Related papers: Perturbed affine arithmetic for invariant computat…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the properties of the inverse of the related pentadiagonal matrices, associated with the fourth-order nonlinear beam equation. This nonlinear problem is…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

Convolutional Neural Networks (CNNs) define an exceptionally powerful class of models for image classification, but the theoretical background and the understanding of how invariances to certain transformations are learned is limited. In a…

We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…

Program behavior may depend on parameters, which are either configured before compilation time, or provided at run-time, e.g., by sensors or other input devices. Parametric program analysis explores how different parameter settings may…

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

In this paper, we consider the computation of controlled invariant sets (CIS) of discrete-time nonlinear control affine systems. We propose an iterative refinement procedure based on polytopic inclusion functions, which is able to…

We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…

We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…

An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…

Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…

Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…

There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…