We derive a method for the analysis of weight quantization effects in multilayer perceptrons based on the application of interval arithmetic. Differently from previous results, we find worst case bounds on the errors due to weight quantization, that are valid for every distribution of the input or weight values. Given a trained network, our method allows us to easily compute the minimum number of bits needed to encode its weights.

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Worst case analysis of weight inaccuracy effects in multilayer perceptrons

A verification method and a verification apparatus of a neural network for guaranteeing the operation of the neural network to any input signals which might be inputted The neural network verification apparatus comprises a data file storage section for storing a verification data file DFK concerning on the structure of the neural network to be verified, a network structuring section for structuring a neural network NET to be verified by reading the neural network data file DFN from the data file storage section, an input data generating section for generating initial interval input vector database DBI by reading the verification data file DFK from the data file storage section, a verification executing section for executing the verification of the neural network NET based on the neural network NET structured by the network structuring section and the initial interval input vector database DBI created by the input data generating section and for generating a verification result database DBO based on the verification result, and others The verification apparatus generates an interval input vector signal per input signal subspace which is obtained by dividing an input signal space formed by the input signal to the neural network NET into a plurality of input signal subspaces and accumulates them in a stack

Verification method of neural network and verification apparatus thereof

In this paper a real-time quality control system for steel industry is presented. The system implements the surface defect classification of steel strips in flat rolled mills in real-time. To achieve reliable classification accuracy the system implements a MLP_based hierarchical neural network. A dedicated hardware implementation has been designed and manufactured to meet the realtime constraints of the application. An ASIC neural chip directly implements the neural network and it is integrated on a custom high speed co-processor board, compatible with many commercial carrier board. The entire system has been tested with data coming from the plant.

A Hardware Implementation of Hierarchical Neural Networks for Real-Time Quality Contol Systems in Industrial Applications

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? "Backpropagation of accuracy" is developed to solve this problem.

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Backpropagation of accuracy

Two generalizations of multilayer feedforward and backpropagation to interval arithmetic were proposed several years ago. These generalizations have several applications like the codification of rules in the training set, "don't care attributes", missing inputs, etc. There are two generalizations what means that there are two different training algorithms and there is no way, at first, to consider one of them better than the other. We present an in depth comparison between the two training algorithms. We have used a total number of 75 different problems and five different performance definitions for the comparison. The results are that the performance of the algorithms depends on the performance definition, but we can consider one of them as the "usual" one and in this sense one algorithm outperforms the other.

A comparison between two interval arithmetic learning algorithms

We address in this work the problem of weight inaccuracies in digital and analog feedforward networks. Both kind of implementations suffer from this problem due to physical limits of the particular technology. This work presents a novel and effective approach through the application of interval arithmetic to the multilayer perceptron. Results show that our method allows one to (1) compute strict bounds of the output error of the network, (2) find robust solutions respect to weight inaccuracies and (3) compute the minimum weight precision required to obtain the desired performance of the network.

S. Rovetta

Papers

Limiting the effects of weight errors in feedforward networks using interval arithmetic