Calculus of Variations and Geometric Measure Theory

M. Datres - G. P. Leonardi - A. Figalli - D. Sutter

A Two-Scale Complexity Measure for Deep Learning Models

created by leonardi on 31 Jan 2024



Inserted: 31 jan 2024

Year: 2024

ArXiv: 2401.09184 PDF


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.