AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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10 Pith papers cite this work, alongside 1,071 external citations. Polarity classification is still indexing.
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The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.
VGF solves behavior-regularized RL by transporting particles from a reference distribution to the value-induced optimal policy via discrete value-guided gradient flow.
Newton's recursive mixture estimator is a discrete gradient flow on the Fisher-Rao manifold of probability measures.
wAR-Tok adds a Wasserstein-gradient-flow prior-matching term to tokenizer training so that discrete tokens become easier for autoregressive priors to model, cutting AR loss and raising generation FID on CIFAR-10 and ImageNet while keeping reconstruction quality comparable.
Galaxy evolution is cast as a geometrically constrained reaction-transport process on probability measures, using Wasserstein distance and CD(K,∞) conditions to enforce energy dissipation and interaction closure.
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.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
Establishes stability bounds for SHK flows yielding dimension-free controls on log-likelihood ratios and divergences, then applies them to time-dependent Pure-DP and Approximate-DP certificates for exponential-mechanism samplers.
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The physics of AI weather models
AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
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A stiff limit of non-homogeneous conservation laws for crowd motion modeling
A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.
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Reinforcement Learning via Value Gradient Flow
VGF solves behavior-regularized RL by transporting particles from a reference distribution to the value-induced optimal policy via discrete value-guided gradient flow.
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Newton's Algorithm as a Gradient Flow: A Geometric Framework for Recursive Mixture Estimation
Newton's recursive mixture estimator is a discrete gradient flow on the Fisher-Rao manifold of probability measures.
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Learning Discrete Autoregressive Priors with Wasserstein Gradient Flow
wAR-Tok adds a Wasserstein-gradient-flow prior-matching term to tokenizer training so that discrete tokens become easier for autoregressive priors to model, cutting AR loss and raising generation FID on CIFAR-10 and ImageNet while keeping reconstruction quality comparable.
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A Measure-Theoretic Transport Formulation of Galaxy Evolution on the Galaxy Manifold: Geometric Constraints
Galaxy evolution is cast as a geometrically constrained reaction-transport process on probability measures, using Wasserstein distance and CD(K,∞) conditions to enforce energy dissipation and interaction closure.
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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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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
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On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy
Establishes stability bounds for SHK flows yielding dimension-free controls on log-likelihood ratios and divergences, then applies them to time-dependent Pure-DP and Approximate-DP certificates for exponential-mechanism samplers.