Related papers: From Dyson to Hopfield: Processing on hierarchical…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…
It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a…
In many complex systems, elementary units live in a chaotic environment and need to adapt their strategies to perform a task, by extracting information from the environment and controlling the feedback loop on it. One of the main example of…
Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences…
Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity…
Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear…
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…
The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…
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…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…
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…
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…