Modeling the Nonsmoothness of Modern Neural Networks

TL;DR

This paper investigates the nonsmoothness in modern neural networks caused by operations like ReLU and max pooling, modeling and quantifying it to better understand its propagation and potential forensic applications.

Contribution

It introduces a novel measure called SMP to quantify nonsmoothness and models its propagation through neural network layers, providing new insights into neural network behavior.

Findings

ReLU and max pooling induce nonsmoothness in neural networks

The SMP feature accurately predicts nonsmoothness propagation

Nonsmoothness can serve as a forensic tool for neural network analysis

Abstract

Modern neural networks have been successful in many regression-based tasks such as face recognition, facial landmark detection, and image generation. In this work, we investigate an intuitive but understudied characteristic of modern neural networks, namely, the nonsmoothness. The experiments using synthetic data confirm that such operations as ReLU and max pooling in modern neural networks lead to nonsmoothness. We quantify the nonsmoothness using a feature named the sum of the magnitude of peaks (SMP) and model the input-output relationships for building blocks of modern neural networks. Experimental results confirm that our model can accurately predict the statistical behaviors of the nonsmoothness as it propagates through such building blocks as the convolutional layer, the ReLU activation, and the max pooling layer. We envision that the nonsmoothness feature can potentially be used as a forensic tool for regression-based applications of neural networks.