Related papers: On abstract normalisation beyond neededness
In this work, we develop an alternating nonlinear Generalized Minimum Residual (NGMRES) algorithm with depth $m$ and periodicity $p$, denoted by aNGMRES($m, p$), applied to linear systems. We provide a theoretical analysis to quantify by…
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure…
In many applications, it is necessary to retrieve pairs of vertices with the path between them satisfying certain constraints, since regular expression is a powerful tool to describe patterns of a sequence. To meet such requirements, in…
Maximally parallel multiset rewriting systems (MPMRS) give a convenient way to express relations between unstructured objects. The functioning of various computational devices may be expressed in terms of MPMRS (e.g., register machines and…
Generalization is a central challenge for the deployment of reinforcement learning (RL) systems in the real world. In this paper, we show that the sequential structure of the RL problem necessitates new approaches to generalization beyond…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
For the lambda-calculus with letrec we develop an optimisation, which is based on the contraction of a certain class of 'future' (also: virtual) redexes. In the implementation of functional programming languages it is common practice to…
Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by…
We generalize the Brezzi-Rappaz-Raviart approximation theorem, which allows to obtain existence and a priori error estimates for approximations of solutions to some nonlinear partial differential equations. Our contribution lies in the fact…
Abstractive summarization has been studied using neural sequence transduction methods with datasets of large, paired document-summary examples. However, such datasets are rare and the models trained from them do not generalize to other…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the…
In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears…
Allreduce is one of the most frequently used MPI collective operations, and thus its performance attracts much attention in the past decades. Many algorithms were developed with different properties and purposes. We present a novel approach…