Related papers: Subinvariant kernel dynamics
We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Ito-integration. Our…
The evolution kernels that govern the scale dependence of the generalized parton distributions are invariant under transformations of the $\mathrm{SL}(2,\mathrm R)$ collinear subgroup of the conformal group. Beyond one loop the symmetry…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…
Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…
When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we…
Let $M$ be a complex manifold with boundary $X$, which admits a holomorphic Lie group $G$-action preserving $X$. We establish a full asymptotic expansion for the $G$-invariant Bergman kernel under certain assumptions. As an application, we…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of random vectors, namely probability measures or more simply…
Qualitatively different systems of molecular energy bands are studied on example of a parametric family of effective Hamiltonians describing rotational structure of triply degenerate vibrational state of a cubic symmetry molecule. The…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
Random operator tuples possess a rich second-moment structure that is not visible at the level of pointwise operator inequalities. This paper shows that their averaged word moments form a positive kernel whose behavior is controlled by a…
We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel. Moreover, we study boundary regular fixed points of…
We analyze feature learning in infinite-width neural networks trained with gradient flow through a self-consistent dynamical field theory. We construct a collection of deterministic dynamical order parameters which are inner-product kernels…
We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close…
New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group.…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…