A Lightweight and Gradient-Stable Neural Layer

We propose a neural-layer architecture based on Householder weighting and absolute-value activating, hence called Householder-absolute neural layer or simply Han-layer. Compared to a fully connected layer with $d$-neurons and $d$ outputs, a Han-layer reduces the number of parameters and the corresponding complexity from $O(d^2)$ to $O(d)$. The Han-layer structure guarantees two desirable properties: (1) gradient stability (free of vanishing or exploding gradient), and (2) 1-Lipschitz continuity. Extensive numerical experiments show that one can strategically use Han-layers to replace fully connected (FC) layers, reducing the number of model parameters while maintaining or even improving the generalization performance. We will also showcase the capabilities of the Han-layer architecture on a few small stylized models, and discuss its current limitations.