Architopes: An Architecture Modification for Composite Pattern Learning, Increased Expressiveness, and Reduced Training Time

We introduce a simple neural network architecture modification that enables composite pattern learning, increases expressiveness, and reduces training time. This expressibility improvement is explained by the density of the modified architecture in a new refined local $L^p$-space describing composite patterns. In contrast, most feed-forward neural network architectures with sigmoid activation functions are shown not to be dense in this space. In practice, restrictions have to be placed on the dimension of any architecture's parameter space. $L^1$ approximation bounds are obtained in terms of the number of the trainable parameters. Likewise, convergence guarantees are obtained as the imposed restrictions are asymptotically removed. By exploiting the new architecture's structure, a parallelizable training meta-algorithm is provided, and numerical evaluations are made using the California housing dataset.