Lattice theory framework for deep convolutional learning using mathematical morphology

A recent publication on arXiv has introduced an innovative algebraic framework for deep convolutional neural networks (CNNs), including ResNets and UNet-style architectures. By integrating principles from lattice theory and mathematical morphology, the study utilizes the Matheron-Maragos-Banon-Barrera (MMBB) universal representation theory to enhance translation-invariant operations at each layer of the model. A key finding indicates that the conventional CNN methodology, which consists of linear convolution, ReLU activation, and max-pooling, operates as a cross-lattice operator. Furthermore, it was discovered that the upper adjoint of ReLU acts as a global operator within the pointwise lattice for certain functions.