AttentionInfluence: Adopting Attention Head Influence for Weak-to-Strong
  Pretraining Data Selection
Authors: name: Kai Hua, name: Steven Wu, name: Ge Zhang, name: Ke Shen

Recently, there has been growing interest in collecting reasoning-intensive
pretraining data to improve LLMs' complex reasoning ability. Prior approaches
typically rely on supervised classifiers to identify such data, which requires
labeling by humans or LLMs, often introducing domain-specific biases. Due to
the attention heads being crucial to in-context reasoning, we propose
AttentionInfluence, a simple yet effective, training-free method without
supervision signal. Our approach enables a small pretrained language model to
act as a strong data selector through a simple attention head masking
operation. Specifically, we identify retrieval heads and compute the loss
difference when masking these heads. We apply AttentionInfluence to a
1.3B-parameter dense model to conduct data selection on the SmolLM corpus of
241B tokens, and mix the SmolLM corpus with the selected subset comprising 73B
tokens to pretrain a 7B-parameter dense model using 1T training tokens and WSD
learning rate scheduling. Our experimental results demonstrate substantial
improvements, ranging from 1.4pp to 3.5pp, across several knowledge-intensive
and reasoning-heavy benchmarks (i.e., MMLU, MMLU-Pro, AGIEval-en, GSM8K, and
HumanEval). This demonstrates an effective weak-to-strong scaling property,
with small models improving the final performance of larger models-offering a
promising and scalable path for reasoning-centric data selection.