# Is Haar Enough? Exploring Symlets and Coiflets for Wavelet Convolution Layers

arXiv: https://arxiv.org/abs/2608.17662 · HTML: https://mlsanity.com/paper/2608.17662/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 21 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [Visual Attention Network](https://mlsanity.com/paper/2202.09741/) (2022)
- [Wave-ViT: Unifying Wavelet and Transformers for Visual Representation Learning](https://mlsanity.com/paper/2207.04978/) (2022)
- [Wavelet Convolutions for Large Receptive Fields](https://mlsanity.com/paper/2407.05848/) (2024)
- [Adaptive Frequency Filters As Efficient Global Token Mixers](https://mlsanity.com/paper/2307.14008/) (2023)
- [WaveMix: Resource-efficient Token Mixing for Images](https://mlsanity.com/paper/2203.03689/) (2022)
- [Multiscale Attention via Wavelet Neural Operators for Vision Transformers](https://mlsanity.com/paper/2303.12398/) (2023)

## Abstract (arXiv)

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.