arXiv research

Novel model detects communities in noisy multilayer networks.

I-BBS identifies latent sub-manifolds from distance matrices, robust to noise.

Geometry-aware noise improves model generalization on complex manifolds.

Recent progress in separating the speech signals from multiple overlapping speakers using a single audio channel has brought us closer to solving the cocktail party problem. However, most studies in this area use a constrained problem setup, comparing performance when speakers overlap almost completely, at artificially…

Study recovers Riemannian quantities from noisy data densities.

The paper tackles transfer learning for growing matrix representations, improving estimation accuracy.

High-dimensional models trained on smooth manifolds achieve optimal rates in Wasserstein metrics.

Proposes a new method for efficient manifold denoising robust to high dimensional noise.

The existence of the pricing kernel is shown to imply the existence of an ambient information process that generates market filtration. This information process consists of a signal component concerning the value of the random variable X that can be interpreted as the timing of future cash demand, and an independent no…

Gaussians as noise in NCE lead to exponentially bad conditioning, hindering its efficiency.

Proposes a learned Bayesian Cramér-Rao bound for unknown measurement models.

Paper improves sparse linear bandits by accounting for noise variance.

BDDMs eliminate noise conditioning in diffusion models, simplifying training and sampling.

Doubly-stochastic normalization improves robustness to heteroskedastic noise.

Geodesic distance is the shortest path between two points in a Riemannian manifold. Manifold learning algorithms, such as Isomap, seek to learn a manifold that preserves geodesic distances. However, such methods operate on the ambient dimensionality, and are therefore fragile to noise dimensions. We developed an unsupe…

Study on detecting and recovering hidden dense cycles in random graphs.

We present a machine-learning approach to classifying the phases of surface wave dispersion curves. Standard FTAN analysis of surfaces observed on an array of receivers is converted to an image, of which, each pixel is classified as fundamental mode, first overtone, or noise. We use a convolutional neural network (U-ne…

DSM on manifolds removes singularities and computes small-noise expansions.

New method reduces memorization in diffusion models without sacrificing image quality.

Projective DP-SGD reduces privacy error by identifying low-dimensional gradient subspaces.

New method uses Wasserstein loss for data unfolding, offering better accuracy than classical techniques.

Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.

We prove existence and uniqueness of weighted ambient metric for manifolds with density.

DP-SGD can update fewer coordinates while maintaining privacy.

Extended solitons show constant curvature on compact manifolds.

This paper studies the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman-Graham ambient metric of the conformal manifold. It is shown that the infinitesimal confo…

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as aff…

DVAO predicts volumetric ambient occlusion for real-time volume rendering.

Proves existence and uniqueness of weighted metrics for smooth spaces.

We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the $D$-dimensional ambient space and belong to a $d<D$ dimensional space. We call them "singular features." Hunting for singular features corresponds to f…

We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal …

In this paper we relate the Fefferman-Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tract…

The paper characterizes ambient metrics using conformal completion and null infinity properties.

An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the logarithm of a defining function homogeneous of degree 2, and an invariant procedur…

The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are assumed unknown. We propose a simple low-complexity subspace clustering algorithm, w…

The conformal Fefferman-Graham ambient metric construction is one of the most fundamental constructions in conformal geometry. It embeds a manifold with a conformal structure into a pseudo-Riemannian manifold whose Ricci tensor vanishes up to a certain order along the original manifold. Despite the general existence re…

This work optimizes signal estimation for sparse MRA with collision-free signals.

Research into automated systems for detecting and classifying marine mammals in acoustic recordings is expanding internationally due to the necessity to analyze large collections of data for conservation purposes. In this work, we present a Convolutional Neural Network that is capable of classifying the vocalizations o…

Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays the foundati…

A new method for manifold learning using sparse regularised optimal transport.

New property: polygons have a fixed dimension regardless of ambient space dimensions.

The (Fefferman-Graham) ambient obstruction tensor is a conformally invariant symmetric trace-free 2-tensor on even-dimensional Riemannian and pseudo-Riemannian manifolds. The conformal deformation complex is a differential complex related to infinitesimal deformations of conformal structure. We construct a conformally …

Chart autoencoders learn latent features preserving manifold topology and geometry, with robust denoising capabilities.

We present conformal structures in signature (3,2) for which the holonomy of the Fefferman-Graham ambient metric is equal to the non-compact exceptional Lie group G_{2(2)}. We write down the resulting 8-parameter family of G_{2(2)}-metrics in dimension seven explicitly in an appropriately chosen coordinate system on th…

Curve shortening flow shrinks curves to points under certain conditions.

New algorithm catches moving subspaces in bandit problems.

Uniform convergence of isotopies implies ambient isotopy, aiding knot equivalence.

We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.