Bridging soft and hard morphological optimization

Bridge softened morphological operators and hard morphological operators in a way that overcomes the increasing optimization difficulty associated with the hard limit as the temperature parameter approaches zero.

Background

The paper introduces a correlation-based multiplicative-weights update for training morphological neural networks, motivated by the sparsity and limited informativeness of ordinary gradient signals. The method is evaluated in both softened morphology, using a positive temperature parameter, and hard morphology, corresponding to the zero-temperature limit. Although the proposed method improves optimization in the hard regime on the PMLB experiments, the authors report that softened morphology is more competitive for image classification. They therefore identify the transition between soft and hard morphology as an unresolved optimization challenge.