Extends VAEs to handle complex Bayesian network structures.
problem Handling complex dependency structures in Bayesian networks.
method Extends VAEs with graphical residual flows to model arbitrary dependency structures.
result Demonstrates improved performance on synthetic datasets.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
New framework learns nonlinear cyclic causal models from data.
problem Challenges in learning causal relationships from real-world, cyclic systems.
method NODAGS-Flow: a novel framework using residual normalizing flows for likelihood estimation.
result Significant performance improvements in structure recovery and predictive performance compared to state-of-the-art methods.
Consider a mean curvature flow of hypersurfaces in Euclidean space, that is initially graphical inside a cylinder. There exists a period of time during which the flow is graphical inside the cylinder of half the radius. Here we prove a lower bound on this period depending on the Lipschitz-constant of the initial graphi…
The study proves stability of various graphical translators in mean curvature flow.
problem Stability of graphical translators in mean curvature flow.
method Existence of longtime solution to mean curvature flow, dynamical stability results for various graphical translators.
result Dynamical stability of various types of graphical translators.
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
Study preserves planar and graphical properties of curves under elastic flow.
problem Maintaining planar and graphical properties of non-compact curves under elastic flow.
method Extended recent work on adapted elastic energy to derive thresholds for planar and graphical embeddedness.
result Derived new Li--Yau type inequality for complete planar curves.
We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provides an ele- mentary proof to the known rigidity results for graphical and almost graphical shrinkers of mean curvature flows.
New estimate for Curve Shortening Flow improves graphical solutions.
problem Improving regularity estimates for Curve Shortening Flow.
method Generalizing delayed parabolic regularity for Curve Shortening Flow.
result Interior graphical estimate for Curve Shortening Flow.
Study on rigidity of translating hypersurfaces not in graphical direction.
problem Rigidity of translating hypersurfaces not in graphical direction.
method Proved rigidity results for complete graphical translating hypersurfaces under specific conditions.
result Entire graphical translating surfaces are flat under certain conditions.
We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying graphical mean curvature flow wit…
VFG model embeds flow-based models with hierarchical structures using variational inference.
problem Flow-based models struggle with high-dimensional latent spaces and lack of tractable inference for graphical structures.
method Integrates flow-based functions through variational inference with aggregation nodes for hierarchical information integration.
result VFG models achieve improved ELBO and likelihood values on multiple datasets.
Sharp estimate for flow in any dimension.
problem Interior gradient estimate for graphical mean curvature flow.
method Proving sharp interior gradient estimate for area decreasing graphical mean curvature flow in arbitrary codimension.
result Generalized result in arbitrary codimension.
The study examines the graphical mean curvature flow on compact manifolds with bounded bi-Ricci curvature.
problem Analyzing the graphical mean curvature flow of maps between manifolds with bounded bi-Ricci curvature.
method Proving long-time existence and preserving the strictly area decreasing property under bounded bi-Ricci curvature conditions.
result Smooth convergence to a minimal map under certain conditions on Ricci curvature.
Develops c-GNF for personalized social science policy analysis.
problem Challenges in estimating causal effects and counterfactual inference in social sciences.
method causal-Graphical Normalizing Flow (c-GNF) method.
result c-GNF performs well in estimating causal effects and counterfactual inference.
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
Researchers relax the CVF's smoothness requirement to create more flexible flow models.
problem Challenges in constructing flexible density models due to the CVF's smoothness requirement.
method Introduce L-diffeomorphisms as generalized transformations that may violate smoothness on zero Lebesgue-measure sets. result The relaxation allows for the use of non-smooth activation functions like ReLU in residual flows.
Invertible DenseNets improve model efficiency and performance.
problem Improving model efficiency and performance in neural networks.
method Enforcing invertibility in DenseNets by satisfying the Lipschitz constraint and proposing a learnable concatenation.
result i-DenseNets outperform Residual Flows in negative log-likelihood on various datasets.
The paper studies a flow of spacelike curves in a Lorentz-Minkowski plane, showing convergence to a constant function.
problem Evolution of spacelike graphic curves in Lorentz-Minkowski plane.
method Anisotropic inverse mean curvature flow with vanishing Neumann boundary condition.
result The evolving curves converge to a constant function as time tends to infinity.
Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…
New method controls latent variables in graphical models to improve causal inference and prediction.
problem Uncertainty in causal relationships due to unobserved confounders.
method Iteratively derives proxies for latent variables from model residuals.
result Improves structural inference and prediction performance of causal models.
Paper proposes a natural hedging framework with graphical assessment for longevity risk management.
problem Lack of a unified framework for natural hedging and graphical risk assessment.
method Structured natural hedging framework integrated with a graphical risk metric.
result Demonstrates flexibility, interpretability, and practical value for longevity risk management.
New Harnack inequality for curve shortening flow without convexity.
problem Proving a Harnack inequality for curve shortening flow without convexity.
method Developed a new Harnack inequality for one-dimensional mean curvature flow (curve shortening flow) that doesn't require convexity.
result Explicit time by which an initial curve becomes graphical under curve shortening flow.
