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Title: On limited fan-in optimal neural networks

Abstract

Because VLSI implementations do not cope well with highly interconnected nets the area of a chip growing as the cube of the fan-in--this paper analyses the influence of limited fan in on the size and VLSI optimality of such nets. Two different approaches will show that VLSI- and size-optimal discrete neural networks can be obtained for small (i.e. lower than linear) fan-in values. They have applications to hardware implementations of neural networks. The first approach is based on implementing a certain sub class of Boolean functions, IF{sub n,m} functions. The authors will show that this class of functions can be implemented in VLSI optimal (i.e., minimizing AT{sup 2}) neural networks of small constant fan ins. The second approach is based on implementing Boolean functions for which the classical Shannon`s decomposition can be used. Such a solution has already been used to prove bounds on neural networks with fan-ins limited to 2. They generalize the result presented there to arbitrary fan-in, and prove that the size is minimized by small fan in values, while relative minimum size solutions can be obtained for fan-ins strictly lower than linear. Finally, a size-optimal neural network having small constant fan-ins will be suggested for IF{submore » n,m} functions.« less

Authors:
;  [1];  [2]
  1. Los Alamos National Lab., NM (United States)
  2. Wayne State Univ., Detroit, MI (United States). Vision and Neural Networks Lab.
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)
OSTI Identifier:
654140
Report Number(s):
LA-UR-97-4314; CONF-971235-
ON: DE98004666; TRN: AHC2DT05%%228
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: 4. Brasilian symposium on neural networks, Boifnia (Brazil), 3-5 Dec 1997; Other Information: PBD: Mar 1998
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; NEURAL NETWORKS; INTEGRATED CIRCUITS; FUNCTIONS; SIZE; OPTIMIZATION

Citation Formats

Beiu, V, Makaruk, H E, and Draghici, S. On limited fan-in optimal neural networks. United States: N. p., 1998. Web.
Beiu, V, Makaruk, H E, & Draghici, S. On limited fan-in optimal neural networks. United States.
Beiu, V, Makaruk, H E, and Draghici, S. 1998. "On limited fan-in optimal neural networks". United States. https://www.osti.gov/servlets/purl/654140.
@article{osti_654140,
title = {On limited fan-in optimal neural networks},
author = {Beiu, V and Makaruk, H E and Draghici, S},
abstractNote = {Because VLSI implementations do not cope well with highly interconnected nets the area of a chip growing as the cube of the fan-in--this paper analyses the influence of limited fan in on the size and VLSI optimality of such nets. Two different approaches will show that VLSI- and size-optimal discrete neural networks can be obtained for small (i.e. lower than linear) fan-in values. They have applications to hardware implementations of neural networks. The first approach is based on implementing a certain sub class of Boolean functions, IF{sub n,m} functions. The authors will show that this class of functions can be implemented in VLSI optimal (i.e., minimizing AT{sup 2}) neural networks of small constant fan ins. The second approach is based on implementing Boolean functions for which the classical Shannon`s decomposition can be used. Such a solution has already been used to prove bounds on neural networks with fan-ins limited to 2. They generalize the result presented there to arbitrary fan-in, and prove that the size is minimized by small fan in values, while relative minimum size solutions can be obtained for fan-ins strictly lower than linear. Finally, a size-optimal neural network having small constant fan-ins will be suggested for IF{sub n,m} functions.},
doi = {},
url = {https://www.osti.gov/biblio/654140}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1998},
month = {3}
}

Conference:
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