# Active Budget Can Kill Sensitivity: Diagnosing and Repairing TopK Sparse Autoencoder Reliability

arXiv: https://arxiv.org/abs/2609.37857 · HTML: https://mlsanity.com/paper/2609.37857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Mechanistic interpretability / [SAE features and their applications](https://mlsanity.com/mechinterp/sae-features-and-their-applications/)

## Builds on (most cited first, 30 of 37)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Adversarial Examples for Evaluating Reading Comprehension Systems](https://mlsanity.com/paper/1707.07328/) (2017)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Adversarial Example Generation with Syntactically Controlled Paraphrase Networks](https://mlsanity.com/paper/1804.06059/) (2018)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)

## Abstract (arXiv)

Sparse autoencoders (SAEs) are increasingly scaled to wider dictionaries to recover fine-grained structure from large language model activations. However, a feature is useful for interpretation only if it remains a stable unit of analysis when the same meaning is expressed in different surface forms. We study this reliability question for TopK SAEs via feature sensitivity. Experiments demonstrate that scaling selectively reduces the sensitivity of rare features, while common features remain comparatively stable. A controlled width(× k) factorial experiment identifies the active budget k as the root cause: the degradation arises from the selection boundary rather than dictionary width alone. We attribute this failure to the geometry of TopK selection. The active margin, the distance to the cutoff, predicts feature loss without thresholds. Guided by this margin diagnosis, we introduce pairwise rank stabilization. Our method targets ordering failures at the cutoff and improves rare-feature sensitivity by (8.83) percentage points, while keeping reconstruction and alive-feature coverage near the baseline. Overall, our results suggest that wide TopK SAEs should be evaluated not only by reconstruction, sparsity, and feature count, but also by feature reliability under semantic variation and boundary geometry for stable interpretability.