An Approach to Stable Gradient Descent Adaptation of Higher-Order Neural Units

TL;DR

This paper introduces a spectral radius-based method for ensuring stability during gradient descent adaptation of higher-order neural units with polynomial input aggregation, applicable to both feedforward and recurrent architectures.

Contribution

It presents a novel stability monitoring approach using spectral radius for HONUs, enabling stable online adaptation at each step and extending to any linear-in-parameters neural architecture.

Findings

Stability can be maintained at every adaptation step.

The approach guarantees overall architecture stability.

Applicable to both feedforward and recurrent HONUs.

Abstract

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.