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Models of Neural Development

Lupe

Topographic projections between neural sheets, orientation columns and ocular dominance columns in early visual areas have served as paradigmatic model systems for understanding the mechanisms underlying neural plasticity and development. Using mathematical models and computer simulations we investigated how activity driven and intrinsic processes interact in order to generate the observed anatomical connectivity patterns and response properties of neurons. We describe the development of those patterns as a goal-oriented (in the sense of underlying cost-functions) self-organizing process, which extracts information from the environment and imprints this knowledge into neural circuits. Particular emphasis was given to competitive networks including the Self-Organizing Map, which are known to trade smoothness vs. completeness of representations and which lead to patterns which fit experimental data surprisingly well.The mathematical properties of self-organizing maps were also analysed in a machine learning context. For details see "Research" page "Learning Vector Quantization and Self-organizing Maps"

Acknowledgements: Research was funded by BMBF, DFG, and the Technische Universität Berlin.

Selected Publications:

The Effect of Intracortical Competition on the Formation of Topographic Maps in Models of Hebbian Learning
Citation key Piepenbrock2000
Author Piepenbrock, C. and Obermayer, K.
Pages 345 – 353
Year 2000
ISSN 0340-1200
DOI 10.1007/s004220050588
Journal Biological Cybernetics
Volume 82
Number 4
Publisher Springer-Verlag
Abstract Correlation based learning models (CBL) and self-organizing maps (SOM) are two classes of Hebbian models that have both been proposed to explain the activity driven formation of cortical maps. Both models differ significantly in the way lateral cortical interactions are treated leading to different predictions for the formation of receptive fields. The linear CBL models predict that receptive field profiles are determined by the average values and the spatial correlations of second order of the afferent activity patterns, wheras SOM models map stimulus features. Here we investigate a class of models which are characterized by a variable degree of lateral competition and which have the CBL and SOM models as limit cases. We show that there exists a critical value for intracortical competition below which the model exhibits CBL properties and above which feature mapping sets in. The class of models is then analyzed with respect to the formation of topographic maps between two layers of neurons. For Gaussian input stimuli we find that localized receptive fields and topographic maps emerge above the critical value for intracortical competition and we calculate this value as a function of the size of the input stimuli and the range of the lateral interaction function. Additionally, we show that the learning rule can be derived via the optimization of a global cost function in a framework of probabilistic output neurons which represent a set of input stimuli by a sparse code.
Bibtex Type of Publication Selected:development
Link to publication Link to original publication Download Bibtex entry

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