A KANERVA NETWORK MODEL OF SYNTACTIC PARAMETERS

Sparse Distributed Memory (or Kanerva Networks) is a technique first introduced as a model of memory in neuroscience, [2] (see also §13 of [1] for a quick summary). In a large Boolean space FN2 one chooses a uniform random sample of hard locations. The number 2k of hard locations is small compared to the size 2N of the ambient space. At each of these hard locations a datum (a Boolean string of length N) is stored. Compute the median Hamming distance between hard locations. An access sphere of a point in the Boolean space FN2 is a Hamming sphere of radius slightly larger than the median distance of hard locations (see some estimates in §6 of [2]). The a given location ξ in FN2, the datum D(ξ) assigned to that location is distributively stored by writing it at all the hard locations within the access sphere of ξ. When the operation is performed for a set of locations ξ, each hard location stores a datum whose i-th entry is determined by the majority rule of the corresponding entries D(ξ)i for all the stored data D(ξ). Similarly one reads at the location ξ a new datum D′(ξ) whose i-th entry D′(ξ)i is given by the majority rule on the i-th entries of all the data stored at all the hard locations accessible from ξ. If the datum D(ξ) stored at ξ is ξ itself as a Boolean string of length N, this method works at reconstructing the correct datum D′(ξ) = D(ξ) = ξ because the intersections between access spheres are small and so copies of th