Orthogonal Transforms in Neural Networks Amount to Effective Regularization
This work addresses efficiency and regularization in neural networks for system identification, but it appears incremental as it builds on known orthogonal transform concepts.
The paper tackles the problem of improving neural network performance in nonlinear system identification by incorporating orthogonal transforms, showing that this approach acts as effective regularization and that using the Fourier transform specifically outperforms equivalent models without orthogonality.
We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in an efficient neural network retaining its universal properties. We show that such a structure is a universal approximator and that using any orthogonal transform in a proposed way implies regularization during training by adjusting the learning rate of each parameter individually. We empirically show in particular, that such a structure, using the Fourier transform, outperforms equivalent models without orthogonality support.