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Neural Network Computations with DOMINATION Functions

Kilic, Kordag Mehmet and Bruck, Jehoshua (2021) Neural Network Computations with DOMINATION Functions. In: 2021 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 1029-1034. ISBN 978-1-5386-8209-8. https://resolver.caltech.edu/CaltechAUTHORS:20211110-155100881

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Abstract

We study a new representation of neural networks based on DOMINATION functions. Specifically, we show that a threshold function can be computed by its variables connected via an unweighted bipartite graph to a universal gate computing a DOMINATION function. The DOMINATION function consists of fixed weights that are ascending powers of 2. We derive circuit-size upper and lower bounds for circuits with small weights that compute DOMINATION functions. Interestingly, the circuit-size bounds are dependent on the sparsity of the bipartite graph. In particular, functions with sparsity 1 (like the EQUALITY function) can be implemented by small-size constant-weight circuits.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/isit45174.2021.9517872DOIArticle
ORCID:
AuthorORCID
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© 2021 IEEE.
DOI:10.1109/isit45174.2021.9517872
Record Number:CaltechAUTHORS:20211110-155100881
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211110-155100881
Official Citation:K. M. Kilic and J. Bruck, "Neural Network Computations with DOMINATION Functions," 2021 IEEE International Symposium on Information Theory (ISIT), 2021, pp. 1029-1034, doi: 10.1109/ISIT45174.2021.9517872
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111819
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Nov 2021 19:08
Last Modified:11 Nov 2021 19:08

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