# Geometry-Adaptive Explainer for Faithful Dictionary-Based Interpretability under Distribution Shift

arXiv: https://arxiv.org/abs/2605.21849 · HTML: https://mlsanity.com/paper/2605.21849/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 30 of 32)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Tilted Empirical Risk Minimization](https://mlsanity.com/paper/2007.01162/) (2020)
- [EDGAR-CORPUS: Billions of Tokens Make The World Go Round](https://mlsanity.com/paper/2109.14394/) (2021)
- [Transcoders Beat Sparse Autoencoders for Interpretability](https://mlsanity.com/paper/2501.18823/) (2025)
- [On the Robustness of Removal-Based Feature Attributions](https://mlsanity.com/paper/2306.07462/) (2023)
- [Decoding Dark Matter: Specialized Sparse Autoencoders for Interpreting Rare Concepts in Foundation Models](https://mlsanity.com/paper/2411.00743/) (2024)
- [Normalized AOPC: Fixing Misleading Faithfulness Metrics for Feature Attribution Explainability](https://mlsanity.com/paper/2408.08137/) (2024)

## Abstract (arXiv)

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 controls OOD faithfulness degradation. To reduce this gap, we propose the Geometry-Adaptive Explainer (GAE), which realigns the explainer's dictionary with the OOD-active subspace while preserving the original feature structure. This requires only unlabeled OOD activations and no gradient updates. We prove that GAE improves over the unadapted ID explainer, with excess loss bounded quadratically by the second-moment shift. Empirically, GAE even matches or surpasses all training-based baselines in causal faithfulness across multiple models and OOD settings.