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In this paper, we propose a a gradient-based neural network model to solve the mathematical programming problems with complementary constraints (MPCC). In order to facilitate tractable optimization, the problem MPCC is transformed via a…

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…

We address the structure identification and the uniform approximation of two fully nonlinear layer neural networks of the type $f(x)=1^T h(B^T g(A^T x))$ on $\mathbb R^d$ from a small number of query samples. We approach the problem by…

We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on using a finite set of Laurent coefficients as input information,…

Image superresolution methods process an input image sequence of a scene to obtain a still image with increased resolution. Classical approaches to this problem involve complex iterative minimization procedures, typically with high…

Neural Networks (NN) with ReLU activation functions are used to model multiparametric quadratic optimization problems (mp-QP) in diverse engineering applications. Researchers have suggested leveraging the piecewise affine property of deep…

Modern Hopfield Networks (MHNs) have emerged as powerful components in deep learning, serving as effective replacements for pooling layers, LSTMs, and attention mechanisms. While recent advancements have significantly improved their storage…

Deep Convolution Neural Networks (CNN) have achieved significant performance on single image super-resolution (SR) recently. However, existing CNN-based methods use artificially synthetic low-resolution (LR) and high-resolution (HR) image…

Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…

There exist many problem domains where the interpretability of neural network models is essential for deployment. Here we introduce a recurrent architecture composed of input-switched affine transformations - in other words an RNN without…

In this short paper we present a linear constraint solver for the UniCalc system, an environment for reliable solution of mathematical modeling problems.

Although Recurrent Neural Network (RNN) has been a powerful tool for modeling sequential data, its performance is inadequate when processing sequences with multiple patterns. In this paper, we address this challenge by introducing a novel…

We investigate to what extent it is possible to solve linear inverse problems with $ReLu$ networks. Due to the scaling invariance arising from the linearity, an optimal reconstruction function $f$ for such a problem is positive homogeneous,…

We consider the problem of recovering the topology and the edge conductance value, as well as characterizing a set of electrical networks that satisfy the limitedly available Thevenin impedance measurements. The measurements are obtained…

In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…

A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…

Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for…

We introduce Neural Radiosity, an algorithm to solve the rendering equation by minimizing the norm of its residual similar as in traditional radiosity techniques. Traditional basis functions used in radiosity techniques, such as piecewise…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Neuromorphic computing systems overcome the limitations of traditional von Neumann computing architectures. These computing systems can be further improved upon by using emerging technologies that are more efficient than CMOS for neural…