Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

Deep neural networks (DNNs) excel on clean images but struggle with corrupted ones. Incorporating specific corruptions into the data augmentation pipeline can improve robustness to those corruptions but may harm performance on clean images and other types of distortion. In this paper, we introduce an alternative approach that improves the robustness of DNNs to a wide range of corruptions without compromising accuracy on clean images. We first demonstrate that input perturbations can be mimicked by multiplicative perturbations in the weight space. Leveraging this, we propose Data Augmentation via Multiplicative Perturbation (DAMP), a training method that optimizes DNNs under random multiplicative weight perturbations. We also examine the recently proposed Adaptive Sharpness-Aware Minimization (ASAM) and show that it optimizes DNNs under adversarial multiplicative weight perturbations. Experiments on image classification datasets (CIFAR-10/100, TinyImageNet and ImageNet) and neural network architectures (ResNet50, ViT-S/16, ViT-B/16) show that DAMP enhances model generalization performance in the presence of corruptions across different settings. Notably, DAMP is able to train a ViT-S/16 on ImageNet from scratch, reaching the top-1 error of 23.7% which is comparable to ResNet50 without extensive data augmentations.

Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational complexity of large-scale architectures and datasets. Node-based BNNs have recently been introduced as scalable alternatives, which induce epistemic uncertainty by multiplying each hidden node with latent random variables, while learning a point-estimate of the weights. In this paper, we interpret these latent noise variables as implicit representations of simple and domain-agnostic data perturbations during training, producing BNNs that perform well under covariate shift due to input corruptions. We observe that the diversity of the implicit corruptions depends on the entropy of the latent variables, and propose a straightforward approach to increase the entropy of these variables during training. We evaluate the method on out-of-distribution image classification benchmarks, and show improved uncertainty estimation of node-based BNNs under covariate shift due to input perturbations. As a side effect, the method also provides robustness against noisy training labels.