The paper proves a reverse isoperimetric inequality and applies it to analyze surface flows.
problem Analyzing the negative gradient flow of the Willmore energy plus volume.
method Proved a quantitative reverse isoperimetric inequality and applied it to the flow.
result Initial surfaces converge to a round point in finite or infinite time.
GraphNVP generates molecular graphs efficiently and reversibly.
problem Generating valid molecular graphs with desired properties.
method Decomposes graph generation into adjacency tensor and node attributes, using reversible flows.
result Efficiently generates valid molecular graphs with minimal duplicates and latent space for property generation.
Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-rever…
Unified framework for efficient trans-dimensional Bayesian inference using VI and NFs.
problem Efficient trans-dimensional Bayesian inference with reduced computational cost.
method Variational inference with normalizing flows to train transport proposals.
result Our approach minimizes reverse KL divergence and reduces computational cost.
New invertible transformations improve flow-based generative models.
problem Improving flow-based generative models for better performance.
method Proposed new invertible transformations and coupling layers.
result New coupling layers achieve better results in IDF.
The study proves the existence of geodesics on reversible Finsler spheres.
problem Existence of closed geodesics on Finsler 2-spheres.
method Generalization of Grayson's curve shortening flow.
result Existence of three simple closed geodesics and infinitely many closed geodesics.
Graph normalizing flows use neural networks for graph prediction and generation.
problem Efficiently processing and generating graph data with reduced memory usage.
method Reversible graph neural network model combining auto-encoder and normalizing flows.
result Graph normalizing flows achieve competitive results in graph generation and prediction.
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
DFM simplifies CNF training without interpolants.
problem Efficiently training CNFs with computationally expensive ODE solving.
method DFM optimizes dual vector fields for bijective transformations.
result DFM outperforms CNF trained with FM or ML objectives.
Entropy rigidity for Finsler flows but collapse for Reeb flows.
problem Entropy behavior of Reeb and Finsler flows on contact manifolds.
method Analysis of topological entropy for Reeb and Finsler flows.
result Uniform positive lower bound for Finsler flows but arbitrarily small topological entropy for Reeb flows.
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…
Enhances RJMCMC efficiency with non-linear transport-based proposals.
problem Designing efficient RJMCMC proposals for complex models.
method Applies non-linear transport-based approach to construct efficient transdimensional jumps.
result Acceptance probability depends only on model probabilities when exact transports are used.
We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We …
The main result of this paper is a construction of solutions to the reverse Yang-Mills-Higgs flow converging in the C∞ topology to a critical point. The construction uses only the complex gauge group action, which leads to an algebraic classification of the isomorphism classes of points in the unstable set of a…
We show uniqueness of classical solutions of the normalised two-dimensional Hamilton-Ricci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural space-time L2-bound for the time derivative of the solution. The result is s…
Study counts and equidistributes geodesic orbits on curved spaces.
problem Counting and equidistribution of strongly reversible closed geodesics in negatively curved spaces.
method Generalized techniques from Sarnak and Erlandsson-Souto, thermodynamic formalism, and graphs of groups with 2-torsion.
result Asymptotic counting and equidistribution of geodesic orbits towards the Bowen-Margulis measure.
Flow-based models generate data with improved theoretical guarantees.
problem Theoretical analysis of flow-based generative models.
method Proximal gradient descent in Wasserstein space for JKO flow model.
result KL guarantee of data generation by JKO flow model is O(ε2). Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wassers…
We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the 2D case. On one hand we construct examples of nonuniqueness by showing that surfaces with cusps can evolve either by keeping the cusps or by contracting them…
We study solutions of the mean curvature flow which are defined for all negative curvature times, usually called ancient solutions. We give various conditions ensuring that a closed convex ancient solution is a shrinking sphere. Examples of such conditions are: a uniform pinching condition on the curvatures, a suitable…
Method uses normalizing flows to efficiently sample from complex target densities.
problem Sampling from complex target densities with zero values in regions of transformation.
method Normalizing flows to address exploding reverse Kullback-Leibler divergence.
result Demonstrated efficient sampling from multi-mode complex density function.
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
SurVAE Flows combine VAEs and flows using surjective transformations.
problem Combining the strengths of VAEs and flows to model complex densities.
method Modular framework of composable deterministic and stochastic transformations.
result Exact likelihood computation and lower bound on likelihood.
A new method for reconstructing flows from perturbed distributions.
problem Reconstructing flows from perturbed probability distributions.
method Integrable vector fields and Green's functions.
result A nonparametric flow can be computed to generate samples from a perturbed distribution.
We present two approaches to the heat flow on a Finsler manifold (M,F): either as gradient flow on L2(M,m) for the energy; or as gradient flow on the reverse L2-Wasserstein space P2(M) of probability measures on M for the relative entropy. Both approaches depend on the choice of a measure m on …
We consider the geodesic flow of reversible Finsler metrics on the 2-sphere and the 2-torus, whose geodesic flow has vanishing topological entropy. Following a construction of A. Katok, we discuss examples of Finsler metrics on both surfaces, which have large ergodic components for the geodesic flow in the unit tangent…
We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible…
Study of intersections in Hamiltonian orbits on cotangent bundles.
problem Understanding intersections of projected Hamiltonian orbits in cotangent bundles.
method Generic submersive level set analysis, multi-jet transversality theorem.
result Projected Hamiltonian orbits have discrete intersections, which can be perturbed away under certain conditions.
