An Approach to Stable Gradient Descent Adaptation of Higher-Order Neural Units
This addresses stability issues in training polynomial neural networks, which is an incremental improvement for researchers working with these architectures.
The paper tackles the stability problem in gradient descent adaptation of higher-order neural units (HONUs) by introducing a stability evaluation method based on the spectral radius of the weight-update system, enabling stability monitoring and maintenance at each adaptation step to ensure overall adaptation stability.
Stability evaluation of a weight-update system of higher-order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring stability of the weight-update system (at every single adaptation step) naturally results in adaptation stability of the whole neural architecture that adapts to target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.