# Decoder-Preserving Sparse Autoencoders: Which Readouts Survive Sparse Compression?

arXiv: https://arxiv.org/abs/2607.17425 · HTML: https://mlsanity.com/paper/2607.17425/

## 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 18 of its 21 references that are in the map.
- First posted on arXiv 19 Jul 2026.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry](https://mlsanity.com/paper/2503.01822/) (2025)
- [From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit](https://mlsanity.com/paper/2506.03093/) (2025)
- [Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs](https://mlsanity.com/paper/2410.11179/) (2024)
- [What Representational Similarity Measures Imply about Decodable Information](https://mlsanity.com/paper/2411.08197/) (2024)
- [Temporal Sparse Autoencoders: Leveraging the Sequential Nature of Language for Interpretability](https://mlsanity.com/paper/2511.05541/) (2025)
- [GULP: a prediction-based metric between representations](https://mlsanity.com/paper/2210.06545/) (2022)
- [Measuring and Guiding Monosemanticity](https://mlsanity.com/paper/2506.19382/) (2025)
- [Cross-Modal Redundancy and the Geometry of Vision-Language Embeddings](https://mlsanity.com/paper/2602.06218/) (2026)
- [Revisiting End-To-End Sparse Autoencoder Training: A Short Finetune Is All You Need](https://mlsanity.com/paper/2503.17272/) (2025)
- [AdaptiveK: Complexity-Driven Sparse Autoencoders for Interpretable Language Model Representations](https://mlsanity.com/paper/2508.17320/) (2025)
- [Unveiling Decision-Making in LLMs for Text Classification : Extraction of influential and interpretable concepts with Sparse Autoencoders](https://mlsanity.com/paper/2506.23951/) (2025)

## Abstract (arXiv)

Sparse autoencoders (SAEs) compress model activations into sparse codes, but equal reconstruction error and sparsity can preserve different linearly decodable signals. We formalize this ambiguity as a matrix-valued distortion between optimal ridge-prediction operators and train decoder-preserving SAEs by combining this distortion with reconstruction loss. In a rank relaxation, an isotropic task prior saturates per-mode omission costs without changing PCA's ordering, whereas a structured prior can change which modes are retained. A controlled sparse experiment shows that a declared prior protects held-out combinations from its task subspace. On GPT-2 small block 8, DPSAE reduces held-out decoder distortion by 10.6--11.4% across three paired runs while matching reconstruction NMSE. The same checkpoints pass an average natural-text output-KL noninferiority test, but one matched Pythia pair shows no improvement in probes restricted to a few sparse features. These results show that reconstruction quality does not determine which refitted linear readouts survive sparse compression, and that readout preservation is distinct from learning cleaner benchmark concepts or preserving every frozen-model behavior.