Related papers: RDNF Oriented Analytics to Random Boolean Function…

A Boolean network (BN) is a discrete dynamical system defined by a Boolean function that maps to the domain itself. A trap space of a BN is a generalization of a fixed point, which is defined as the sub-hypercubes closed by the function of…

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…

Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation…

Understanding and controlling the informational complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based…

We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…

Deep neural networks have been successfully deployed in a wide variety of applications including computer vision and speech recognition. However, computational and storage complexity of these models has forced the majority of computations…

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…

Background: The huge quantity of data produced in Biomedical research needs sophisticated algorithmic methodologies for its storage, analysis, and processing. High Performance Computing (HPC) appears as a magic bullet in this challenge.…

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…

Biclustering is a powerful approach to search for patterns in data, as it can be driven by a function that measures the quality of diverse types of patterns of interest. However, due to its computational complexity, the exploration of the…

We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN)…

We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…

Deep learning networks excel at classification, yet identifying minimal architectures that reliably solve a task remains challenging. We present a computational methodology for systematically exploring and analyzing the relationships among…

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…

Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the…

In this paper we analyse the complexity of boolean functions takes value 0 on a sufficiently small number of points. For many functions this leads to the analysis of a single function attains 0 only on unsigned representation of numbers…

In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…

Machine learning tasks are generally formulated as optimization problems, where one searches for an optimal function within a certain functional space. In practice, parameterized functional spaces are considered, in order to be able to…

We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass…