Interleaved Noise Injection Improves Clean, Corrupted, and OOD Performance
Authors: Matt L. Wiemann, Peter Melchior, Andrew K. Saydjari
Organizations: Princeton University
Abstract
Noise injection is a well-known technique in stochastic optimization. We report its surprising effectiveness with an interleaved (on-off-on-off...) rather than the usual monotonic decay schedule. We present a theoretical analysis of noise injection, which confirms that corruption by impulse noise approximates a Jacobian regularization, whereas Gaussian noise acts as a curvature penalty. This regularization behavior has been invoked to explain why noise injection increases model robustness. But the interleaved nature of our proposed schedule produces superior results even for the optimization objective: mixing phases of noisy data permits the optimizer to escape local minima and increase exploration without the risk of catastrophically forgetting the important features from the clean data. To stabilize this training scheme against the rapid changes of the loss when switching between clean and noisy data, we introduce a gradient-norm stabilization technique that scales noisy updates based on clean gradient magnitudes. We compare this method with other common augmentation methods and find substantial improvements in corruption tolerance and robustness to real-world distribution shifts on CIFAR-100-C, ImageNet-C, and ImageNet-R for ResNet and ViT architectures, with the best results being achieved by stacking our method on top of other augmentations. Through saliency and attention maps we show that the effect of interleaved noise injection stems from penalizing the failure modes encouraged by the inductive bias of the models: impulse noise works against the locality bias of convolutional (ResNet) architectures, and Gaussian noise reduces the tendency of attention-based models to pick up large-scale spurious features. Interleaved noise injection is therefore an effective tool to improve the test performance on clean, noisy, and out-of-distribution data at essentially zero computational cost.
Injecting noise into the optimization process is a well-established technique for improving the training and generalization of deep neural networks. Yet, despite the breadth of existing approaches, it remains unclear which design choices truly matter in practice. In this work, we investigate parameter noise injection for stochastic gradient descent, focusing on two key questions: how to efficiently pair each training example with its own perturbation in mini-batch training, and whether sophisticated noise parameterizations or multi-sample gradient averaging yield meaningful gains over simpler alternatives. To address the first question, we leverage a distributional identity for linear layers that allows per-example noise injection without breaking batched computation. To address the second, we systematically compare several diagonal Gaussian parameterizations against an isotropic baseline across varying noise levels on CIFAR100. Our results consistently show that simple, lightweight strategies, isotropic noise with a single perturbed forward pass per update step, recover most of the benefit of more complex schemes. These findings suggest that simplicity suffices for parameter noise injection, and that practitioners need not resort to elaborate perturbation designs to reap the optimization and generalization benefits of noisy SGD.
Benjamin Leblanc, Louis-Jacob Lebel, Teddy Kana +1
We propose a novel training-free method for inpainting with off-the-shelf text-to-image models. While guidance-based methods in theory allow generic models to be used for inverse problems such as inpainting -- in practice their effectiveness is limited, leading to the necessity of specialized inpainting-specific models. In this work, we argue the missing ingredient for training-free generic model usage is proper optimization of the initial noise sample. We optimize the initial noise to approximately reproduce the unmasked image, in as few as tens of optimization steps, then use it with a conventional training-free inpainting method. Critically, we propose two core ideas that make this possible: (i) we perform linear approximation that avoids the costly and often impractical unrolling required to relate the initial noise sample to model output -- which potentially is why this relationship was previously overlooked; and (ii) perform spectral preconditioning by optimizing the initial noise sample in the spectral domain with Adam, which stabilizes the optimization. We demonstrate our method on various inpainting tasks, outperforming the state of the art. Project website: https://ubc-vision.github.io/sonic/
Model robustness against natural image corruptions is essential for safety-critical applications. While existing methods primarily focus on implicit representation learning, we provide the first systematic exploration of computational pathways to explicitly characterize internal robustness. We identify a progressive decay of robust features across network layers and establish a functional dependency between the prevalence of these features and model performance. To exploit these insights, we propose Suppress and Diversify (S&D), a non-intrusive refinement approach that enhances robustness by dynamically selecting robust pathways and diversifying them through symmetry-preserving transformations. S&D is architecture-agnostic, parameter-free, and incurs zero test-time overhead. Extensive evaluations across eight benchmarks demonstrate that S&D consistently improves performance across multiple vision tasks, diverse backbones, and complex real-world scenarios, highlighting its broad efficacy and scalability.