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Self-Organization of Symmetry Networks: Transformation Invariance from the Spontaneous Symmetry-Breaking Mechanism

Defence Evaluation and Research Agency, Malvern WR14 3PS, U.K.

Symmetry networks use permutation symmetries among synaptic weights to achieve transformation-invariant response. This article proposes a generic mechanism by which such symmetries can develop during unsupervised adaptation: it is shown analytically that spontaneous symmetry breaking can result in the discovery of unknown invariances of the data's probability distribution. It is proposed that a role of sparse coding is to facilitate the discovery of statistical invariances by this mechanism. It is demonstrated that the statistical dependences that exist between simple-cell-like threshold feature detectors, when exposed to temporally uncorrelated natural image data, can drive the development of complex-cell-like invariances, via single-cell Hebbian adaptation. A single learning rule can generate both simple-cell-like and complex-cell-like receptive fields.

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				C. J. S. Webber Predictions of the Spontaneous Symmetry-Breaking Theory for Visual Code Completeness and Spatial Scaling in Single-Cell Learning Rules Neural Comput., May 1, 2001; 13(5): 1023 - 1043. [Abstract] [Full Text]