Related papers: Analytical Discovery of Manifold with Machine Lear…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations,…

In the domain of scientific imaging, interpreting visual data often demands an intricate combination of human expertise and deep comprehension of the subject materials. This study presents a novel methodology to linguistically emulate and…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Large Language Models (LLMs) have demonstrated substantial efficacy in advancing graph-structured data analysis. Prevailing LLM-based graph methods excel in adapting LLMs to text-rich graphs, wherein node attributes are text descriptions.…

The (variational) graph auto-encoder is widely used to learn representations for graph-structured data. However, the formation of real-world graphs is a complicated and heterogeneous process influenced by latent factors. Existing encoders…

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…

Unsupervised attributed graph representation learning is challenging since both structural and feature information are required to be represented in the latent space. Existing methods concentrate on learning latent representation via…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

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…

We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly…

Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…

Graphs provide a powerful framework for modeling complex systems, but their structural variability poses significant challenges for analysis and classification. To address these challenges, we introduce GAUDI (Graph Autoencoder Uncovering…

Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…

Implicit spatial relations and deep semantic structures encoded in object attributes are crucial for procedural planning in embodied AI systems. However, existing approaches often over rely on the reasoning capabilities of vision language…

Unsupervised graph-level anomaly detection (UGLAD) is a critical and challenging task across various domains, such as social network analysis, anti-cancer drug discovery, and toxic molecule identification. However, existing methods often…