Learning of correlated patterns in spin-glass networks by local learning rules

1987 ◽  
Vol 58 (9) ◽  
pp. 949-952 ◽  
Author(s):  
Sigurd Diederich ◽  
Manfred Opper
1992 ◽  
Vol 4 (5) ◽  
pp. 703-711 ◽  
Author(s):  
Günther Palm

A simple relation between the storage capacity A for autoassociation and H for heteroassociation with a local learning rule is demonstrated: H = 2A. Both values are bounded by local learning bounds: A ≤ LA and H ≤ LH. LH = 2LA is evaluated numerically.


2018 ◽  
Vol 30 (1) ◽  
pp. 84-124 ◽  
Author(s):  
Cengiz Pehlevan ◽  
Anirvan M. Sengupta ◽  
Dmitri B. Chklovskii

Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet derivations of single-layer networks with such local learning rules from principled optimization objectives became possible only recently, with the introduction of similarity matching objectives. What explains the success of similarity matching objectives in deriving neural networks with local learning rules? Here, using dimensionality reduction as an example, we introduce several variable substitutions that illuminate the success of similarity matching. We show that the full network objective may be optimized separately for each synapse using local learning rules in both the offline and online settings. We formalize the long-standing intuition of the rivalry between Hebbian and anti-Hebbian rules by formulating a min-max optimization problem. We introduce a novel dimensionality reduction objective using fractional matrix exponents. To illustrate the generality of our approach, we apply it to a novel formulation of dimensionality reduction combined with whitening. We confirm numerically that the networks with learning rules derived from principled objectives perform better than those with heuristic learning rules.


1995 ◽  
Vol 52 (3) ◽  
pp. 2860-2871 ◽  
Author(s):  
Michael Haft ◽  
Martin Schlang ◽  
Gustavo Deco

1992 ◽  
Vol 4 (5) ◽  
pp. 666-681 ◽  
Author(s):  
Peter König ◽  
Bernd Janosch ◽  
Thomas B. Schillen

A temporal structure of neuronal activity has been suggested as a potential mechanism for defining cell assemblies in the brain. This concept has recently gained support by the observation of stimulus-dependent oscillatory activity in the visual cortex of the cat. Furthermore, experimental evidence has been found showing the formation and segregation of synchronously oscillating cell assemblies in response to various stimulus conditions. In previous work, we have demonstrated that a network of neuronal oscillators coupled by synchronizing and desynchronizing delay connections can exhibit a temporal structure of responses, which closely resembles experimental observations. In this paper, we investigate the self-organization of synchronizing and desynchronizing coupling connections by local learning rules. Based on recent experimental observations, we modify synchronizing connections according to a two-threshold learning rule, involving synaptic potentiation and depression. This rule is generalized to its functional inverse for weight changes of desynchronizing connections. We show that after training, the resulting network exhibits stimulus-dependent formation and segregation of oscillatory assemblies in agreement with the experimental data. These results indicate that local learning rules during ontogenesis can suffice to develop a connectivity pattern in support of the observed temporal structure of stimulus responses in cat visual cortex.


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