Related papers: Grassmann Manifold Flows for Stable Shape Generati…
We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models,…
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
Grasp synthesis is a fundamental task in robotic manipulation which usually has multiple feasible solutions. Multimodal grasp synthesis seeks to generate diverse sets of stable grasps conditioned on object geometry, making the robust…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…
Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…
Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…
Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…
Despite the growing interest in generative adversarial networks (GANs), training GANs remains a challenging problem, both from a theoretical and a practical standpoint. To address this challenge, in this paper, we propose a novel way to…
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…
A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…
High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…
Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…
Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining…