Related papers: Fixed points of competitive threshold-linear netwo…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…
Text classification is a fundamental task in natural language processing (NLP). Several recent studies show the success of deep learning on text processing. Convolutional neural network (CNN), as a popular deep learning model, has shown…
Graph neural networks (GNN) are powerful models for many graph-structured tasks. Existing models often assume that the complete structure of the graph is available during training. In practice, however, graph-structured data is usually…
Linear recurrent neural networks (RNNs) and state-space models (SSMs) such as Mamba have become promising alternatives to softmax-attention as sequence mixing layers in Transformer architectures. Current models, however, do not exhibit the…
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore,…
We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…
Graph-structured data consisting of objects (i.e., nodes) and relationships among objects (i.e., edges) are ubiquitous. Graph-level learning is a matter of studying a collection of graphs instead of a single graph. Traditional graph-level…
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 establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global…
Temporal Graph Networks (TGNs) have demonstrated significant success in dynamic graph tasks such as link prediction and node classification. Both tasks comprise transductive settings, where the model predicts links among known nodes, and in…
Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision…
Relational learning deals with data that are characterized by relational structures. An important task is collective classification, which is to jointly classify networked objects. While it holds a great promise to produce a better accuracy…
Exploring the application of large language models (LLMs) to graph learning is a emerging endeavor. However, the vast amount of information inherent in large graphs poses significant challenges to this process. This work focuses on the link…
A dynamic graph (DG) is frequently encountered in numerous real-world scenarios. Consequently, A dynamic graph convolutional network (DGCN) has been successfully applied to perform precise representation learning on a DG. However,…
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}.…
The mining and exploitation of graph structural information have been the focal points in the study of complex networks. Traditional structural measures in Network Science focus on the analysis and modelling of complex networks from the…