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We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such…
Reasoning about spatial relationships between objects is essential for many real-world robotic tasks, such as fetch-and-delivery, object rearrangement, and object search. The ability to detect and disambiguate different objects and identify…
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
In this paper, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present CPL-SLAM, an efficient and…
We explore the application of large language models (LLMs) to empower domain experts in integrating large, heterogeneous, and noisy urban spatial datasets. Traditional rule-based integration methods are unable to cover all edge cases,…
A novel approach to exploiting the log-convex structure present in many design problems is developed by modifying the classical Sequential Quadratic Programming (SQP) algorithm. The modified algorithm, Logspace Sequential Quadratic…
Recent advancements in large language models (LLMs) underscore the need for stronger reasoning capabilities to solve complex problems effectively. While Chain-of-Thought (CoT) reasoning has been a step forward, it remains insufficient for…
We introduce FloorplanQA, a diagnostic benchmark for evaluating spatial reasoning in large language models (LLMs). FloorplanQA is grounded in structured representations of indoor scenes, such as (e.g., kitchens, living rooms, bedrooms,…
Spatial reasoning is an essential problem in embodied AI research. Efforts to enhance spatial reasoning abilities through supplementary spatial data and fine-tuning have proven limited and ineffective when addressing complex embodied tasks,…
Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To…
Spatial reasoning in Large Language Models (LLMs) is the foundation for embodied intelligence. However, even in simple maze environments, LLMs still encounter challenges in long-term path-planning, primarily influenced by their spatial…
The rise of large language models (LLMs) has significantly advanced various natural language processing (NLP) tasks. However, the resource demands of these models pose substantial challenges. Structured pruning is an effective approach to…
Structured pruning reduces LLM inference cost by removing low-importance architectural components. This can be viewed as learning a multiplicative gate for each component under an l0 sparsity constraint. Due to the discreteness of the l0…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains…
Enhancing the reasoning capabilities of language models (LMs) remains a key challenge, especially for tasks that require complex, multi-step decision-making where existing Chain-of-Thought (CoT) approaches struggle with consistency and…
Reliable spatial reasoning remains a core bottleneck for vision-language models (VLMs). Existing mainstream training paradigms for spatial reasoning largely rely on outcome alignment or process imitation, lacking explicit constraints on the…
We introduce LaySPA, a reinforcement learning framework that equips large language models (LLMs) with explicit and interpretable spatial reasoning for content-aware graphic layout design. LaySPA addresses two key challenges: LLMs' limited…