Paper discusses conditions for deforming coupled Kähler-Einstein metrics.
problem Conditions for deforming coupled Kähler-Einstein metrics.
method Analyzes deformation of coupled Kähler-Einstein metrics on Fano manifolds.
result Necessary and sufficient condition for deformation of coupled Kähler-Einstein metrics.
This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.
problem Understanding the representational power of affine coupling flows for log-concave distributions.
method Leveraging connections between affine coupling architectures, Langevin dynamics, and Hénon maps to prove log-concave approximation.
result Any log-concave distribution can be approximated using well-conditioned affine-coupling flows.
Unified Jacobi coupling construction for various geometric settings.
problem Constructing Jacobi structures on associated bundles.
method Extending Sternberg--Weinstein coupling to Jacobi geometry.
result Associated bundles inherit Jacobi structures from base spaces.
Numerical observations on martingale couplings are confirmed under certain conditions.
problem Understanding the validity of numerical observations on maximizers and minimizers of martingale couplings.
method Investigation of sufficient conditions and counterexamples for the property to hold.
result The non-decreasing property of martingale couplings is preserved for maximizers under specific conditions.
A new method for conditional sampling using paired Wasserstein Autoencoders.
problem Conditional sampling from complex data distributions.
method Derive a novel loss function for Wasserstein Autoencoders to enable sampling from OT-type couplings.
result Learned cost-optimal transport maps and conditional sampling from an OT-type coupling.
Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.
problem Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
method Develop a framework for barycentric projections of transport couplings on Riemannian manifolds.
result The intrinsic projection maps each source point to the conditional Fréchet mean of its destination law and is shown to be the best deterministic representative under squared geodesic loss.
We review coupled SU(3)-structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behaviour of flows of SU(3)-structures with respect to the coupled condition.
Two probability distributions μ and ν in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are al…
We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled Kähler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson conjecture. We also obtain a necessary and sufficient condition for…
We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds. In particular, we get necessary and sufficient conditions for existence of coupled Kähler-Ricci solitons, Mabuchi metrics and twisted Kähler-Einstein metrics in t…
We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod e…
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability conditions on a solution. We then discuss a procedure for coupling known solutions of …
We propose new types of canonical metrics on Kähler manifolds, called coupled Kähler-Einstein metrics, generalizing Kähler-Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and when the manifold is Kähler-Einstein Fano. In the Fano case we also prove that existe…
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
ReDi improves few-step generation for discrete data models.
problem Slow sampling speeds in discrete flow-based models.
method Rectified Discrete Flow (ReDi) reduces factorization error by rectifying coupling.
result Empirically, ReDi reduces Conditional Total Correlation and enables few-step generation.
New framework explains normalizing flows' power and limitations.
problem Understanding the expressive power and limitations of normalizing flows.
method Theoretical framework for well-conditioned coupling-based normalizing flows and volume-preserving flows.
result RealNVP is distributionally universal, but volume-preserving flows are not.
We give sufficient conditions for the existence of a Dirac structure on the total space of a Poisson fiber bundle endowed with a compatible connection. We also show that Cartan and Cartan-Hannay-Berry connections give rise to coupling Dirac structures.
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
This work introduces a new method for coupling base and target densities in generative models.
problem Generating samples from complex target distributions using simple base distributions.
method Developed a framework of stochastic interpolants with data-dependent couplings.
result Constructing dynamical transport maps that serve as conditional generative models.
In this paper we show how a natural coupling of the Dirac equation with the generalized Jang equation, leads to a proof of the rigidity statement in the positive mass theorem with charge, without the maximal slicing condition, provided a solution to the coupled system exists.
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
problem Proving geometric ergodicity of SGLD in nonconvex, log-concave settings.
method Reflection coupling technique to handle SGLD's time discretization and minibatch issues.
result SGLD has an invariant distribution and geometric ergodicity in W1 distance. Proposes a model for semi-supervised learning using both labeled and unlabeled data.
problem Semi-supervised learning with limited labeled data.
method Semi-conditional normalizing flow model with conditional coupling layer.
result Model outperforms variational auto-encoders on MNIST dataset.
We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a 5-dimensional orientable fibered manifolds with 2-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their …
Study finds critical points of volume functionals on Sasaki manifolds.
problem Finding Kähler-Einstein metrics on Sasaki manifolds.
method Revisited moment polytopes, applied to volume minimization.
result Transverse coupled Kähler-Einstein metrics found as critical points.
The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.
problem Approximating posterior measures in inverse problems using conditional Wasserstein distances.
method Introduces a conditional Wasserstein distance with restricted couplings and derives its dual.
result Shows that conditional Wasserstein GANs can yield favorable properties for posterior sampling.