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…
Proves strong solutions for graphical Brakke flows with L2 normal velocity.
problem Proving strong solutions for graphical Brakke flows with specific velocity conditions.
method Combining L2 normal velocity with parabolic regularity theory. result Graphical Brakke flows with forcing term in Lp,q and C0,α are strong and classical solutions. JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph…
We show that (a) any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in Cm with the Euclidean metric is flat; (b) any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in Cm with the pseudo-Euclidean metric is flat if the H…
The paper studies a flow of spacelike surfaces in Lorentz-Minkowski space, proving convergence to a hyperbolic plane.
problem Evolution of spacelike graphic hypersurfaces in Lorentz-Minkowski space.
method Anisotropic inverse mean curvature flow with Neumann boundary condition.
result The flow converges to a hyperbolic plane as time tends to infinity.
The paper studies how certain spacelike surfaces evolve over time in a specific space.
problem Evolution of spacelike graphic hypersurfaces in Lorentz-Minkowski space.
method Inverse mean curvature flow with vanishing Neumann boundary condition.
result The evolving surfaces converge to a hyperbolic plane as time goes to infinity.
Smooth convergence to an enveloping cylinder proved for mean curvature flow of complete graphical hypersurfaces.
problem Proving smooth convergence of mean curvature flow to an enveloping cylinder.
method Analyzing mean curvature flow of complete graphical hypersurfaces over domains Ωt, proving convergence under certain circumstances. result Smooth convergence of Mt−hen+1 to the enveloping cylinder under specific conditions. This paper improves bond market making by adjusting hit-ratios for client flow quality.
problem Economic misleading of raw hit-ratios in corporate bond market making.
method Stochastic-control framework with residual-quality-adjusted hit-ratio.
result Optimal quotes decompose into various components, improving service/economics frontier.
i-DenseNets improve parameter efficiency and performance in density estimation.
problem Improving parameter efficiency and performance in density estimation models.
method Invertible Dense Networks (i-DenseNets) with learnable weighted concatenation and Concatenated LipSwish activation function.
result i-DenseNets outperform Residual Flows and other flow-based models in bits per dimension.
A finite simple graph Γ determines a quotient PΓ of the pure braid group, called a graphic arrangement group. We analyze homomorphisms of these groups defined by deletion of sets of vertices, using methods developed in prior joint work with R. Randell. We show that, for a K4-free graph Γ, a product of deletio…
The purpose of this paper is twofold: firstly, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface, and secondly, to illustrate the application of Killing vector fields in the preser…
Study on mean curvature flow of graphs in higher dimensions.
problem Analyzing the evolution of graphs under mean curvature flow.
method Derives estimates using a new maximum principle for submanifolds, applies to uniformly area decreasing maps.
result Graphicality and area decreasing property are preserved for uniformly area decreasing maps.
Study of mean curvature flow in de Sitter space, showing convergence to flat slicing.
problem Mean curvature flow in de Sitter space.
method Analysis of mean convex mean curvature flow of local spacelike graphs in de Sitter space.
result As s goes to infinity, Ms becomes graphical in expanding balls, converging to the flat slicing of de Sitter space. Study of mean curvature flow in warped products preserving equivariance.
problem Analyzing mean curvature flow in warped products.
method Deriving flow equation and proving existence for infinite time.
result Mean curvature flow exists for infinite time under specific conditions.
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
A GPU-based workflow for building physics emulators of hypersonic flows
problem Resolving complex physical phenomena in hypersonic flows
method Fully GPU-based workflow integrating accelerated data generation and neural emulators
result Physics emulators remain reliable beyond their training distribution
Consider an integral Brakke flow (μt), t∈[0,T], inside some ball in Euclidean space. If μ0 has small height, its measure does not deviate too much from that of a plane and if μT is non-empty, then Brakke's local regularity theorem yields that (μt) is actually smooth and graphical inside a smaller b…
A new method for learning gradient flows from population dynamics.
problem Reconstructing population dynamics from limited data.
method Residual approach to enforce continuity equations, combining with data-fitting divergence.
result Demonstrated state-of-the-art performance across trajectory inference benchmarks.
ELF simplifies normalizing flows, making them more efficient and universal.
problem Computational inefficiency of normalizing flows.
method ELF introduces a simple, one-layer network with closed-form Lipschitz constants, combining the ease of residual flows with the performance of autoregressive flows.
result ELF is a provably universal density approximator, more efficient computationally and parameter-wise.
Paper proves unique tangent flow at infinity for entropy-limited curve shortening.
problem Proving uniqueness of tangent flows for finite-entropy curve shortening.
method Rescaled backward convergence to a line, entropy analysis, and geometric properties.
result Ancient smooth curve shortening flow has a unique tangent flow at infinity.
The paper studies how spacelike surfaces evolve in Lorentz-Minkowski space over time.
problem Evolution of spacelike graphic hypersurfaces in Lorentz-Minkowski space.
method Inverse Gauss curvature flow with Neumann boundary condition.
result The evolving surfaces converge to a constant function as time goes to infinity.
Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, resp…