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Attractor neural networks (ANNs) are one of the leading theoretical frameworks for the formation and retrieval of memories in networks of biological neurons. In this framework, a pattern imposed by external inputs to the network is said to…

Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…

The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfy constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining…

We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths…

We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…

Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based models have been successfully implemented as…

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…

We study the associative-memory network of Kuramoto-type oscillators that stores a set of memorized patterns (memories). In [Phys. Rev. Lett., 92 (2004), 108101], Nishikawa, Lai and Hoppensteadt showed that the capacity of this system for…

Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical…

Neural encoding of objects and cognitive states remains an elusive yet crucial aspect of brain function. While traditional feed-forward machine learning neural networks have enormous potential to encode information, modern architectures…

Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…

Operation of the array of coupled oscillators underlying the associative memory function is demonstrated for various interconnection schemes (cross-connect, star phase keying and star frequency keying) and various physical implementation of…

We consider the class of Hopfield models of associative memory with activation function $F$ and state space $\{-1,1\}^N$, where each vertex of the cube describes a configuration of $N$ binary neurons. $M$ randomly chosen configurations,…

Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…

Identifying computational mechanisms for memorization and retrieval of data is a long-standing problem at the intersection of machine learning and neuroscience. Our main finding is that standard overparameterized deep neural networks…

The associative memory model is a typical neural network model, which can store discretely distributed fixed-point attractors as memory patterns. When the network stores the memory patterns extensively, however, the model has other…

We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…

In the context of attractor neural networks, we study how the equilibrium analog neural activities, reached by the network dynamics during memory retrieval, may improve storage performance by reducing the interferences between the recalled…

Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…