A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks.

Alemi, Alireza

Baldassi, Carlo

Brunel, Nicolas

Zecchina, Riccardo

Latham, Peter E

United States

2017-08-01T13:17:36Z

2017-08-01T13:17:36Z

2015-08

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network scenario, whose prototype is the Hopfield model. The model simplicity and the locality of the synaptic update rules come at the cost of a poor storage capacity, compared with the capacity achieved with perceptron learning algorithms. Here, by transforming the perceptron learning rule, we present an online learning rule for a recurrent neural network that achieves near-maximal storage capacity without an explicit supervisory error signal, relying only upon locally accessible information. The fully-connected network consists of excitatory binary neurons with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the memory patterns to be memorized are presented online as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs. Synapses corresponding to active inputs are modified as a function of the value of the local fields with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. We simulated and analyzed a network of binary neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction. The storage capacity obtained through numerical simulations is shown to be close to the value predicted by analytical calculations. We also measured the dependence of capacity on the strength of external inputs. Finally, we quantified the statistics of the resulting synaptic connectivity matrix, and found that both the fraction of zero weight synapses and the degree of symmetry of the weight matrix increase with the number of stored patterns.

https://www.ncbi.nlm.nih.gov/pubmed/26291608

PCOMPBIOL-D-15-00533

1553-7358

https://hdl.handle.net/10161/15109

eng

Public Library of Science (PLoS)

PLoS Comput Biol

10.1371/journal.pcbi.1004439

Algorithms

Computational Biology

Computer Simulation

Memory

Models, Neurological

Nerve Net

Neural Networks (Computer)

Neurons

A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks.

Journal article

Brunel, Nicolas|0000-0002-2272-3248

https://www.ncbi.nlm.nih.gov/pubmed/26291608

e1004439

8

Basic Science Departments

Duke

Neurobiology

Physics

School of Medicine

Trinity College of Arts & Sciences

Published online

11