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Statistical Mechanics of Unsupervised Hebbian Learning
| Content Provider | Semantic Scholar |
|---|---|
| Author | Department, Jonathan L. Shapiro |
| Copyright Year | 1995 |
| Abstract | A model describing the dynamics of the synaptic weights of a single neuron performing Hebbian learning is described. The neuron is repeatedly excited by a set of input patterns. Its response is modeled as a continuous, nonlinear function of its excitation. We study how the model forms a self-organized representation of the set of input patterns. The dynamical equations are solved directly in a few simple cases. The model is studied for random patterns by a signal to noise analysis, and by introducing a partition function and applying the replica approach. As the number of patterns is increased a rst order phase transitions occurs where the neuron becomes unable to remember one pattern but rather learns to a mixture of very many patterns. The critical number of patterns for this transition scales as N b , where N is the number of synapses and b is the degree of nonlinearity. The leading order nite size corrections are calculated and compared with numerical simulations. It is shown how the representation of the input patterns learned by the neuron depends upon the nonlinearity in the neuron's response. Two types of behaviour can be identiied depending on the degree of nonlinearity: either the neuron learns to discriminate one pattern from all the others, or it will learn to a complex mixture of many of the patterns. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://ecs.soton.ac.uk/~apb/ps/unsuper.ps.Z |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Computer simulation Dynamical system Excitation Hebbian theory Neuron Nonlinear system Numerical analysis Partition function (mathematics) Phase Transition Respiratory Mechanics Self-organization Synapses Synaptic Package Manager Synaptic weight |
| Content Type | Text |
| Resource Type | Article |
