A two-scale Complexity Measure for Deep Learning Models

Massimiliano Datres, Gian Paolo Leonardi, Alessio Figalli, David Sutter

Keywords: Statistical learning theory, complexity measures, covering number estimates, Fisher metric, Markovian models.

Abstract: We introduce a novel capacity measure 2sED for statistical models based on the effective dimension. The new quantity provably bounds the generalization error under mild assumptions on the model. Furthermore, simulations on standard data sets and popular model architectures show that 2sED correlates well with the training error. For Markovian models, we show how to efficiently approximate 2sED from below through a layerwise iterative approach, which allows us to tackle deep learning models with a large number of parameters. Simulation results suggest that the approximation is good for different prominent models and data sets.

Primary Area: Learning theory

Submission Number: 10330