In this paper, we study an emerging class of neural networks, the Morphological Neural networks, from some modern perspectives. Our approach utilizes ideas from tropical geometry and mathematical morphology. First, we state the training of a binary morphological classifier as a Difference-of-Convex optimization problem and extend this method to multiclass tasks. We then focus on general morphological networks trained with gradient descent variants and show, quantitatively via pruning schemes as well as qualitatively, the sparsity of the resulted representations compared to FeedForward networks with ReLU activations as well as the effect the training optimizer has on such compression techniques. Finally, we show how morphological networks can be employed to guarantee monotonicity and present a softened version of a known architecture, based on Maslov Dequantization, which alleviates issues of gradient propagation associated with its "hard" counterparts and moderately improves performance.

Finding optimal channel dimensions (i.e., the number of filters in DNN layers) is essential to design DNNs that perform well under computational resource constraints. Recent work in neural architecture search aims at automating the optimization of the DNN model implementation. However, existing neural architecture search methods for channel dimensions rely on fixed search spaces, which prevents achieving an efficient and fully automated solution. In this work, we propose a novel differentiable neural architecture search method with an efficient dynamic channel allocation algorithm to enable a flexible search space for channel dimensions. We show that the proposed framework is able to find DNN architectures that are equivalent to previous methods in task accuracy and inference latency for the CIFAR-10 dataset with an improvement of 1.3−1.7× in GPU-hours and 1.5−1.7× in the memory requirements during the architecture search stage. Moreover, the proposed frameworks do not require a well-engineered search space a priori, which is an important step towards fully automated design of DNN architectures.