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We introduce autoboot, a Mathematica program which automatically generates mixed-correlator bootstrap equations of an arbitrary number of scalar external operators, given the global symmetry group and the representations of the operators.…

Recent advancements have seen Large Language Models (LLMs) and Large Multimodal Models (LMMs) surpassing general human capabilities in various tasks, approaching the proficiency level of human experts across multiple domains. With…

Graph model generation from natural language description is an important task with many applications in software engineering. With the rise of large language models (LLMs), there is a growing interest in using LLMs for graph model…

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…

Graph neural networks (GNNs) have emerged as state-of-the-art methods to learn from graph-structured data for recommendation. However, most existing GNN-based recommendation methods focus on the optimization of model structures and learning…

Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…

Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…

Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories:…

Recent years have witnessed an upsurge in research interests and applications of machine learning on graphs. However, manually designing the optimal machine learning algorithms for different graph datasets and tasks is inflexible,…

Meibography is a non-contact imaging technique used by ophthalmologists to assist in the evaluation and diagnosis of meibomian gland dysfunction (MGD). While artificial qualitative analysis of meibography images could lead to low…

Geometric reasoning inherently requires "thinking with constructions" -- the dynamic manipulation of visual aids to bridge the gap between problem conditions and solutions. However, existing Multimodal Large Language Models (MLLMs) are…

The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a…

We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening…

This paper introduces GLLM, an innovative tool that leverages Large Language Models (LLMs) to automatically generate G-code from natural language instructions for Computer Numerical Control (CNC) machining. GLLM addresses the challenges of…

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…

We describe the first version (v1.0.0) of the code ADG that automatically (1) generates all valid Bogoliubov many-body perturbation theory (BMBPT) diagrams and (2) evaluates their algebraic expression to be implemented for numerical…

A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…

Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…

This paper presents GO-GAN, a novel Generative Adversarial Network (GAN) architecture for geometry optimization (GO), specifically to generate structures based on user-specified input parameters. The architecture for GO-GAN proposed here…