A Gentle Introduction to Gradient-Based Optimization and Variational Inequalities for Machine Learning

The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and multi-agent problems. In these broader settings, new mathematical challenges emerge that involve equilibria and game theory instead of optima. Gradient-based methods remain essential -- given the high dimensionality and large scale of machine-learning problems -- but simple gradient descent is no longer the point of departure for algorithm design. We provide a gentle introduction to a broader framework for gradient-based algorithms in machine learning, beginning with saddle points and monotone games, and proceeding to general variational inequalities. While we provide convergence proofs for several of the algorithms that we present, our main focus is that of providing motivation and intuition.Comment: 36 pages, 7 figure

SCANN: Synthesis of Compact and Accurate Neural Networks

Deep neural networks (DNNs) have become the driving force behind recent artificial intelligence (AI) research. An important problem with implementing a neural network is the design of its architecture. Typically, such an architecture is obtained manually by exploring its hyperparameter space and kept fixed during training. This approach is time-consuming and inefficient. Another issue is that modern neural networks often contain millions of parameters, whereas many applications and devices require small inference models. However, efforts to migrate DNNs to such devices typically entail a significant loss of classification accuracy. To address these challenges, we propose a two-step neural network synthesis methodology, called DR+SCANN, that combines two complementary approaches to design compact and accurate DNNs. At the core of our framework is the SCANN methodology that uses three basic architecture-changing operations, namely connection growth, neuron growth, and connection pruning, to synthesize feed-forward architectures with arbitrary structure. SCANN encapsulates three synthesis methodologies that apply a repeated grow-and-prune paradigm to three architectural starting points. DR+SCANN combines the SCANN methodology with dataset dimensionality reduction to alleviate the curse of dimensionality. We demonstrate the efficacy of SCANN and DR+SCANN on various image and non-image datasets. We evaluate SCANN on MNIST and ImageNet benchmarks. In addition, we also evaluate the efficacy of using dimensionality reduction alongside SCANN (DR+SCANN) on nine small to medium-size datasets. We also show that our synthesis methodology yields neural networks that are much better at navigating the accuracy vs. energy efficiency space. This would enable neural network-based inference even on Internet-of-Things sensors.Comment: 13 pages, 8 figure

A Digital Neuromorphic Architecture Efficiently Facilitating Complex Synaptic Response Functions Applied to Liquid State Machines

Information in neural networks is represented as weighted connections, or synapses, between neurons. This poses a problem as the primary computational bottleneck for neural networks is the vector-matrix multiply when inputs are multiplied by the neural network weights. Conventional processing architectures are not well suited for simulating neural networks, often requiring large amounts of energy and time. Additionally, synapses in biological neural networks are not binary connections, but exhibit a nonlinear response function as neurotransmitters are emitted and diffuse between neurons. Inspired by neuroscience principles, we present a digital neuromorphic architecture, the Spiking Temporal Processing Unit (STPU), capable of modeling arbitrary complex synaptic response functions without requiring additional hardware components. We consider the paradigm of spiking neurons with temporally coded information as opposed to non-spiking rate coded neurons used in most neural networks. In this paradigm we examine liquid state machines applied to speech recognition and show how a liquid state machine with temporal dynamics maps onto the STPU-demonstrating the flexibility and efficiency of the STPU for instantiating neural algorithms.Comment: 8 pages, 4 Figures, Preprint of 2017 IJCN