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 | ||||||
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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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