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README.md

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+---
+pipeline_tag: text-generation
+license: other
+language:
+- en
+- zh
+tags:
+- math
+---
+
+# InternLM-Math
+
+<div align="center">
+
+<img src="https://raw.githubusercontent.com/InternLM/InternLM/main/assets/logo.svg" width="200"/>
+  <div> </div>
+  <div align="center">
+    <b><font size="5">InternLM-Math</font></b>
+    <sup>
+      <a href="https://internlm.intern-ai.org.cn/">
+        <i><font size="4">HOT</font></i>
+      </a>
+    </sup>
+    <div> </div>
+  </div>
+
+State-of-the-art bilingual open-sourced Math reasoning LLMs.
+</div>
+
+# Introduction
+- **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. 
+- **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.
+- **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.
+- **A Math LM Augment Helper** and **Code Intepreter**. InternLM2-Math can help augment math reasoning problems and solve them using the code interpreter which makes you generate synthesis data quicker!
+
+# Models
+| Model | Transformers(HF) |Release Date |
+|---|---|---|
+| **InternLM2-Math-Base-7B**    | [🤗internlm/internlm2-math-base-7b](https://huggingface.co/internlm/internlm2-math-base-7b) | 2024-01-23|
+| **InternLM2-Math-Base-20B**    | [🤗internlm/internlm2-math-base-20b](https://huggingface.co/internlm/internlm2-math-base-20b) | 2024-01-23|
+| **InternLM2-Math-7B**    | [🤗internlm/internlm2-math-7b](https://huggingface.co/internlm/internlm2-math-7b) | 2024-01-23|
+| **InternLM2-Math-20B**    | [🤗internlm/internlm2-math-20b](https://huggingface.co/internlm/internlm2-math-20b) | 2024-01-23|
+
+
+# Performance
+
+## Pretrain Performance
+We evaluate pretrain checkpoints based on greedy decoding with few-shot COT. Details of pretraining will be introduced in the tech report.
+| Model                  |  GSM8K  | MATH   |
+|------------------------|---------|--------|
+| Llama2-7B |  11.8 | 3.2 |
+| Llemma-7B |  36.4 | 18.0 |
+| InternLM2-Base-7B |  36.5 | 8.6 |
+| **InternLM2-Math-Base-7B** |  **49.2** | **21.5** |
+| Minerva-8B |  16.2 | 14.1 |
+| InternLM2-Base-20B |  54.6 | 13.7 |
+| **InternLM2-Math-Base-20B** |  **63.7** | **27.3** |
+| Llemma-34B |  51.5 | 25.0 |
+| Minerva-62B |  52.4 | 27.6 |
+| Minerva-540B |  58.8 | 33.6 |
+
+
+## SFT Peformance
+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. 
+| Model                  | Model Type           | GSM8K  | MATH   | Hungary | 
+|------------------------|----------------------|--------|--------|---------|
+| Qwen-7B-Chat           | Genearl              | 51.7   | 11.6   | -       |
+| DeepSeek-7B-Chat       | General              | 63.0   | 15.8   | 28.5    | 
+| InternLM2-Chat-7B      | General              | 70.7   | 23.0   | -       |
+| ChatGLM3-6B            | General              | 53.8   | 20.4   | 32      |
+| MetaMath-Mistral-7B    | Mathematics          | 77.7   | 28.2   | 29      |
+| MetaMath-Llemma-7B     | Mathematics          | 69.2   | 30.0   | -       |
+| **InternLM2-Math-7B**      | Mathematics          | **78.1**   | **34.6**   | **55**      |
+| InternLM2-Chat-20B     | General              | 79.6   | 31.9   | -       | 
+| MetaMath-Llemma-34B    | Mathematics          | 75.8   | 34.8   | -       | 
+| **InternLM2-Math-20B**     | Mathematics          | **82.6**   | **37.7**   | **66**      | 
+| Qwen-72B               | General              | 78.9   | 35.2   | 52      | 
+| DeepSeek-67B           | General              | 84.1   | 32.6   | 58      | 
+| ChatGPT (GPT-3.5)      | General              | 80.8   | 34.1   | 41      |
+| GPT4 (First version)   | General              | 92.0   | 42.5   | 68      | 
+
+# Inference
+
+## LMDeploy
+We suggest using [LMDeploy](https://github.com/InternLM/LMDeploy)(>=0.2.1) for inference.