Flow-based models detect anomalies in industrial time series data.
problem Novelty detection in industrial time series data.
method Normalizing flows, specifically Masked Autoregressive Flows and Free-form Jacobian of Reversible Dynamics.
result Flow-based models outperform traditional methods in novelty detection of industrial time series data.
We address the problem of reverse engineering of stripped executables, which contain no debug information. This is a challenging problem because of the low amount of syntactic information available in stripped executables, and the diverse assembly code patterns arising from compiler optimizations. We present a novel ap…
Study on Gaussian interpolation flows for generative modeling.
problem Theoretical properties and regularizing effect of Gaussian denoising in continuous normalizing flows.
method Unified framework of Gaussian interpolation flow, Lipschitz regularity, existence and uniqueness of flow, stability analysis.
result Established theoretical properties of Gaussian interpolation flows, including Lipschitz continuity and existence of flow.
Sharp Gaussian isoperimetry proven along Ricci flow.
problem Proving sharp Gaussian isoperimetric inequality for Ricci flow.
method Using monotonicity formula to prove inequality.
result Exact Gaussian enlargement theorem and concentration estimates.
In my previaou paper of K. Horihata, we have proposed a Ginzburg-Landau system with a time-dependent parameter and then passing to the limit we have constructed a harmonic heat flow into spheres. Thanks to this scheme, we establish a few energy inequalities of our flow: (i) monotonical inequalities and (ii) a reverse P…
Maps on infinite-type surfaces linked to 3-manifold flows.
problem Understanding maps on infinite-type surfaces using 3-manifold flows.
method Using pseudo-Anosov flows to construct maps from fibered hyperbolic 3-manifolds.
result Maps on infinite-type surfaces can be derived from fibered structures in 3-manifolds.
In this article, we show that a Finsler--Laplacian introduced previously can detect changes in the Finsler metric that the marked length spectrum cannot. We also construct examples of non-reversible Finsler metrics in negative curvature such that 4λ1>h2, where λ1 is the bottom of the L2-spectrum and h the…
Flow on weighted graphs sharpens Bakry-Émery curvature.
problem Sharp curvature in weighted graphs.
method Bakry-Émery curvature flow on mixed weighted graphs.
result Limits of curvature flow are curvature sharp.
New sampling and diffusion models methods introduced without density function assumptions.
problem Sampling and diffusion models without regularity assumptions.
method Inspired by reverse diffusion process, novel sampling and diffusion algorithms.
result Explicit convergence rate and dimension-free particle approximation convergence result.
A new method uses MCMC-assisted normalizing flows for efficient Bayesian sampling.
problem Sampling from complex posterior distributions in Bayesian statistics.
method Training a normalizing flow using direct KL divergence and MCMC assistance.
result The method improves sampling efficiency for complicated posterior distributions.
The paper proposes a new way to approximate Riemannian metrics using discrete wall systems.
problem Approximating Riemannian metrics and proving geometric conjectures.
method Discretization of metrics using walls and triangulations.
result The discrete filling area conjecture is equivalent to Gromov's original conjecture.
Study finds stock prices rarely appreciate during capital inflows but often appreciate during normal flows.
problem Understanding stock price behavior during capital inflows and outflows.
method Identified capital flow episodes using threshold and k-means clustering; detected stock index changepoints using PELT method; combined results over identified capital flows.
result Stock prices rarely appreciate during capital inflows but often appreciate during normal flows.
We analyse a multiplex of networks between OECD countries during the decade 2002-2010, which consists of five financial layers, given by foreign direct investment, equity securities, short-term, long-term and total debt securities, and five environmental layers, given by emissions of N O x, P M 10 SO 2, CO 2 equivalent…
The paper improves the probability flow ODE sampler for faster sampling of natural images.
problem Improving the convergence rate of the probability flow ODE sampler.
method Adapting the probability flow ODE sampler to exploit intrinsic low-dimensional structures in natural image data.
result Achieves a dimension-free convergence rate of O(k/T) in total variation distance, improving upon existing results. New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative 5/2-order L2-accuracy in approximating Hamiltonian flows. The paper explores the geometry of holomorphic flows and orbits.
problem Understanding the local geometry of holomorphic flows and their equilibria.
method Analyzing the local geometry of first-order equilibria and higher-order equilibria under holomorphic conditions.
result Holomorphic Poincaré-Bendixson theorem: bounded non-periodic orbits are homoclinic or heteroclinic.
MetFlow combines MCMC and VI efficiently for better inference.
problem Combining MCMC and VI for efficient inference.
method Introduces MetFlow, a novel MCMC algorithm with Normalizing Flows, and a new method to combine it with VI.
result MetFlow produces expressive variational families with improved computational efficiency.
Classifies reversible and strongly reversible elements in quaternionic groups.
problem Classifying reversible and strongly reversible elements in quaternionic groups.
method Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
result Proves elements are reversible if and only if they are products of skew-involutions (resp. involutions).
The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.
problem Classifying reversible and strongly reversible elements in Hermitian isometry groups.
method Classification through group theory and algebraic manipulation.
result New classification of strongly reversible elements in Sp(n).
We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We …