Nearest Neighbor Representations of Neurons
Kordag Mehmet Kilic Jin Sima Jehoshua Bruck
The Nearest Neighbor (NN) Representation is an emerging computational model
that is inspired by the brain. We study the complexity of representing a neuron
(threshold function) using the NN representations. It is known that two anchors
(the points to which NN is computed) are sufficient for a NN representation of
a threshold function, however, the resolution (the maximum number of bits
required for the entries of an anchor) is $O(n\log{n})$. In this work, the
trade-off between the number of anchors and the resolution of a NN
representation of threshold functions is investigated. We prove that the
well-known threshold functions EQUALITY, COMPARISON, and ODD-MAX-BIT, which
require 2 or 3 anchors and resolution of $O(n)$, can be represented by
polynomially large number of anchors in $n$ and $O(\log{n})$ resolution. We
conjecture that for all threshold functions, there are NN representations with
polynomially large size and logarithmic resolution in $n$.