Manifold Regularized Discriminative Neural Networks

TL;DR

This paper introduces manifold regularization techniques for discriminative neural networks, improving generalization by modeling input data distribution and leveraging the manifold hypothesis, applicable to both supervised and semi-supervised learning.

Contribution

It proposes two novel regularizers that incorporate the data manifold into DNN training, enhancing generalization especially in semi-supervised settings.

Findings

Significant performance improvements on MNIST, CIFAR10, and SVHN datasets.

Effective semi-supervised learning with label-independent regularization.

Enhanced generalization by modeling data distribution within discriminative frameworks.

Abstract

Unregularized deep neural networks (DNNs) can be easily overfit with a limited sample size. We argue that this is mostly due to the disriminative nature of DNNs which directly model the conditional probability (or score) of labels given the input. The ignorance of input distribution makes DNNs difficult to generalize to unseen data. Recent advances in regularization techniques, such as pretraining and dropout, indicate that modeling input data distribution (either explicitly or implicitly) greatly improves the generalization ability of a DNN. In this work, we explore the manifold hypothesis which assumes that instances within the same class lie in a smooth manifold. We accordingly propose two simple regularizers to a standard discriminative DNN. The first one, named Label-Aware Manifold Regularization, assumes the availability of labels and penalizes large norms of the loss function w.r.t. data points. The second one, named Label-Independent Manifold Regularization, does not use label information and instead penalizes the Frobenius norm of the Jacobian matrix of prediction scores w.r.t. data points, which makes semi-supervised learning possible. We perform extensive control experiments on fully supervised and semi-supervised tasks using the MNIST, CIFAR10 and SVHN datasets and achieve excellent results.