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An enhancement of the dynamic geometry system GeoGebra for the automatic symbolic computation of algebraic loci and envelopes is presented. Given a GeoGebra construction, the prototype, after rewriting the construction as a polynomial…
Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems…
Machine learning is a novel and powerful technology and has been widely used in various science topics. We demonstrate a machine-learning based approach built by a set of general metrics and rules inspired by physics. Taking advantages of…
A good state representation is crucial to solving complicated reinforcement learning (RL) challenges. Many recent works focus on designing auxiliary losses for learning informative representations. Unfortunately, these handcrafted…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum…
Geolocation, the task of identifying an image's location, requires complex reasoning and is crucial for navigation, monitoring, and cultural preservation. However, current methods often produce coarse, imprecise, and non-interpretable…
Gaussian Process (GP) kernels are central to Bayesian optimization (BO), yet designing effective kernels for high-dimensional problems still relies on extensive manual engineering. Existing automated approaches struggle in high dimensions…
AlphaEvolve (Novikov et al., 2025) is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
The algorithms given in Karney, J. Geodesy 87, 43-55 (2013), to compute geodesics on terrestrial ellipsoids are extended to apply to ellipsoids of revolution with arbitrary eccentricity. For the direct and inverse geodesic problems, this…
Automated algorithm selection for continuous black-box optimization depends on representing problem information under limited probing and selecting solvers under heavy-tailed performance distributions. This paper proposes a geometric…
Detecting oriented objects along with estimating their rotation information is one crucial step for analyzing remote sensing images. Despite that many methods proposed recently have achieved remarkable performance, most of them directly…
Recently, large language models (LLMs) have gained much attention for the emergence of human-comparable capabilities and huge potential. However, for open-domain implicit question-answering problems, LLMs may not be the ultimate solution…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts,…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available…