-Base-20B** | Base| [🤗internlm/internlm2-math-base-20b](https://huggingface.co/internlm/internlm2-math-base-20b) |[](https://openxlab.org.cn/models/detail/OpenLMLab/InternLM2-Math-Base-20B)|[<img src="https://raw.githubusercontent.com/InternLM/InternLM-Math/main/assets/modelscope_logo.png" width="20px" /> internlm2-math-base-20b](https://modelscope.cn/models/Shanghai_AI_Laboratory/internlm2-math-base-20b/summary)| 2024-01-23| |
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| **InternLM2-Math-7B** | Chat| [🤗internlm/internlm2-math-7b](https://huggingface.co/internlm/internlm2-math-7b) |[](https://openxlab.org.cn/models/detail/OpenLMLab/InternLM2-Math-7B)|[<img src="https://raw.githubusercontent.com/InternLM/InternLM-Math/main/assets/modelscope_logo.png" width="20px" /> internlm2-math-7b](https://modelscope.cn/models/Shanghai_AI_Laboratory/internlm2-math-7b/summary)| 2024-01-23| |
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| **InternLM2-Math-20B** | Chat| [🤗internlm/internlm2-math-20b](https://huggingface.co/internlm/internlm2-math-20b) |[](https://openxlab.org.cn/models/detail/OpenLMLab/InternLM2-Math-20B)|[<img src="https://raw.githubusercontent.com/InternLM/InternLM-Math/main/assets/modelscope_logo.png" width="20px" /> internlm2-math-20b](https://modelscope.cn/models/Shanghai_AI_Laboratory/internlm2-math-20b/summary)| 2024-01-23| |
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# Performance |
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## Pretrain Performance |
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We evaluate pretrain checkpoints based on greedy decoding with few-shot COT. Details of pretraining will be introduced in the tech report. |
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| Model | GSM8K | MATH | |
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|------------------------|---------|--------| |
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| Llama2-7B | 11.8 | 3.2 | |
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| Llemma-7B | 36.4 | 18.0 | |
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| InternLM2-Base-7B | 36.5 | 8.6 | |
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| **InternLM2-Math-Base-7B** | **49.2** | **21.5** | |
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| Minerva-8B | 16.2 | 14.1 | |
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| InternLM2-Base-20B | 54.6 | 13.7 | |
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| **InternLM2-Math-Base-20B** | **63.7** | **27.3** | |
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| Llemma-34B | 51.5 | 25.0 | |
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| Minerva-62B | 52.4 | 27.6 | |
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| Minerva-540B | 58.8 | 33.6 | |
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## SFT Peformance |
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All performance is based on greedy decoding with COT. We notice that the performance of Hungary has a big variance between our different checkpoints, while other performance is very stable. This may be due to the problem amount about Hungary. |
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| Model | Model Type | GSM8K | MATH | Hungary | |
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|------------------------|----------------------|--------|--------|---------| |
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| Qwen-7B-Chat | Genearl | 51.7 | 11.6 | - | |
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| DeepSeek-7B-Chat | General | 63.0 | 15.8 | 28.5 | |
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| InternLM2-Chat-7B | General | 70.7 | 23.0 | - | |
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| ChatGLM3-6B | General | 53.8 | 20.4 | 32 | |
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| MetaMath-Mistral-7B | Mathematics | 77.7 | 28.2 | 29 | |
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| MetaMath-Llemma-7B | Mathematics | 69.2 | 30.0 | - | |
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| **InternLM2-Math-7B** | Mathematics | **78.1** | **34.6** | **55** | |
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| InternLM2-Chat-20B | General | 79.6 | 31.9 | - | |
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| MetaMath-Llemma-34B | Mathematics | 75.8 | 34.8 | - | |
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| **InternLM2-Math-20B** | Mathematics | **82.6** | **37.7** | **66** | |
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| Qwen-72B | General | 78.9 | 35.2 | 52 | |
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| DeepSeek-67B | General | 84.1 | 32.6 | 58 | |
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| ChatGPT (GPT-3.5) | General | 80.8 | 34.1 | 41 | |
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| GPT4 (First version) | General | 92.0 | 42.5 | 68 | |
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# Inference |
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## LMDeploy |
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We suggest using [LMDeploy](https://github.com/InternLM/LMDeploy)(>=0.2.1) for inference. |
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```python |
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from lmdeploy import pipeline, TurbomindEngineConfig, ChatTemplateConfig |
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backend_config = TurbomindEngineConfig(model_name='internlm2-chat-7b', tp=1, cache_max_entry_count=0.3) |
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chat_template = ChatTemplateConfig(model_name='internlm2-chat-7b', system='', eosys='', meta_instruction='') |
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pipe = pipeline(model_path='internlm/internlm2-math-7b', chat_template_config=chat_template, backend_config=backend_config) |
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problem = '1+1=' |
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result = pipe([problem], request_output_len=1024, top_k=1) |
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``` |
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## Huggingface |
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```python |
