Hierarchical multi-scale parametric optimization of deep neural networks

Traditionally, sensitivity analysis has been utilized to determine the importance of input variables to a deep neural network (DNN). However, the quantification of sensitivity for each neuron in a network presents a significant challenge. In this article, a selective method for calculating neuron sensitivity in layers of neurons concerning network output is proposed. This approach incorporates scaling factors that facilitate the evaluation and comparison of neuron importance. Additionally, a hierarchical multi-scale optimization framework is proposed, where layers with high-importance neurons are selectively optimized. Unlike the traditional backpropagation method that optimizes the whole network at once, this alternative approach focuses on optimizing the more important layers. This paper provides fundamental theoretical analysis and motivating case study results for the proposed neural network treatment. The framework is shown to be effective in network optimization when applied to simulated and UCI Machine Learning Repository datasets. This alternative training generates local minima close to or even better than those obtained with the backpropagation method, utilizing the same starting points for comparative purposes within a multi-start optimization procedure. Moreover, the proposed approach is observed to be more efficient for large-scale DNNs. These results validate the proposed algorithmic framework as a rigorous and robust new optimization methodology for training (fitting) neural networks to input/output data series of any given system.