Necessary and sufficient conditions for convergence of low-intensity Poisson–Voronoi diagrams to a unique ideal tessellation, applied to symmetric spaces and Diestel–Leader graphs.
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Grundlehren der mathematischen Wissenschaften [Fun- damental Principles of Mathematical Sciences], vol
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representative citing papers
Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
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The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.
Proves unique stationary law for Clifford random monitored quantum circuits and computes leading asymptotics of steady magic, linear for odd-prime dimension mana and quadratic for qubit 2-stabilizer Rényi entropy.
Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
Derivation of a stochastic maximum principle for McKean-Vlasov SDEs with common noise that requires a third adjoint state to linearize all second-order terms in the cost expansion.
OTP-FM extends conditional flow matching by incorporating dynamic optimal transport potentials to enable efficient multimarginal transport learning with intermediate observed marginals.
Attention in minimal transformers under corruption performs in-context empirical Bayes via a single kernel-weighted posterior mean step followed by depth-driven particle dynamics refinement.
CausalHealth detects lithium-ion battery degradation with 100% sensitivity and up to 402-cycle lead time using causal anomaly scores from voltage, current, temperature, and resistance time series across seven cells.
Presents a likelihood-free transport map learned by minimizing an averaged energy-distance objective to amortize Bayesian inference for inverse problems, including PDE-constrained cases with neural operator representations.
Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.
A Deep Set encoder plus normalizing flow model trained on five million CRPropa 3 events recovers UHECR source parameters without bias and classifies primary composition at over 98 percent accuracy.
Derives Õ(d β² A² / ε⁴) oracle complexity for AIS estimating normalizing constant Z to relative error ε and introduces reverse diffusion sampler for geometric paths with large action.
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
Proves the conditional minimal-intermediate-entropy property holds for topologically expanding maps, transitive countable Markov shifts, and symbolic systems with non-uniform structure via adapted multi-horseshoe constructions.
A Minkowski-type Wasserstein framework for location-scale mixtures reduces multimarginal OT to discrete component transport with linear complexity and shows competitive domain adaptation performance.
GalSBI extended with optimal transport subhalo matching and SBI to forward-model galaxy population plus clustering, validated against DES Y3 and HSC data with public code release.
Non-closing Lie brackets of intervention-response fields can serve as a high-recall screen for causal edges under latent confounding, but do not by themselves identify general DAGs.
Proposes and analyzes a homogeneity test using squared L2 distance of empirical EOT maps to uniform-on-ball reference, with FCLT, Gaussian quadratic null limit, consistency, local power, and weighted multiplier bootstrap.
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Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
Proves SLiCEs are universal time-series generators approximating path laws in W_∞ and proposes G-SLiCEs for path-space flow matching with benefits on irregular grids.
Introduces extended bridge functions and derives identification results for joint interventional distributions retaining proxy variables in proximal causal inference.
citing papers explorer
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Convergence towards Ideal Poisson--Voronoi tessellations with a focus on Diestel--Leader graphs
Necessary and sufficient conditions for convergence of low-intensity Poisson–Voronoi diagrams to a unique ideal tessellation, applied to symmetric spaces and Diestel–Leader graphs.
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Function graph transformers universally approximate operators between function spaces
Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
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A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
Introduces structured DRO for learned inverse problem reconstructions with ambiguity sets aligned to the forward operator, yielding explicit dual representations and a worst-case bound that induces Tikhonov regularization on the operator Lipschitz constant.
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The Mortensen observer on the space of probability measures
The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.
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Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
Proves unique stationary law for Clifford random monitored quantum circuits and computes leading asymptotics of steady magic, linear for odd-prime dimension mana and quadratic for qubit 2-stabilizer Rényi entropy.
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Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
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Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations with Common Noise
Derivation of a stochastic maximum principle for McKean-Vlasov SDEs with common noise that requires a third adjoint state to linearize all second-order terms in the cost expansion.
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Multimarginal flow matching with optimal transport potentials
OTP-FM extends conditional flow matching by incorporating dynamic optimal transport potentials to enable efficient multimarginal transport learning with intermediate observed marginals.
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Attention as In-Context Empirical Bayes: A Two-Stage View via Particle Dynamics
Attention in minimal transformers under corruption performs in-context empirical Bayes via a single kernel-weighted posterior mean step followed by depth-driven particle dynamics refinement.
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Causal Anomaly Detection for Lithium-Ion Battery Degradation
CausalHealth detects lithium-ion battery degradation with 100% sensitivity and up to 402-cycle lead time using causal anomaly scores from voltage, current, temperature, and resistance time series across seven cells.
