A Two-Scale Complexity Measure for Deep Learning Models

TL;DR

This paper introduces 2sED, a new complexity measure for deep learning models based on effective dimension, which bounds generalization error and correlates with training error, with an efficient approximation method for large models.

Contribution

The paper proposes 2sED, a novel capacity measure for deep models, along with an efficient layerwise approximation technique for large-scale models.

Findings

2sED bounds generalization error under mild assumptions.

2sED correlates well with training error across datasets.

Layerwise approximation of 2sED is effective for large 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.