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We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

In this paper we introduce the DMR -- a prototype-based method and network architecture for deep learning which is using a decision tree (DT)-based inference and synthetic data to balance the classes. It builds upon the recently introduced…

Determinantal point processes (DPPs) are well known models for diverse subset selection problems, including recommendation tasks, document summarization and image search. In this paper, we discuss a greedy deterministic adaptation of k-DPP.…

Human-robot interactive decision-making is increasingly becoming ubiquitous, and trust is an influential factor in determining the reliance on autonomy. However, it is not reasonable to trust systems that are beyond our comprehension, and…

Recent advances in large language models (LLMs) have revolutionized the landscape of reasoning tasks. To enhance the capabilities of LLMs to emulate human reasoning, prior studies have focused on modeling reasoning steps using various…

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…

Markovian processes have long been used to model stochastic environments. Reinforcement learning has emerged as a framework to solve sequential planning and decision-making problems in such environments. In recent years, attempts were made…

Large language models often fail at logical reasoning when semantic heuristics conflict with decisive evidence - a phenomenon we term cognitive traps. To address this fundamental limitation, we introduce the Deliberative Reasoning Network…

The potential of large language models (LLMs) as decision support tools is increasingly being explored in fields such as business, engineering, and medicine, which often face challenging tasks of decision-making under uncertainty. In this…

Recommender systems often grapple with noisy implicit feedback. Most studies alleviate the noise issues from data cleaning perspective such as data resampling and reweighting, but they are constrained by heuristic assumptions. Another…

Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…

This paper serves as a review and discussion of the recent works on memcomputing. In particular, the $\textit{universal memcomputing machine}$ (UMM) and the $\textit{digital memcomputing machine}$ (DMM) are discussed. We review the…

The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information…