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A Logical/Linear Model of Cortical Subunit Interactions

A. Dobbins (Caltech), L. Iverson (SRI International), S.W. Zucker Visual cortical neurons vary dramatically in their tuning along different stimulus dimensions, and in whether those selectivities are adequately captured by linear models. Certain properties, such as spatial frequency selectivity, seem adequately explained by linear models; while others, such as direction selectivity and endstopping, may involve nonlinearities. We have developed a calculus for the logical combination of local evidence from subunits in which support is accumulated linearly, but incompatible evidence enters nonlinearly. This leads to a class of operators that appears linear for one class of stimuli but markedly nonlinear for others -- we call these logical-linear operators. They exhibit dual advantages: they are considerably more stimulus-specific than purely linear operators, while more robust to incidental stimulus variation than logical operators. The viability of such operators as models of visual cortical neurons (e.g. simple cells) is examined by comparing simulations of purely linear and logical-linear models to the responses of cortical neurons. Operators with properties specialised for spatial contours are examined with stimuli containing vernier offsets, interruptions, and opposite contrast segments. The results are consistent with the well-known ``linear'' properties (e.g., sensitivity to spatial frequency gratings) while exhibiting the nonlinear behaviour associated with high vernier sensitivities (Swindale and Cynader, 1989) and strong suppressive effects for opposite contrast segments (Hammond and MacKay, 1983, 1985). Finally, we relate the abstract description of subunit combination to nonlinear synaptic interactions.

Thierry Baron
Mon Apr 7 12:54:24 EDT 1997