Inherent Weight Normalization in Stochastic Neural Networks

Multiplicative stochasticity such as Dropout improves the robustness and generalizability of deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons are sufficient operations for deep neural networks. We call such models Neural Sampling Machines (NSM). We find that the probability of activation of the NSM exhibits a self-normalizing property that mirrors Weight Normalization, a previously studied mechanism that fulfills many of the features of Batch Normalization in an online fashion. The normalization of activities during training speeds up convergence by preventing internal covariate shift caused by changes in the input distribution. The always-on stochasticity of the NSM confers the following advantages: the network is identical in the inference and learning phases, making the NSM suitable for online learning, it can exploit stochasticity inherent to a physical substrate such as analog non-volatile memories for in-memory computing, and it is suitable for Monte Carlo sampling, while requiring almost exclusively addition and comparison operations. We demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and event-based classification benchmarks (N-MNIST and DVS Gestures). Our results show that NSMs perform comparably or better than conventional artificial neural networks with the same architecture

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE