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The subjective evaluation of early stage engineering designs, such as conceptual sketches, traditionally relies on human experts. However, expert evaluations are time-consuming, expensive, and sometimes inconsistent. Recent advances in…

Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs' abilities in constructive geometric problem-solving one…

Evaluating the capability of Large Language Models (LLMs) in following instructions has heavily relied on a powerful LLM as the judge, introducing unresolved biases that deviate the judgments from human judges. In this work, we reevaluate…

We introduce \textbf{GAUSS} (\textbf{G}eneral \textbf{A}ssessment of \textbf{U}nderlying \textbf{S}tructured \textbf{S}kills in Mathematics), a benchmark that evaluates LLMs' mathematical abilities across twelve core skill dimensions,…

Continual Learning models aim to learn a set of tasks under the constraint that the tasks arrive sequentially with no way to access data from previous tasks. The Online Continual Learning framework poses a further challenge where the tasks…

Recent neuro-symbolic geometry theorem provers have made significant progress on Euclidean problems by coupling neural guidance with symbolic verification. However, most existing systems operate almost exclusively in a symbolic space,…

Evaluating the symbolic reasoning of large language models (LLMs) calls for geometry benchmarks that require multi-step proofs grounded in both text and diagrams. However, existing benchmarks are often limited in scale and rarely provide…

We consider the problem of visual imitation learning without human supervision (e.g. kinesthetic teaching or teleoperation), nor access to an interactive reinforcement learning (RL) training environment. We present a geometric perspective…

Vision-Language Models (VLMs) have recently gained attention due to their competitive performance on multiple downstream tasks, achieved by following user-input instructions. However, VLMs still exhibit several limitations in visual…

We propose Knowledge Crosswords, a geometric knowledge reasoning benchmark consisting of incomplete knowledge networks bounded by structured factual constraints, where LLMs are tasked with inferring the missing facts to meet all…

Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their performance…

Spatial reasoning remains a fundamental challenge for Vision-Language Models (VLMs), with current approaches struggling to achieve robust performance despite recent advances. We identify that this limitation stems from a critical gap:…

Advancing towards artificial superintelligence requires rich and intelligent perceptual capabilities. A critical frontier in this pursuit is overcoming the limited spatial understanding of Multimodal Large Language Models (MLLMs), where…

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models'…

The increasing reliance on Large Language Models (LLMs) across various domains extends to education, where students progressively use generative AI as a tool for learning. While prior work has examined LLMs' mathematical ability, their…

Skills have become the de facto way to enable LLM agents to perform complex real-world tasks with customized instructions, workflows, and tools, but how to learn them automatically and effectively remains unclear. We introduce…

Supporting learners' understanding of taught skills in online settings is a longstanding challenge. While exercises and chat-based agents can evaluate understanding in limited contexts, this challenge is magnified when learners seek…

Online education platforms enable teachers to share a large number of educational resources such as questions to form exercises and quizzes for students. With large volumes of available questions, it is important to have an automated way to…

Understanding geometry relies heavily on vision. In this work, we evaluate whether state-of-the-art vision language models (VLMs) can understand simple geometric concepts. We use a paradigm from cognitive science that isolates visual…

360 panoramic images are increasingly used in virtual reality, autonomous driving, and robotics for holistic scene understanding. However, current Vision-Language Models (VLMs) struggle with 3D spatial reasoning on Equirectangular…