Parameter-Efficient Architectural Modifications for Translation-Invariant CNNs
Authors: Nuria Alabau-Bosque, Jorge Vila-Tomas, Paula Dauden-Oliver, Valero Laparra, Jesus Malo
Abstract
Convolutional Neural Networks (CNNs) are widely assumed to be translation-invariant, yet standard architectures exhibit a startling fragility: even a single-pixel shift can drastically degrade performance due to their reliance on spatially dependent fully connected layers. In this work, we resolve this vulnerability by proposing a lightweight 'Online Architecture' strategy. By strategically inserting Global Average Pooling (GAP) layers at various network depths, we effectively decouple feature recognition from spatial location. Using VGG-16 as a primary case study, we demonstrate that this architectural modification achieves a massive 98% reduction in trainable parameters (from 5.2M to just 82K) and a 90% reduction in total network size (138M to 14M). Despite this drastic pruning, our variants maintain competitive Top-1 accuracy on ImageNet (66.4%) while doubling translational robustness, reducing average relative loss from 0.09 to 0.05. Furthermore, our analysis identifies a fundamental limit to invariance: while GAP resolves macroscopic sensitivity, discrete pooling operations introduce a residual periodic aliasing that prevents perfect pixel-level stability. Finally, we extend these findings to Perceptual Image Quality Assessment (IQA) by integrating our invariant backbones into the LPIPS framework. The resulting metric significantly outperforms the retrained baseline in generalization across the KADID-10k dataset (Spearman 0.89 vs. 0.75) and achieves a near-perfect alignment with human psychophysical response curves on the RAID dataset (Spearman 0.95). These results confirm that enforcing architectural invariance is a far more efficient and biologically plausible path to robustness than traditional data augmentation. Data and code are publicly available. The data and code are publicly available to facilitate validation and further research.
Vision models have been found to be susceptible to perturbations such as motion blur induced at runtime by a shaking camera. This impedes their deployment in critical applications since phenomena such as slightly blurred vision might lead to failures, for example an object detector missing objects. While methods such as data augmentation or Adversarial Training can improve empirical robustness, they lack formal safety guarantees, making it difficult to identify and mitigate hidden vulnerabilities. We introduce a novel Certified Training approach that leverages an efficient encoding of convolutional perturbations to train provably robust models. Our method significantly outperforms Adversarial Training, achieving, for example, over 80% robust accuracy against motion blur of reasonable intensity on CIFAR10 while maintaining comparable standard accuracy.
Robustness to natural corruptions remains a fundamental challenge for deep neural networks. In this paper, we identify a robustness fading phenomenon where shallow layers spontaneously develop robust representations and flat loss landscapes in early training, yet these properties are not preserved during standard convergence. To address this, we propose a framework that performs strategic interventions on training dynamics to stabilize the empirically identified early-emergent robust priors. Our approach includes two parameter-free strategies: Early-Phase Stabilization~(EPS) and Asymmetric Weight Reversion~(AWR), which stabilize or recover robust shallow configurations without modifying the model architecture or introducing learnable parameters. Extensive experiments demonstrate the efficacy of our framework across various benchmarks and architectures, yielding significant gains in downstream transfer, dynamic adaptation, and diverse computer vision applications.
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(ay+b1)=af(y)+b1 for all a>0 and b∈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× slower.