用Coiflet波小波替代传统Haar，减少参数和计算量
Is Haar Enough? Exploring Symlets and Coiflets for Wavelet Convolution Layers
- 比较了不同小波基在卷积层中的表现，发现长滤波器小波可降低分解深度
- 在图像分类与分割任务中，使用Coiflet比Haar少32%参数、33%计算量
- 为波小波架构设计提供可落地的新选择，适合追求效率的工程师
波小波卷积层通过多分辨率分析有效扩展感受野，但以往工作固定使用Haar或Daubechies小波，未探索其他基函数的潜力。本文揭示并刻画了一个未被关注的权衡：具有更强逼近性能的小波（滤波器更长）虽每层变换成本更高，但可显著降低所需分解层级，从而在整体上减少参数和浮点运算量。我们将其形式化为滤波器长度（F）与分解层数（L）之间的权衡，并在控制架构与预算下系统比较了Haar、Daubechies、Symlets和Coiflets。在CIFAR-10、ImageNet-1K图像分类及Cityscapes语义分割任务中，基于Coiflet的波小波卷积在更深层次达到与Haar相当的精度，额外参数减少约32%，额外计算量减少约33%，为构建高效波小波网络提供了明确且可操作的设计选择。
原文摘要 · Abstract (English)
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.
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