Haar足够了吗？探索Symlets和Coiflets用于小波卷积层
Is Haar Enough? Exploring Symlets and Coiflets for Wavelet Convolution Layers
- Bangladesh Univeristy of Engineering and Technology（孟加拉工程技术大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究探究小波卷积层的基选择，发现Coiflet基在图像分类、语义分割任务中，相较Haar基可减少约32%额外参数、33%额外FLOPs，为相关架构设计提供了可行选择。
AI中文摘要：
小波卷积层近期成为了一种通过多分辨率分析扩大感受野的高效机制，但现有研究已将小波基固定为所选分解深度下的Haar或Daubechies，未探究不同基是否能改变潜在的效率边界。我们在该场景中识别并表征了此前未被探索的权衡：具有更强近似特性（更长滤波器）的基可降低达到可比精度所需的分解深度，尽管每层变换成本更高，但仍能净减少参数和浮点运算量（FLOPs）。我们将此形式化为F-vs.-L权衡（滤波器长度vs.分解层数），并在受控架构和预算下，针对Haar、Daubechies、Symlets和Coiflets系统研究该权衡。在图像分类（CIFAR-10、ImageNet-1K）和语义分割（Cityscapes）任务中，基于Coiflet的小波卷积在更深层级上与Haar性能相当，额外参数减少约32%，额外FLOPs减少约33%，为构建基于小波的架构的从业者提供了具体可行的设计选择。
英文摘要：
Wavelet convolution layers have recently emerged as an efficient mechanism for enlarging receptive fields through multiresolution analysis, but prior work has fixed the wavelet basis to Haar or Daubechies at a chosen decomposition depth, leaving open whether a different basis can shift the underlying efficiency frontier. We identify and characterize a previously unexplored trade-off in this setting: bases with stronger approximation properties (longer filters) can reduce the decomposition depth required for competitive accuracy, yielding a net reduction in parameters and FLOPs despite higher perlevel transform cost. We formalize this as an F-vs.-L tradeoff (filter length vs. decomposition levels) and study it systematically across Haar, Daubechies, Symlets, and Coiflets under controlled architectures and budgets. On image classification (CIFAR-10, ImageNet-1K) and semantic segmentation (Cityscapes), Coiflet-based wavelet convolutions match Haar at deeper levels with approximately 32% fewer additional parameters and 33% fewer additional FLOPs, providing a concrete and actionable design choice for practitioners building wavelet-based architectures.
