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Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase…

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise…

Given the rapid changes in telecommunication systems and their higher dependence on artificial intelligence, it is increasingly important to have models that can perform well under different, possibly adverse, conditions. Deep Neural…

In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean…

In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of these types of signals by a stable mathematical tool. Gabardo and Nashed and Gabardo and Yu…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

This article describes a series of new results outlining equivalences between certain "rewirings" of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to…

Computing the optimal solution to a spatial filtering problems in a Wireless Sensor Network can incur large bandwidth and computational requirements if an approach relying on data centralization is used. The so-called distributed adaptive…

Fully convolutional neural networks can process input of arbitrary size by applying a combination of downsampling and pooling. However, we find that fully convolutional image classifiers are not agnostic to the input size but rather show…

In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…

We present first empirical results from our ongoing investigation of distribution shifts in image data used for various computer vision tasks. Instead of analyzing the original training and test data, we propose to study shifts in the…

This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…

Learning in a non-stationary environment is an inevitable problem when applying machine learning algorithm to real world environment. Learning new tasks without forgetting the previous knowledge is a challenge issue in machine learning. We…

In many practical applications, signals and environments are time- varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify…

This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…

The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

Convolutional neural networks are based on a huge number of trained weights. Consequently, they are often data-greedy, sensitive to overtraining, and learn slowly. We follow the line of research in which filters of convolutional neural…

Quaternion wavelets are redundant wavelet transforms generalizing complex-valued non-decimated wavelet transforms. In this paper we propose a matrix-formulation for non-decimated quaternion wavelet transforms and define spectral tools for…

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…