mlsanityData to 14 Oct 2026

Learning Multi-Level Features with Matryoshka Sparse Autoencoders

arXiv 2503.17547 ↗First posted 21 Mar 2025cs.LG cs.AIcited by 143

On the map: Mechanistic interpretability → Sparse autoencoder training and evaluation

Abstract (arXiv)

Sparse autoencoders (SAEs) have emerged as a powerful tool for interpreting neural networks by extracting the concepts represented in their activations. However, choosing the size of the SAE dictionary (i.e. number of learned concepts) creates a tension: as dictionary size increases to capture more relevant concepts, sparsity incentivizes features to be split or absorbed into more specific features, leaving high-level features missing or warped. We introduce Matryoshka SAEs, a novel variant that addresses these issues by simultaneously training multiple nested dictionaries of increasing size, forcing the smaller dictionaries to independently reconstruct the inputs without using the larger dictionaries. This organizes features hierarchically - the smaller dictionaries learn general concepts, while the larger dictionaries learn more specific concepts, without incentive to absorb the high-level features. We train Matryoshka SAEs on Gemma-2-2B and TinyStories and find superior performance on sparse probing and targeted concept erasure tasks, more disentangled concept representations, and reduced feature absorption. While there is a minor tradeoff with reconstruction performance, we believe Matryoshka SAEs are a superior alternative for practical tasks, as they enable training arbitrarily large SAEs while retaining interpretable features at different levels of abstraction.

Key facts. Cited by 143 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 20 of its 28 references that are in the map. First posted on arXiv 21 Mar 2025.

Builds on

20 of 28 references.

Closest ancestors · 6

Same direction, newest first

  1. 2025Sparse Autoencoders Do Not Find Canonical Units of Analysis7 Feb
  2. 2024Evaluating Sparse Autoencoders on Targeted Concept Erasure Tasks28 Nov
  3. 2024Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 29 Aug
  4. 2024Interpreting Attention Layer Outputs with Sparse Autoencoders25 Jun
  5. 2024Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control14 May
  6. 2022Toy Models of Superposition21 Sep

Other references · 14

  1. 2020Scaling Laws for Neural Language Modelscited by 6,586
  2. 2022Training Compute-Optimal Large Language Modelscited by 3,019
  3. 2020The Pile: An 800GB Dataset of Diverse Text for Language Modelingcited by 2,411
  4. 2023Sparse Autoencoders Find Highly Interpretable Features in Language Modelscited by 1,420
  5. 2024Scaling and evaluating sparse autoencoderscited by 553
  6. 2024Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Modelscited by 435
  7. 2024Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoderscited by 300
  8. 2024Improving Dictionary Learning with Gated Sparse Autoencoderscited by 179
  9. 2024A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoderscited by 160
  10. 2024BatchTopK Sparse Autoencoderscited by 130
  11. 2025SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretabilitycited by 124
  12. 2024Automatically Interpreting Millions of Features in Large Language Modelscited by 113
2 more
  1. 2024Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Modelscited by 51
  2. 2024Relational Composition in Neural Networks: A Survey and Call to Actioncited by 23

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 50; 2026: 93.

143 papers.

