Related papers: Estimates of gradient perturbation series
Integrated Gradients has become a popular method for post-hoc model interpretability. De-spite its popularity, the composition and relative impact of different regions of the integral path are not well understood. We explore these effects…
Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data…
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…
Gradients and subgradients are central to optimization and sensitivity analysis of buffered failure probabilities. We furnish a characterization of subgradients based on subdifferential calculus in the case of finite probability…
Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.
We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…
This paper presents bounds for the variation of the spectral radius $\lambda(G)$ of a graph $G$ after some perturbations or local vertex/edge modifications of $G$. The perturbations considered here are the connection of a new vertex with,…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
An approximation of the density of states for the Ising and Potts models based on the high- and low-temperature series are developed.
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small)…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
The statistical uncertainty in measuring the primordial density perturbations on a given comoving scale is dictated by the number of independent regions of that scale that are accessible to an observer. This number varies with cosmic time…
We consider a functional obtained by adding a trace term to the Allen-Cahn phase segregation model and we prove some density estimates for the level sets of the interfaces. We treat in a unified way also the cases of possible degeneracy and…
The standard calculation of the spectrum of density perturbations produced during inflation assumes (i) |n-1| << 1 and (ii) |dn/dlnk| << |n-1|. Slow-roll predicts and observations require (i), but neither slow-roll nor observations require…
Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by…
We develop the gradient expansion formalism for shift-symmetric Galileon-type actions. We focus on backgrounds that undergo inflation, work in the synchronous gauge, and obtain a general solution up to second order without imposing extra…
We study boundary gradient estimates for second-order divergence type parabolic and elliptic systems in $C^{1,\alpha}$ domains. The coefficients and data are assumed to be H\"older in the time variable and all but one spatial variables.…