How Does the Cerebral Cortex Work? Developement, Learning, Attention, and 3D Vision by Laminar Circuits of Visual Cortex

A key goal of behavioral and cognitive neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how the visual cortex sees. Visual cortex, like many parts of perceptual and cognitive neocortex, is organized into six main layers of cells, as well as characteristic sub-lamina. Here it is proposed how these layered circuits help to realize the processes of developement, learning, perceptual grouping, attention, and 3D vision through a combination of bottom-up, horizontal, and top-down interactions. A key theme is that the mechanisms which enable developement and learning to occur in a stable way imply properties of adult behavior. These results thus begin to unify three fields: infant cortical developement, adult cortical neurophysiology and anatomy, and adult visual perception. The identified cortical mechanisms promise to generalize to explain how other perceptual and cognitive processes work.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.