The paper introduces a scalable method for uncertainty quantification in neural networks by applying a low‑rank generalized Laplace approximation within a data‑informed active subspace. It constructs a local Gaussian posterior around pretrained weights, calibrates the prior variance via empirical Bayes, and compares two posterior scalings: standard Bayesian and mean‑loss scaling. The study finds that mean‑loss scaling yields a more stable, lower‑dimensional subspace and produces calibrated, coherent predictive confidence intervals, whereas standard scaling can cause posterior variance contraction and degrade predictive coherence.
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.
arXiv:2605. 09075v2 Announce Type: replace-cross Abstract: Although the Laplace approximation offers a simple route to uncertainty quantification in deep neural networks, its reliance on inverting large Hessian matrices has motivated a range of computationally feasible low-dimensional or sparse approximations.
arXiv:2606. 15479v1 Announce Type: cross Abstract: Steerable convolutional neural networks (Steerable-CNNs) guarantee SE(3)-equivariance by parameterizing kernels as linear combinations of steerable basis functions, but their deterministic nature precludes uncertainty quantification - limiting their use in settings where confidence estimates are essential.
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
arXiv:2607. 25376v1 Announce Type: cross Abstract: In Bayesian neural networks (BNNs), variational inference is a widely adopted framework for modeling uncertainty in a distributional way, with the evidence lower bound (ELBO) serving as the standard objective function.
arXiv:2606. 27269v1 Announce Type: cross Abstract: Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models.
arXiv:2610.19074v1 Announce Type: new Abstract: Reliable uncertainty quantification remains an important challenge in AI. Hierarchical Bayesian methods provide a principled framework for this by repr...
arXiv:2502.00550v2 Announce Type: replace Abstract: Surrogate models of parametric dynamical systems are essential for many-query and real-time predictions in engineering applications such as design...
The paper introduces an uncertainty‑driven training framework for 3D CT lung nodule classification that uses validation‑based uncertainty estimates to reweight the loss, aiming to improve predictive performance and probability calibration. Two uncertainty quantification methods—Monte Carlo Dropout and Evidential Deep Learning—are evaluated across multiple backbone architectures (ResNet, DenseNet, EfficientNet, ViT, Swin) on the LIDC‑IDRI and NoduleMNIST3D datasets. The approach yields comparable classification accuracy to conventional training while substantially reducing expected calibration error, especially on convolutional backbones, and shows that simple temperature scaling can also achieve strong calibration.
The paper introduces Latent-Posterior Alignment (LPA), a phenomenon where predictive uncertainty in Graph Neural Networks with Bayesian output layers decreases as latent representations align with lower‑variance posterior directions, even without posterior variance contraction. Through interventional experiments, the authors demonstrate LPA’s functional role in shaping uncertainty and propose Alignment‑Guided Learning (AGL) to explicitly promote this alignment during training. AGL reduces predictive uncertainty, preserves accuracy, and improves structural calibration, ensuring model confidence reflects data density.
arXiv:2608.29349v1 Announce Type: new Abstract: Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-e...
arXiv:2609.08620v1 Announce Type: cross Abstract: We address the challenge of scalable uncertainty quantification in large-scale scientific applications, where complex state-of-the-art machine learni...