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We propose Neuro-Symbolic Visual Dialog (NSVD) -the first method to combine deep learning and symbolic program execution for multi-round visually-grounded reasoning. NSVD significantly outperforms existing purely-connectionist methods on…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
To reduce cycles of rejection and redesign -- especially in the absence of clear acceptance criteria and the diversity of possible development paths -- User-Centered Design (UCD) has become a central methodology in computer science,…
Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
Typeclasses provide an elegant and effective way of managing ad-hoc polymorphism in both programming languages and interactive proof assistants. However, the increasingly sophisticated uses of typeclasses within proof assistants, especially…
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…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial…
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,…
This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…
Inspired by the linear programming method developed by Cohn and Elkies (Ann. Math. 157(2): 689-714, 2003), we introduce a new linear programming method to solve the sphere packing problem. More concretely, we consider sequences of auxiliary…
As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…
This paper describes a user-friendly frontend to a Fortran program that integrates coupled nonlinear ordinary differential equations. The user interface is built using the NeXTstep Interface Builder, together with a public-domain graphical…
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…
The design of nuclear imaging scanners is crucial for optimizing detection and imaging processes. While advancements have been made in simplistic, symmetrical modalities, current research is progressing towards more intricate structures,…
3D Slicer is a powerful platform for 3D data visualization and analysis, but has a significant learning curve for new users. Generative AI applications, such as ChatGPT, have emerged as a potential method of bridging the gap between various…
Extending the success of 2D Large Kernel to 3D perception is challenging due to: 1. the cubically-increasing overhead in processing 3D data; 2. the optimization difficulties from data scarcity and sparsity. Previous work has taken the first…
RNA 3D architectures are stabilized by sophisticated networks of (non-canonical) base pair interactions, which can be conveniently encoded as multi-relational graphs and efficiently exploited by graph theoretical approaches and recent…
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…