Exact Phase Transitions in Deep Learning

TL;DR

This paper uncovers phase transitions in deep learning models, linking them to statistical physics phenomena, and explains their implications for neural network optimization and posterior collapse issues.

Contribution

It provides a theoretical framework identifying first- and second-order phase transitions in neural networks based on layer count, connecting physics concepts to deep learning.

Findings

Identifies first- and second-order phase transitions in neural networks

Links phase transitions to optimization challenges and posterior collapse

Provides a physics-inspired theoretical understanding of deep learning behavior

Abstract

This work reports deep-learning-unique first-order and second-order phase transitions, whose phenomenology closely follows that in statistical physics. In particular, we prove that the competition between prediction error and model complexity in the training loss leads to the second-order phase transition for nets with one hidden layer and the first-order phase transition for nets with more than one hidden layer. The proposed theory is directly relevant to the optimization of neural networks and points to an origin of the posterior collapse problem in Bayesian deep learning.