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Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial…
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…
The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review…
This thesis addresses the challenge of understanding Neural Networks through the lens of their most fundamental component: the weights, which encapsulate the learned information and determine the model behavior. At the core of this thesis…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
This work examines the deep disconnect between existing theoretical analyses of gradient-based algorithms and the practice of training deep neural networks. Specifically, we provide numerical evidence that in large-scale neural network…
Recurrent Neural Networks (RNNs) are general-purpose parallel-sequential computers. The program of an RNN is its weight matrix. How to learn useful representations of RNN weights that facilitate RNN analysis as well as downstream tasks?…
Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are…
The interpretability of neural networks (NNs) is a challenging but essential topic for transparency in the decision-making process using machine learning. One of the reasons for the lack of interpretability is random weight initialization,…
The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by…
Single layer feedforward networks with random weights are known for their non-iterative and fast training algorithms and are successful in a variety of classification and regression problems. A major drawback of these networks is that they…
The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems; in this situation, the modelbased methods need be revisited. A data-driven method, as…
Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…
Deep neural networks (DNN) are black box algorithms. They are trained using a gradient descent back propagation technique which trains weights in each layer for the sole goal of minimizing training error. Hence, the resulting weights cannot…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
Deep neural networks (DNNs) have been successfully applied to many real-world problems, but a complete understanding of their dynamical and computational principles is still lacking. Conventional theoretical frameworks for analysing DNNs…