Related papers: Asymptotically Stable Quaternion-valued Hopfield-s…

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…

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…

Neural networks that can capture key principles underlying brain computation offer exciting new opportunities for developing artificial intelligence and brain-like computing algorithms. Such networks remain biologically plausible while…

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…

Previous work on predicting or generating 3D human pose sequences regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler…

We propose a custom learning algorithm for shallow over-parameterized neural networks, i.e., networks with single hidden layer having infinite width. The infinite width of the hidden layer serves as an abstraction for the…

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel…

Equivariant quantum neural networks (QNNs) are promising variational models that exploit symmetries to improve machine learning capabilities. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum…

The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…

Hypercomplex neural networks are gaining increasing interest in the deep learning community. The attention directed towards hypercomplex models originates from several aspects, spanning from purely theoretical and mathematical…

Physical neural networks using physical materials and devices to mimic synapses and neurons offer an energy-efficient way to implement artificial neural networks. Yet, training physical neural networks are difficult and heavily relies on…

Graph Convolution Network (GCN) has been widely applied in recommender systems for its representation learning capability on user and item embeddings. However, GCN is vulnerable to noisy and incomplete graphs, which are common in real…

Many real-world interactions are group-based rather than pairwise such as papers with multiple co-authors and users jointly engaging with items. Hypergraph neural networks have shown great promise at modeling higher-order relations, but…

In neural network's Literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i.e., definite patterns that are experienced just once to form the synaptic…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…

Spiking Neural Networks are often touted as brain-inspired learning models for the third wave of Artificial Intelligence. Although recent SNNs trained with supervised backpropagation show classification accuracy comparable to deep networks,…

This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…