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In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a…

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in ML. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D/3D…

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their…

Autonomous navigation in unknown environments is challenging and demands the consideration of both geometric and semantic information in order to parse the navigability of the environment. In this work, we propose a novel space modeling…

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g.,…

Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories:…

Achieving human-like reasoning in deep learning models for complex tasks in unknown environments remains a critical challenge in embodied intelligence. While advanced vision-language models (VLMs) excel in static scene understanding, their…

Unstructured environments are difficult for autonomous driving. This is because various unknown obstacles are lied in drivable space without lanes, and its width and curvature change widely. In such complex environments, searching for a…

Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem…

3D visual grounding (3DVG) is a critical task in scene understanding that aims to identify objects in 3D scenes based on text descriptions. However, existing methods rely on separately pre-trained vision and text encoders, resulting in a…

The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…

Robotic pick and place tasks are symmetric under translations and rotations of both the object to be picked and the desired place pose. For example, if the pick object is rotated or translated, then the optimal pick action should also…

Estimating the 6D pose of an object from a single RGB image is a critical task that becomes additionally challenging when dealing with symmetric objects. Recent approaches typically establish one-to-one correspondences between image pixels…

Simultaneous Localization and Planning (SLAP) under process and measurement uncertainties is a challenge. It involves solving a stochastic control problem modeled as a Partially Observed Markov Decision Process (POMDP) in a general…

Light decoder-based solvers have gained popularity for solving vehicle routing problems (VRPs) due to their efficiency and ease of integration with reinforcement learning algorithms. However, they often struggle with generalization to…

Robot motion planning has made vast advances over the past decades, but the challenge remains: robot mobile manipulators struggle to plan long-range whole-body motion in common household environments in real time, because of…

The well-established modular autonomous driving system is decoupled into different standalone tasks, e.g. perception, prediction and planning, suffering from information loss and error accumulation across modules. In contrast, end-to-end…

This paper proposes online sampling in the parameter space of a neural network for GPU-accelerated motion planning of autonomous vehicles. Neural networks are used as controller parametrization since they can handle nonlinear non-convex…

Unsupervised text encoding models have recently fueled substantial progress in NLP. The key idea is to use neural networks to convert words in texts to vector space representations based on word positions in a sentence and their contexts,…

Vision-and-Language Navigation (VLN) empowers agents to associate time-sequenced visual observations with corresponding instructions to make sequential decisions. However, generalization remains a persistent challenge, particularly when…