# SoftSAE: Dynamic Top-K Selection for Adaptive Sparse Autoencoders

arXiv: https://arxiv.org/abs/2605.06610 · HTML: https://mlsanity.com/paper/2605.06610/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 7 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, 21 of 21)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [Natural Language Descriptions of Deep Visual Features](https://mlsanity.com/paper/2201.11114/) (2022)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [SAeUron: Interpretable Concept Unlearning in Diffusion Models with Sparse Autoencoders](https://mlsanity.com/paper/2501.18052/) (2025)
- [Interpreting CLIP with Hierarchical Sparse Autoencoders](https://mlsanity.com/paper/2502.20578/) (2025)
- [One-Step is Enough: Sparse Autoencoders for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2410.22366/) (2024)
- [Labeling Neural Representations with Inverse Recognition](https://mlsanity.com/paper/2311.13594/) (2023)
- [LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood](https://mlsanity.com/paper/2206.14882/) (2022)
- [An X-Ray Is Worth 15 Features: Sparse Autoencoders for Interpretable Radiology Report Generation](https://mlsanity.com/paper/2410.03334/) (2024)
- [Beyond Interpretability: The Gains of Feature Monosemanticity on Model Robustness](https://mlsanity.com/paper/2410.21331/) (2024)
- [LapSum -- One Method to Differentiate Them All: Ranking, Sorting and Top-k Selection](https://mlsanity.com/paper/2503.06242/) (2025)

## Built on by (most cited first, 1 of 1)

- [Beyond the Hard Budget: Sparsity Regularizers for More Interpretable Top-k Sparse Autoencoders](https://mlsanity.com/paper/2606.27321/) (2026)

## Abstract (arXiv)

Sparse Autoencoders (SAEs) have become an important tool in mechanistic interpretability, helping to analyze internal representations in both Large Language Models (LLMs) and Vision Transformers (ViTs). By decomposing polysemantic activations into sparse sets of monosemantic features, SAEs aim to translate neural network computations into human-understandable concepts. However, common architectures such as TopK SAEs rely on a fixed sparsity level. They enforce the same number of active features (K) across all inputs, ignoring the varying complexity of real-world data. Natural data often lies on manifolds with varying local intrinsic dimensionality, meaning the number of relevant factors can change significantly across samples. This suggests that a fixed sparsity level is not optimal. Simple inputs may require only a few features, while more complex ones need more expressive representations. Using a constant K can therefore introduce noise in simple cases or miss important structure in more complex ones. To address this issue, we propose SoftSAE, a sparse autoencoder with a Dynamic Top-K selection mechanism. Our method uses a differentiable Soft Top-K operator to learn an input-dependent sparsity level k. This allows the model to adjust the number of active features based on the complexity of each input. As a result, the representation better matches the structure of the data, and the explanation length reflects the amount of information in the input. Experimental results confirm that SoftSAE not only finds meaningful features, but also selects the right number of features for each concept. The source code is available at: https://github.com/St0pien/SoftSAE.