Influence Dynamics and Stagewise Data Attribution

Jin Hwa Lee, Matthew J. A. Smith, Maxwell Adam, Jesse Hoogland

Keywords: Training data attribution, influence functions, singular learning theory, stagewise development, phase transitions, developmental interpretability, Bayesian influence functions

TL;DR: We demonstrate that neural network influence functions can change dramatically over training due to stagewise development, which challenges the static attribution paradigm and motivates a shift to stagewise data attribution.

Abstract: Current training data attribution (TDA) methods treat the influence one sample has on another as static, but neural networks learn in distinct stages that exhibit changing patterns of influence. In this work, we introduce a framework for stagewise data attribution grounded in singular learning theory. We predict that influence can change non-monotonically, including sign flips and sharp peaks at developmental transitions. We first validate these predictions analytically and empirically in a toy model, showing that dynamic shifts in influence directly map to the model's progressive learning of a semantic hierarchy. Finally, we demonstrate these phenomena at scale in language models, where token-level influence changes align with known developmental stages.

Primary Area: interpretability and explainable AI

Submission Number: 20207