Related papers: Learning Geometric Combinatorial Optimization Prob…
Recent deep reinforcement learning methods have achieved remarkable success in solving multi-objective combinatorial optimization problems (MOCOPs) by decomposing them into multiple subproblems, each associated with a specific weight…
Neural Combinatorial Optimization (NCO) has emerged as a powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance…
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…
Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and…
Convolutional networks have been the paradigm of choice in many computer vision applications. The convolution operation however has a significant weakness in that it only operates on a local neighborhood, thus missing global information.…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
Geometry problem solving (GPS) is a challenging mathematical reasoning task requiring multi-modal understanding, fusion, and reasoning. Existing neural solvers take GPS as a vision-language task but are short in the representation of…
Many existing learning-based grasping approaches concentrate on a single embodiment, provide limited generalization to higher DoF end-effectors and cannot capture a diverse set of grasp modes. We tackle the problem of grasping using…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4,…
Modern deep learning heavily relies on large labeled datasets, which often comse with high costs in terms of both manual labeling and computational resources. To mitigate these challenges, researchers have explored the use of informative…
Solving large-scale Generalized Eigenvalue Problems (GEPs) is a fundamental yet computationally prohibitive task in science and engineering. As a promising direction, contour integral (CI) methods, such as the CIRR algorithm, offer an…
Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to…
We present Convolutional Oriented Boundaries (COB), which produces multiscale oriented contours and region hierarchies starting from generic image classification Convolutional Neural Networks (CNNs). COB is computationally efficient,…
Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…
Accurate feature matching and correspondence in endoscopic images play a crucial role in various clinical applications, including patient follow-up and rapid anomaly localization through panoramic image generation. However, developing…
Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising…
The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…
We propose a novel optimization algorithm for continuous functions using geodesics and contours under conformal mapping.The algorithm can find multiple optima by first following a geodesic curve to a local optimum then traveling to the next…
Neural approaches for combinatorial optimization (CO) equip a learning mechanism to discover powerful heuristics for solving complex real-world problems. While neural approaches capable of high-quality solutions in a single shot are…