# Supervised sparse auto-encoders for interpretable and compositional representations

arXiv: https://arxiv.org/abs/2602.00924 · HTML: https://mlsanity.com/paper/2602.00924/

## 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 22 of its 34 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers](https://mlsanity.com/paper/2012.05420/) (2020)
- [Sparse Modeling for Image and Vision Processing](https://mlsanity.com/paper/1411.3230/) (2014)
- [Deep Neural Collapse Is Provably Optimal for the Deep Unconstrained Features Model](https://mlsanity.com/paper/2305.13165/) (2023)
- [Interpreting Attention Layer Outputs with Sparse Autoencoders](https://mlsanity.com/paper/2406.17759/) (2024)
- [One-Step is Enough: Sparse Autoencoders for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2410.22366/) (2024)
- [SAEmnesia: Erasing Concepts in Diffusion Models with Supervised Sparse Autoencoders](https://mlsanity.com/paper/2509.21379/) (2025)
- [Sparse Autoencoder as a Zero-Shot Classifier for Concept Erasing in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2503.09446/) (2025)
- [AlignSAE: Concept-Aligned Sparse Autoencoders](https://mlsanity.com/paper/2512.02004/) (2025)
- [CASL: Concept-Aligned Sparse Latents for Interpreting Diffusion Models](https://mlsanity.com/paper/2601.15441/) (2026)

## Abstract (arXiv)

Sparse auto-encoders (SAEs) have re-emerged as a prominent method for mechanistic interpretability, yet they face two significant challenges: the non-smoothness of the L1 penalty, which hinders reconstruction and scalability, and a lack of alignment between learned features and human semantics. In this paper, we address these limitations by adapting unconstrained feature models, a mathematical framework from neural collapse theory, and by supervising the task. We supervise (decoder-only) SAEs to reconstruct feature vectors by jointly learning sparse concept embeddings and decoder weights. Validated on Stable Diffusion 3.5, our approach demonstrates compositional generalization, successfully reconstructing images with concept combinations unseen during training, and enabling feature-level intervention for semantic image editing without prompt modification.