Distributional Training Data Attribution: What do Influence Functions Sample?

TL;DR

This paper introduces distributional training data attribution (d-TDA), a method to account for stochasticity in deep learning training, revealing influence functions as a distributional limit and demonstrating practical benefits in vision and diffusion models.

Contribution

The paper proposes d-TDA to incorporate training randomness into data attribution, revealing influence functions as a distributional limit without convexity assumptions.

Findings

Influence functions are shown to be 'secretly distributional'

d-TDA improves data pruning in vision transformers

d-TDA helps identify influential examples in diffusion models

Abstract

Randomness is an unavoidable part of training deep learning models, yet something that traditional training data attribution algorithms fail to rigorously account for. They ignore the fact that, due to stochasticity in the initialisation and batching, training on the same dataset can yield different models. In this paper, we address this shortcoming through introducing distributional training data attribution (d-TDA), the goal of which is to predict how the distribution of model outputs (over training runs) depends upon the dataset. Intriguingly, we find that influence functions (IFs), a popular data attribution tool, are 'secretly distributional': they emerge from our framework as the limit to unrolled differentiation, without requiring restrictive convexity assumptions. This provides a new perspective on the effectiveness of IFs in deep learning. We demonstrate the practical utility of d-TDA in experiments, including improving data pruning for vision transformers and identifying influential examples with diffusion models.