Related papers: Adjusting Dynamics of Hopfield Neural Network via …

In this paper, we explore the dynamics of structured complex-valued Hopfield neural networks (CvHNNs), which arise when the synaptic weight matrix possesses specific structural properties. We begin by analyzing CvHNNs with a Hermitian…

We associate learning and adaptation in living systems with the shaping of the velocity vector field in the respective dynamical systems in response to external, generally random, stimuli. With this, a mathematical concept of self-shaping…

Spiking Neural Networks (SNNs) offer biologically inspired, energy-efficient alternatives to traditional Deep Neural Networks (DNNs) for real-time control systems. However, their training presents several challenges, particularly for…

Memory-augmented spiking neural networks (SNNs) promise energy-efficient neuromorphic computing, yet their generalization across sensory modalities remains unexplored. We present the first comprehensive cross-modal ablation study of memory…

We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…

Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that updating all weights is…

Multivariate geo-sensory time series prediction is challenging because of the complex spatial and temporal correlation. In urban water distribution systems (WDS), numerous spatial-correlated sensors have been deployed to continuously…

Neural population activity in cortical and hippocampal circuits can be flexibly reorganized by context, suggesting that cognition relies on dynamic manifolds rather than static representations. However, how such dynamic organization can be…

The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…

This paper investigates the controllability of a broad class of recurrent neural networks widely used in theoretical neuroscience, including models of large-scale human brain dynamics. Motivated by emerging applications in non-invasive…

Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…

This paper proposes two projector-based Hopfield neural network (HNN) estimators for online, constrained parameter estimation under time-varying data, additive disturbances, and slowly drifting physical parameters. The first is a…

Network architectures and learning principles are key in forming complex functions in artificial neural networks (ANNs) and spiking neural networks (SNNs). SNNs are considered the new-generation artificial networks by incorporating more…

Spiking Neural Networks (SNNs), models inspired by neural mechanisms in the brain, allow for energy-efficient implementation on neuromorphic hardware. However, SNNs trained with current direct training approaches are constrained to a…

While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…

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…

Spiking neural networks (SNNs) promise low-power event-driven computation for temporally rich tasks, but commonly used neuron models often trade off gradient-based trainability, dynamical richness, and high activity sparsity. These…

Neuronal excitability is known to be affected by transcranial electrical stimulation. However, due to the existence of both excitatory and inhibitory neurons in the cortex, the mechanism of neuronal excitability shift is still not clear.…

Flexible cognition demands discovering hidden rules to quickly adapt stimulus-response mappings. Standard neural networks struggle in such tasks requiring rapid, context-driven remapping. Recently, Hummos (2023) introduced a fast-and-slow…

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…