Chapter 1 strongly advocates the stochastic back-propagation method to train neural networks. This is in fact an instance of a more general technique called stochastic gradient descent (SGD). This chapter provides background material, explains why SGD is a good learning algorithm when the training set is large, and provides useful recommendations.

There is widespread sentiment that fast gradient methods (e.g. Nesterov’s acceleration, conjugate gradient, heavy ball) are not effective for the purposes of stochastic optimization due to their instability and error accumulation. Numerous works have attempted to quantify these instabilities in the face of either statistical or non-statistical errors (Paige, 1971; Proakis, 1974; Polyak, 1987; G...

Executive Summary Echo state networks (ESNs) are a novel approach to modeling the nonlinear dynamical systems that abound in the sciences and engineering. They employ artificial recurrent neural networks in a way that has been independently proposed as a learning mechanism in biological brains and lead to a fast and simple algorithm for supervised training. ESNs are controlled by several global...

Prior work has demonstrated that exploiting the sparsity can dramatically improve the energy efficiency and reduce the memory footprint of Convolutional Neural Networks (CNNs). However, these sparsity-centric optimization techniques might be less effective for Long Short-Term Memory (LSTM) based Recurrent Neural Networks (RNNs), especially for the training phase, because of the significant stru...

We consider two questions at the heart of machine learning; how can we predict if a minimum will generalize to the test set, and why does stochastic gradient descent find minima that generalize well? Our work responds to Zhang et al. (2016), who showed deep neural networks can easily memorize randomly labeled training data, despite generalizing well on real labels of the same inputs. We show th...