Manifold Regularized Discriminative Neural Networks
This work addresses generalization issues in deep learning for practitioners, but it is incremental as it builds on existing regularization techniques.
The paper tackled overfitting in deep neural networks by proposing two manifold-based regularizers that incorporate input distribution assumptions, achieving excellent results on MNIST, CIFAR10, and SVHN datasets in supervised and semi-supervised tasks.
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.