Related papers: Graph Hopfield Networks: Energy-Based Node Classif…
Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…
The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent…
Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily…
We introduce a three-dimensional vectorial extension of the Hopfield associative-memory model in which each neuron is a unit vector on $S^2$ and synaptic couplings are $3\times 3$ blocks generated through a vectorial Hebbian rule. The…
Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…
Assessing homophily in large-scale networks is central to understanding structural regularities in graphs, and thus inform the choice of models (such as graph neural networks) adopted to learn from network data. Evaluation of smoothness…
In this paper, a novel 3D deep learning network is proposed for brain MR image segmentation with randomized connection, which can decrease the dependency between layers and increase the network capacity. The convolutional LSTM and 3D…
Graph neural networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs, as a result of their ability to exploit node features and topological information simultaneously. However, most GNNs…
Semi-supervised learning has received a lot of recent attention as it alleviates the need for large amounts of labelled data which can often be expensive, requires expert knowledge and be time consuming to collect. Recent developments in…
Graph Neural Networks (GNNs) have demonstrated significant success in learning from graph-structured data but often struggle on heterophilous graphs, where connected nodes differ in features or class labels. This limitation arises from…
We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to…
Equilibrium Propagation (EP) is a powerful and more bio-plausible alternative to conventional learning frameworks such as backpropagation. The effectiveness of EP stems from the fact that it relies only on local computations and requires…
This paper designs and implements an explainable recommendation model that integrates knowledge graphs with structure-aware attention mechanisms. The model is built on graph neural networks and incorporates a multi-hop neighbor aggregation…
We study a fully connected Hopfield-type associative memory network with online activity-dependent synaptic plasticity, where neural states and synaptic couplings coevolve during retrieval. Using the generating-functional formalism, we…
The study of brain states, ranging from highly synchronous to asynchronous neuronal patterns like the sleep-wake cycle, is fundamental for assessing the brain's spatiotemporal dynamics and their close connection to behavior. However, the…
The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…