Theory of linear and integer programming
Theory of linear and integer programming
The interpolation capabilities of the binary CMAC
Neural Networks
Fourier analysis of the generalized CMAC neural network
Neural Networks
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
Basis function models of the CMAC network
Neural Networks
Acyclic Database Schemes (of Various Degrees): A Painless Introduction
CAAP '83 Proceedings of the 8th Colloquium on Trees in Algebra and Programming
Hierarchical image coding via cerebellar model arithmetic computers
IEEE Transactions on Image Processing
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The CMAC is a neural net for computing real-valued functions. Conceptually, the CMAC maps a point in the function's domain to a set of locations in an associative memory. Each location "contains" a weight, and the sum of the weights is taken to be the function's value at that point. The overall process may be modeled as the multiplication of an input vector by an "association matrix." This paper highlights some aspects of the CMAC's mapping and function computation procedures. Regarding the mapping procedure, it is shown that the associative matrix of a univariate CMAC has the consecutive-ones property; this implies that the matrix is totally-unimodular, a property of great importance in integer optimization. For a multivariate CMAC, the association matrix can be partitioned into sub-matrices, each with the consecutive-ones property. Regarding the function computation procedure, it is shown that a univariate CMAC can compute a function exactly iff a certain distribution is reconstructible from its one dimensional marginals. A CMAC extension, free of this limitation and derived from the theory of balanced matrices, is briefly discussed. These results are generalizable to multivariate CMACs in a relatively straightforward manner.