用小波变换提升神经网络，兼顾效率与量子兼容性
WTHaar-Net: a Hybrid Quantum-Classical Approach
- 以哈尔小波替换哈达玛变换，实现多分辨率空间局部表示
- 在Tiny-ImageNet上参数量显著减少，精度优于ResNet和哈达玛基线
- 可部署于近中期量子硬件，适合追求轻量化与量子融合的视觉任务
卷积神经网络依赖线性滤波操作，可在特定变换域中高效重述。量子计算进展表明，某些结构化线性变换可通过浅层量子电路实现，为增强深度学习模型提供了混合量子-经典路径。本文提出WTHaar-Net，将先前混合架构中的哈达玛变换替换为哈尔小波变换（HWT）。与哈达玛变换不同，哈尔变换提供空间局部化、多分辨率表示，更符合视觉任务的归纳偏置。我们证明HWT可通过结构化哈达玛门实现量子化，其分解为适用于量子电路的酉操作。在CIFAR-10和Tiny-ImageNet上的实验表明，WTHaar-Net在保持竞争力准确率的同时实现显著参数压缩。在Tiny-ImageNet上，本方法超越了ResNet及基于哈达玛的基线。我们还在IBM Quantum云硬件上验证了量子实现，证明其与近中期量子设备兼容。
原文摘要 · Abstract (English)
Convolutional neural networks rely on linear filtering operations that can be reformulated efficiently in suitable transform domains. At the same time, advances in quantum computing have shown that certain structured linear transforms can be implemented with shallow quantum circuits, opening the door to hybrid quantum-classical approaches for enhancing deep learning models. In this work, we introduce WTHaar-Net, a convolutional neural network that replaces the Hadamard Transform used in prior hybrid architectures with the Haar Wavelet Transform (HWT). Unlike the Hadamard Transform, the Haar transform provides spatially localized, multi-resolution representations that align more closely with the inductive biases of vision tasks. We show that the HWT admits a quantum realization using structured Hadamard gates, enabling its decomposition into unitary operations suitable for quantum circuits. Experiments on CIFAR-10 and Tiny-ImageNet demonstrate that WTHaar-Net achieves substantial parameter reduction while maintaining competitive accuracy. On Tiny-ImageNet, our approach outperforms both ResNet and Hadamard-based baselines. We validate the quantum implementation on IBM Quantum cloud hardware, demonstrating compatibility with near-term quantum devices.
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