Related papers: Reconstructing the Hopfield network as an inverse …
Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…
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…
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
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…
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…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…
Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the…
While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student…
We investigate a recently proposed model for cortical computation which performs relational inference. It consists of several interconnected, structurally equivalent populations of leaky integrate-and-fire (LIF) neurons, which are trained…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…
In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and…
The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…
Associative memory architectures such as the Hopfield network have long been important conceptual and theoretical models for neuroscience and artificial intelligence. However, translating these abstract models into spiking neural networks…
Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We…
Simulations of complex-valued Hopfield networks based on spin-torque oscillators can recover phase-encoded images. Sequences of memristor-augmented inverters provide tunable delay elements that implement complex weights by phase shifting…
A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
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…