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Different fields in applied machine learning such as computer vision, speech or natural language processing have been building domain-specialised solutions. Currently, we are witnessing an opposing trend towards developing more generalist…
In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems,…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We introduce a unified method for constructing the basis functions of a wide variety of partially continuous tensor-valued finite elements on simplices using polytopal templates. These finite element spaces are essential for achieving…
In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for…
Machine learning models that are developed with invariance to certain types of data transformations have demonstrated superior generalization performance in practice. However, the underlying mechanism that explains why invariance leads to…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…
Consider the problem of imputing missing values in a dataset. One the one hand, conventional approaches using iterative imputation benefit from the simplicity and customizability of learning conditional distributions directly, but suffer…
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
We describe the LoopInvGen tool for generating loop invariants that can provably guarantee correctness of a program with respect to a given specification. LoopInvGen is an efficient implementation of the inference technique originally…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
Formal program specifications in the form of preconditions, postconditions, and class invariants have several benefits for the construction and maintenance of programs. They not only aid in program understanding due to their unambiguous…
This paper is a tutorial in a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group. The procedure is based on basic notions of representation theory of finite groups. As…
Verification of programs operating on heap-allocated data structures, for instance lists or trees, poses significant challenges due to the potentially unbounded size of such data structures. We present time-indexed heap invariants, a novel…
We consider the problem of type-directed component based synthesis where, given a set of (typed) components and a query type, the goal is to synthesize a term that inhabits the query. Classical approaches based on proof search in…
In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain…