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Enhanced storage capacity with errors in scale-free Hopfield neural networks: An analytical study.

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.

SUBMITTER: Kim DH

PROVIDER: S-EPMC5659639 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Enhanced storage capacity with errors in scale-free Hopfield neural networks: An analytical study.

Kim Do-Hyun DH Park Jinha J Kahng Byungnam B

PloS one 20171027 10

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, et ...[more]

PMID: 29077721

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Project description:BackgroundMany complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks.ResultsThis article addresses the impact of erroneous links on network topological inference and explores possible error mechanisms for scale-free networks with an emphasis on Saccharomyces cerevisiae protein interaction networks. We study this issue by both theoretical derivations and simulations. We show that the ignorance of erroneous links in network analysis may lead to biased estimates of the scale parameter and recommend robust estimators in such scenarios. Possible error mechanisms of yeast protein interaction networks are explored by comparisons between real data and simulated data.ConclusionOur studies show that, in the presence of erroneous links, the connectivity distribution of scale-free networks is still scale-free for the middle range connectivities, but can be greatly distorted for low and high connecitivities. It is more appropriate to use robust estimators such as the least trimmed mean squares estimator to estimate the scale parameter gamma under such circumstances. Moreover, we show by simulation studies that the scale-free property is robust to some error mechanisms but untenable to others. The simulation results also suggest that different error mechanisms may be operating in the yeast protein interaction networks produced from different data sources. In the MIPS gold standard protein interaction data, there appears to be a high rate of false negative links, and the false negative and false positive rates are more or less constant across proteins with different connectivities. However, the error mechanism of yeast two-hybrid data may be very different, where the overall false negative rate is low and the false negative rates tend to be higher for links involving proteins with more interacting partners.

Dataset Information

Enhanced storage capacity with errors in scale-free Hopfield neural networks: An analytical study.

Publications

Enhanced storage capacity with errors in scale-free Hopfield neural networks: An analytical study.

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