A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper constructs wild Cantor sets in high dimensions.
Proposes GDTW for aligning time series on different, incomparable spaces.
This thesis tackles Optimal Transport on incomparable spaces, proposing new tools and properties.
A new Wasserstein distance method for comparing incomparable distributions.
Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension)…
New method detects Kaehler scalar flat metrics and minimal hypersurfaces.
Local surrogate explainers vary in objectives, leading to incomparable explanations.
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
Faster GW alignment for incomparable point clouds via low-rank couplings.
Framework benchmarks optimizers on multiple criteria.
Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.
We prove existence and uniqueness of weighted ambient metric for manifolds with density.
Two commonly arising computational tasks in Bayesian learning are Optimization (Maximum A Posteriori estimation) and Sampling (from the posterior distribution). In the convex case these two problems are efficiently reducible to each other. Recent work (Ma et al. 2019) shows that in the non-convex case, sampling can som…
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 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 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…
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 …
A new algorithmic framework is proposed for learning autoencoders of data distributions. We minimize the discrepancy between the model and target distributions, with a \emph{relational regularization} on the learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the la…
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.
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.
Given an -dimensional manifold with an affine connection , we show that the associated Patterson-Walker metric on admits a global and explicit Fefferman-Graham ambient metric. This provides a new and large class of conformal structures which are generically not conformally Einstein but for which th…
We study deformations of free boundary constant mean curvature (CMC) hypersurfaces whose Jacobi operator is degenerate due to symmetries of the ambient space. The value of the mean curvature and the ambient metric are allowed to vary simultaneously, provided that the infinitesimal ambient symmetries change smoothly. We…
It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.
We study piecewise linear co-dimension two embeddings of closed oriented manifolds in Euclidean space, and show that any such embedding can always be isotoped to be a closed braid as long as the ambient dimension is at most five, extending results of Alexander (in ambient dimension three), and Viro and independently Ka…
Unbalanced COOT improves feature alignment robustly to outliers.
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension …
Generative adversarial models are powerful tools to model structure in complex distributions for a variety of tasks. Current techniques for learning generative models require an access to samples which have high quality, and advanced generative models are applied to generate samples from noisy training data through amb…
This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is e…
Researchers analyze neural process architectures and their representational capacities.
Generative models use Riemannian manifolds to improve latent space interpretation.
Researchers study solitons on homogeneous manifolds, proving properties of specific types of solitons.
Researchers create a family of conformally covariant operators.
Extends submanifold theorem to general spaces.
The paper extends knot contact homology to tangles and proves a gluing formula.
This paper benchmarks speech LVMs against deterministic models and adapts a video model to speech.
We provide an explicit formula for the Fefferman-Graham-ambient metric of an -dimensional conformal -wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional -waves that are Bach-flat, and give a large class of Bach-flat examp…
We provide a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint…
We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to a large class of invariant operators. This procedure can be also applied to CR g…