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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Optimal transport , volume 338 of Grundlehren der math- ematischen Wissenschaften [Fundamental Principles of Mathematical Sci- ences]
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UNVERDICTED 22representative citing papers
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)).
Introduces extended bridge functions and derives identification results for joint interventional distributions retaining proxy variables in proximal causal inference.
SPIN performs bidirectional domain transfer in SBI to retain parameter mutual information from unlabeled real observations, improving real-world posterior inference under increasing misspecification.
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.
VSLP infers dense segmentations from global label proportions via a pre-trained transformer for initial confidence maps followed by variational optimization using Wasserstein fidelity and a learned regularizer, outperforming prior weakly supervised methods on histopathology datasets.
The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.
RL agents' rationality is quantified via expected value discrepancy to optimal actions, with the training-deployment gap decomposed and bounded by Wasserstein distance and Rademacher complexity, supported by experiments on regularizers.
A framework of four reference images and sensitive metrics for tomography that reveals reconstruction discrepancies missed by global image quality measures.
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
Presents an optimal transport framework for simulating particle systems with arbitrary cell shapes and volumes that automatically handles exclusion constraints.
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.
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.
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.
Causal PDE-Control Models combine causal drivers with PDE control and filtering to deliver interpretable dynamic portfolio rules that outperform benchmarks in Sharpe ratio and turnover on U.S. equity data.
Defines p-Wasserstein distances and divergences via quantum channels and proves triangle inequality for quadratic divergences assuming one state is pure.
MoRER builds an ER model repository via feature distribution clustering of tasks, achieving competitive results with limited labels versus active learning, transfer learning, and self-supervised methods on three multi-source datasets.
citing papers explorer
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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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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)).
-
Identifying Interventional Joint Distributions via Extended Bridge Functions
Introduces extended bridge functions and derives identification results for joint interventional distributions retaining proxy variables in proximal causal inference.
-
Information-Preserving Domain Transfer with Unlabeled Data in Misspecified Simulation-Based Inference
SPIN performs bidirectional domain transfer in SBI to retain parameter mutual information from unlabeled real observations, improving real-world posterior inference under increasing misspecification.
-
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.
-
Semantic Segmentation for Histopathology using Learned Regularization based on Global Proportions
VSLP infers dense segmentations from global label proportions via a pre-trained transformer for initial confidence maps followed by variational optimization using Wasserstein fidelity and a learned regularizer, outperforming prior weakly supervised methods on histopathology datasets.
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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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Rationality Measurement and Theory for Reinforcement Learning Agents
RL agents' rationality is quantified via expected value discrepancy to optimal actions, with the training-deployment gap decomposed and bounded by Wasserstein distance and Rademacher complexity, supported by experiments on regularizers.
-
Standardized Images and Evaluation Metrics for Tomography
A framework of four reference images and sensitive metrics for tomography that reveals reconstruction discrepancies missed by global image quality measures.
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Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
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Multicellular simulations with shape and volume constraints using optimal transport
Presents an optimal transport framework for simulating particle systems with arbitrary cell shapes and volumes that automatically handles exclusion constraints.
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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.
-
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.
-
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.
-
Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers
Causal PDE-Control Models combine causal drivers with PDE control and filtering to deliver interpretable dynamic portfolio rules that outperform benchmarks in Sharpe ratio and turnover on U.S. equity data.
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Wasserstein distances and divergences of order $p$ by quantum channels
Defines p-Wasserstein distances and divergences via quantum channels and proves triangle inequality for quadratic divergences assuming one state is pure.
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Efficient Model Repository for Entity Resolution: Construction, Search, and Integration
MoRER builds an ER model repository via feature distribution clustering of tasks, achieving competitive results with limited labels versus active learning, transfer learning, and self-supervised methods on three multi-source datasets.