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The neural operator (NO) framework has emerged as a powerful tool for solving partial differential equations (PDEs). Recent NOs are dominated by the Transformer architecture, which offers NOs the capability to capture long-range…
Deep learning has enabled remarkable improvements in grasp synthesis for previously unseen objects from partial object views. However, existing approaches lack the ability to explicitly reason about the full 3D geometry of the object when…
Generative artificial intelligence, and large language models in particular, have emerged as one of the most transformative paradigms in modern computer science. This automated survey provides an accessible treatment of the field as of…
By systematically applying ten well-known and inequivalent two-part relations between hypergeometric sums 3F2(...|1) to the published database of all such sums, 62 new sums are obtained. The existing literature is summarized, and many…
Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, Gemini-2.5-Pro,…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Recent years have seen a significant progress in the general-purpose problem solving abilities of large vision and language models (LVLMs), such as ChatGPT, Gemini, etc.; some of these breakthroughs even seem to enable AI models to…
We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…
Benchmarks are the primary tool for assessing progress in artificial intelligence (AI), yet current practice evaluates models on isolated test suites and provides little guidance for reasoning about generality or autonomous…
We introduce a new symbolic solver for geometry, called Newclid, which is based on AlphaGeometry. Newclid contains a symbolic solver called DDARN (derived from DDAR-Newclid), which is a significant refactoring and upgrade of AlphaGeometry's…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
In this report, we pose the following question: Who is the most intelligent AI model to date, as measured by the OlympicArena (an Olympic-level, multi-discipline, multi-modal benchmark for superintelligent AI)? We specifically focus on the…
Artificial intelligence (AI) is poised to transform education, but the research community lacks a robust, general benchmark to evaluate AI models for learning. To assess state-of-the-art support for educational use cases, we ran an "arena…
In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…
Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge,…
Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs.…
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…
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
Graph similarity is critical in graph-related tasks such as graph retrieval, where metrics like maximum common subgraph (MCS) and graph edit distance (GED) are commonly used. However, exact computations of these metrics are known to be…
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…