Related papers: Learning Manifolds from Non-stationary Streaming D…
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…
PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an It\^o equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for…
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…
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…
Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an…
Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…
We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…
We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal…
Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…
In the real world, data streams are ubiquitous -- think of network traffic or sensor data. Mining patterns, e.g., outliers or clusters, from such data must take place in real time. This is challenging because (1) streams often have high…
Deep generative models learn the data distribution, which is concentrated on a low-dimensional manifold. The geometric analysis of distribution transformation provides a better understanding of data structure and enables a variety of…
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…
Can we modify the training data distribution to encourage the underlying optimization method toward finding solutions with superior generalization performance on in-distribution data? In this work, we approach this question for the first…
Neural network pruning is an essential approach for reducing the computational complexity of deep models so that they can be well deployed on resource-limited devices. Compared with conventional methods, the recently developed dynamic…
Streaming 3D reconstruction demands long-horizon state updates under strict latency constraints, yet stateful recurrent models often suffer from geometric drift as errors accumulate over time. We revisit this problem from a Grassmannian…
Diffusion has shown great success in improving accuracy of unsupervised image retrieval systems by utilizing high-order structures of image manifold. However, existing diffusion methods suffer from three major limitations: 1) they usually…
Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian…
Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While…
Data collection at a massive scale is becoming ubiquitous in a wide variety of settings, from vast offline databases to streaming real-time information. Learning algorithms deployed in such contexts must rely on single-pass inference, where…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…