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

Wavelet convolution (WTConv) has emerged as an increasingly popular drop-in replacement for standard convolutions, expanding a network's receptive field exponentially with the number of decomposition levels while keeping the parameter count linear. However, its reference implementation is severely memory-bound due to excessive data movement through high-bandwidth memory (HBM). We develop an I/O model of WTConv to characterize this bottleneck and use it to guide three algebraic reformulations: (1) recomputing the inexpensive Haar analysis butterfly on chip, (2) collapsing the multi-level synthesis cascade into a single closed-form pass indexed by output-coordinate bits, and (3) folding learned per-channel scales into the convolution weights. Together, these reformulations enable an I/O-aware fused implementation that substantially reduces HBM traffic. We evaluate the WTConvNeXt configuration across decomposition levels and a broad range of tensor shapes. Despite performing comparable arithmetic, the reference WTConv is substantially slower than the depthwise convolution it replaces. Our reformulation reduces modeled HBM traffic by approximately $2.55\times$, yielding up to a $4.35\times$ training speedup over the reference while roughly halving peak memory usage. Thus, our reformulation preserves the benefits of WTConv while substantially reducing its execution time and memory footprint, removing the systems overhead that previously limited its practical efficiency.

We introduce CoLoRA (Convolutional Low-Rank Adaptation), a parameter-efficient fine-tuning method for convolutional neural networks (CNNs). CoLoRA extends LoRA to convolutional layers by decomposing kernel updates into lightweight depthwise and pointwise components. This design reduces the number of trainable convolutional-update parameters by over 80% compared with full convolutional fine-tuning, while allowing the learned updates to be merged into the pretrained convolutional kernels, thereby preserving the original model size and inference complexity. Experiments on MedMNIST datasets, particularly OCTMNISTv2, demonstrate that CoLoRA applied to VGG16 and ResNet50 achieves competitive classification performance while substantially reducing the number of trainable parameters. Comparisons with transfer learning, adapters, BitFit, and convolutional LoRA variants further characterize the trade-offs among predictive performance, trainable parameters, and training cost. Additional experiments on CIFAR-100 and Cats vs. Dogs provide preliminary evidence that the proposed adaptation strategy also transfers to non-medical image-classification tasks. Peak GPU-memory measurements further show that parameter efficiency does not translate directly into proportional training-memory savings, with memory consumption depending strongly on the placement of the adapted convolutional layers. Overall, CoLoRA provides a parameter-efficient and deployment-efficient alternative to full fine-tuning for convolutional models.

Adapting large pretrained vision models to medical image classification is often limited by memory, computation, and task-specific specializations. Parameter-efficient fine-tuning (PEFT) methods like LoRA reduce this cost by learning low-rank updates, but operating directly in feature space can struggle to capture the localized, multi-scale features common in medical imaging. We propose WaRA, a wavelet-structured adaptation module that performs low-rank adaptation in a wavelet domain. WaRA reshapes patch tokens into a spatial grid, applies a fixed discrete wavelet transform, updates subband coefficients using a shared low-rank adapter, and reconstructs the additive update through an inverse wavelet transform. This design provides a compact trainable interface while biasing the update toward both coarse structure and fine detail. For extremely low-resource settings, we introduce Tiny-WaRA, which further reduces trainable parameters by learning only a small set of coefficients in a fixed basis derived from the pretrained weights through a truncated SVD. Experiments on medical image classification across four modalities and datasets demonstrate that WaRA consistently improves performance over strong PEFT baselines, while retaining a favorable efficiency profile. Our code is publicly available at https://github.com/moeinheidari7829/WaRA.