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In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a…

Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is of paramount importance but still challenging. Considering that these interactions may…

Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…

Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…

We study the synchronous dynamics of the Hopfield model when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. We use a generating functional technique to derive analytical expressions for the order parameters…

Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies…

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…

Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to…

Transformer-based Language Models have become ubiquitous in Natural Language Processing (NLP) due to their impressive performance on various tasks. However, expensive training as well as inference remains a significant impediment to their…