Perturbation Theory for Spherical Hellinger-Kantorovich Flows with Differential Privacy Guarantees
This paper develops a perturbation theory for Spherical Hellinger-Kantorovich (SHK) gradient flows, which couple transport and reaction dynamics and coincide with birth-death Langevin dynamics. The authors derive dimension-free bounds on log-likelihood ratios and Rényi/KL divergences when two potentials differ, quantifying how perturbations propagate over time. These results are applied to differential privacy: the likelihood-ratio control yields explicit Pure-DP guarantees for SHK-based samplers implementing the exponential mechanism, while KL bounds provide Approximate-DP certificates. A utility bound is also derived that separates intrinsic exponential-mechanism suboptimality from finite-time sampling error.
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Predictability as a Fine-Grained Privacy Metric Complementary to Differential Privacy
A new arXiv preprint introduces 'privacy via predictability,' a framework that measures privacy leakage as the incremental gain in an attacker's ability to predict sensitive information after observing an algorithm's output, conditioned on the attacker's prior knowledge. The authors show predictability and differential privacy are generally incomparable, but that predictability implies mutual-information DP in worst-case regimes. They develop a generalized method of moments framework for asymptotic analysis and derive a predictability-calibrated output perturbation scheme for empirical risk minimization. The work positions predictability as a complementary, finer-grained alternative to DP for settings where attacker knowledge and query families can be specified.
IntraShuffler: Privacy-Preserving Framework for Heterogeneous DP Federated Learning
This paper identifies a novel Privacy Inference Attack against heterogeneous differential privacy federated learning (HDP-FL) systems, where an honest-but-curious server exploits epsilon-aware aggregation and gradient denoising to infer client data distributions and link updates across rounds. To counter this, the authors propose IntraShuffler, a middleware framework that groups clients into privacy-compatible buckets and performs parameter-level shuffling within buckets, preserving epsilon-aware aggregation while disrupting persistent gradient structure. Experiments on four datasets show IntraShuffler reduces gradient recoverability by over 60% and drops surrogate inference accuracy from 0.78 to 0.33 with minimal utility loss.
The Privacy Price of Tail-Risk Learning: Effective Tail Sample Size in Differentially Private CVaR Optimization
This paper characterizes how differential privacy affects the statistical complexity of CVaR (Conditional Value at Risk) optimization, showing that the effective sample size governing private tail-risk learning is εnτ rather than n, where τ is the tail mass. Complete minimax rates are derived for scalar estimation and finite classes under pure DP, with lower bounds extending to approximate DP. For convex Lipschitz learning, the CVaR-specific privacy cost necessarily scales as 1/(εnτ), with dimension dependence inherited from private stochastic convex optimization. The results reduce private CVaR learning to private learning on Θ(nτ) tail records as the canonical hard subproblem.
Global Convergence Theory for Wasserstein Policy Gradient in Entropy-Regularized RL
This paper establishes the first global convergence theory for Wasserstein Policy Gradient (WPG), a continuous-control RL optimization method that uses optimal-transport geometry over action distributions. The authors show that the Bellman recursion structure of entropy-regularized RL induces a Polyak–Łojasiewicz (PL) geometry that substitutes for classical convexity, enabling global convergence analysis. Key technical contributions include a statewise KL representation of the soft Bellman residual, a Bellman resolvent identity linking value improvement to relative Fisher information, and a uniform log-Sobolev inequality for the evolving Gibbs policy family. The result yields geometric contraction up to discretization bias, providing theoretical grounding for WPG in continuous-action settings.
Kolmogorov Regression lifts diffusion policies to Cameron-Martin space for robust long-horizon control
Researchers introduce a backward Kolmogorov equation framework that reformulates diffusion policy training as a deterministic boundary-value PDE problem in Cameron-Martin space, replacing stochastic score matching. The approach uses a precision-weighted Cameron-Martin loss and a Kolmogorov residual as an inference-time failure detector, yielding convergence guarantees tied to kernel effective rank rather than action dimension. Validation on the PushT manipulation benchmark shows 17% improvement in episode reward and 67.6% reduction in inter-step drift; a 6-station manufacturing scheduling task shows 28.4% lower RMSE than LSTM baselines and 96% reduction in deadlock events via Hamilton-Jacobi reachability certification.
PTL-Diffusion: Diffusion framework with periodic terminal laws for manifold-aware generation
PTL-Diffusion is a new diffusion modeling framework that replaces the standard single Gaussian terminal distribution with a periodic family of Gaussian terminal laws, embedding phase structure directly into the forward noising dynamics rather than only in the denoising network. The authors derive closed-form forward marginals and reverse posteriors for a periodically forced Ornstein-Uhlenbeck process, enabling standard noise-prediction training. Experiments on torus, cylinder, and face datasets show improvements in manifold-level distributional matching over DDPM baselines. The work is a proof-of-concept motivating structured terminal reference laws as a direction for geometry-aware generative modeling.
Finite-Sample Lens for Understanding Diffusion Posterior Sampler Failures
This paper introduces a finite-sample theoretical framework for analyzing diffusion model posterior samplers used in imaging inverse problems. The authors show that popular likelihood approximations at intermediate timesteps systematically under- or over-estimate posterior spread, leading to failure modes including sensitivity to early stopping, incorrect weighting of posterior modes, and hallucination of prior or likelihood modes. Crucially, they demonstrate these failures can arise from a multimodal prior alone, without requiring nonlinear measurement models or multimodal posteriors. The framework is model-agnostic and can serve as a diagnostic tool for evaluating existing and future posterior samplers.
KAFFEE: Addressing the Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling
This paper identifies a 'dynamic-probabilistic consistency (DPC) gap' in dynamical systems reconstruction (DSR), where optimizing finite-horizon probabilistic objectives can degrade learned dynamics or decouple predictive uncertainty from local tangent dynamics. Three failure mechanisms are isolated: core collapse, noise masking, and blind uncertainty. The authors propose KAFFEE, a differentiable extended Kalman filter-based training framework that evaluates likelihood on local predictive residuals while transporting covariance through learned Jacobians, reducing these failure modes on stochastic hyperchaotic Lorenz-96 and across 13 chaotic systems when adapting a DSR foundation model.