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High-capacity associative memories based on Kernel Logistic Regression (KLR) achieve strong retrieval performance but typically require substantial computational resources. This paper investigates the compressibility of KLR Hopfield…
A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…
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…
Krotov and Hopfield (2021) proposed a biologically plausible two-layer associative memory network with memory storage capacity exponential in the number of visible neurons. However, the capacity was only linear in the number of hidden…
We introduce Graph Hopfield Networks, whose energy function couples associative memory retrieval with graph Laplacian smoothing for node classification. Gradient descent on this joint energy yields an iterative update interleaving Hopfield…
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…
Associative memory retrieves complete patterns from partial or corrupted inputs and constitutes a primitive form of generative inference. Classical Hopfield networks (CHN) provide a canonical framework for associative memory but suffer from…
The retrieval capabilities of associative neural networks can be impaired by different kinds of noise: the fast noise (which makes neurons more prone to failure), the slow noise (stemming from interference among stored memories), and…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…
Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where…
Memory systems can store vastly different amounts of information despite similar hardware constraints. Here, we show that superior spatial memory emerges from a discrete stiffening of hippocampal population geometry-a transition from…
Dense Hopfield networks are known for their feature to prototype transition and adversarial robustness. However, previous theoretical studies have been mostly concerned with their storage capacity. We bridge this gap by studying the phase…
In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…
Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…
Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…