Nearest Neighbor Representations of Neurons
<|reference_start|>Nearest Neighbor Representations of Neurons: 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 $n$.<|reference_end|>
@article{kilic2024nearest,
    title={Nearest Neighbor Representations of Neurons},
    author={Kordag Mehmet Kilic, Jin Sima, and Jehoshua Bruck},
    journal={arXiv preprint arXiv:2402.08748},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08748},
    primaryClass={cs.CC cs.DM cs.LG cs.NE}
}