Biologically Plausible Neural Circuits for Realization of Maximum Operations

Object recognition in the visual cortex is based on a hierarchical architecture, in which specialized brain regions along the ventral pathway extract object features of increasing levels of complexity, accompanied by greater invariance in stimulus size, position, and orientation. Recent theoretical studies postulate a non-linear pooling function, such as the maximum (MAX) operation could be fundamental in achieving such invariance. In this paper, we are concerned with neurally plausible mechanisms that may be involved in realizing the MAX operation. Four canonical circuits are proposed, each based on neural mechanisms that have been previously discussed in the context of cortical processing. Through simulations and mathematical analysis, we examine the relative performance and robustness of these mechanisms. We derive experimentally verifiable predictions for each circuit and discuss their respective physiological considerations.

Measure Fields for Function Approximation

The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function may then be computed as the optimal estimator with respect to this measure field. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components.