Mechanistic interpretability aims to explain a model's behavior by identifying causally responsible internal structures. Dictionary-based explainers such as sparse autoencoders and transcoders are a primary tool, but their faithfulness under out-of-distribution (OOD) shift has received little systematic attention. We show that distribution shift rotates the subspace that the model actively uses, misaligning the explainer's dictionary trained on in-distribution (ID) activations. We formalize this misalignment as the faithfulness gap, a geometric distance between the ID dictionary and the OOD-active subspace, and show that it bounds excess OOD projection loss. To reduce this gap, we propose the Geometry-Adaptive Explainer (GAE), which realigns the dictionary with the OOD-active subspace while preserving the original sparse feature activations. This requires only unlabeled OOD activations and no gradient updates. For the adapted dictionary, we also bound the excess projection loss caused by any remaining faithfulness gap. Empirically, GAE even matches or surpasses all training-based baselines in causal faithfulness across multiple models and OOD settings.

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