TASER: Task-Aware Stein Regularisation for Geometry-Driven Robustness

Modern deep networks remain fragile under distribution shift and adversarial perturbations, often due to excessive or poorly structured input sensitivity. We introduce TASER (Task-Aware Stein Regularisation), a training-time regularisation framework derived from Langevin Stein operators. By penalising pointwise Stein residuals under the training distribution, TASER encourages geometric compatibility between predictors and data density, inducing anisotropic, data-aware smoothness. We provide theoretical links between Stein regularisation and reduced first-order shift sensitivity, develop scalable implementation variants compatible with modern architectures, and demonstrate improved robustness and stability across regression and vision benchmarks. Across CIFAR-10 experiments, TASER consistently improves the adversarial robustness of established training methods without incurring statistically significant clean-accuracy degradation.

TASTE: Task-Aware Out-of-Distribution Detection via Stein Operators

Out-of-distribution detection methods are often either data-centric, detecting deviations from the training input distribution irrespective of their effect on a trained model, or model-centric, relying on classifier outputs without explicit reference to data geometry. We propose TASTE (Task-Aware STEin operators): a task-aware framework based on so-called Stein operators, which allows us to link distribution shift to the input sensitivity of the model. We show that the resulting operator admits a clear geometric interpretation as a projection of distribution shift onto the sensitivity field of the model, yielding theoretical guarantees. Beyond detecting the presence of a shift, the same construction enables its localisation through a coordinate-wise decomposition, and for image data-provides interpretable per-pixel diagnostics. Experiments on controlled Gaussian shifts, MNIST under geometric perturbations, and CIFAR-10 perturbed benchmarks demonstrate that the proposed method aligns closely with task degradation while outperforming established baselines.