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In the context of post-hoc interpretability, this paper addresses the task of explaining the prediction of a classifier, considering the case where no information is available, neither on the classifier itself, nor on the processed data…
We propose an interactive-predictive neural machine translation framework for easier model personalization using reinforcement and imitation learning. During the interactive translation process, the user is asked for feedback on uncertain…
Despite the wide use of $k$-Nearest Neighbors as classification models, their explainability properties remain poorly understood from a theoretical perspective. While nearest neighbors classifiers offer interpretability from a ``data…
In this paper, we investigate the attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are…
The Earth Mover's Distance is a popular similarity measure in several branches of computer science. It measures the minimum total edge length of a perfect matching between two point sets. The Earth Mover's Distance under Translation…
We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
The ring of integer-valued polynomials on an arbitrary integral domain is well-studied. In this paper we initiate and provide motivation for the study of integer-valued polynomials on commutative rings and modules. Several examples are…
We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number…
We give explicit formulas of the Bethe approximation with multipoint correlations for systems with magnetic field. The obtained formulas include the closed form of the magnetization and the correlations between adjacent degrees of freedom.…
The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two…
Solid state quantum computing proposals rely on adiabatic operations of the exchange gate among localized spins in nanostructures. We study corrections to the Heisenberg interaction between lateral semiconductor quantum dots in an external…
This is a journey through integrals of involutions and surprising consequences of the Lagrange inversion theorem. On the way, we meet unexpected logarithmic identities, hypergeometric functions with a linear regime and other mysterious…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
We provide a direct proof of a result regarding the asymptotic behavior of alternating nearest point projections onto two closed and convex sets in a Hilbert space. Our arguments are based on nonexpansive mapping theory.
Revised version, a few typing errors that might cause confusion of physics argument in the article have been corrected.