Bayesian Deep Learning

Neural networks are often biased to spuriously correlated features that provide misleading statistical evidence that does not generalize. This raises an interesting question: "Does an optimal unbiased functional subnetwork exist in a severely biased network? If so, how to extract such subnetwork?" While empirical evidence has been accumulated about the existence of such unbiased subnetworks, these observations are mainly based on the guidance of ground-truth unbiased samples. Thus, it is unexplored how to discover the optimal subnetworks with biased training datasets in practice. To address this, here we first present our theoretical insight that alerts potential limitations of existing algorithms in exploring unbiased subnetworks in the presence of strong spurious correlations. We then further elucidate the importance of bias-conflicting samples on structure learning. Motivated by these observations, we propose a Debiased Contrastive Weight Pruning (DCWP) algorithm, which probes unbiased subnetworks without expensive group annotations. Experimental results demonstrate that our approach significantly outperforms state-of-the-art debiasing methods despite its considerable reduction in the number of parameters.

Recently deep learning techniques have significantly advanced image super-resolution (SR). Due to the black-box nature, quantifying reconstruction uncertainty is crucial when employing these deep SR networks. Previous approaches for SR uncertainty estimation mostly focus on capturing pixel-wise uncertainty in the spatial domain. SR uncertainty in the frequency domain which is highly related to image SR is seldom explored. In this paper, we propose to quantify spectral Bayesian uncertainty in image SR. To achieve this, a Dual-Domain Learning (DDL) framework is first proposed. Combined with Bayesian approaches, the DDL model is able to estimate spectral uncertainty accurately, enabling a reliability assessment for high frequencies reasoning from the frequency domain perspective. Extensive experiments under non-ideal premises are conducted and demonstrate the effectiveness of the proposed spectral uncertainty. Furthermore, we propose a novel Spectral Uncertainty based Decoupled Frequency (SUDF) training scheme for perceptual SR. Experimental results show the proposed SUDF can evidently boost perceptual quality of SR results without sacrificing much pixel accuracy.

Recent research in robust optimization has shown an overfitting-like phenomenon in which models trained against adversarial attacks exhibit higher robustness on the training set compared to the test set. Although previous work provided theoretical explanations for this phenomenon using a robust PAC-Bayesian bound over the adversarial test error, related algorithmic derivations are at best only loosely connected to this bound, which implies that there is still a gap between their empirical success and our understanding of adversarial robustness theory. To close this gap, in this paper we consider a different form of the robust PAC-Bayesian bound and directly minimize it with respect to the model posterior. The derivation of the optimal solution connects PAC-Bayesian learning to the geometry of the robust loss surface through a Trace of Hessian (TrH) regularizer that measures the surface flatness. In practice, we restrict the TrH regularizer to the top layer only, which results in an analytical solution to the bound whose computational cost does not depend on the network depth. Finally, we evaluate our TrH regularization approach over CIFAR-10/100 and ImageNet using Vision Transformers (ViT) and compare against baseline adversarial robustness algorithms. Experimental results show that TrH regularization leads to improved ViT robustness that either matches or surpasses previous state-of-the-art approaches while at the same time requires less memory and computational cost.

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While current efforts focus on improving uncertainty quantification accuracy and efficiency, there is a need to identify uncertainty sources and take actions to mitigate their effects on predictions. Therefore, we propose to develop explainable and actionable Bayesian deep learning methods to not only perform accurate uncertainty quantification but also explain the uncertainties, identify their sources, and propose strategies to mitigate the uncertainty impacts. Specifically, we introduce a gradient-based uncertainty attribution method to identify the most problematic regions of the input that contribute to the prediction uncertainty. Compared to existing methods, the proposed UA-Backprop has competitive accuracy, relaxed assumptions, and high efficiency. Moreover, we propose an uncertainty mitigation strategy that leverages the attribution results as attention to further improve the model performance. Both qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of our proposed methods.

Reliable uncertainty from deterministic single-forward pass models is sought after because conventional methods of uncertainty quantification are computationally expensive. We take two complex single-forward-pass uncertainty approaches, DUQ and SNGP, and examine whether they mainly rely on a well-regularized feature space. Crucially, without using their more complex methods for estimating uncertainty, we find that a single softmax neural net with such a regularized feature-space, achieved via residual connections and spectral normalization, outperforms DUQ and SNGP's epistemic uncertainty predictions using simple Gaussian Discriminant Analysis post-training as a separate feature-space density estimator---without fine-tuning on OoD data, feature ensembling, or input pre-procressing. Our conceptually simple Deep Deterministic Uncertainty (DDU) baseline can also be used to disentangle aleatoric and epistemic uncertainty and performs as well as Deep Ensembles, the state-of-the art for uncertainty prediction, on several OoD benchmarks (CIFAR-10/100 vs SVHN/Tiny-ImageNet, ImageNet vs ImageNet-O), active learning settings across different model architectures, as well as in large scale vision tasks like semantic segmentation, while being computationally cheaper.

We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochastic ensembles are formulated as families of distributions and trained to approximate the Bayesian posterior with variational inference. We implement stochastic ensembles based on Monte Carlo dropout, DropConnect and a novel non-parametric version of dropout and evaluate them on a toy problem and CIFAR image classification. For both tasks, we test the quality of the posteriors directly against Hamiltonian Monte Carlo simulations. Our results show that stochastic ensembles provide more accurate posterior estimates than other popular baselines for Bayesian inference.