Related papers: Algorithmic Boundedness-From-Below Conditions for …
We consider the problem of estimating a probability of failure $\alpha$, defined as the volume of the excursion set of a function $f:\mathbb{X} \subseteq \mathbb{R}^{d} \to \mathbb{R}$ above a given threshold, under a given probability…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
In this paper we provide in $\bFp$ expanding lower bounds for two variables functions $f(x,y)$ in connection with the product set or the sumset. The sum-product problem has been hugely studied in the recent past. A typical result in…
Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…
Let F:=(f_1,...,f_n) be a random polynomial system with fixed n-tuple of supports. Our main result is an upper bound on the probability that the condition number of f in a region U is larger than 1/epsilon. The bound depends on an integral…
It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Many studies have observed that modern neural networks achieve high accuracy while producing poorly calibrated probabilities, making calibration a critical practical issue. In this work, we propose probability bounding (PB), a novel…
In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
The explorations of models beyond the Standard Model (BSM) naturally involve scans over the unknown BSM parameters. On the other hand, high precision predictions require calculations at the loop-level and thus a renormalization of (some of)…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
Searching for an intermediate-range force has been considerable interests in gravity experiments. In this paper, aiming at a scalar-tensor theory with an intermediate-range force, we have derived the metric and equations of motion (EOMs) in…
Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…
In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms…