mailitics

Tag: manifold

  • Flow Matching is Adaptive to Manifold Structures

    Flow Matching is Adaptive to Manifold Structures arXiv:2602.22486v1 Announce Type: new Abstract: Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods…

  • Generative Modeling with Manifold Percolation

    Generative Modeling with Manifold Percolation arXiv:2511.20503v1 Announce Type: new Abstract: Generative modeling is typically framed as learning mapping rules, but from an observer’s perspective without access to these rules, the task manifests as disentangling the geometric support from the probability distribution. We propose that Continuum Percolation is uniquely suited for this support analysis, as the…

  • Robust Multi-Manifold Clustering via Simplex Paths

    Robust Multi-Manifold Clustering via Simplex Paths arXiv:2507.10710v1 Announce Type: new Abstract: This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a locality graph on d-simplices, using the dihedral angle in between adjacent simplices as the…

  • Active Learning for Manifold Gaussian Process Regression

    Active Learning for Manifold Gaussian Process Regression arXiv:2506.20928v1 Announce Type: new Abstract: This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a neural network for dimensionality reduction and a Gaussian process regressor in the…

  • Data-Driven Dynamic Factor Modeling via Manifold Learning

    Data-Driven Dynamic Factor Modeling via Manifold Learning arXiv:2506.19945v1 Announce Type: new Abstract: We propose a data-driven dynamic factor framework where a response variable depends on a high-dimensional set of covariates, without imposing any parametric model on the joint dynamics. Leveraging Anisotropic Diffusion Maps, a nonlinear manifold learning technique introduced by Singer and Coifman, our framework…

  • Analytical Discovery of Manifold with Machine Learning

    Analytical Discovery of Manifold with Machine Learning arXiv:2504.02511v1 Announce Type: new Abstract: Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited global insight and the lack of interpretable analytical descriptions-remain unresolved. In this work, we introduce a…