Efficient Parametric Approximations of Neural Network Function Space Distance

TL;DR

This paper introduces LAFTR, an efficient parametric method to approximate the Function Space Distance between neural networks, enabling scalable analysis of model similarity, influence, and data quality in continual learning scenarios.

Contribution

The paper presents LAFTR, a novel linearized approximation technique for ReLU networks that requires minimal parameters and outperforms existing methods in estimating function space distance.

Findings

LAFTR outperforms other parametric approximations with less memory.

It is effective in continual learning and influence estimation.

It can detect mislabeled data without extensive dataset iteration.

Abstract

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.