# AdaptiveK: Complexity-Driven Sparse Autoencoders for Interpretable Language Model Representations

arXiv: https://arxiv.org/abs/2508.17320 · HTML: https://mlsanity.com/paper/2508.17320/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 24 Aug 2025.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [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)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)
- [Dissecting Contextual Word Embeddings: Architecture and Representation](https://mlsanity.com/paper/1808.08949/) (2018)
- [Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models](https://mlsanity.com/paper/2408.00113/) (2024)
- [A Language Model's Guide Through Latent Space](https://mlsanity.com/paper/2402.14433/) (2024)
- [Enhancing Neural Network Interpretability with Feature-Aligned Sparse Autoencoders](https://mlsanity.com/paper/2411.01220/) (2024)
- [Evaluating and Designing Sparse Autoencoders by Approximating Quasi-Orthogonality](https://mlsanity.com/paper/2503.24277/) (2025)

## Built on by (most cited first, 4 of 4)

- [MonoLoss: A Training Objective for Interpretable Monosemantic Representations](https://mlsanity.com/paper/2602.12403/) (2026)
- [Decoder-Preserving Sparse Autoencoders: Which Readouts Survive Sparse Compression?](https://mlsanity.com/paper/2607.17425/) (2026)
- [A Survey on the Linear Representation Hypothesis](https://mlsanity.com/paper/2609.22695/) (2026)
- [Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utility](https://mlsanity.com/paper/2610.20139/) (2026)

## Abstract (arXiv)

Understanding the internal representations of large language models (LLMs) remains a central challenge for interpretability research. Sparse autoencoders (SAEs) offer a promising solution by decomposing activations into interpretable features, but existing approaches rely on fixed sparsity constraints that fail to account for input complexity. We propose AdaptiveK SAE (Adaptive Top K Sparse Autoencoders), a novel framework that dynamically adjusts sparsity levels based on the semantic complexity of each input. Leveraging linear probes, we demonstrate that context complexity is linearly encoded in LLM representations, and we use this signal to guide feature allocation during training. Experiments across ten language models demonstrate that this complexity-driven adaptation outperforms fixed-sparsity approaches on reconstruction fidelity, explained variance, cosine similarity and interpretability metrics while eliminating the burden of extensive hyperparameter tuning. Our code is available at: https://github.com/hiyukie/adaptiveK.