Related papers: Pattern-recalling processes in quantum Hopfield ne…
Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory…
Fully connected Blume-Emery-Griffiths neural networks performing pattern recognition and associative memory have been heuristically studied in the past (mainly via the replica trick and under the replica symmetric assumption) as…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
Associative memory models retrieve stored information through content-based addressing, mimicking the neural processes of animal brains. The classical Hopfield network-based models store memories as vectors of discrete values and have good…
We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of…
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…
A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…
We present a computational model based on the CRISP theory (Content Representation, Intrinsic Sequences, and Pattern completion) of the hippocampus that allows to continuously store pattern sequences online in a one-shot fashion. Rather…
Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…
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…
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…
Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the…
The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances raises the question how these models relate to each other. In particular it is hard to distinguish between…
Quantum computing, with its ability to do exponentially faster computation compared to classical systems, has found novel applications in various fields such as machine learning and recommendation systems. Quantum Machine Learning (QML),…
Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…
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…
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…
Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…
We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…
The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We…