[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!
hungarian
Models
InternLM2-Math-Base-7B and InternLM2-Math-Base-20B are pretrained checkpoints. InternLM2-Math-7B and InternLM2-Math-20B are SFT checkpoints.
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.
1import torch
2from transformers import AutoTokenizer, AutoModelForCausalLM
3tokenizer = AutoTokenizer.from_pretrained("internlm/internlm2-math-base-20b", trust_remote_code=True)4# Set `torch_dtype=torch.float16` to load model in float16, otherwise it will be loaded as float32 and might cause OOM Error.5model = AutoModelForCausalLM.from_pretrained("internlm/internlm2-math-base-20b", trust_remote_code=True, torch_dtype=torch.float16).cuda()6model = model.eval()7response, history = model.chat(tokenizer,"1+1=", history=[], meta_instruction="")8print(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:
nl2lean3
Using Lean 3 to solve GSM8K problem:
gsm8k_lean
Generate problem based on Lean 3 code:
lean_problem
Play 24 point game:
24
Augment a harder math problem:
augment_hard
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 Code}
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{LEAN State}
Rephrase Problem
Describe this problem in another way. {Question}
Augment Problem
Please augment a new problem based on: {Question}
Augment a harder Problem
Increase the complexity of the problem: {Question}
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.
