arXiv research

New linear flows using exponential of linear transformations improve generative models.

In this paper, we propose a new volume-preserving flow and show that it performs similarly to the linear general normalizing flow. The idea is to enrich a linear Inverse Autoregressive Flow by introducing multiple lower-triangular matrices with ones on the diagonal and combining them using a convex combination. In the …

We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three--manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which characterizes a way of Ricci flow averaging metric dependent geometrical data. …

Ancient flows by curvature powers in 2D have finite entropy.

Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.

Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure of the flow, this partial differential equation problem can be resolved using a…

Study on Hermitian curvature flow on special linear groups, disproving a conjecture and finding non-algebraic solitons.

New method for natural policy gradients converges linearly.

Gradient flow in parameters equals linear interpolation in outputs.

Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…

Proofs for flows of linear vector fields and their applications.

Geodesic flows on surfaces have specific fractional-linear integrals related to constant cross-ratios.

We give a geometric interpretation of the linear trace Harnack inequality for the Ricci flow.

Regularization leads to balancedness in deep linear networks.

This paper develops an ensemble learning-based linearization approach for power flow, which differs from the network-parameter based direct current (DC) power flow or other extended versions of linearization. As a novel data-driven linearization through data mining, it firstly applies the polynomial regression (PR) as …

As a step toward understanding the analytic behavior of Type-III Ricci flow singularities, i.e. immortal solutions that exhibit |Rm|<C/t curvature decay, we examine the linearization of an equivalent flow at fixed points discovered recently by Baird--Danielo and Lott: nongradient homogeneous expanding Ricci solitons on…

Investigates stability of piecewise flat Ricci flow using analysis and simulations.

This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given set of piecewise linear spaces we define and discuss (normalized) Ricci flows. …

Homogeneous magnetic trajectories in a special linear group proven.

Superdense flows on surfaces imply bounded geodesics, and vice versa.

New tensor formulation reveals gradient flow's bias in linear neural networks.

Rectified flows achieve optimal sample complexity for generating data.

In this paper, we introduce a parameterized discrete curvature ($α$-curvature) for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical discrete curvature. A discrete uniformization theorem is established for the parameterized discrete curvature, which generalizes the discrete uni…

We show a connection between the linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow and the monotonicity formula for the positive currents. As an application of the linear trace Li-Yau-Hamilton stated in this paper and the one proved by Chow-Hamiltonm, we give another proof on the classification of the …

Unified piecewise-linear Ricci flows improve community detection.

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

New Ricci flows found with Einstein orbifolds at infinity.

Pruning method removes less important features in linear models.

Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.

We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests…

We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and the Ricci flow.

Researchers found a new type of singularity in surface evolution equations.

The study provides a criterion for fractional-linear integrals of geodesics on surfaces.

The paper proves stability for a modified Bach flow on various manifolds.

$\mathscr{W}$-entropy and reduced volume for the Ricci flow were introduced by Perelman, which had proved their importance in the study of the Ricci flow. L. Ni studied the analogous concepts for the linear heat equation on the static manifolds, and established an equation which links the large time behavior of these t…

Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by density estimation performance issues as compared to state-of-the-art autoregressive…

Study geometric flow on curves with positive torsion, finding stationary solutions and their stability.

LOL method simplifies forming linear combinations of latent variables.

In the 1950's Hopf gave examples of non-round convex 2-spheres in Euclidean 3-space with rotational symmetry that satisfy a linear relationship between their principal curvatures. In this paper we investigate conditions under which evolving a smooth rotationally symmetric sphere by a linear combination of its radii of …

We prove an estimate for solutions to the linearized Ricci flow system on closed 3-manifolds. This estimate is a generalization of Hamilton's pinching is preserved estimate for the Ricci curvatures of solutions to the Ricci flow on 3-manifolds with positive Ricci curvature. In our estimate we make no assumption on the …

A new MDP with Bandits approach for sequential decision making in linear-flow scenarios.

Cash managers make daily decisions based on predicted monetary inflows from debtors and outflows to creditors. Usual assumptions on the statistical properties of daily net cash flow include normality, absence of correlation and stationarity. We provide a comprehensive study based on a real-world cash flow data set from…

The paper examines how parabolic frequency behaves under Ricci flow and Ricci-harmonic flow on manifolds.

We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional $\mathcal{F}$. The other one is a dynamical stability and it refers to a convergence of a Ricci flow starting at any metric in a neighbourhood of a considere…

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an epsi…

We study the long time behavior of the volume preserving $p$-flow in $\mathbb{R}^{n+1}$ for $1\leq p<\frac{n+1}{n-1}$. By extending Andrews' technique for the flow along the affine normal, we prove that every centrally symmetric solution to the volume preserving $p$-flow converges sequentially to the unit ball in the $…

The paper studies non-integer curvature flows and proves convergence to spheres under specific conditions.