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Neural Networks Computations with DOMINATION Functions

Kilic, Kordag Mehmet and Bruck, Jehoshua (2021) Neural Networks Computations with DOMINATION Functions. Parallel and Distributed Systems Group Technical Reports, etr151. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210624-214748102

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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:Report or Paper (Technical Report)
Related URLs:
URLURL TypeDescription
http://www.paradise.caltech.edu/papers/etr151.pdfAuthorTechnical Report
ORCID:
AuthorORCID
Bruck, Jehoshua0000-0001-8474-0812
Group:Parallel and Distributed Systems Group
Series Name:Parallel and Distributed Systems Group Technical Reports
Issue or Number:etr151
Record Number:CaltechAUTHORS:20210624-214748102
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210624-214748102
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109572
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Jun 2021 14:37
Last Modified:25 Jun 2021 14:37

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