Input Space Mode Connectivity in Deep Neural Networks

TL;DR

This paper explores the existence of low-loss paths connecting similar input images in deep neural networks, extending the concept of mode connectivity from parameter space to input space, with implications for adversarial detection and interpretability.

Contribution

It introduces the concept of input space mode connectivity, providing theoretical and empirical evidence, and demonstrates its applications in adversarial detection and interpretability.

Findings

Connected images with similar predictions are common in trained models.

Paths between such images are often nearly linear with small deviations.

Input space mode connectivity exists even in untrained models, explained by percolation theory.

Abstract

We extend the concept of loss landscape mode connectivity to the input space of deep neural networks. Mode connectivity was originally studied within parameter space, where it describes the existence of low-loss paths between different solutions (loss minimizers) obtained through gradient descent. We present theoretical and empirical evidence of its presence in the input space of deep networks, thereby highlighting the broader nature of the phenomenon. We observe that different input images with similar predictions are generally connected, and for trained models, the path tends to be simple, with only a small deviation from being a linear path. Our methodology utilizes real, interpolated, and synthetic inputs created using the input optimization technique for feature visualization. We conjecture that input space mode connectivity in high-dimensional spaces is a geometric effect that takes place even in untrained models and can be explained through percolation theory. We exploit mode connectivity to obtain new insights about adversarial examples and demonstrate its potential for adversarial detection. Additionally, we discuss applications for the interpretability of deep networks.