Layerwise Tunable Lifting Scheme for the Convolutional Neural Network

Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and $b\in\mathbb{R}$. Existing NE methods constrain every internal layer to NE-compatible operations. These constraints add runtime cost and exclude standard transformer components such as softmax attention and LayerNorm. We introduce Wrapped Normalization Equivariance (WNE), a parameter-free wrapper that normalizes the input, applies any backbone, and denormalizes the output. We prove every NE function admits this factorization, so the wrapper exactly parameterizes the class of NE functions. On blind denoising, wrapping CNN and transformer architectures improves robustness under noise-level mismatch with no measurable GPU overhead, while architectural NE baselines are up to $1.6\times$ slower.

This paper proposes a new method to improve the training efficiency of deep convolutional neural networks. During training, the method evaluates scores to measure how much each layer's parameters change and whether the layer will continue learning or not. Based on these scores, the network is scaled down such that the number of parameters to be learned is reduced, yielding a speed up in training. Unlike state-of-the-art methods that try to compress the network to be used in the inference phase or to limit the number of operations performed in the backpropagation phase, the proposed method is novel in that it focuses on reducing the number of operations performed by the network in the forward propagation during training. The proposed training strategy has been validated on two widely used architecture families: VGG and ResNet. Experiments on MNIST, CIFAR-10 and Imagenette show that, with the proposed method, the training time of the models is more than halved without significantly impacting accuracy. The FLOPs reduction in the forward propagation during training ranges from 17.83% for VGG-11 to 83.74% for ResNet-152. These results demonstrate the effectiveness of the proposed technique in speeding up learning of CNNs. The technique will be especially useful in applications where fine-tuning or online training of convolutional models is required, for instance because data arrive sequentially.

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.