One of the issues faced in training Generative Adversarial Nets (GANs) and their variants is the problem of mode collapse, wherein the training stability in terms of the generative loss increases as more training data is used. In this paper, we propose an alternative architecture via the Low-Complexity Neural Network (LCNN), which attempts to learn models with low complexity. The motivation is that controlling model complexity leads to models that do not overfit the training data. We incorporate the LCNN loss function for GANs, Deep Convolutional GANs (DCGANs) and Spectral Normalized GANs (SNGANs), in order to develop hybrid architectures called the LCNN-GAN, LCNN-DCGAN and LCNN-SNGAN respectively. On various large benchmark image datasets, we show that the use of our proposed models results in stable training while avoiding the problem of mode collapse, resulting in better training stability. We also show how the learning behavior can be controlled by a hyperparameter in the LCNN functional, which also provides an improved inception score.

Twin Support Vector Machines (TWSVMs) have emerged as an efficient alternative to Support Vector Machines (SVM) for learning from imbalanced datasets. The TWSVM learns two non-parallel classifying hyperplanes by solving a couple of smaller sized problems. However, it is unsuitable for large datasets, as it involves matrix operations. In this paper, we discuss a Twin Neural Network (Twin NN) architecture for learning from large unbalanced datasets. The objective functions of the networks in the Twin NN are designed to realize the idea of the Twin SVM with non-parallel decision boudaries for the respective classes, while also being able to reduce model complexity. The Twin NN optimizes the feature map, allowing for better discrimination between classes. The paper also discusses an extension of the Twin NN for multiclass datasets. This architecture trains as many neural networks as the number of classes, and has the additional advantage that it does not have any hyper-parameter which requires tuning. Results presented in the paper demonstrate that the Twin NN generalizes well and scales well on large unbalanced datasets.

Deep neural networks are over-parameterized, which implies that the number of parameters are much larger than the number of samples used to train the network. Even in such a regime deep architectures do not overfit. This phenomenon is an active area of research and many theories have been proposed trying to understand this peculiar observation. These include the Vapnik Chervonenkis (VC) dimension bounds and Rademacher complexity bounds which show that the capacity of the network is characterized by the norm of weights rather than the number of parameters. However, the effect of input noise on these measures for shallow and deep architectures has not been studied. In this paper, we analyze the effects of various regularization schemes on the complexity of a neural network which we characterize with the loss, $L_2$ norm of the weights, Rademacher complexities (Directly Approximately Regularizing Complexity-DARC1), VC dimension based Low Complexity Neural Network (LCNN) when subject to varying degrees of Gaussian input noise. We show that $L_2$ regularization leads to a simpler hypothesis class and better generalization followed by DARC1 regularizer, both for shallow as well as deeper architectures. Jacobian regularizer works well for shallow architectures with high level of input noises. Spectral normalization attains highest test set accuracies both for shallow and deeper architectures. We also show that Dropout alone does not perform well in presence of input noise. Finally, we show that deeper architectures are robust to input noise as opposed to their shallow counterparts.

This paper introduces an ACO model and associated algorithm, called Coupled EigenAnt, for the problem of finding the shortest of N paths between a source and a destination node. It is based on the recently introduced EigenAnt algorithm, the novelty being that it allows probabilistic path choice on both the forward and return journeys, as well as the fact that it introduces decay of pheromone deposition following a geometric progression. Equilibrium points of the model are calculated and the local stability of the two path synchronous version analyzed. Simulations illustrate the main features of the algorithm.

A technique for building a multilayer perceptron classifier network is presented. Initially, a single perceptron tries to correctly classify as many samples as possible. Misclassified samples are taken care of by adding as bias the output of up to two neurons to the parent neuron. The final classification boundary between the two disjoint half spaces at the output of the parent neuron is determined by a maximum margin classifier type SVM applied jointly to the training set of the parent neuron along with the correcting inputs from its child neuron(s). The growth of a branch in the network ceases when the terminal neuron is able to correctly classify all samples from its training set. No a priori assumptions need to be made regarding the number of neurons in the network or the kernel of the SVM classifier. Examples are presented to illustrate the effectiveness of the technique.