+```python
+from lmdeploy import pipeline, TurbomindEngineConfig, ChatTemplateConfig
+
+backend_config = TurbomindEngineConfig(model_name='internlm2-chat-7b', tp=1, cache_max_entry_count=0.3)
+chat_template = ChatTemplateConfig(model_name='internlm2-chat-7b', system='', eosys='', meta_instruction='')
+pipe = pipeline(model_path='internlm/internlm2-math-7b', chat_template_config=chat_template, backend_config=backend_config)
+
+problem = '1+1='
+result = pipe([problem], request_output_len=1024, top_k=1)
+```
+
+## Huggingface
+```python
+import torch
+from transformers import AutoTokenizer, AutoModelForCausalLM
+tokenizer = AutoTokenizer.from_pretrained("internlm/internlm2-math-7b", trust_remote_code=True)
+# Set `torch_dtype=torch.float16` to load model in float16, otherwise it will be loaded as float32 and might cause OOM Error.
+model = AutoModelForCausalLM.from_pretrained("internlm/internlm2-math-7b", trust_remote_code=True, torch_dtype=torch.float16).cuda()
+model = model.eval()
+response, history = model.chat(tokenizer, "1+1=", history=[], meta_instruction="")
+print(response)
+```
+
+# Special usages
+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.
+
+| Description | Query |
+| --- | --- |
+| Solving question via chain-of-thought | {Question} |
+| Solving question via Lean 3 | {Question}\nSolve this via Lean 3 |
+| Outcome reward model | Given a question and an answer, check is it correct?\nQuestion:{Question}\nAnswer:{COT} |
+| Process reward model | Given a question and an answer, check correctness of each step.\nQuestion:{Question}\nAnswer:{COT} |
+| Reward model | Given a question and two answers, which one is better? \nQuestion:{Question}\nAnswer 1:{COT}\nAnswer 2:{COT} |
+| Convert chain-of-thought to Lean 3 | Convert this answer into Lean3. Question:{Question}\nAnswer:{COT} |
+| Convert Lean 3 to chain-of-thought | Convert this lean 3 code into a natural language problem with answers:\n{LEAN} |
+| Translate question and chain-of-thought answer to a proof statement | Convert this question and answer into a proof format.\nQuestion:{Question}\nAnswer:{COT} |
+| Translate proof problem to Lean 3 | Convert this natural langauge statement into a Lean 3 theorem statement:{Theorem} |
+| Translate Lean 3 to proof problem | Convert this Lean 3 theorem statement into natural language:{STATEMENT} |
+| Suggest a tactic based on Lean state | Given the Lean 3 tactic state, suggest a next tactic:\n{State} |
+| Rephrase Problem | Describe this problem in another way. {STATEMENT} |
+| Augment Problem | Please augment a new problem based on: {Question} |
+| Augment a harder Problem | Increase the complexity of the problem: {Question} |
+| Change specific numbers | Change specific numbers: {Question}|
+| Introduce fractions or percentages | Introduce fractions or percentages: {Question}|
+| Code Intepreter | [lagent](https://github.com/InternLM/InternLM/blob/main/agent/lagent.md) |
+| In-context Learning | Question:{Question}\nAnswer:{COT}\n...Question:{Question}\nAnswer:{COT}|
+
+# Fine-tune and others
+Please refer to [InternLM](https://github.com/InternLM/InternLM/tree/main).
+
+# Known issues
+Our model is still under development and will be upgraded. There are some possible issues of InternLM-Math.
+- Jump the calculating step.
+- Perform badly at Chinese fill-in-the-bank problems and English choice problems due to SFT data composition.
+- The reward model mode can be better leveraged with assigned token probabilities.
+- Code switch due to SFT data composition.
+- 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.
+
+# Citation and Tech Report
+To be appended.

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original_repo_url.txt

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