Lightweight Adaptive ReduNet via Hyperspherical Manifold Learning

2026-08-20

AI Summary

为减少ReduNet层数与参数存储，提出LA-ReduNet，通过超球面流形学习和自适应步长，以更少的层达到稳定的MCR^2目标。

Abstract

In recent years, a white-box neural network called ReduNet has been proposed, which employs the maximal coding rate reduction (MCR$^2$) principle to transform raw data into low-dimensional discriminative features via a forward layer-wise construction process. Unlike traditional deep networks that rely on backpropagation, ReduNet explicitly derives the parameters of each layer from the features of its preceding layer, offering a mathematically interpretable paradigm. However, this layer-wise construction often requires a large number of layers for the MCR$^2$ objective to reach a stable value, which increases the parameter storage of the unfolded module. To address this issue, we propose LA-ReduNet, a lightweight adaptive architecture that refines the layer-wise update rule and enables discriminative feature representations to be obtained with substantially fewer unfolded layers. Specifically, LA-ReduNet employs hyperspherical manifold learning and adaptive step sizes, thereby reducing by an order of magnitude the number of layers required for the MCR$^2$ objective to reach a stable value. Simulation results demonstrate that, while maintaining comparable classification accuracy, LA-ReduNet requires significantly fewer layers for the MCR$^2$ objective to reach a stable value. Remarkably, under the considered experimental settings, LA-ReduNet requires only approximately $1/29$ of the parameter storage of the unfolded ReduNet module for the MCR$^2$ objective to reach a stable value.

Problem

• Lightweight Adaptive ReduNet
• Hyperspherical Manifold Learning
• Maximal Coding Rate Reduction (MCR^2)
• Layer-wise Construction
• Parameter Storage

Innovation

• hyperspherical manifold learning
• adaptive step sizes
• lightweight adaptive architecture
• reduced layer count
• MCR^2