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Amortized Energy-Based Bayesian Inference
Presents a likelihood-free transport map learned by minimizing an averaged energy-distance objective to amortize Bayesian inference for inverse problems, including PDE-constrained cases with neural operator representations.
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Primitive Sequences for Probability Measures on Compact Intervals
Primitive sequences obtained from iterated antiderivatives of the CDF are homeomorphic to probability measures on compact intervals, equivalent to factorial-rescaled moments of the reflected variable, and yield sharp bounds on functionals when the first m terms are fixed.
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Neural Posterior Estimation for UHECR source inference from 3D propagation simulations
A Deep Set encoder plus normalizing flow model trained on five million CRPropa 3 events recovers UHECR source parameters without bias and classifies primary composition at over 98 percent accuracy.
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Complexity Analysis of Normalizing Constant Estimation: from Jarzynski Equality to Annealed Importance Sampling and beyond
Derives Õ(d β² A² / ε⁴) oracle complexity for AIS estimating normalizing constant Z to relative error ε and introduces reverse diffusion sampler for geometric paths with large action.
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Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
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Abundance of minimal measures via entropy and multifractal analysis
Proves the conditional minimal-intermediate-entropy property holds for topologically expanding maps, transitive countable Markov shifts, and symbolic systems with non-uniform structure via adapted multi-horseshoe constructions.
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Minkowski-Type Wasserstein Metrics and Barycenters for Location-Scale Mixtures with Application to Domain Adaptation
A Minkowski-type Wasserstein framework for location-scale mixtures reduces multimarginal OT to discrete component transport with linear complexity and shows competitive domain adaptation performance.
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GalSBI: Forward Modelling Galaxy Clustering and Population
GalSBI extended with optimal transport subhalo matching and SBI to forward-model galaxy population plus clustering, validated against DES Y3 and HSC data with public code release.
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Latent Confounded Causal Discovery via Lie Bracket Geometry
Non-closing Lie brackets of intervention-response fields can serve as a high-recall screen for causal edges under latent confounding, but do not by themselves identify general DAGs.
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Two-Sample Homogeneity Test via Entropic Optimal Transport
Proposes and analyzes a homogeneity test using squared L2 distance of empirical EOT maps to uniform-on-ball reference, with FCLT, Gaussian quadratic null limit, consistency, local power, and weighted multiplier bootstrap.
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Generate in Reconstruction Space, Match in Semantic Space: Transport Geometry for One-Step Generation
Matching in semantic SSL feature space via Sinkhorn divergence enables effective one-step generation on ImageNet by inducing compact geometry for distribution matching, with training and evaluation features best kept distinct.
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Wasserstein Least Squares: A Canonical Regression Method for Probability Distributions
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
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Universal Time Series Generation with Neural Controlled Differential Equations
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Identifying Interventional Joint Distributions via Extended Bridge Functions
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Information-Preserving Domain Transfer with Unlabeled Data in Misspecified Simulation-Based Inference
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Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
Quantitative 2-Wasserstein bounds are established between finite-width deep neural networks and their infinite-width Gaussian limits using a Lindeberg principle for successive Gaussian replacement of weights.
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Semantic Segmentation for Histopathology using Learned Regularization based on Global Proportions
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Quantitative Stability of the Shadow for Wasserstein Projections and Sample Complexity
The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.
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Standardized Images and Evaluation Metrics for Tomography
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Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
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Multicellular simulations with shape and volume constraints using optimal transport
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Flow-Corrected Thompson Sampling for Non-Stationary Contextual Bandits
fcTS corrects and reweights historical observations via drift models for linear, periodic, and regime-switching non-stationarities in contextual bandits, outperforming forgetting baselines in structured cases.
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Linear quadratic optimal transport and interpolation inequalities
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.
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Convergence rate of the occupation measure of classes of ergodic processes toward their invariant distribution in mean Wasserstein distance
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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Reduced-Precision Stochastic Simulation for Mathematical Biology
Mixed-precision SSA with stochastic rounding preserves ensemble statistics across five biological models while cutting memory use by 2-4x and delivering up to 1.5x CPU speedup.
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Rationality Measurement and Theory for Reinforcement Learning Agents
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Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers
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Wasserstein distances and divergences of order $p$ by quantum channels
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Efficient Model Repository for Entity Resolution: Construction, Search, and Integration
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Hierarchical Semantic-Augmented Navigation: Optimal Transport and Graph-Driven Reasoning for Vision-Language Navigation
HSAN integrates hierarchical semantic graphs, optimal transport-based goal selection, and graph-aware RL to claim SOTA results on VLN-CE tasks.