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We revisit the adaptive Lasso as well as the thresholded Lasso with refitting, in a high-dimensional linear model, and study prediction error, $\ell_q$-error ($q \in \{1, 2 \} $), and number of false positive selections. Our theoretical…

It is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive…

Recurrent neural networks (RNNs) have shown promising performance for language modeling. However, traditional training of RNNs using back-propagation through time often suffers from overfitting. One reason for this is that stochastic…

A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical…

Recursion is a fundamental concept in the design of filters and audio systems. In particular, artificial reverberation systems that use delay networks depend on recursive paths to control both echo density and the decay rate of modal…

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…

Deploying deep convolutional neural networks (CNNs) on resource-constrained devices presents significant challenges due to their high computational demands and rigid, static architectures. To overcome these limitations, this thesis explores…

Recent contrastive methods show significant improvement in self-supervised learning in several domains. In particular, contrastive methods are most effective where data augmentation can be easily constructed e.g. in computer vision.…

Neural networks can be compressed to reduce memory and computational requirements, or to increase accuracy by facilitating the use of a larger base architecture. In this paper we focus on pruning individual neurons, which can simultaneously…

Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to…

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…

In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general synchronization transition becomes more difficult to meet when memory range increases,…

Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…

Convolutional neural networks can automatically learn features via deep network architectures and given input samples. However, the robustness of obtained models may face challenges in varying scenes. Bigger differences in network…

In this work we propose the use of adaptive stochastic search as a building block for general, non-convex optimization operations within deep neural network architectures. Specifically, for an objective function located at some layer in the…

Deep neural networks are state-of-the-art models for understanding the content of images, video and raw input data. However, implementing a deep neural network in embedded systems is a challenging task, because a typical deep neural…

We investigate the synaptic noise as a novel mechanism for creating critical avalanches in the activity of neural networks. We model neurons and chemical synapses by dynamical maps with a uniform noise term in the synaptic coupling. An…

Contemporary machine learning models, including large language models, exhibit remarkable capabilities in static tasks yet falter in non-stationary environments due to rigid architectures that hinder continual adaptation and lifelong…

Neuromorphic computing leveraging spiking neural network has emerged as a promising solution to tackle the security and reliability challenges with the conventional cyber-physical infrastructure of microgrids. Its event-driven paradigm…