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We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points…
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…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…
The concept of space-bounded computability has become significantly important in handling vast data sets on memory-limited computing devices. To replenish the existing short list of NL-complete problems whose instance sizes are dictated by…
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the…
The study of control mechanisms of biological systems allows for interesting applications in bioengineering and medicine, for instance in cell reprogramming or drug target identification. A control strategy often consists of a set of…
Probabilistic Boolean networks (PBNs) is an important mathematical framework widely used for modelling and analysing biological systems. PBNs are suited for modelling large biological systems, which more and more often arise in systems…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
This paper addresses the $\epsilon$-close parameter tuning problem for Bayesian Networks (BNs): find a minimal $\epsilon$-close amendment of probability entries in a given set of (rows in) conditional probability tables that make a given…
This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification…
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…
The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…
Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…
Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…
Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…
Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be…
Prob-solvable loops are probabilistic programs with polynomial assignments over random variables and parametrised distributions, for which the full automation of moment-based invariant generation is decidable. In this paper we extend…
Universal approximation theorems show that neural networks can approximate any continuous function; however, the number of parameters may grow exponentially with the ambient dimension, so these results do not fully explain the practical…
Emergence of robustness in biological networks is a paramount feature of evolving organisms, but a study of this property in vivo, for any level of representation such as Genetic, Metabolic, or Neuronal Networks, is a very hard challenge.…