Disentangling Model Multiplicity in Deep Learning

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.