Two-Phase Dynamics of Interactions Explains the Starting Point of a DNN Learning Over-Fitted Features

TL;DR

This paper reveals that DNNs learn interactions in two distinct phases, first penalizing medium/high-order interactions and then gradually learning higher-order ones, explaining the evolution of their generalization capabilities.

Contribution

The paper uncovers the two-phase learning dynamics of interactions in DNNs and links this to the model's generalization power during training.

Findings

DNNs learn interactions in two phases.

High-order interactions have weaker generalization.

Two-phase dynamics are consistent across architectures.

Abstract

This paper investigates the dynamics of a deep neural network (DNN) learning interactions. Previous studies have discovered and mathematically proven that given each input sample, a well-trained DNN usually only encodes a small number of interactions (non-linear relationships) between input variables in the sample. A series of theorems have been derived to prove that we can consider the DNN's inference equivalent to using these interactions as primitive patterns for inference. In this paper, we discover the DNN learns interactions in two phases. The first phase mainly penalizes interactions of medium and high orders, and the second phase mainly learns interactions of gradually increasing orders. We can consider the two-phase phenomenon as the starting point of a DNN learning over-fitted features. Such a phenomenon has been widely shared by DNNs with various architectures trained for different tasks. Therefore, the discovery of the two-phase dynamics provides a detailed mechanism for how a DNN gradually learns different inference patterns (interactions). In particular, we have also verified the claim that high-order interactions have weaker generalization power than low-order interactions. Thus, the discovered two-phase dynamics also explains how the generalization power of a DNN changes during the training process.