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Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Published on: August 12, 2018

Neural subnet design by direct polynomial mapping.

K Rohani¹, M S Chen, M T Manry

¹Motorola Inc., Fort Worth, TX.

IEEE Transactions on Neural Networks

|January 1, 1992

Summary

This summary is machine-generated.

This study extends universal approximation for neural networks, introducing a mapping method for designing feedforward networks. This approach efficiently creates polynomial approximations, avoiding local minima common in backpropagation.

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Area of Science:

Artificial Intelligence
Machine Learning
Neural Networks

Background:

Multilayer perceptron neural networks have demonstrated universal approximation capabilities for forming products of inputs.
Previous work established the theoretical foundation for neural network universal approximation.

Purpose of the Study:

To extend the universal approximation results for neural networks.
To develop a method for the analysis and synthesis of single-input, single-output neural subnetworks.
To implement polynomial approximations of functions using feedforward neural networks.

Main Methods:

Extending theoretical results on neural network universal approximation.
Designing feedforward neural networks using a mapping approach for function approximation.
Comparing the mapping approach with classical backpropagation training.

Main Results:

The mapping method successfully designs feedforward neural networks for polynomial approximation with arbitrary accuracy.
Mapped neural subnetworks avoid local minima, a common issue with backpropagation.
The mapping approach demonstrates significantly faster training times compared to backpropagation.

Conclusions:

The proposed mapping method offers an efficient and robust alternative to backpropagation for training neural networks.
This work provides a constructive approach to universal approximation in neural networks.
The findings have implications for designing accurate and fast neural network models for function approximation.