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Residual neural networks can be viewed as the forward Euler discretization of an Ordinary Differential Equation (ODE) with a unit time step. This has recently motivated researchers to explore other discretization approaches and train ODE…

In this paper, we consider the problem of prototype-based vision-language reasoning problem. We observe that existing methods encounter three major challenges: 1) escalating resource demands and prolonging training times, 2) contending with…

Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…

Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…

The rapid scaling of large language models~(LLMs) has made inference efficiency a primary bottleneck in the practical deployment. To address this, semi-structured sparsity offers a promising solution by strategically retaining $N$ elements…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Nystr\"om approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a…

$\textbf{Purpose:}$ To develop and evaluate an operator learning framework for nonlinear inversion (NLI) of brain magnetic resonance elastography (MRE) data, which enables real-time inversion of elastograms with comparable spatial accuracy…

One of the limiting factors of using support vector machines (SVMs) in large scale applications are their super-linear computational requirements in terms of the number of training samples. To address this issue, several approaches that…

Spiking Neural Networks (SNNs) provide an energy-efficient way to extract 3D spatio-temporal features. However, existing SNNs still exhibit a significant performance gap compared to Artificial Neural Networks (ANNs) due to inadequate…

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

One Class Slab Support Vector Machines (OCSSVM) have turned out to be better in terms of accuracy in certain classes of classification problems than the traditional SVMs and One Class SVMs or even other One class classifiers. This paper…

Kernel methods provide a powerful framework for non parametric learning. They are based on kernel functions and allow learning in a rich functional space while applying linear statistical learning tools, such as Ridge Regression or Support…

Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…

We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…