The Memory Perturbation Equation: Understanding Model's Sensitivity to Data

TL;DR

The paper introduces the Memory-Perturbation Equation (MPE), a Bayesian-derived formula that links a model's sensitivity to data perturbations with its generalization ability, aiding robust and adaptive learning.

Contribution

It presents the MPE, unifying and generalizing existing sensitivity measures, and demonstrates its effectiveness in predicting model generalization during training.

Findings

Sensitivity estimates predict test performance accurately.

MPE unifies existing sensitivity measures.

Useful for developing robust learning algorithms.

Abstract

Understanding model's sensitivity to its training data is crucial but can also be challenging and costly, especially during training. To simplify such issues, we present the Memory-Perturbation Equation (MPE) which relates model's sensitivity to perturbation in its training data. Derived using Bayesian principles, the MPE unifies existing sensitivity measures, generalizes them to a wide-variety of models and algorithms, and unravels useful properties regarding sensitivities. Our empirical results show that sensitivity estimates obtained during training can be used to faithfully predict generalization on unseen test data. The proposed equation is expected to be useful for future research on robust and adaptive learning.