Which Data Attributes Stimulate Math and Code Reasoning? An
  Investigation via Influence Functions
Authors: name: Siqi Kou, name: Qingyuan Tian, name: Hanwen Xu, name: Zihao Zeng, name: Zhijie Deng

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.