Input and Weight Space Smoothing for Semi-supervised Learning

We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the minimality of the resulting representation, the other insensitivity to nuisance variability. We propose a method to perform such smoothing, which combines known input-space smoothing with a novel weight-space smoothing, based on a min-max (adversarial) optimization. The resulting Adversarial Block Coordinate Descent (ABCD) algorithm performs gradient ascent with a small learning rate for a random subset of the weights, and standard gradient descent on the remaining weights in the same mini-batch. It achieves comparable performance to the state-of-the-art without resorting to heavy data augmentation, using a relatively simple architecture

Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting

We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after every task with a Gaussian, leading to a quadratic penalty on changes to the weights. The Laplace approximation requires calculating the Hessian around a mode, which is typically intractable for modern architectures. In order to make our method scalable, we leverage recent block-diagonal Kronecker factored approximations to the curvature. Our algorithm achieves over 90% test accuracy across a sequence of 50 instantiations of the permuted MNIST dataset, substantially outperforming related methods for overcoming catastrophic forgetting.Comment: 13 pages, 6 figure

A jamming transition from under- to over-parametrization affects loss landscape and generalization

We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. Under some general conditions, we show that this transition is sharp for the hinge loss. In the whole over-parametrized regime, poor minima of the loss are not encountered during training since the number of constraints to satisfy is too small to hamper minimization. Our findings support a link between this transition and the generalization properties of the network: as we increase the number of parameters of a given model, starting from an under-parametrized network, we observe that the generalization error displays three phases: (i) initial decay, (ii) increase until the transition point --- where it displays a cusp --- and (iii) slow decay toward a constant for the rest of the over-parametrized regime. Thereby we identify the region where the classical phenomenon of over-fitting takes place, and the region where the model keeps improving, in line with previous empirical observations for modern neural networks.Comment: arXiv admin note: text overlap with arXiv:1809.0934