Disentangling Model Multiplicity in Deep Learning

TL;DR

This paper investigates the phenomenon of model multiplicity in deep learning, analyzing how different models with similar training performance can vary internally and in predictions, affecting generalization.

Contribution

It introduces a new setup for analyzing representational multiplicity using SVCCA, and explores how training methods influence this multiplicity and its relation to predictive multiplicity.

Findings

Training methods systematically affect representational multiplicity.

Representational multiplicity correlates with predictive multiplicity in test predictions.

Measuring multiplicity can help understand and predict model generalization.

Abstract

Model multiplicity is a well-known but poorly understood phenomenon that undermines the generalisation guarantees of machine learning models. It appears when two models with similar training-time performance differ in their predictions and real-world performance characteristics. This observed 'predictive' multiplicity (PM) also implies elusive differences in the internals of the models, their 'representational' multiplicity (RM). We introduce a conceptual and experimental setup for analysing RM by measuring activation similarity via singular vector canonical correlation analysis (SVCCA). We show that certain differences in training methods systematically result in larger RM than others and evaluate RM and PM over a finite sample as predictors for generalizability. We further correlate RM with PM measured by the variance in i.i.d. and out-of-distribution test predictions in four standard image data sets. Finally, instead of attempting to eliminate RM, we call for its systematic measurement and maximal exposure.