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The authors design a family of layerwise tunable, lattice-structured lifting schemes鈥攕panning low-pass, high-pass, and sequential joint adaptations鈥攖hat integrate learnable biorthogonal wavelet filter banks into convolutional backbones. By formulating the lifting steps via a lattice structure, the architecture mathematically guarantees invertibility and numerical stability for arbitrary parameter values during gradient updates. Evaluated on a ResNet-18 backbone, the framework achieves consistent performance gains across texture classification on DTD and visual anomaly detection on MVTec-AD and KRC102S.
Wavelet transforms in deep learning no longer require trading off learnability for mathematical stability: lattice-structured lifting steps guarantee perfect invertibility and stability under arbitrary network parameter updates.
This work introduces a family of tunable lifting schemes for biorthogonal wavelet filter banks. We propose three lifting strategies: low-pass tuning (LS-LayLatt-LP), high-pass tuning (LS-LayLatt-HP), and a sequential lifting scheme that jointly adapts low- and high-frequency branches (LS-LayLatt-Sequential). All proposed designs are formulated using a lattice-based lifting structure, which guarantees invertibility and stability for arbitrary parameter values within the lifting functions. We evaluated the proposed methods by integrating them into a ResNet-18 backbone for image classification on the Describable Textures Dataset (DTD), as well as for anomaly detection on hazelnut images from the MVTec-AD dataset and private KRC102S dataset. Experimental results demonstrate consistent performance improvements across all evaluated tasks.
