arXiv research

Note establishes a local maximum principle for Ricci flow under curvature conditions.

Residual flows are shown to approximate MMD well.

This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operato…

A new gradient flow for MMD with closed-form implementation.

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…

Study on mean curvature flow of graphs in higher dimensions.

This paper improves normalizing flows by combining MLE and sliced-Wasserstein distance for better data fidelity.

In this paper we mainly study the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a K ähler-Einstein surface. We show the relation between the maximum of the Kähler angle and the maximum of $|H|^2$ on the limit flow.

We derive a parabolic version of Omori-Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on $\ell$-sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean spaces with uniform bounded second fundamenta…

Paper proposes efficient training for normalizing flows in Boltzmann generators.

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explici…

New particle algorithms optimize latent variable models.

Study CR Yamabe constant, flow, and soliton on CR manifolds.

We introduce the new notion of Bianchi-convex sets, a generalization of convex sets of algebraic curvature tensors inspired by the second Bianchi identity. It turns out that Hamilton's maximum principle for the Ricci flow can be generalized for Bianchi-convex sets.

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that …

Curve shortening flow shrinks curves to points.

A new layer, funnel, reduces dimensionality in flows for better performance.

We provide a new proof of the following inequality: the maximum curvature $k_\mathrm{max}$ and the enclosed area $A$ of a smooth Jordan curve satisfy $k_\mathrm{max}\ge \sqrt{π/A}$. The feature of our proof is the use of the curve shortening flow.

In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, we investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over …

Study proposes curvature flow model for Drosophila dorsal closure.

Mirror flow optimizes separable data problems, converging to a maximum margin classifier.

New perspective on Ricci flow on spheres using Minkowski spacetime.

A new path gradient estimator speeds up normalizing flows without sacrificing accuracy.

The maximum principle is one of the most important tools in the analysis of geometric partial differential equations. Traditionally, the maximum principle is applied to a scalar function defined on a manifold, but in recent years more sophisticated versions have emerged. One particularly interesting direction involves …

Neural execution solves complex graph problems like bipartite matching.

New proof of Kähler-Einstein Fano manifold $L^\infty$ estimates.

This work concerns with the existence and detailed asymptotic analysis of Type II singularities for solutions to complete non-compact conformally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate of the maximum curvature and show that the solution converges, after blowing-up a…

We solve image inverse problems using a flow-based noise model.

M-flows learn data manifolds and densities, improving manifold learning and inference.

Study classifies translators for mean curvature flow in 3D.

We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton $(M,g)$ is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton. If $g$ is not a local maxim…

We give a maximum principle proof of interior derivative estimates for the Kähler-Ricci flow, assuming local uniform bounds on the metric.

We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on probability measures for a sufficiently rich RKHS. We obtain conditions for conv…

Paper proposes energy objective for training normalizing flows without determinants.

Paper proposes CoopFlow, a two-flow generator for energy-based models.

The paper studies global Yamabe flow on AF manifolds, preserving ADM mass.

DFM simplifies CNF training without interpolants.

Proposes a new method for high-dimensional density estimation.

Paper relaxes convexity assumptions in mean curvature flow results.

Assuming local uniform bounds on the metric for a solution of the Chern-Ricci flow, we establish local Calabi and curvature estimates using the maximum principle.

Proposes a new method for posterior sampling using MMD with negative distance kernel.

This work analyzes the maximum-margin bias in quasi-homogeneous neural networks.

MGD combines maximum entropy and diffusion methods for efficient sampling.

In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …

Paper explores Fisher-Rao gradient flows and their kernel approximations.

Maximum likelihood training improves the performance of score-based diffusion models.

Study sub-Riemannian geodesics on a Heisenberg 3D nil-manifold.

A graph (digraph) $G=(V,E)$ with a set $T\subseteq V$ of terminals is called inner Eulerian if each nonterminal node $v$ has even degree (resp. the numbers of edges entering and leaving $v$ are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint $T$-paths in an inner Eulerian graph $G…