Related papers: Invariant Subspace Approach to Boolean (Control) N…
Humans routinely confront the following key question which could be viewed as a probabilistic variant of the controllability problem: While faced with an uncertain environment governed by causal structures, how should they practice their…
Nanoparticles interconnected by insulating organic molecules exhibit nonlinear switching behavior at low temperatures. By assembling these switches into a network and manipulating charge transport dynamics through surrounding electrodes,…
The application of Bayesian networks (BNs) to cognitive assessment and intelligent tutoring systems poses new challenges for model construction. When cognitive task analyses suggest constructing a BN with several latent variables, empirical…
Compact neural networks are essential for affordable and power efficient deep learning solutions. Binary Neural Networks (BNNs) take compactification to the extreme by constraining both weights and activations to two levels, $\{+1, -1\}$.…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
The notion of Boolean logic backpropagation was introduced to build neural networks with weights and activations being Boolean numbers. Most of computations can be done with Boolean logic instead of real arithmetic, both during training and…
The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated…
Computational properties of networks that can undergo cascades are examined. It is shown that universal Boolean logic circuits can be computed by a global cascade having antagonistic interactions. Determinism and cascade frequency of this…
In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and…
Random Boolean networks (RBNs) have been a popular model of genetic regulatory networks for more than four decades. However, most RBN studies have been made with random topologies, while real regulatory networks have been found to be…
Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior…
One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is…
A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often…
Network Calculus is a theoretical model that aims at providing upper bounds of worst-case performance (such as delay or buffer occupancy). This is a mathematical framework that handles both network modeling and network analysis. As such it…
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…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…
The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or…
Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…