Related papers: Reconstructing the Hopfield network as an inverse …
We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
High-capacity associative memory models, such as Kernel Logistic Regression (KLR) Hopfield networks, have demonstrated strong storage capabilities but typically rely on computationally expensive synchronous updates. This reliance poses a…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
Real-world physical signals are continuous and high-dimensional, yet the statistical-mechanics machinery of associative memory operates on discrete Ising spins. We bridge this divide through a multilayer Ising framework that couples a…
The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of…
The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…
Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for…
We study a variant of the pseudo-inverse learning rule for Hopfield-like Neural Networks, which allows the network to infer archetypal concepts on the basis of a limited number of examples. The mean-field replica theory for this model…
We propose a decentralized online learning algorithm for distributed random inverse problems over network graphs with online measurements, and unifies the distributed parameter estimation in Hilbert spaces and the least mean square problem…
The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns…
An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns…
Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…
We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly…
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others.…
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…
Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…
Reasoning is the ability to integrate internal states and external inputs in a meaningful and semantically consistent flow. Contemporary machine learning (ML) systems increasingly rely on such sequential reasoning, from language…
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
The zero-temperature Glauber dynamics of the ferromagnetic Ising model on small-world networks, rewired from a two-dimensional square lattice, has been studied by numerical simulations. For increasing disorder in finite networks, the…