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This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus…

Graph-structured data typically exhibits complex topological heterogeneity, making it difficult to model accurately within a single Riemannian manifold. While emerging mixed-curvature methods attempt to capture such diversity, they often…

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets.…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods…

Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

Model merging offers a promising avenue for knowledge integration and parallel development without retraining. Yet, existing methods either ignore the geometry of the loss landscape or rely on intractable full-space Hessian approximations.…

High-fidelity interactive digital assets are essential for embodied intelligence and robotic interaction, yet articulated objects remain challenging to reconstruct due to their complex structures and coupled geometry-motion relationships.…

Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled…

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical…

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared…

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…