Self-organization of orientation maps in a formal neuron model using a cluster learning rule

Self-organization of orientation maps due to external stimuli in the primary visual area of the cerebral cortex is studied in a two-layered neural network which consists of formal neuron models with a sigmoidal output function. A cluster learning rule is proposed as an extended Hebbian learning rule, where a modification of synaptic connections is influenced by an activation of neighboring output neurons. By making use of self-consistent Monte Carlo method, we evaluate output responses of neurons against explicit inputs after the learning. An orientation map calculated from the output responses reproduces characteristic features of biological ones. Moreover quantitative analysis of our results are consistent with those of experimental results. It is shown that the cluster learning rule plays an important role in forming smooth changes of preferred orientations.

[1]  KD Miller A model for the development of simple cell receptive fields and the ordered arrangement of orientation columns through activity-dependent competition between ON- and OFF-center inputs , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[2]  G. Blasdel,et al.  Differential imaging of ocular dominance and orientation selectivity in monkey striate cortex , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[3]  G. Blasdel,et al.  Voltage-sensitive dyes reveal a modular organization in monkey striate cortex , 1986, Nature.

[4]  Tobias Bonhoeffer,et al.  Development of identical orientation maps for two eyes without common visual experience , 1996, Nature.

[5]  Shogo Miyake,et al.  Mean Field Theory and Self-Consistent Monte Carlo Method for Self-Organization of Formal Neuron Model , 2000 .

[6]  J. Nicholls From neuron to brain , 1976 .

[7]  G. Blasdel,et al.  Orientation selectivity, preference, and continuity in monkey striate cortex , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[8]  Klaus Obermayer,et al.  Singularities in Primate Orientation Maps , 1997, Neural Computation.

[9]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[10]  D. Hubel,et al.  Sequence regularity and geometry of orientation columns in the monkey striate cortex , 1974, The Journal of comparative neurology.

[11]  S. Geman SOME AVERAGING AND STABILITY RESULTS FOR RANDOM DIFFERENTIAL EQUATIONS , 1979 .

[12]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[13]  Amiram Grinvald,et al.  Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns , 1991, Nature.

[14]  D. Hubel,et al.  Receptive fields and functional architecture of monkey striate cortex , 1968, The Journal of physiology.

[15]  Tobias Bonhoeffer,et al.  Reverse occlusion leads to a precise restoration of orientation preference maps in visual cortex , 1994, Nature.

[16]  Klaus Schulten,et al.  Models of Orientation and Ocular Dominance Columns in the Visual Cortex: A Critical Comparison , 1995, Neural Computation.

[17]  K. Obermayer,et al.  Statistical-mechanical analysis of self-organization and pattern formation during the development of visual maps. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  Roman Bek,et al.  Discourse on one way in which a quantum-mechanics language on the classical logical base can be built up , 1978, Kybernetika.

[19]  D. W. Mann A mathematical model of the self. , 1992, Psychiatry.

[20]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[21]  T. Bonhoeffer,et al.  Reverse occlusion leads to a precise restoration of orientation preference maps in visual cortex , 1994, Nature.

[22]  Y. Tamori,et al.  Hamiltonian formalism for self-organization of formal neurons , 1996 .

[23]  A. Grinvald,et al.  The layout of iso-orientation domains in area 18 of cat visual cortex: optical imaging reveals a pinwheel-like organization , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[24]  M. Miyashita,et al.  A mathematical model for the self-organization of orientation columns in visual cortex. , 1992, Neuroreport.

[25]  R. Linsker From basic network principles to neural architecture (series) , 1986 .