On the Importance of Normalisation Layers in Deep Learning with Piecewise Linear Activation Units

Deep feedforward neural networks with piecewise linear activations are currently producing the state-of-the-art results in several public datasets. The combination of deep learning models and piecewise linear activation functions allows for the estimation of exponentially complex functions with the use of a large number of subnetworks specialized in the classification of similar input examples. During the training process, these subnetworks avoid overfitting with an implicit regularization scheme based on the fact that they must share their parameters with other subnetworks. Using this framework, we have made an empirical observation that can improve even more the performance of such models. We notice that these models assume a balanced initial distribution of data points with respect to the domain of the piecewise linear activation function. If that assumption is violated, then the piecewise linear activation units can degenerate into purely linear activation units, which can result in a significant reduction of their capacity to learn complex functions. Furthermore, as the number of model layers increases, this unbalanced initial distribution makes the model ill-conditioned. Therefore, we propose the introduction of batch normalisation units into deep feedforward neural networks with piecewise linear activations, which drives a more balanced use of these activation units, where each region of the activation function is trained with a relatively large proportion of training samples. Also, this batch normalisation promotes the pre-conditioning of very deep learning models. We show that by introducing maxout and batch normalisation units to the network in network model results in a model that produces classification results that are better than or comparable to the current state of the art in CIFAR-10, CIFAR-100, MNIST, and SVHN datasets

Adaptive Normalized Risk-Averting Training For Deep Neural Networks

This paper proposes a set of new error criteria and learning approaches, Adaptive Normalized Risk-Averting Training (ANRAT), to attack the non-convex optimization problem in training deep neural networks (DNNs). Theoretically, we demonstrate its effectiveness on global and local convexity lower-bounded by the standard $L_p$-norm error. By analyzing the gradient on the convexity index $\lambda$, we explain the reason why to learn $\lambda$ adaptively using gradient descent works. In practice, we show how this method improves training of deep neural networks to solve visual recognition tasks on the MNIST and CIFAR-10 datasets. Without using pretraining or other tricks, we obtain results comparable or superior to those reported in recent literature on the same tasks using standard ConvNets + MSE/cross entropy. Performance on deep/shallow multilayer perceptrons and Denoised Auto-encoders is also explored. ANRAT can be combined with other quasi-Newton training methods, innovative network variants, regularization techniques and other specific tricks in DNNs. Other than unsupervised pretraining, it provides a new perspective to address the non-convex optimization problem in DNNs.Comment: AAAI 2016, 0.39%~0.4% ER on MNIST with single 32-32-256-10 ConvNets, code available at https://github.com/cauchyturing/ANRA

Hyper-parameter optimization of Deep Convolutional Networks for object recognition

Recently sequential model based optimization (SMBO) has emerged as a promising hyper-parameter optimization strategy in machine learning. In this work, we investigate SMBO to identify architecture hyper-parameters of deep convolution networks (DCNs) object recognition. We propose a simple SMBO strategy that starts from a set of random initial DCN architectures to generate new architectures, which on training perform well on a given dataset. Using the proposed SMBO strategy we are able to identify a number of DCN architectures that produce results that are comparable to state-of-the-art results on object recognition benchmarks.Comment: 4 pages, 1 figure, 3 tables, Submitted to ICIP 201