EdgeLDR: Quaternion Low-Displacement Rank Neural Networks for Edge-Efficient Deep Learning

TL;DR

EdgeLDR introduces quaternion block-circulant layers for deep neural networks, enabling efficient FFT-based computation that reduces memory and compute costs on edge devices while maintaining competitive accuracy.

Contribution

The paper proposes a novel quaternion block-circulant layer framework, combining channel mixing with structured matrices and FFT evaluation for efficient edge deployment.

Findings

FFT-based evaluation significantly speeds up computation.

EdgeLDR achieves high compression with minimal accuracy loss.

Latency remains stable with larger block sizes.

Abstract

Deploying deep neural networks on edge devices is often limited by the memory traffic and compute cost of dense linear operators. While quaternion neural networks improve parameter efficiency by coupling multiple channels through Hamilton products, they typically retain unstructured dense weights; conversely, structured matrices enable fast computation but are usually applied in the real domain. This paper introduces EdgeLDR, a practical framework for quaternion block-circulant linear and convolutional layers that combines quaternion channel mixing with block-circulant parameter structure and enables FFT-based evaluation through the complex adjoint representation. We present reference implementations of EdgeLDR layers and compare FFT-based computation against a naive spatial-domain realization of quaternion circulant products. FFT evaluation yields large empirical speedups over the naive implementation and keeps latency stable as block size increases, making larger compression factors computationally viable. We further integrate EdgeLDR layers into compact CNN and Transformer backbones and evaluate accuracy-compression trade-offs on 32x32 RGB classification (CIFAR-10/100, SVHN) and hyperspectral image classification (Houston 2013, Pavia University), reporting parameter counts and CPU/GPU latency. The results show that EdgeLDR layers provide significant compression with competitive accuracy.