InternLM-Math

News

• [2024.01.29] We add checkpoints from ModelScope. Tech report is on the way!
• [2024.01.26] We add checkpoints from OpenXLab, which ease Chinese users to download!

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 Interpreter. InternLM2-Math can help augment math reasoning problems and solve them using the code interpreter which makes you generate synthesis data quicker!

Models

InternLM2-Math-Base-7B and InternLM2-Math-Base-20B are pretrained checkpoints. InternLM2-Math-7B and InternLM2-Math-20B are SFT checkpoints.

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.

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.

Inference

LMDeploy

We suggest using LMDeploy(>=0.2.1) for inference.

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

import torch
from transformers import AutoTokenizer, AutoModelForCausalLM
tokenizer = AutoTokenizer.from_pretrained("internlm/internlm2-math-20b", 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-20b", 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.

Translate proof problem to Lean:

Using Lean 3 to solve GSM8K problem:

Generate problem based on Lean 3 code:

Play 24 point game:

Augment a harder math problem:

Fine-tune and others

Please refer to InternLM.

Known issues

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.

• Jump the calculating step.
• Perform badly at Chinese fill-in-the-bank problems and English choice problems due to SFT data composition.
• Tend to generate Code Interpreter when facing Chinese 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.