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Recurrent Neural Cascades (RNCs) are the recurrent neural networks with no cyclic dependencies among recurrent neurons. This class of recurrent networks has received a lot of attention in practice. Besides training methods for a fixed…

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…

This paper presents a new family of backpropagation-free neural architectures, Gated Linear Networks (GLNs). What distinguishes GLNs from contemporary neural networks is the distributed and local nature of their credit assignment mechanism;…

For most deep learning practitioners, sequence modeling is synonymous with recurrent networks. Yet recent results indicate that convolutional architectures can outperform recurrent networks on tasks such as audio synthesis and machine…

Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small…

In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may…

Graph processes model a number of important problems such as identifying the epicenter of an earthquake or predicting weather. In this paper, we propose a Graph Convolutional Recurrent Neural Network (GCRNN) architecture specifically…

Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…

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…

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse…

Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called…

We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which…

Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}.…

Central Pattern Generators (CPGs) are biological neural circuits capable of producing coordinated rhythmic outputs in the absence of rhythmic input. As a result, they are responsible for most rhythmic motion in living organisms. This…

The cell cycle is a tightly controlled process, yet its underlying genetic network shows marked differences across species. Which of the associated structural features follow solely from the ability to impose the appropriate gene expression…

Models of simple excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This subject is a topic of practical relevance to diverse fields, ranging from neuroscience to…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…

Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…