Training neural networks to jointly predict mean and uncertainty estimates from noisy observations can be unstable, prompting a series of independent stabilization efforts. We argue that these interventions highlight a common underlying issue where gradient steps are poorly aligned with the geometry of the loss landscape.
arXiv:2608. 10374v1 Announce Type: new Abstract: Training neural networks to jointly predict mean and uncertainty estimates from noisy observations can be unstable, prompting a series of independent stabilization efforts.
arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.
arXiv:2608. 07630v1 Announce Type: new Abstract: We adapt two classical statistical estimators for quantifying uncertainty to modern deep learning, in order to provide clearer insights into uncertainty attributable to two sources : aleatoric uncertainty, or locally scarce data.
arXiv:2605. 25811v2 Announce Type: replace-cross Abstract: We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure.
arXiv:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.
arXiv:2608. 04442v1 Announce Type: new Abstract: Robustness to natural corruptions remains a fundamental challenge for deep neural networks.
arXiv:2605. 29547v2 Announce Type: replace-cross Abstract: Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators.
arXiv:2606. 08799v1 Announce Type: cross Abstract: We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual--curvature term.
arXiv:2502. 17055v5 Announce Type: replace Abstract: Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence.
arXiv:2607. 05536v1 Announce Type: cross Abstract: Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers.
arXiv:2606. 10196v1 Announce Type: cross Abstract: Parameter-efficient fine-tuning (PEFT) aims to adapt pretrained models with a small trainable parameter subset, however, most existing methods choose this subset from fixed architectural heuristics rather than using dynamic, task-aware criteria.
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.