This paper introduces a novel recurrent model for music composition that is tailored to the structure of polyphonic music. We propose an efficient new conditional probabilistic factorization of musical scores, viewing a score as a collection of concurrent, coupled sequences: i.e. voices. To model the conditional distri…
Introduces new equations linking Kähler-Einstein and Hermitian-Yang-Mills theories.
problem Existence of solutions to coupled Kähler-Einstein and Hermitian-Yang-Mills equations.
method Moment map interpretation, Futaki invariant, Matsushima-Lichnerowicz theorem, deformation results.
result Nontrivial solutions produced under certain conditions.
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
A one-parameter family of coupled flows depending on a parameter κ>0 is introduced which reduces when κ=1 to the coupled flow of a metric ω with a (1,1)-form α due recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for κ=1, estimates for derivatives of all orders would follow from…
Developed MF-PINNs to solve coupled Stokes-Darcy equations more accurately.
problem Solving coupled Stokes-Darcy equations with varying physical constants.
method Combining VP and SV forms with adjusted weights in MF-PINNs.
result Improved accuracy of streamline and pressure fields in numerical experiments.
Proves Hadamard states for Dirac fields on manifolds with timelike boundaries.
problem Existence of Hadamard states for Dirac fields with MIT boundary conditions.
method Introducing geometric Møller operator to implement unitary isomorphism between spaces of initial data.
result Existence of Hadamard states for Dirac fields with MIT boundary conditions.
Rényi Neural Processes replace KL divergence with Rényi divergence to improve NP performance.
problem Parameterization coupling in Neural Processes leads to prior misspecification.
method Propose Rényi Neural Processes (RNP) by replacing KL divergence with Rényi divergence.
result Significant performance improvements in real-world problems, including better log-likelihoods.
ANODEV2 extends Neural ODEs to include evolving parameters.
problem Training and accuracy of neural networks.
method Coupled ODE-based framework for evolving neural network parameters.
result ANODEV2 achieves higher accuracy than baseline models and Neural ODEs.
Augmented bridge matching preserves coupling information between distributions.
problem Preserving the original empirical pairing in flow and bridge matching processes.
method Augmenting the velocity field with initial sample point information.
result Simple modification recovers coupling information without losing Markovian property.
Wilson loops in N=4 supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in AdS5. We study a class of extremal surfaces known as special Legendrian submanifolds. The "hemisphere" corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and w…
In our previous paper (arXiv:1306.5449) we have given a sufficient and necessary condition when the coupling between Lie algebra bundle (LAB) and the tangent bundle exists in the sense of Mackenzie (\cite{Mck-2005}, Definition 7.2.2) for the theory of transitive Lie algebroids. Namely we have defined a new topology on …
Survey on Kähler-Einstein and weighted solitons on Fano manifolds.
problem Existence of coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds.
method Generalization of algebraic conditions for K-polystability.
result Existence of coupled Kähler-Einstein metrics and weighted solitons is equivalent to algebraic conditions.
New method uncovers zero entropy in dependent observations after finite samples.
problem Understanding uncertainty reduction in dependent observations.
method Minimum list entropy coupling, greedy algorithm.
result Zero entropy achieved with O(log(1/P_min)) samples for dependent observations.
We address representational challenges in normalizing flows, particularly depth and conditioning issues.
problem Challenges in training normalizing flows, including vanishing/exploding gradients and poor conditioning.
method Analyzes representational aspects of depth and conditioning in normalizing flows, proving theoretical bounds and investigating phenomena.
result Proves that shallow affine coupling networks are universal approximators in Wasserstein distance if ill-conditioning is allowed.
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-Kähler case, by its analogues. To this end we…
MUSIC learns coupled systems with sparse data and incomplete physics.
problem Learning coupled systems with incomplete physical constraints and missing data.
method Sparsity induced multitask neural network framework integrating partial physical constraints with data-driven learning.
result MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions.
We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of …
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror des…
A new method estimates protein evolutionary fields and couplings from alignments.
problem Estimating evolutionary fields and couplings from protein sequence alignments.
method Boltzmann machine with parallel, persistent Markov chain Monte Carlo method.
result Improved precision in predicting contact residue pairs.
The paper characterizes metallic pseudo-Riemannian manifolds using conjugate connections and tensor structures.
problem Characterizing metallic pseudo-Riemannian manifolds.
method Using conjugate connections and tensor structures, the paper derives new characterizations and conditions for these manifolds.
result A necessary and sufficient condition for a non-integrable metallic pseudo-Riemannian manifold to be a quasi metallic pseudo-Riemannian manifold is derived.
The paper proves existence of solutions for Einstein-type elliptic systems on AE manifolds.
problem Analyzing semi-linear systems of partial differential equations motivated by the conformal formulation of Einstein constraint equations.
method Proving existence theorems under suitable conditions, including smallness assumptions on free parameters.
result Existence of far from CMC (near CMC) Yamabe positive (Yamabe non-positive) solutions for charged dust coupled to the Einstein equations.
Model simulates correlation emergence in two coupled limit order books.
problem Modeling correlation emergence in coupled limit order books.
method Simulated two coupled diffusive limit order books using random walks in the fluid limit, with trader interactions.
result Demonstrated the recovery of an Epps effect from the model.