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<p>Every optimization problem shares the common objective of finding a minima/maxima, but its application spans over a wide variety of fields ranging from solving NP-hard problems to training a neural network. This thesis addresses two crucial aspects of the above-mentioned fields. The first project is concerned with designing a hardware-system for efficiently solving Traveling Salesman Problem (TSP). It involves encoding  the solution to the ground state of an Ising Hamiltonian and finding the minima of the energy landscape. To that end, we i) designed a stochastic nanomagnet-based device as a building block for the system, ii) developed a unique approach to encode any TSP into an array of these blocks, and finally, iii) established the operating principle to make the system converge to an optimal solution. We used this method to solve TSPs having more than 600 nodes.</p> <p>  </p> <p>The next parts of the thesis deal with another genre of optimization problems involving deep neural networks (DNN) in image-classification tasks. DNNs are trained by finding the minima of a loss landscape aimed at mapping input images to a set of discrete labels. Adversarial attacks tend to disrupt this mapping by corrupting the inputs with subtle perturbations, imperceptible to human eyes. Although it is imperative to deploy some external defense mechanisms to guard against these attacks, the defense procedure can be aided by some intrinsic robust properties of the network. In the quest for an inherently resilient neural network, we explored the robustness of biologically-inspired Spiking Neural Networks (SNN) in the second part of the thesis. We demonstrated that accuracy degradation is less severe in SNNs than in their non-spiking counterparts. We attribute this robustness to two fundamental characteristics of SNNs: (i) input discretization  and (ii) leak rate in Leaky-Integrate-Fire neurons and analyze their effects.</p> <p><br></p> <p>As mentioned beforehand, this intrinsic robustness is merely an aiding tool to external defense mechanisms. Adversarial training has been established as the stat-of-the-art defense to provide significant robustness against existing attack techniques. This method redefines the boundary of the neural network by augmenting the training dataset with adversarial samples. In the process of achieving robustness, we are faced with a trade-off: a decrease in the prediction accuracy of clean or unperturbed data. The goal of the last section of my thesis is to understand this setback by using Gradient Projection-based sequential learning as an analysis tool. We systematically analyze the interplay between clean training and adversarial training on parameter subspace. In this technique, adversarial training follows clean training task where the parameter update is performed in the orthogonal direction of the previous task (clean training). It is possible to track down the principal component directions responsible for adversarial training by restricting clean and adversarial parameter update to two orthogonal subspaces. By varying the partition of subspace, we showed that the low-variance principal components are not capable of learning adversarial data, rather it is necessary to perform parameter update in a common subspace consisting of higher variance principal components to obtain significant adversarial accuracy. However, disturbing these higher variance components causes the decrease in standard clean accuracy, hence the accuracy-robustness trade-off. Further, we showed that this trade-off is worsened</p> <p>when the network capacity is smaller due to under-parameterization effect.</p>

In this project, a neural network based system is used to classify the promoter regions found in Escherichia coli DNA sequences. An unsupervised algorithm based on the self-organizing feature map is used to classify the sequences and a dynamic programming algorithm is used too query the trained neural networks. In order to generalize the neural network's weights for display purposes, a back propagation supervised learning algorithm based on the conjugate gradient method is used to map the weights to one of the fifteen combinations of adenine, cytosine, guanine, and thymine (the chemical components of DNA). The results show that this method is able to classify the training sequences into discrete sub-classes which provide a query base for classifying new sequences. This method can be used for any class of sequences and can be extended for use in searching sequence databases. / Thesis / Master of Science (MS)

Biophysically detailed representations of neural network models provide substantial insight to underlying neural processing mechanisms in the auditory systems of the brain. For simple biological systems the behavior can be represented by simple equations or flow charts. But for complex systems, more detailed descriptions of individual neurons and their synaptic connectivity are typically required. Creating extensive network models allows us to test hypotheses, apply specific manipulations that cannot be done experimentally and provide supporting evidence for experimental results. Several studies have been made on establishing realistic models of the cochlear nucleus (Manis and Campagnola, 2018; Eager et al., 2004), the part of the brainstem where sound signals enter the brain, both on individual neuron and networked structure levels. These models are based on both in vitro and in vivo physiological data, and they successfully demonstrate certain aspects of the neural processing of sound signals. Even though these models have been tested with tone bursts and isolated phonemes, the representation of speech in the cochlear nucleus and how it may support robust speech intelligibility remains to be explored with these detailed biophysical models. In this study, the basis of creating a biophysically detailed model of microcircuits in the cochlear nucleus is formed following the approach of Manis and Campagnola (2018). The focus of this thesis is more on bushy cell microcircuits. We have updated Manis and Campagnola (2018) model to take inputs from the new phenomenological auditory periphery model of Bruce et al. (2018). Different cell types in the cochlear nucleus are modelled by detailed cell models of Rothman and Manis (2003c) and updated Manis and Campagnola (2018) cell models. Networked structures are built out of them according to published anatomical and physiological data. The outputs of these networked structures are used to create post-stimulus-time-histograms (PSTH) and response maps to investigate the representation of tone bursts and average localized synchronized rate (ALSR) of phoneme 'e' and are compared to published physiological data (Blackburn and Sachs, 1990). / Thesis / Master of Applied Science (MASc)

Since its inception in the nineteenth century, the Internal Combustion Engine (ICE) remains the most prevalent technology in transportation systems to date. In order to minimize emissions, it is important that ICE is operated according to its optimized design conditions. As such, condition monitoring and Fault Detection and Diagnosis (FDD) tools can play an important role in detecting conditions that would affect the operability of the engine. In this research, different signal-based Fault Detection and Diagnosis (FDD) techniques are researched and implemented for fault condition monitoring of ICE. The implementation of prognostics for the engine in an automated form has important consequences that include cost savings, increased reliability, reduction of GHG emissions, better safety, and extended life for the vehicle. In this research, in order to carry out FDD onboard, a low-cost and flexible internet-based data-acquisition system (DAQ) was designed and implemented. The main part of the system is an embedded hardware running a full desktop version of Linux. This sensory system leverages the positive aspects of both real-time and general-purpose architectures to ensure engine monitoring at high sampling rates. Unlike other commercial DAQ systems, the software of this device is open-source, free of charge, and highly expandable to suit other FDD applications. In addition to data collection at high sampling rates, the FDD system includes advanced FDD strategies. The Fault Detection and Diagnosis strategies considered use a combination of Fourier Transforms (FT), Wavelet Transforms (WT), and Principal Component Analysis (PCA). Meanwhile, Fault Classification was carried using Neural Networks consisting of the Multi-Layer Perceptron (MLP). Three strategies were comparatively considered for the training of the Neural Network (NN), namely the Levenberg-Marquardt (LM), the Extended Kalman Filter (EKF), and the Smooth Variable Structure Filter (SVSF) techniques. The proposed FDD system was able to achieve 100% accuracy in classifying a set of engine faults. / Thesis / Master of Applied Science (MASc)