This paper proposes a novel Decentralized Spike-based Learning (DSL) framework for the discrete Perimeter Defense Problem (d-PDP). A team of defenders is operating on the perimeter to protect the circular territory from radially incoming intruders. At first, the d-PDP is formulated as a spatio-temporal multi-task assignment problem (STMTA). The problem of STMTA is then converted into a multi-label learning problem to obtain labels of segments that defenders have to visit in order to protect the perimeter. The DSL framework uses a Multi-Label Classifier using Synaptic Efficacy Function spiking neuRON (MLC-SEFRON) network for deterministic multi-label learning. Each defender contains a single MLC-SEFRON network. Each MLC-SEFRON network is trained independently using input from its own perspective for decentralized operations. The input spikes to the MLC-SEFRON network can be directly obtained from the spatio-temporal information of defenders and intruders without any extra pre-processing step. The output of MLC-SEFRON contains the labels of segments that a defender has to visit in order to protect the perimeter. Based on the multi-label output from the MLC-SEFRON a trajectory is generated for a defender using a Consensus-Based Bundle Algorithm (CBBA) in order to capture the intruders. The target multi-label output for training MLC-SEFRON is obtained from an expert policy. Also, the MLC-SEFRON trained for a defender can be directly used for obtaining labels of segments assigned to another defender without any retraining. The performance of MLC-SEFRON has been evaluated for full observation and partial observation scenarios of the defender. The overall performance of the DSL framework is then compared with expert policy along with other existing learning algorithms. The scalability of the DSL has been evaluated using an increasing number of defenders.

Mammographic image analysis requires accurate localisation of salient mammographic masses. In mammographic computer-aided diagnosis, mass or Region of Interest (ROI) is often marked by physicians and features are extracted from the marked ROI. In this paper, we present a novel mammographic mass localisation framework, based on the maximal class activations of the stacked auto-encoders. We hypothesize that the image regions activating abnormal classes in mammographic images will be the breast masses which causes the anomaly. The experiment is conducted using randomly selected 200 mammographic images (100 normal and 100 abnormal) from IRMA mammographic dataset. Abnormal mass regions marked by an expert radiologist are used as the ground truth. The proposed method outperforms existing Deep Convolutional Neural Network (DCNN) based techniques in terms of salient region detection accuracy. The proposed greedy backtracking method is more efficient and does not require a vast number of labelled training images as in DCNN based method. Such automatic localisation method will assist physicians to make accurate decisions on biopsy recommendations and treatment evaluations.

Occlusion is a prevalent and easily realizable semantic perturbation to deep neural networks (DNNs). It can fool a DNN into misclassifying an input image by occluding some segments, possibly resulting in severe errors. Therefore, DNNs planted in safety-critical systems should be verified to be robust against occlusions prior to deployment. However, most existing robustness verification approaches for DNNs are focused on non-semantic perturbations and are not suited to the occlusion case. In this paper, we propose the first efficient, SMT-based approach for formally verifying the occlusion robustness of DNNs. We formulate the occlusion robustness verification problem and prove it is NP-complete. Then, we devise a novel approach for encoding occlusions as a part of neural networks and introduce two acceleration techniques so that the extended neural networks can be efficiently verified using off-the-shelf, SMT-based neural network verification tools. We implement our approach in a prototype called OccRob and extensively evaluate its performance on benchmark datasets with various occlusion variants. The experimental results demonstrate our approach's effectiveness and efficiency in verifying DNNs' robustness against various occlusions, and its ability to generate counterexamples when these DNNs are not robust.

Dynamical systems theory has recently been applied in optimization to prove that gradient descent algorithms avoid so-called strict saddle points of the loss function. However, in many modern machine learning applications, the required regularity conditions are not satisfied. In particular, this is the case for rectified linear unit (ReLU) networks. In this paper, we prove a variant of the relevant dynamical systems result, a center-stable manifold theorem, in which we relax some of the regularity requirements. Then, we verify that shallow ReLU networks fit into the new framework. Building on a classification of critical points of the square integral loss of shallow ReLU networks measured against an affine target function, we deduce that gradient descent avoids most saddle points. We proceed to prove convergence to global minima if the initialization is sufficiently good, which is expressed by an explicit threshold on the limiting loss.