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import torch |
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from transformers import AutoTokenizer, AutoModelForCausalLM |
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tokenizer = AutoTokenizer.from_pretrained("internlm/internlm2-math-20b", trust_remote_code=True) |
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# Set `torch_dtype=torch.float16` to load model in float16, otherwise it will be loaded as float32 and might cause OOM Error. |
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model = AutoModelForCausalLM.from_pretrained("internlm/internlm2-math-20b", trust_remote_code=True, torch_dtype=torch.float16).cuda() |
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model = model.eval() |
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response, history = model.chat(tokenizer, "1+1=", history=[], meta_instruction="") |
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print(response) |
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``` |
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# Special usages |
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We list some instructions used in our SFT. You can use them to help you. You can use the other ways to prompt the model, but the following are recommended. InternLM2-Math may combine the following abilities but it is not guaranteed. |
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Translate proof problem to Lean: |
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Using Lean 3 to solve GSM8K problem: |
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Generate problem based on Lean 3 code: |
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Play 24 point game: |
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Augment a harder math problem: |
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| Description | Query | |
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| Solving question via chain-of-thought | {Question} | |
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| Solving question via Lean 3 | {Question}\nSolve this via Lean 3 | |
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| Outcome reward model | Given a question and an answer, check is it correct?\nQuestion:{Question}\nAnswer:{COT} | |
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| Process reward model | Given a question and an answer, check correctness of each step.\nQuestion:{Question}\nAnswer:{COT} | |
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| Reward model | Given a question and two answers, which one is better? \nQuestion:{Question}\nAnswer 1:{COT}\nAnswer 2:{COT} | |
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| Convert chain-of-thought to Lean 3 | Convert this answer into Lean3. Question:{Question}\nAnswer:{COT} | |
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| Convert Lean 3 to chain-of-thought | Convert this lean 3 code into a natural language problem with answers:\n{LEAN Code} | |
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| Translate question and chain-of-thought answer to a proof statement | Convert this question and answer into a proof format.\nQuestion:{Question}\nAnswer:{COT} | |
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| Translate proof problem to Lean 3 | Convert this natural langauge statement into a Lean 3 theorem statement:{Theorem} | |
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| Translate Lean 3 to proof problem | Convert this Lean 3 theorem statement into natural language:{STATEMENT} | |
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| Suggest a tactic based on Lean state | Given the Lean 3 tactic state, suggest a next tactic:\n{LEAN State} | |
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| Rephrase Problem | Describe this problem in another way. {Question} | |
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| Augment Problem | Please augment a new problem based on: {Question} | |
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| Augment a harder Problem | Increase the complexity of the problem: {Question} | |
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| Change specific numbers | Change specific numbers: {Question}| |
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| Introduce fractions or percentages | Introduce fractions or percentages: {Question}| |
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| Code Interpreter | [lagent](https://github.com/InternLM/InternLM/blob/main/agent/lagent.md) | |
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| In-context Learning | Question:{Question}\nAnswer:{COT}\n...Question:{Question}\nAnswer:{COT}| |
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# Fine-tune and others |
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Please refer to [InternLM](https://github.com/InternLM/InternLM/tree/main). |
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# Known issues |
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Our model is still under development and will be upgraded. There are some possible issues of InternLM-Math. If you find performances of some abilities are not great, welcome to open an issue. |
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- Jump the calculating step. |
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- Perform badly at Chinese fill-in-the-bank problems and English choice problems due to SFT data composition. |
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- Tend to generate Code Interpreter when facing Chinese problems due to SFT data composition. |
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- The reward model mode can be better leveraged with assigned token probabilities. |
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- Code switch due to SFT data composition. |
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- Some abilities of Lean can only be adapted to GSM8K-like problems (e.g. Convert chain-of-thought to Lean 3), and performance related to Lean is not guaranteed. |
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# Citation and Tech Report |
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To be appended. |
