Abstract
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 O(N), where N is the system size. Beyond the threshold, they are completely lost. Since the introduction of the Hopfield model, the theory of neural networks has been further developed toward realistic neural networks using analog neurons, spiking neurons, etc. Nevertheless, those advances are based on fully connected networks, which are inconsistent with recent experimental discovery that the number of connections of each neuron seems to be heterogeneous, following a heavy-tailed distribution. Motivated by this observation, we consider the Hopfield model on scale-free networks and obtain a different pattern of associative memory retrieval from that obtained on the fully connected network: the storage capacity becomes tremendously enhanced but with some error in the memory retrieval, which appears as the heterogeneity of the connections is increased. Moreover, the error rates are also obtained on several real neural networks and are indeed similar to that on scale-free model networks.
Highlights
Human neuroscience has attracted increasing attention through various studies
Neural network models of associative memory have been used to explain how the brain stores and recalls long-term memories. These models incorporate the so-called Hebbian rule for a cell assembly, a group of excitatory neurons mutually coupled by strong synapses [3]: Memory storage occurs when a cell assembly is created by Hebbian synaptic plasticity, and memory retrieval or recall occurs when the neurons in the cell assembly are activated by a stimulus
We obtained the results that as the network changes from a hub-absent network to a SF network with degree exponent just above two, the storage capacity becomes tremendously enhanced, but some error occurs
Summary
Human neuroscience has attracted increasing attention through various studies Among such activities, the retrieval or recall of associative memory in neural networks is a historically noticeable issue [1, 2]. Neural network models of associative memory have been used to explain how the brain stores and recalls long-term memories. These models incorporate the so-called Hebbian rule for a cell assembly, a group of excitatory neurons mutually coupled by strong synapses [3]: Memory storage occurs when a cell assembly is created by Hebbian synaptic plasticity, and memory retrieval or recall occurs when the neurons in the cell assembly are activated by a stimulus. Neural network models of associative memory assume that information exists alternatively as neural activity or as synaptic
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