Which Data Attributes Stimulate Math and Code Reasoning? An Investigation via Influence Functions

TL;DR

This paper uses influence functions to analyze how specific data attributes affect LLMs' math and coding reasoning, revealing insights that lead to improved dataset curation and performance.

Contribution

It introduces a systematic influence-based attribution method to understand data effects on reasoning, and proposes a data reweighting strategy that significantly enhances model accuracy.

Findings

High-difficulty math data benefits both math and code reasoning.

Low-difficulty code data most improves code reasoning.

Sequence and token-level influences reveal distinct patterns for math and coding.

Abstract

Large language models (LLMs) have demonstrated remarkable reasoning capabilities in math and coding, often bolstered by post-training on the chain-of-thoughts (CoTs) generated by stronger models. However, existing strategies for curating such training data predominantly rely on heuristics, limiting generalizability and failing to capture subtleties underlying in data. To address these limitations, we leverage influence functions to systematically attribute LLMs' reasoning ability on math and coding to individual training examples, sequences, and tokens, enabling deeper insights into effective data characteristics. Our Influence-based Reasoning Attribution (Infra) uncovers nontrivial cross-domain effects across math and coding tasks: high-difficulty math examples improve both math and code reasoning, while low-difficulty code tasks most effectively benefit code reasoning. Based on these findings, we introduce a simple yet effective dataset reweighting strategy by flipping task difficulty, which doubles AIME24 accuracy from 10\% to 20\% and boosts LiveCodeBench accuracy from 33.8\% to 35.3\% for Qwen2.5-7B-Instruct. Moreover, our fine-grained attribution reveals that the sequence-level exploratory behaviors enhance reasoning performance in both math and code, and the token-level influence patterns are distinct for math and code reasoning: the former prefers natural language logic connectors and the latter emphasizes structural syntax.