Permutation Binary Neural Networks: Analysis of Periodic Orbits and Its Applications

TL;DR

This paper introduces permutation binary neural networks with local and global connections, analyzing their periodic orbits and demonstrating their potential for hardware implementation and precise dynamic analysis.

Contribution

It provides a novel framework for analyzing permutation binary neural networks, including new tools for visualization and classification of periodic orbits, and demonstrates FPGA-based hardware implementation.

Findings

Generated various periodic orbits depending on network connections

Developed visualization and classification tools for network dynamics

Successfully implemented FPGA prototype for practical applications

Abstract

This paper presents a permutation binary neural network characterized by local binary connection, global permutation connection, and the signum activation function. The dynamics is described by a difference equation of binary state variables. Depending on the connection, the network generates various periodic orbits of binary vectors. The binary/permutation connection brings benefits to precise analysis and to FPGA based hardware implementation. In order to consider the periodic orbits, we introduce three tools: a composition return map for visualization of the dynamics, two feature quantities for classification of periodic orbits, and an FPGA based hardware prototype for engineering applications. Using the tools, we have analyzed all the 6-dimensional networks. Typical periodic orbits are confirmed experimentally.