to appear in Frank Eeckman
نویسندگان
چکیده
We describe a theoretical model of spatial representation in cortex, including computer simulations, that is compatible with data from single neuron recordings. Our proposed architecture, called a sinusoidal array, encodes a polar vector ~ v = (r;) as distributed activity across a neuronal population. We demonstrate how sinusoidal arrays might be used for vector computations such as addition, subtraction, and rotation in tasks such as primate reaching and rodent navigation. 1 The Sinusoidal Array Spatial representation in the mammalian brain has been widely studied in hippocampus, parietal cortex, and throughout the motor system. But most of the modeling work to date has focused on place cells in hippocam-pus and on the transformation of retinal to head centered coordinates in parietal cortex. Our work models spatial representations in the motor system, but it is also applicable to certain navigational tasks. We ooer a general computation mechanism, the sinusoidal array, which is capable of representing n-dimensional vectors. (We will be primarily concerned with 2 and 3 dimensional spatial vectors.) The sinusoidal array is an encoding of a vector as a distributed pattern of activity over N neurons. The ring rate of each neuron i encodes the value F(r; ; i) = bi + ki r cos(? i) where bi is a baseline value that attempts to keep F(r; ; i) positive, ki is a scale factor, and i is a preferred direction. We assume that preferred directions are uniformly distributed. Thus, for each cell we associate a preferred vector (in polar coordinates) ~ i = (ki; i). With ~ v = (r;) the vector being represented, and SA ~ v the sinusoidal array represention of ~ v, the ring rate of neuron i is F(SA ~ v ; i) = bi + ~ v:~ i where the dot denotes inner product. The si-nusoidal array is an extension of the population vector 6]. Because the sinusoidal array includes magnitude information, it is capable of supporting vector arithmetic.
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Frank Eeckman Lawrence Livermore National Laboratory, P.O. Box 808 (L-270), Livermore, Ca. 94550, [email protected] We show how an "Elman" network architecture, constructed from recurrently connected oscillatory associative memory network modules, can employ selective "attentional" control of synchronization to direct the flow of communication and computation within the architecture to solve a ...
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