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 links distribution shift to the input sensitivity of the model. The resulting operators admit a geometric interpretation as a projection of distribution shift onto the sensitivity field of the model, with theoretical guarantees. Beyond detecting a shift, the 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/ImageNet-1K perturbed benchmarks demonstrate that TASTE aligns closely with task degradation while showing competitive performance compared to established baselines, with gains that depend on the shift regime.

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