# Sparse Autoencoders, Again?

arXiv: https://arxiv.org/abs/2506.04859 · HTML: https://mlsanity.com/paper/2506.04859/

## Key facts

- Cited by 3 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 27 of its 54 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Sparse Autoencoders Learn Monosemantic Features in Vision-Language Models](https://mlsanity.com/paper/2504.02821/) (2025)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Rectangular Flows for Manifold Learning](https://mlsanity.com/paper/2106.01413/) (2021)
- [A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models](https://mlsanity.com/paper/2406.03537/) (2024)
- [Evaluating Open-Source Sparse Autoencoders on Disentangling Factual Knowledge in GPT-2 Small](https://mlsanity.com/paper/2409.04478/) (2024)
- [Sparse Autoencoders for Hypothesis Generation](https://mlsanity.com/paper/2502.04382/) (2025)
- [Interpretable and Testable Vision Features via Sparse Autoencoders](https://mlsanity.com/paper/2502.06755/) (2025)
- [On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models](https://mlsanity.com/paper/2402.03845/) (2024)
- [Disentangling Dense Embeddings with Sparse Autoencoders](https://mlsanity.com/paper/2408.00657/) (2024)
- [Learning Manifold Dimensions with Conditional Variational Autoencoders](https://mlsanity.com/paper/2302.11756/) (2023)

## Built on by (most cited first, 3 of 3)

- [ELROND: Exploring and decomposing intrinsic capabilities of diffusion models](https://mlsanity.com/paper/2602.10216/) (2026)
- [From Insight to Action: A Novel Framework for Interpretability-Guided Data Selection in Large Language Models](https://mlsanity.com/paper/2604.25167/) (2026)
- [Invariant Atoms: Sparse Coordinates of Local Semantic Geometry in Language Model Representations](https://mlsanity.com/paper/2609.36451/) (2026)

## Abstract (arXiv)

Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could reflect, among other things, correlation patterns in large language model activations, or complex natural image manifolds. And yet despite the wide-ranging applicability, there have been relatively few changes to SAEs beyond the original recipe from decades ago, namely, standard deep encoder/decoder layers trained with a classical/deterministic sparse regularizer applied within the latent space. One possible exception is the variational autoencoder (VAE), which adopts a stochastic encoder module capable of producing sparse representations when applied to manifold data. In this work we formalize underappreciated weaknesses with both canonical SAEs, as well as analogous VAEs applied to similar tasks, and propose a hybrid alternative model that circumvents these prior limitations. In terms of theoretical support, we prove that global minima of our proposed model recover certain forms of structured data spread across a union of manifolds. Meanwhile, empirical evaluations on synthetic and real-world datasets substantiate the efficacy of our approach in accurately estimating underlying manifold dimensions and producing sparser latent representations without compromising reconstruction error. In general, we are able to exceed the performance of equivalent-capacity SAEs and VAEs, as well as recent diffusion models where applicable, within domains such as images and language model activation patterns.