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Multimodal large language models (MLLMs) have achieved significant progress in image and language tasks due to the strong reasoning capability of large language models (LLMs). Nevertheless, most MLLMs suffer from limited spatial reasoning…

Recent advancements in large language models (LLMs) have spurred interest in robotic navigation that incorporates complex spatial, mathematical, and conditional constraints from natural language into the planning problem. Such constraints…

Multimodal Large Language Models (MLLMs) have demonstrated impressive performance in general vision-language tasks. However, recent studies have exposed critical limitations in their spatial reasoning capabilities. This deficiency in…

Semantic communication, an intelligent communication paradigm that aims to transmit useful information in the semantic domain, is facilitated by deep learning techniques. Robust semantic features can be learned and transmitted in an analog…

Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme…

Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…

Humans naturally understand 3D spatial relationships, enabling complex reasoning like predicting collisions of vehicles from different directions. Current large multimodal models (LMMs), however, lack of this capability of 3D spatial…

We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…

This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential…

This thesis introduces "Embodied Spatial Intelligence" to address the challenge of creating robots that can perceive and act in the real world based on natural language instructions. To bridge the gap between Large Language Models (LLMs)…

Large language models (LLMs) have achieved significant progress across various domains, but their increasing scale results in high computational and memory costs. Recent studies have revealed that LLMs exhibit sparsity, providing the…

We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…

Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…

Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…

3D spatial understanding is essential in real-world applications such as robotics, autonomous vehicles, virtual reality, and medical imaging. Recently, Large Language Models (LLMs), having demonstrated remarkable success across various…

Uncertainty in Logic Programming has been investigated since about 25 years, publishing papers dealing with various approaches to semantics and different applications. This report is intended as a first step towards the investigation of…

We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…

As spatial intelligence becomes an increasingly important capability for foundation models, it remains unclear whether large language models' (LLMs) performance on spatial reasoning benchmarks reflects structured internal spatial…

Large Language Models (LLMs) and Vision Language Models (VLMs) have shown impressive reasoning abilities, yet they struggle with spatial understanding and layout consistency when performing fine-grained visual editing. We introduce a…

Vision-Language Models often struggle with complex visual reasoning due to the visual information loss in textual CoT. Existing methods either add the cost of tool calls or rely on localized patch-based embeddings that are insufficient to…