Analysis of Generalizability of Deep Neural Networks Based on the Complexity of Decision Boundary

TL;DR

This paper introduces the Decision Boundary Complexity (DBC) score, a novel method to quantify the complexity of DNN decision boundaries, demonstrating that simpler boundaries correlate with better generalization performance.

Contribution

The paper proposes a new DBC score based on entropy of eigenvalues from adversarial examples, providing a quantitative measure of decision boundary complexity and generalizability in DNNs.

Findings

DBC score correlates with test accuracy

Simpler decision boundaries lead to better generalization

Method works effectively for high-dimensional data

Abstract

For supervised learning models, the analysis of generalization ability (generalizability) is vital because the generalizability expresses how well a model will perform on unseen data. Traditional generalization methods, such as the VC dimension, do not apply to deep neural network (DNN) models. Thus, new theories to explain the generalizability of DNNs are required. In this study, we hypothesize that the DNN with a simpler decision boundary has better generalizability by the law of parsimony (Occam's Razor). We create the decision boundary complexity (DBC) score to define and measure the complexity of decision boundary of DNNs. The idea of the DBC score is to generate data points (called adversarial examples) on or near the decision boundary. Our new approach then measures the complexity of the boundary using the entropy of eigenvalues of these data. The method works equally well for high-dimensional data. We use training data and the trained model to compute the DBC score. And, the ground truth for model's generalizability is its test accuracy. Experiments based on the DBC score have verified our hypothesis. The DBC is shown to provide an effective method to measure the complexity of a decision boundary and gives a quantitative measure of the generalizability of DNNs.