Connectionists: coupled cortical maps paper

[Peter Thomas]

Dear Colleagues:

I am pleased to draw your attention to the following article,  
available at

http://imammb.oxfordjournals.org/cgi/rapidpdf/dql006? 
ijkey=TjqJPARL6JsfmFT&keytype=ref

> Simultaneous constraints on pre- and post-synaptic cells couple  
> cortical
> feature maps in a 2D geometric model of orientation preference
>
> Peter J. Thomas (Oberlin College & Case Western Reserve University)
> Jack D. Cowan (The University of Chicago)
>
> The most prominent feature of mammalian striate cortex (V1) is the  
> spatial organization of response preferences for the position and  
> orientation of elementary visual stimuli. Models for the formation  
> of cortical maps of orientation and retinotopic position typically  
> rely on a combination of Hebbian or correlation-based synaptic  
> plasticity, and constraints on the distribution of synaptic  
> weights. We consider a simplified model of orientation and  
> retinotopic specificity based on the geometry of the feedforward  
> synaptic weight distribution from an unoriented layer of cells to a  
> first weakly oriented layer. We model the feed-forward weight  
> distribution as a system of planar Gaussian receptive fields each  
> elongated in the direction matching the preferred orientation of  
> the postsynaptic cell. Under the constraint of presynaptic weight  
> normalization (each cell in the oriented layer receives the same  
> net synaptic weight) and a uniform retinotopic map (displacement of  
> centres of mass of receptive fields in the unoriented layer is  
> strictly proportional to the displacement of the corresponding  
> cells in the oriented layer), we find that imposing a pattern of  
> orientation preference forces the system to violate postsynaptic  
> weight normalization (each cell in the unoriented layer no longer  
> sends forth the same net synaptic weight). We study this deviation  
> from uniformity of the postsynaptic weight, and find that the  
> deviation has a distinct form in the vicinity of the pinwheel  
> singularities of the orientation map. We show that uniform synaptic  
> coverage of the unoriented layer can be restored by introducing a  
> distortion in the retinotopic locations of the receptive fields. We  
> calculate, to first order in the relative elongation of the  
> receptive fields, the retinotopic distortion vector field. Both the  
> pattern of postsynaptic weight non-uniformity and the corrective  
> retinotopic distortion vector field fail to possess the reflection  
> symmetry commonly assumed to relate orientation singularities with  
> topological index +-pi. Hence, we show that right-handed and left- 
> handed orientation singularities are fundamentally distinct  
> anatomical structures when full 2D synaptic architecture is taken  
> into account. Finally, we predict specific patterns of retinotopic  
> distortion that should obtain in the vicinity of +-pi-fold  
> orientation singularities, if uniform pre- and post-synaptic weight  
> constraints are strongly enforced.
>
> Keywords: visual cortex; orientation; retinotopy; fan-in; fan-out;  
> neural network; cortical map.

Best wishes,

Peter J. Thomas

[as of July 1, 2006:]
Assistant Professor of Mathematics, Biology & Cognitive Science
Case Western Reserve University
Department of Mathematics
Yost Hall, 10900 Euclid Ave, Cleveland, OH 44106-7058
pjt9 -- at -- case.edu      //          216-368-8998