### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Publication status | Published - 1992 |

Externally published | Yes |

### Publication series

Name | Memorandum COSOR |
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### Fingerprint

### Cite this

*The minimal number of layers of a perceptron that sorts*. (Memorandum COSOR). Eindhoven: Technische Universiteit Eindhoven.

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*The minimal number of layers of a perceptron that sorts*. Memorandum COSOR, Technische Universiteit Eindhoven, Eindhoven.

**The minimal number of layers of a perceptron that sorts.** / Zwietering, P.J.; Aarts, E.H.L.; Wessels, J.

Research output: Book/Report › Book › Scientific

TY - BOOK

T1 - The minimal number of layers of a perceptron that sorts

AU - Zwietering, P.J.

AU - Aarts, E.H.L.

AU - Wessels, J.

PY - 1992

Y1 - 1992

N2 - In this paper we consider the problem of determining the minimal number of layers required by a multi-layered perceptron for solving the sorting problem. We discuss two formulations of the sorting problem; ABSSORT, which can be considered as the standard form of the sorting problem, and where, given an array of numbers, a new array with the original numbers in non-decreasing order is requested, and RELSORT, where, given an array of numbers, one wants to find the smallest number and for each number -except the largest- one wants to find the next largest number. We show that, if one uses classical multi-layered perceptrons with the hard-limiting response function, the minimal number of layers needed is 3 and 2 for solving ABSSORT and RELSORT, respectively. Keywords: multi-layered perceptrons, minimal number of layers, neural networks, sorting.

AB - In this paper we consider the problem of determining the minimal number of layers required by a multi-layered perceptron for solving the sorting problem. We discuss two formulations of the sorting problem; ABSSORT, which can be considered as the standard form of the sorting problem, and where, given an array of numbers, a new array with the original numbers in non-decreasing order is requested, and RELSORT, where, given an array of numbers, one wants to find the smallest number and for each number -except the largest- one wants to find the next largest number. We show that, if one uses classical multi-layered perceptrons with the hard-limiting response function, the minimal number of layers needed is 3 and 2 for solving ABSSORT and RELSORT, respectively. Keywords: multi-layered perceptrons, minimal number of layers, neural networks, sorting.

M3 - Book

T3 - Memorandum COSOR

BT - The minimal number of layers of a perceptron that sorts

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -