Related papers: Reduction systems and degree bounds for integratio…

A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…

Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…

Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be…

We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…

Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value…

Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…

We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…

It is often useful to perform integration over learned functions represented by neural networks. However, this integration is usually performed numerically, as analytical integration over learned functions (especially neural networks) is…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…

Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has…

This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…

A construction of integrable hamiltonian systems associated with different graded realizations of untwisted loop algebras is proposed. Such systems have the form of Euler - Arnold equations on orbits of loop algebras. The proof of…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…

Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms offer inexpensive iterations by sampling a subset of…