# Layerwise Tunable Lifting Scheme for the Convolutional Neural Network

arXiv: https://arxiv.org/abs/2609.09827 · HTML: https://mlsanity.com/paper/2609.09827/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [WaveCNet: Wavelet Integrated CNNs to Suppress Aliasing Effect for Noise-Robust Image Classification](https://mlsanity.com/paper/2107.13335/) (2021)
- [Learning strides in convolutional neural networks](https://mlsanity.com/paper/2202.01653/) (2022)
- [Wavelet-Attention CNN for Image Classification](https://mlsanity.com/paper/2201.09271/) (2022)
- [Biorthogonal Tunable Wavelet Unit with Lifting Scheme in Convolutional Neural Network](https://mlsanity.com/paper/2507.00739/) (2025)

## Abstract (arXiv)

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.