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We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
We present an application of our new theoretical formulation of quantum dynamics, moment propagation theory (MPT) (Boyer et al., J. Chem. Phys. 160, 064113 (2024)), for employing machine-learning techniques to simulate the quantum dynamics…
Deep learning potentials for complex many-body systems often face challenges of insufficient accuracy and a lack of physical realism. This paper proposes an "Observable-Constrained Variational Framework" (OCVF), a general top-down…
Extreme value theory (EVT) is well suited to model extreme events, such as floods, heatwaves, or mechanical failures, which is required for reliability assessment of systems across multiple domains for risk management and loss prevention.…
Supervised fine-tuning (SFT) is the predominant method for adapting large language models (LLMs), yet it often struggles with generalization compared to reinforcement learning (RL). In this work, we posit that this performance disparity…
Inspired by the tremendous success of the self-attention mechanism in natural language processing, the Vision Transformer (ViT) creatively applies it to image patch sequences and achieves incredible performance. However, the scaled…
The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool by researchers far beyond the optimization community to model many important applications involving structured low rank matrices.…
Large Language Models (LLMs) have revolutionized various domains but encounter substantial challenges in tackling optimization modeling tasks for Operations Research (OR), particularly when dealing with complex problem. In this work, we…
We develop a fitted value iteration (FVI) method to compute bicausal optimal transport (OT) where couplings have an adapted structure. Based on the dynamic programming formulation, FVI adopts a function class to approximate the value…
The objective of this paper is to provide a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems for which the objective space is not necessarily convex. Our approach is…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…
Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…
Open-World Tracking (OWT) aims to track every object of any category, which requires the model to have strong generalization capabilities. Trackers can improve their generalization ability by leveraging Visual Language Models (VLMs).…
Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that…
We explore the impact of coarse quantization on matrix completion in the extreme scenario of dithered one-bit sensing, where the matrix entries are compared with time-varying threshold levels. In particular, instead of observing a subset of…
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…
We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…
In this survey, we analyze the newest machine learning (ML) techniques for optical orthogonal frequency division multiplexing (O-OFDM)-based optical communications. ML has been proposed to mitigate channel and transceiver imperfections. For…
In dynamically varying optical wireless communication (OWC) links, conventional quadrature amplitude modulation (QAM) in optical orthogonal frequency-division multiplexing (OFDM) requires frequent channel estimation and equalization,…