Rethinking generalization requires revisiting old ideas: statistical mechanics approaches and complex learning behavior

TL;DR

This paper revisits classical statistical mechanics ideas to better understand the complex and counterintuitive generalization behaviors of deep neural networks, moving beyond traditional capacity control theories.

Contribution

It introduces a simple deep learning model controlled by two parameters, linking statistical mechanics concepts to explain neural network generalization phenomena.

Findings

Explains overfitting and sharp transitions in generalization.

Describes how noise and early stopping affect model behavior.

Provides qualitative insights into empirical neural network behaviors.

Abstract

We describe an approach to understand the peculiar and counterintuitive generalization properties of deep neural networks. The approach involves going beyond worst-case theoretical capacity control frameworks that have been popular in machine learning in recent years to revisit old ideas in the statistical mechanics of neural networks. Within this approach, we present a prototypical Very Simple Deep Learning (VSDL) model, whose behavior is controlled by two control parameters, one describing an effective amount of data, or load, on the network (that decreases when noise is added to the input), and one with an effective temperature interpretation (that increases when algorithms are early stopped). Using this model, we describe how a very simple application of ideas from the statistical mechanics theory of generalization provides a strong qualitative description of recently-observed empirical results regarding the inability of deep neural networks not to overfit training data, discontinuous learning and sharp transitions in the generalization properties of learning algorithms, etc.