Related papers: Parallel retrieval of correlated patterns
We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…
Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…
We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzman machine and we show its thermodynamical equivalence to an associative working memory able to retrieve multiple patterns in parallel without falling…
We propose a modification of the cost function of the Hopfield model whose salient features shine in its Taylor expansion and result in more than pairwise interactions with alternate signs, suggesting a unified framework for handling both…
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…
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in…
In this work we introduce and investigate the properties of the "relativistic" Hopfield model endowed with temporally correlated patterns. First, we review the "relativistic" Hopfield model and we briefly describe the experimental evidence…
We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…
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…
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…
We study the synchronous dynamics of the Hopfield model when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. We use a generating functional technique to derive analytical expressions for the order parameters…
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…
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…
High-order extensions of the Hopfield model are known to exhibit dramatically enhanced storage capacity at equilibrium, while their dynamical retrieval properties remain less well understood. In our previous work, we carried out a dynamical…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
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…
In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different…
We propose an efficient algorithm to solve inverse problems in the presence of binary clustered datasets. We consider the paradigmatic Hopfield model in a teacher student scenario, where this situation is found in the retrieval phase. This…
Associative memory has been a prominent candidate for the computation performed by the massively recurrent neocortical networks. Attractor networks implementing associative memory have offered mechanistic explanation for many cognitive…
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…