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Geometry problem-solving demands advanced reasoning abilities to process multimodal inputs and employ mathematical knowledge effectively. Vision-language models (VLMs) have made significant progress in various multimodal tasks. Yet, they…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
Advances in large language models (LLMs) offer new possibilities for enhancing math education by automating support for both teachers and students. While prior work has focused on generating math problems and high-quality distractors, the…
The design of complex engineering systems is an often long and articulated process that highly relies on engineers' expertise and professional judgment. As such, the typical pitfalls of activities involving the human factor often manifest…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…
We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This…
We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{\textrm{th}}$ item has width $w(i)$, height $h(i)$, and…
Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Recently, the surge of efficient and automated 3D AI-generated content (AIGC) methods has increasingly illuminated the path of transforming human imagination into complex 3D structures. However, the automated generation of 3D content is…
Urban modeling is essential for city planning, scene synthesis, and gaming. Existing image-based methods generate diverse layouts but often lack geometric continuity and scalability, while graph-based methods capture structural relations…
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…
Recent advancements in large language models (LLMs) have led to significant breakthroughs in mathematical reasoning capabilities. However, existing benchmarks like GSM8K or MATH are now being solved with high accuracy (e.g., OpenAI o1…
Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the…
Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…
Mathematical reasoning poses significant challenges for Large Language Models (LLMs) due to its demand for multi-step reasoning and abstract conceptual integration. While recent test-time scaling techniques rely heavily on high-quality,…
Personalized mathematics education is growing rapidly, creating a strong demand for large sets of similar practice problems. Yet existing studies on mathematics problem generation have focused on data augmentation for training neural…
Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption…
The inherent probabilistic nature of Large Language Models (LLMs) introduces an element of unpredictability, raising concerns about potential discrepancies in their output. This paper introduces an innovative approach aims to generate…
We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a…