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Curvature-driven smoothing: a learning algorithm for feedforward networks.

¹Dept. of Comput. Sci., Aston Univ., Birmingham.

IEEE Transactions on Neural Networks

|January 1, 1993

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This study introduces an efficient learning algorithm for feedforward neural networks, enhancing performance by incorporating prior knowledge like smoothness through regularization terms. The new method overcomes limitations of standard backpropagation for derivative-dependent error functions.

Area of Science:

Artificial Intelligence
Machine Learning
Neural Networks

Background:

Feedforward neural networks (FNNs) performance in real applications can be enhanced using a priori information.
Smoothness requirements are common prior knowledge for interpolation problems, often incorporated via regularization terms in the error function.

Purpose of the Study:

To derive a computationally efficient learning algorithm for FNNs that can minimize error functions dependent on the network mapping's derivatives.
To address the limitations of standard backpropagation when dealing with such derivative-dependent error functions.

Main Methods:

Development of a novel learning algorithm applicable to FNNs of arbitrary topology.
Derivation of a simplified version of the algorithm for FNNs with a single hidden layer.

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Main Results:

The proposed algorithm efficiently minimizes error functions incorporating regularization terms based on network mapping derivatives.
The algorithm is suitable for FNNs with arbitrary network topologies, including a simplified case for single hidden layer networks.

Conclusions:

The new learning algorithm significantly improves FNN performance by effectively utilizing prior information through regularization.
This method provides a viable alternative to standard backpropagation for specific error function formulations in neural network training.