wisdom-dsmath-7b

🧙🏼WISDOM

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WISDOM: PROGRESSIVE CURRICULUM SYNTHESIS MAKES LLMS BETTER MATHEMATICAL REASONER

🤗Datasets&Models@HF | 🐱 Code@GitHub

<div align="center"> <img src="https://anonymous.4open.science/r/Wisdom-math-377B/imgs/main.jpg">

<em> Figure 1: The overall workflow of WISDOM, which leverages Progressive Curriculum Synthesis to generate questions and responses with Deepseek Coder V2 and GPT-4o, including weak teacher guiding, critical expert teaching, experts consistency voting, and hard instruction evolving. </em>

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Main Results on the smaller models

Main Results on the bigger models

† In short of College MATH.

<em>Table 1:Main results on in-domain benchmarks, GSM8K and MATH, and out-of-domain benchmarks, including College MATH, Olympiad, TabMWP, TheoremQA, AMC2023, and AIME2024. We select the current well-performing LLMs to evaluate their test accuracy on these benchmarks. Since KPMath-Plus is not open-sourced, the results are quoted from the corresponding paper.</em>

Introduction of Paper

we introduce WISDOM, which draws inspiration from the human learning process and employs curriculum learning to gradually synthesize high-quality CoT data from easy to hard.

Template

All models were trained using the Alpaca template.

Below is an instruction that describes a task. Write a response that appropriately completes the request.\n### Instruction:\n{question}\n\n### Response:

Training Setup

Data Contamination

we applied a 10-gram hash deduplication method to the questions in both our in-domain and out-of-domain benchmarks, with a condition that the ratio of the longest common sequence must exceed 0.6, Any detected duplicates were removed.

Training details

We employ Llama-factory for fine-tuning the entire suite of models and utilized sequence packing to accelerate the training process.

The training was conducted using 88 NVIDIA A800 GPUs, with a configuration of batch size 1, gradient accumulation of 2, sequence length of 8192, and bf16 precision. We optimized the models with the AdamW optimizer, setting a learning rate warmup using a cosine schedule with a warmup ratio of 0.03, and trained each model for 3 epochs. The learning rates were adjusted slightly for different models: Mistral 7B at 1e-5, DeepSeekMath-7B at 5e-5, Llama3-8B at 4e-5, and both Llama3-70B and Qwen2-72B at 2e-5.