The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement

Post-training discriminative pruning for RBMs

One of the major challenges in the area of artificial neural networks is the identification of a suitable architecture for a specific problem. Choosing an unsuitable topology can exponentially increase the training cost, and even hinder network convergence. On the other hand, recent research indicates that larger or deeper nets can map the problem features into a more appropriate space, and thereby improve the classification process, thus leading to an apparent dichotomy. In this regard, it is interesting to inquire whether independent measures, such as mutual information, could provide a clue to finding the most discriminative neurons in a network. In the present work we explore this question in the context of Restricted Boltzmann Machines, by employing different measures to realize post-training pruning. The neurons which are determined by each measure to be the most discriminative, are combined and a classifier is applied to the ensuing network to determine its usefulness. We find that two measures in particular seem to be good indicators of the most discriminative neurons, producing savings of generally more than 50% of the neurons, while maintaining an acceptable error rate. Further, it is borne out that starting with a larger network architecture and then pruning is more advantageous than using a smaller network to begin with. Finally, a quantitative index is introduced which can provide information on choosing a suitable pruned network.Fil: Sánchez Gutiérrez, Máximo. Universidad Autónoma Metropolitana; MéxicoFil: Albornoz, Enrique Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Rufiner, Hugo Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentina. Universidad Nacional de Entre Ríos; ArgentinaFil: Close, John Goddard. Universidad Autónoma Metropolitana; Méxic

Design and evaluation of neural classifiers

In this paper we propose a method for design of feed-forward neural classifiers based on regularization and adaptive architectures. Using a penalized maximum likelihood scheme we derive a modified form of the entropic error measure and an algebraic estimate of the test error. In conjunction with Optimal Brain Damage pruning the test error estimate is used to optimize the network architecture. The scheme is evaluated on an artificial and a real world problem. INTRODUCTION Pattern recognition is an important aspect of most scientific fields and indeed the objective of most neural network applications. Some of the by now classic applications of neural networks like Sejnowski and Rosenbergs "NetTalk" concern classification of patterns into a finite number of categories. In modern approaches to pattern recognition the objective is to produce class probabilities for a given pattern. Using Bayes decision theory, the "hard" classifier selects the class with the highest class probability, henc..

Pruning artificial neural networks: a way to find well-generalizing, high-entropy sharp minima

Recently, a race towards the simplification of deep networks has begun, showing that it is effectively possible to reduce the size of these models with minimal or no performance loss. However, there is a general lack in understanding why these pruning strategies are effective. In this work, we are going to compare and analyze pruned solutions with two different pruning approaches, one-shot and gradual, showing the higher effectiveness of the latter. In particular, we find that gradual pruning allows access to narrow, well-generalizing minima, which are typically ignored when using one-shot approaches. In this work we also propose PSP-entropy, a measure to understand how a given neuron correlates to some specific learned classes. Interestingly, we observe that the features extracted by iteratively-pruned models are less correlated to specific classes, potentially making these models a better fit in transfer learning approaches