A Lightweight and Gradient-Stable Neural Layer

TL;DR

This paper introduces the Han-layer, a neural network layer that is lightweight, parameter-efficient, and guarantees gradient stability through orthogonal Jacobians, improving resource efficiency without sacrificing performance.

Contribution

The paper proposes the Han-layer architecture based on Householder weighting and absolute-value activation, reducing parameters and ensuring gradient stability in neural networks.

Findings

Han-layer reduces parameter count from O(d^2) to O(d).

Han-layer maintains or improves generalization performance.

Han-layer guarantees orthogonal Jacobian, ensuring gradient stability.

Abstract

To enhance resource efficiency and model deployability of neural networks, we propose a neural-layer architecture based on Householder weighting and absolute-value activating, 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 computational complexity from $O(d^2)$ to $O(d)$. {The Han-layer structure guarantees that the Jacobian of the layer function is always orthogonal, thus ensuring gradient stability (i.e., free of gradient vanishing or exploding issues) for any Han-layer sub-networks.} 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.