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Deep learning (DL) has been shown to outperform traditional, human-defined summary statistics of the Ly{\alpha} forest in constraining key astrophysical and cosmological parameters owing to its ability to tap into the realm of non-Gaussian…

We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by small isotropic normal noise. The addition of such noise may be interpreted as a…

Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…

Quantum communication offers many applications, with teleportation and superdense coding being two of the most fundamental. In these protocols, pre-shared entanglement enables either the faithful transfer of quantum states or the…

We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…

We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…

Spiking and Quantized Neural Networks (NNs) are becoming exceedingly important for hyper-efficient implementations of Deep Learning (DL) algorithms. However, these networks face challenges when trained using error backpropagation, due to…

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation, instead it is based upon a dynamical…

We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…

Recent progress in speech separation has been largely driven by advances in deep neural networks, yet their high computational and memory requirements hinder deployment on resource-constrained devices. A significant inefficiency in…

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…

We present a novel model designed for resource-efficient multichannel speech enhancement in the time domain, with a focus on low latency, lightweight, and low computational requirements. The proposed model incorporates explicit spatial and…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

In the presence of system-environment coupling, classical complex systems undergo stochastic dynamics, where rich phenomena can emerge at large spatio-temporal scales. To investigate these phenomena, numerical approaches for simulating…

A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…

We consider the general problem of describing the dynamics of subnetworks of larger biochemical reaction networks, e.g. protein interaction networks involving complex formation and dissociation reactions. We propose the use of model…

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…