A Note on "Assessing Generalization of SGD via Disagreement"

TL;DR

This paper critically examines the theory linking model disagreement to generalization error in deep neural networks, revealing limitations in the original calibration assumptions and providing simplified, probabilistic proofs.

Contribution

It challenges the practicality of the disagreement-equality theory by showing calibration deterioration and offers simplified theoretical analysis within a probabilistic framework.

Findings

Calibration can worsen as disagreement increases.

The original theory may not hold in practical scenarios.

Simplified proofs clarify the theoretical basis.

Abstract

Several recent works find empirically that the average test error of deep neural networks can be estimated via the prediction disagreement of models, which does not require labels. In particular, Jiang et al. (2022) show for the disagreement between two separately trained networks that this `Generalization Disagreement Equality' follows from the well-calibrated nature of deep ensembles under the notion of a proposed `class-aggregated calibration.' In this reproduction, we show that the suggested theory might be impractical because a deep ensemble's calibration can deteriorate as prediction disagreement increases, which is precisely when the coupling of test error and disagreement is of interest, while labels are needed to estimate the calibration on new datasets. Further, we simplify the theoretical statements and proofs, showing them to be straightforward within a probabilistic context, unlike the original hypothesis space view employed by Jiang et al. (2022).