Back-propagation of accuracy

TL;DR

This paper introduces a method called back-propagation of accuracy to determine the maximum allowable errors in neural network elements, ensuring the output signals meet specified accuracy requirements.

Contribution

It develops a novel back-propagation technique for calculating allowable errors in network signals and parameters based on output accuracy constraints.

Findings

Allows formulation of accuracy requirements for network components

Provides a systematic way to ensure output precision

Enables design of technical devices with specified accuracy

Abstract

In this paper we solve the problem: how to determine maximal allowable errors, possible for signals and parameters of each element of a network proceeding from the condition that the vector of output signals of the network should be calculated with given accuracy? "Back-propagation of accuracy" is developed to solve this problem. The calculation of allowable errors for each element of network by back-propagation of accuracy is surprisingly similar to a back-propagation of error, because it is the backward signals motion, but at the same time it is very different because the new rules of signals transformation in the passing back through the elements are different. The method allows us to formulate the requirements to the accuracy of calculations and to the realization of technical devices, if the requirements to the accuracy of output signals of the network are known.