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Probabilistic programs are key to deal with uncertainty in e.g. controller synthesis. They are typically small but intricate. Their development is complex and error prone requiring quantitative reasoning over a myriad of alternative…

Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…

Learning invariant representations is a critical first step in a number of machine learning tasks. A common approach corresponds to the so-called information bottleneck principle in which an application dependent function of mutual…

This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of…

Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…

In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…

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…

We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…

Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more {system} parameters are not normal, uniform, or closely related…

One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected…

We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…

In experimental control of quantum systems, the precision is often hindered by imperfect applied electronics that distort control pulses delivered to target quantum devices. To mitigate such error, the deconvolution method is commonly used…

Counterfactual explanations represent the minimal change to a data sample that alters its predicted classification, typically from an unfavorable initial class to a desired target class. Counterfactuals help answer questions such as "what…

This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $H\simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of…

We introduce a new method for diverse foreground generation with explicit control over various factors. Existing image inpainting based foreground generation methods often struggle to generate diverse results and rarely allow users to…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers. Building on the recent work of Garg and Schost, we improve on the…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…