Nearest Neighbor Representations of Neurons

Kordag Mehmet Kilic; Jin Sima; Jehoshua Bruck

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arXiv · 2402.08748

Nearest Neighbor Representations of Neurons

Kordag Mehmet Kilic·Jin Sima·Jehoshua Bruck

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Abstract

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 $n$.

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BibTeX RIS

Kordag Mehmet Kilic, Jin Sima, Jehoshua Bruck. 2024-02-13. Nearest Neighbor Representations of Neurons. https://arxiv.org/abs/2402.08748

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