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Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…
In this work we present a novel recurrent neural network architecture designed to model systems characterized by multiple characteristic timescales in their dynamics. The proposed network is composed by several recurrent groups of neurons…
Low-rank recurrent neural networks (lrRNNs) are a class of models that uncover low-dimensional latent dynamics underlying neural population activity. Although their functional connectivity is low-rank, it lacks disentanglement…
This paper extends the fully recursive perceptron network (FRPN) model for vectorial inputs to include deep convolutional neural networks (CNNs) which can accept multi-dimensional inputs. A FRPN consists of a recursive layer, which, given a…
We present a unified framework for the renormalisation of the Hamiltonian and eigenbasis of a system of correlated electrons, unveiling thereby the interplay between electronic correlations and many-particle entanglement. For this, we…
Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the…
Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response…
The hippocampus has the capacity for reactivating recently acquired memories [1-3] and it is hypothesized that one of the functions of sleep reactivation is the facilitation of consolidation of novel memory traces [4-11]. The dynamic and…
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…
Transformers have surpassed RNNs in popularity due to their superior abilities in parallel training and long-term dependency modeling. Recently, there has been a renewed interest in using linear RNNs for efficient sequence modeling. These…
A new computational model is presented suitable for exploring the self-consistent production of energetic electrons during magnetic reconnection in macroscale systems. The equations are based on the recent discovery that parallel electric…
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and…
In order to make data-driven models of physical systems interpretable and reliable, it is essential to include prior physical knowledge in the modeling framework. Hamiltonian Neural Networks (HNNs) implement Hamiltonian theory in deep…
Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the…
Understanding how neuronal networks reorganize in response to external stimuli and give rise to behavior is a central challenge in neuroscience and artificial intelligence. However, existing methods often fail to capture the evolving…
Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…
The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF).…
As a surrogate for computationally intensive meso-scale simulation of woven composites, this article presents Recurrent Neural Network (RNN) models. Leveraging the power of transfer learning, the initialization challenges and sparse data…
Existing FNNs are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep FNN, namely DEVFNN. Fuzzy rules can be automatically…
Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations…