Related papers: High storage capacity in the Hopfield model with a…
I review and expand the model of quantum associative memory that I have recently proposed. In this model binary patterns of n bits are stored in the quantum superposition of the appropriate subset of the computational basis of n qbits.…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
This paper updates the cognitive model, firstly by creating two systems and then unifying them over the same structure. It represents information at the semantic level only, where labelled patterns are aggregated into a 'type-set-match'…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…
Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
Associative memory, traditionally modeled by Hopfield networks, enables the retrieval of previously stored patterns from partial or noisy cues. Yet, the local computational principles which are required to enable this function remain…
Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This…
The Hopfield associative memory model stores random patterns in synaptic couplings according to Hebb's rule and retrieves them through gradient descent on an energy function. This conventional setting, where neurons are assumed to have…
We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric…
We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). For strong coupling, we…
While diffusion models excel at generating high-quality images, their tendency to memorize training data poses significant privacy and copyright risks. In this work, we for the first time identify that memorization induces internal…
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…
The deployment of pre-trained perception models in novel environments often leads to performance degradation due to distributional shifts. Although recent artificial intelligence approaches for metacognition use logical rules to…
We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero-temperature…
The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according to the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…
Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small…
Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors…