Related papers: Criticality of a stochastic modern Hopfield networ…
Spiking Neural Networks (SNNs) provide biological plausibility and energy efficiency, yet systematic investigations of memory augmentation strategies remain limited. We conduct a five-model ablation study integrating Leaky…
We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…
Deep learning models are often trained to approximate dynamical systems that can be modeled using differential equations. Many of these models are optimized to predict one step ahead; such approaches produce calibrated one-step predictions…
We present the Multidimensional Hopfield Network (DHN), a natural generalisation of the Hopfield Network. In our theoretical investigations we focus on DHNs with a certain activation function and provide energy functions for them. We…
Current deep neural networks (DNNs) used in materials modeling often lack explicit physical structure and clear analytical formulations tailored to material systems, which can limit their interpretability. In this work, we integrate…
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule…
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…
The Hopfield network model and its generalizations were introduced as a model of associative, or content-addressable, memory. They were widely investigated both as an unsupervised learning method in artificial intelligence and as a model of…
Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…
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…
The refractory period controls neuron spike firing rate, crucial for network stability and noise resistance. With advancements in spiking neural network (SNN) training methods, low-latency SNN applications have expanded. In low-latency…
We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…
A Hopfield network is an auto-associative, distributive model of neural memory storage and retrieval. A form of error-correcting code, the Hopfield network can learn a set of patterns as stable points of the network dynamic, and retrieve…
We study emerging phenomena in binary neural networks where, with a probability c synaptic intensities are chosen according with a Hebbian prescription, and with probability (1-c) there is an extra random contribution to synaptic weights.…
In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the…
Hopfield networks using Hebbian learning suffer from limited storage capacity. While supervised methods like Linear Logistic Regression (LLR) offer some improvement, kernel methods like Kernel Logistic Regression (KLR) significantly enhance…
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…
We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the…
Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic…
Neural networks are widely used, yet their analysis and verification remain challenging. In this work, we present a Lean 4 formalization of neural networks, covering both deterministic and stochastic models. We first formalize Hopfield…