The paper introduces the expected signature kernel as a similarity measure for probability laws on path space, directly applicable to signature maximum mean discrepancies. It characterizes this kernel for group-valued inhomogeneous Lévy processes by solving an extended Goursat-type system, providing exact solutions in the continuous case and well‑posed infinite‑dimensional systems with error‑controlled truncations for jump processes. The authors also show that conditioning on sampled quadratic variations yields an unbiased, lower‑variance statistic for conditionally Gaussian martingales, and present computable finite‑grid implementations that improve variance and test power.
arXiv:2608. 01547v1 Announce Type: cross Abstract: Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations.
arXiv:2608. 10470v1 Announce Type: new Abstract: Fair representation learning with a continuous sensitive attribute $S$ requires a representation $Z$ that is statistically independent of $S$.
arXiv:2608. 01268v1 Announce Type: cross Abstract: Detecting that a stream of high-dimensional embeddings has changed is usually framed as a choice of statistic.
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
arXiv:2607. 03639v1 Announce Type: cross Abstract: For a multidimensional reflected diffusion, determining whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution is a basic uniqueness problem in the BAR approach.
arXiv:2605. 27478v3 Announce Type: replace-cross Abstract: Schr\"odinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid.
arXiv:2605. 15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends.
arXiv:2609.17287v1 Announce Type: new Abstract: In flow matching (FM), a velocity model $v_{\theta}$ is trained using a predefined path $g_t$ that connects data and noise samples (e.g., $g_t(x_0, x_1...
arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.
arXiv:2605.06866v3 Announce Type: replace Abstract: We study finite-iteration behavior of asynchronous categorical distributional temporal-difference methods, covering scalar categorical TD (CTD) in...
arXiv:2609.09480v1 Announce Type: cross Abstract: We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences genera...
arXiv:2604. 24196v4 Announce Type: replace-cross Abstract: A drifting model is a one-step generator trained by moving each sample along a field of kernel-weighted attraction toward data samples and repulsion between model samples; training halts once this field vanishes.