Neural networks are important tools for data-intensive analysis and are commonly applied to model non-linear relationships between dependent and independent variables. However, neural networks are usually seen as "black boxes" that offer minimal information about how the input variables are used to predict the response in a fitted model. This article describes the \pkg{NeuralSens} package that can be used to perform sensitivity analysis of neural networks using the partial derivatives method. Functions in the package can be used to obtain the sensitivities of the output with respect to the input variables, evaluate variable importance based on sensitivity measures and characterize relationships between input and output variables. Methods to calculate sensitivities are provided for objects from common neural network packages in \proglang{R}, including \pkg{neuralnet}, \pkg{nnet}, \pkg{RSNNS}, \pkg{h2o}, \pkg{neural}, \pkg{forecast} and \pkg{caret}. The article presents an overview of the techniques for obtaining information from neural network models, a theoretical foundation of how are calculated the partial derivatives of the output with respect to the inputs of a multi-layer perceptron model, a description of the package structure and functions, and applied examples to compare \pkg{NeuralSens} functions with analogous functions from other available \proglang{R} packages.

Neural Networks (NN) have recently emerged as backbone of several sensitive applications like automobile, medical image, security, etc. NNs inherently offer Partial Fault Tolerance (PFT) in their architecture; however, the biased PFT of NNs can lead to severe consequences in applications like cryptography and security critical scenarios. In this paper, we propose a revised implementation which enhances the PFT property of NN significantly with detailed mathematical analysis. We evaluated the performance of revised NN considering both software and FPGA implementation for a cryptographic primitive like AES SBox. The results show that the PFT of NNs can be significantly increased with the proposed methodology.

The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural networks, where the activation function is represented as a linear combination of possible candidate functions, and an optimal activation is obtained via minimization of a loss function using gradient descent method. The gradient formulae for the loss function with respect to these expansion coefficients are central for the implementation of gradient descent algorithm, and here we derive these gradient formulae.

A neural network solution is proposed for solving path planning problems faced by mobile robots. The proposed network is a two-dimensional sheet of neurons forming a distributed representation of the robot's workspace. Lateral interconnections between neurons are "cooperative", so that the network exhibits oscillatory behaviour. These oscillations are used to generate solutions of Bellman's dynamic programming equation in the context of path planning. Simulation experiments imply that these networks locate global optimal paths even in the presence of substantial levels of circuit nOlse. 1 Dynamic Programming and Path Planning Consider a 2-DOF robot moving about in a 2-dimensional world. A robot's location is denoted by the real vector, p.

A neural network solution is proposed for solving path planning problems faced by mobile robots. The proposed network is a two-dimensional sheet of neurons forming a distributed representation of the robot's workspace. Lateral interconnections between neurons are "cooperative", so that the network exhibits oscillatory behaviour. These oscillations are used to generate solutions of Bellman's dynamic programming equation in the context of path planning. Simulation experiments imply that these networks locate global optimal paths even in the presence of substantial levels of circuit nOlse. 1 Dynamic Programming and Path Planning Consider a 2-DOF robot moving about in a 2-dimensional world. A robot's location is denoted by the real vector, p.

A neural network solution is proposed for solving path planning problems The proposed network is a two-dimensional sheetfaced by mobile robots. of neurons forming a distributed representation of the robot's workspace. Lateral interconnections between neurons are "cooperative", so that the network exhibits oscillatory behaviour. These oscillations are used to generate solutions of Bellman's dynamic programming equation in the context of path planning. Simulation experiments imply that these networks locate paths even in the presence of substantial levels of circuitglobal optimal nOlse. 1 Dynamic Programming and Path Planning Consider a 2-DOF robot moving about in a 2-dimensional world. A robot's location is denoted by the real vector, p.