Related papers: Nested Canalyzing, unate cascade, and polynomial f…

We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

The study of monotone Boolean functions (MBFs) has a long history. We explore a connection between MBFs and ordinary differential equation (ODE) models of gene regulation, and, in particular, a problem of the realization of an MBF as a…

Graph Neural Networks (GNNs) are a framework for graph representation learning, where a model learns to generate low dimensional node embeddings that encapsulate structural and feature-related information. GNNs are usually trained in an…

We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…

Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…

Boolean functions and binary arithmetic operations are central to standard computing paradigms. Accordingly, many advances in computing have focused upon how to make these operations more efficient as well as exploring what they can…

Neural networks have been proposed as efficient numerical wavefunction ansatze which can be used to variationally search a wide range of functional forms for ground state solutions. These neural network methods are also advantageous in that…

Boolean equivalence allows Boolean networks with identical functionality to exhibit diverse graph structures. This gives more room for exploration in logic optimization, while also posing a challenge for tasks involving consistency between…

We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…

Motivation: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into…

We focus on a convolutional neural network (CNN), which has recently been utilized for fluid flow analyses, from the perspective on the influence of various operations inside it by considering some canonical regression problems with fluid…

Negabent Boolean functions are defined by having a flat magnitude spectrum under the nega-Hadamard transform. They exist in both even and odd dimensions, and the subclass of functions that are simultaneously bent and negabent…

Four terminal switching network is an alternative structure to realize the logic functions in electronic circuit modeling. This network can be used to implement a Boolean function with less number of switches than the two terminal based…

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do…

Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component…

Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline…

Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…