相关论文: Dynamical mean field approach to associative memor…
Hopfield networks are a variant of associative memory that recall information stored in the couplings of an Ising model. Stored memories are fixed points for the network dynamics that correspond to energetic minima of the spin state. We…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners…
Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In…
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with…
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…
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…
Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that…
Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…
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…
We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical…
Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine…
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…
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…
For the Hopfield model with the Hebb connection matrix we investigate the case of $p$ memorized patterns that are distorted copies of the same {\it standard}. In other words, we try to simulate that learning always takes place by means of…
We investigate a recurrent neural network model with common external and bias inputs that can retrieve branching sequences. Retrieval of memory sequences is one of the most important functions of the brain. A lot of research has been done…
We discuss a non-equilibrium dynamical mean-field framework for simulating inhomogeneous Hubbard models with local disorders. Our approach treats electron interactions and disorders on equal footing, by considering only local dynamical…