"Evolutionary Pre-Prompt Optimization for Mathematical Reasoning"

Smart prompt evolution beats brute force optimization for teaching LLMs complex math.

This paper introduces Evolutionary Pre-Prompt Optimization (EPPO), a method that enhances mathematical reasoning in LLMs by optimizing Chain-of-Thought prompts using evolutionary algorithms. EPPO achieves 10% better exact match scores on GSM8k and MathQA benchmarks while providing theoretical guarantees against overfitting.

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https://arxiv.org/abs/2412.04291

🤔 Original Problem:

LLMs struggle with complex mathematical reasoning tasks despite their size. Current prompt optimization methods lack theoretical guarantees and often overfit on small training datasets.

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🔧 Solution in this Paper:

→ EPPO uses evolutionary algorithms to select optimal Chain-of-Thought examples as pre-prompts for mathematical reasoning tasks

→ The method requires only binary comparisons between pre-prompts, enabling information-theoretic generalization bounds

→ EPPO optimizes a small set of 2-16 examples that remain fixed for the entire downstream task

→ The algorithm employs comparison-based optimization to minimize overfitting risks

→ Integration with self-consistency voting further amplifies performance gains

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💡 Key Insights:

→ 4-shot prompts perform better than 8-shot prompts due to reduced overfitting

→ Evolutionary optimization outperforms random search for prompt selection

→ Pre-prompts transfer well across different models and mathematical tasks

→ Limited data feedback helps prevent overfitting compared to gradient-based methods

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📊 Results:

→ 10% improvement in exact match scores on GSM8k and MathQA

→ 64% prediction accuracy on test sets

→ Sharpe ratio of 2.21 on sector rotation strategy

→ Successful transfer from 7B to 70B parameter models