# Concept-SAE: A Controllable and Invertible Concept Interface for Sparse Autoencoders

arXiv: https://arxiv.org/abs/2509.22015 · HTML: https://mlsanity.com/paper/2509.22015/

## 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 31 of its 39 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## 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 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Visual Interpretability for Deep Learning: a Survey](https://mlsanity.com/paper/1802.00614/) (2018)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Sparse Autoencoders Trained on the Same Data Learn Different Features](https://mlsanity.com/paper/2501.16615/) (2025)
- [Discover-then-Name: Task-Agnostic Concept Bottlenecks via Automated Concept Discovery](https://mlsanity.com/paper/2407.14499/) (2024)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [Shield: Fast, Practical Defense and Vaccination for Deep Learning using JPEG Compression](https://mlsanity.com/paper/1802.06816/) (2018)
- [Deflecting Adversarial Attacks with Pixel Deflection](https://mlsanity.com/paper/1801.08926/) (2018)
- [Sparse autoencoders reveal selective remapping of visual concepts during adaptation](https://mlsanity.com/paper/2412.05276/) (2024)
- [Overlooked factors in concept-based explanations: Dataset choice, concept learnability, and human capability](https://mlsanity.com/paper/2207.09615/) (2022)
- [Interpreting Attention Layer Outputs with Sparse Autoencoders](https://mlsanity.com/paper/2406.17759/) (2024)
- [Learning to Receive Help: Intervention-Aware Concept Embedding Models](https://mlsanity.com/paper/2309.16928/) (2023)
- [Efficient Dictionary Learning with Switch Sparse Autoencoders](https://mlsanity.com/paper/2410.08201/) (2024)
- [The Missing Curve Detectors of InceptionV1: Applying Sparse Autoencoders to InceptionV1 Early Vision](https://mlsanity.com/paper/2406.03662/) (2024)
- [Enhancing Neural Network Interpretability with Feature-Aligned Sparse Autoencoders](https://mlsanity.com/paper/2411.01220/) (2024)
- [Rethinking Evaluation of Sparse Autoencoders through the Representation of Polysemous Words](https://mlsanity.com/paper/2501.06254/) (2025)
- [Sparse Autoencoders Enable Scalable and Reliable Circuit Identification in Language Models](https://mlsanity.com/paper/2405.12522/) (2024)
- [Measuring and Guiding Monosemanticity](https://mlsanity.com/paper/2506.19382/) (2025)
- [Probing the Representational Power of Sparse Autoencoders in Vision Models](https://mlsanity.com/paper/2508.11277/) (2025)

## Abstract (arXiv)

Standard Sparse Autoencoders (SAEs) excel at discovering a dictionary of a model's learned features, providing a powerful lens for passive feature discovery. However, this passive nature makes it difficult to systematically evaluate or analyze concepts that users explicitly care about. We introduce Concept-SAE, a framework that augments SAEs with a structured and controllable interface for probing user-defined concepts. Concept-SAE decomposes an activation subspace into two orthogonal components: Concept Tokens, which are aligned to externally specified semantics through dual supervision on both concept existence and spatial localization, and Free Tokens, which operate like standard SAEs to capture all remaining information. This hybrid disentanglement strategy ensures that Concept Tokens are faithful, spatially grounded, and cleanly separated from the residual subspace while preserving the ability of SAEs for open-ended concept discovery. We conduct extensive experiments demonstrating that Concept-SAE yields high-fidelity, well-localized, and strongly disentangled concept representations, outperforming alternatives in interface quality. Finally, we validate the utility of this conceptual interface through three diagnostic evaluations: a detection test on classifying adversarial image samples, a controllability test focusing on controlled counterfactual editing and a stability test using adversarial perturbations. Together, these results show that Concept-SAE equips SAEs with a reliable mechanism for evaluating, probing, and diagnosing user-defined concepts.