Topology of Out-of-Distribution Examples in Deep Neural Networks

TL;DR

This paper introduces a topological method to analyze and detect out-of-distribution examples in deep neural networks by examining the persistence of topological features in latent space embeddings, revealing that OOD examples exhibit longer persistence.

Contribution

It presents a novel topological approach to characterize OOD examples in DNNs, demonstrating that OOD inputs have distinct topological signatures compared to in-distribution data.

Findings

OOD examples have longer topological persistence than training/test data.

Realistic DNNs do not induce topological simplification on OOD inputs.

Topological features can inform OOD detection strategies.

Abstract

As deep neural networks (DNNs) become increasingly common, concerns about their robustness do as well. A longstanding problem for deployed DNNs is their behavior in the face of unfamiliar inputs; specifically, these models tend to be overconfident and incorrect when encountering out-of-distribution (OOD) examples. In this work, we present a topological approach to characterizing OOD examples using latent layer embeddings from DNNs. Our goal is to identify topological features, referred to as landmarks, that indicate OOD examples. We conduct extensive experiments on benchmark datasets and a realistic DNN model, revealing a key insight for OOD detection. Well-trained DNNs have been shown to induce a topological simplification on training data for simple models and datasets; we show that this property holds for realistic, large-scale test and training data, but does not hold for OOD examples. More specifically, we find that the average lifetime (or persistence) of OOD examples is statistically longer than that of training or test examples. This indicates that DNNs struggle to induce topological simplification on unfamiliar inputs. Our empirical results provide novel evidence of topological simplification in realistic DNNs and lay the groundwork for topologically-informed OOD detection strategies.