Jesse M. Zhang

Farzan Farnia, Jesse M. Zhang, David Tse

Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent works have increased the robustness of DNNs by fitting networks using adversarially-perturbed training samples, but the improved performance can still be far below the performance seen in non-adversarial settings. A significant portion of this gap can be attributed to the decrease in generalization performance due to adversarial training. In this work, we extend the notion of margin loss to adversarial settings and bound the generalization error for DNNs trained under several well-known gradient-based attack schemes, motivating an effective regularization scheme based on spectral normalization of the DNN's weight matrices. We also provide a computationally-efficient method for normalizing the spectral norm of convolutional layers with arbitrary stride and padding schemes in deep convolutional networks. We evaluate the power of spectral normalization extensively on combinations of datasets, network architectures, and adversarial training schemes. The code is available at https://github.com/jessemzhang/dl_spectral_normalization.

Soheil Feizi, Hamid Javadi, Jesse Zhang et al.

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper, we take a novel approach to this problem by asking whether one can constrain neural network weights to make its optimization landscape have good theoretical properties while at the same time, be a good approximation for the unconstrained one. For two-layer neural networks, we provide affirmative answers to these questions by introducing Porcupine Neural Networks (PNNs) whose weight vectors are constrained to lie over a finite set of lines. We show that most local optima of PNN optimizations are global while we have a characterization of regions where bad local optimizers may exist. Moreover, our theoretical and empirical results suggest that an unconstrained neural network can be approximated using a polynomially-large PNN.