发表机构
Southwest Jiaotong University（西南交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对ReduNet参数存储量大的问题，提出轻量型自适应LA-ReduNet，采用超球面流形学习和自适应步长，仅需约1/29的参数存储即可使MCR²目标稳定，且保持相当分类准确率。
AI 中文摘要
近年来，一种名为ReduNet的白盒神经网络被提出，该网络采用最大编码率缩减（MCR²）原理，通过逐层前向构建过程将原始数据转换为低维判别特征。与依赖反向传播的传统深度网络不同，ReduNet从其前一层的特征显式推导各层参数，提供了一种具有数学可解释性的范式。然而，这种逐层构建通常需要大量层才能使MCR²目标达到稳定值，这增加了展开模块的参数存储。为解决该问题，我们提出了LA-ReduNet，一种轻量型自适应架构，它改进了逐层更新规则，仅需大幅减少的展开层即可获得判别特征表示。具体而言，LA-ReduNet采用超球面流形学习和自适应步长，从而使MCR²目标达到稳定值所需的层数减少了一个数量级。仿真结果表明，在保持相当分类准确率的同时，LA-ReduNet使MCR²目标达到稳定值所需的层数显著减少。值得注意的是，在所考虑的实验设置下，LA-ReduNet使MCR²目标达到稳定值所需的参数存储仅为展开式ReduNet模块的约1/29。
英文摘要
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.
Comments64 pages, 16 figures, 3 tables
