Modeling the Nonsmoothness of Modern Neural Networks
This work addresses the understudied characteristic of nonsmoothness in neural networks, which could serve as a forensic tool for regression-based applications, but it is incremental as it builds on known properties without introducing a new paradigm.
The authors tackled the problem of quantifying and modeling the nonsmoothness in modern neural networks, showing that operations like ReLU and max pooling cause nonsmoothness, and their model accurately predicts its statistical propagation through network building blocks.
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.