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  1. 2025The Origins of Representation Manifolds in Large Language Modelscited by 51
  2. 2025From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuitcited by 49
  3. 2026Do Sparse Autoencoders Capture Concept Manifolds?cited by 31
  4. 2025What's In My Human Feedback? Learning Interpretable Descriptions of Preference Datacited by 26
  5. 2025Transferring Linear Features Across Language Models With Model Stitchingcited by 21
  6. 2025Position: Use Sparse Autoencoders to Discover Unknownscited by 19
  7. 2025Temporal Sparse Autoencoders: Leveraging the Sequential Nature of Language for Interpretabilitycited by 18
  8. 2025Dense SAE Latents Are Features, Not Bugscited by 17
  9. 2025Feature Hedging: Correlated Features Break Narrow Sparse Autoencoderscited by 16
  10. 2025Position: Mechanistic Interpretability Should Prioritize Feature Consistency in SAEscited by 14
  11. 2025Incorporating Hierarchical Semantics in Sparse Autoencoder Architecturescited by 14
  12. 2025On the Limits of Sparse Autoencoders: A Theoretical Framework and Reweighted Remedycited by 14
38 more
  1. 2025Sparse but Wrong: Incorrect L0 Leads to Incorrect Features in Sparse Autoencoderscited by 14
  2. 2026Sanity Checks for Sparse Autoencoders: Do SAEs Beat Random Baselines?cited by 14
  3. 2026SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Datacited by 11
  4. 2025Measuring and Guiding Monosemanticitycited by 10
  5. 2025SAEdit: Token-level control for continuous image editing via Sparse AutoEncodercited by 9
  6. 2025Mechanistic Indicators of Understanding in Large Language Modelscited by 8
  7. 2025OrtSAE: Orthogonal Sparse Autoencoders Uncover Atomic Featurescited by 8
  8. 2026Unlocking Multimodal Document Intelligence: From Current Triumphs to Future Frontiers of Visual Document Retrievalcited by 8
  9. 2025Superposition as Lossy Compression: Measure with Sparse Autoencoders and Connect to Adversarial Vulnerabilitycited by 7
  10. 2025Safe-SAIL: Towards a Fine-grained Safety Landscape of Large Language Models via Sparse Autoencoder Interpretation Frameworkcited by 6
  11. 2025Route Experts by Sequence, not by Tokencited by 6
  12. 2025Interpretable and Steerable Concept Bottleneck Sparse Autoencoderscited by 6
  13. 2026Tracing Moral Foundations in Large Language Modelscited by 6
  14. 2026CSRv2: Unlocking Ultra-Sparse Embeddingscited by 6
  15. 2026From Atoms to Trees: Building a Structured Feature Forest with Hierarchical Sparse Autoencoderscited by 6
  16. 2026Interpretable Debiasing of Vision-Language Models for Social Fairnesscited by 6
  17. 2025Finding Manifolds With Bilinear Autoencoderscited by 5
  18. 2026Stable and Steerable Sparse Autoencoders with Weight Regularizationcited by 5
  19. 2025Train One Sparse Autoencoder Across Multiple Sparsity Budgets to Preserve Interpretability and Accuracycited by 4
  20. 2025From Noise to Narrative: Tracing the Origins of Hallucinations in Transformerscited by 4
  21. 2025Measuring Sparse Autoencoder Feature Sensitivitycited by 4
  22. 2025Superposition disentanglement of neural representations reveals hidden alignmentcited by 4
  23. 2025Attribution-Guided Distillation of Matryoshka Sparse Autoencoderscited by 4
  24. 2026Putting a Face to Forgetting: Continual Learning meets Mechanistic Interpretabilitycited by 4
  25. 2026Tree SAE: Learning Hierarchical Feature Structures in Sparse Autoencoderscited by 4
  26. 2026Are Sparse Autoencoder Benchmarks Reliable?cited by 4
  27. 2026Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretabilitycited by 4
  28. 2026ICA Lens: Interpreting Language Models Without Training Another Dictionarycited by 4
  29. 2025Ensembling Sparse Autoencoderscited by 3
  30. 2025Mechanistic Interpretability with Sparse Autoencoder Neural Operatorscited by 3
  31. 2025A Unified Theory of Sparse Dictionary Learning in Mechanistic Interpretability: Piecewise Biconvexity and Spurious Minimacited by 3
  32. 2026PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decodingcited by 3
  33. 2026Towards Worst-Case Guarantees with Scale-Aware Interpretabilitycited by 3
  34. 2026The Rate-Distortion-Polysemanticity Tradeoff in SAEscited by 3
  35. 2026Inside the Visual Mind: Neuroscience-Motivated Concept Circuits for Interpreting and Steering Vision Transformerscited by 3
  36. 2025DB-KSVD: Scalable Alternating Optimization for Disentangling High-Dimensional Embedding Spacescited by 2
  37. 2025Evaluating Steering Techniques using Human Similarity Judgmentscited by 2
  38. 2025Factual Self-Awareness in Language Models: Representation, Robustness, and Scalingcited by 2

50 most cited of 143 All 143 (JSON)

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  1. 2024Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning
  2. 2026Toward Identifiable Sparse Autoencoders
  3. 2025Empirical Evaluation of Progressive Coding for Sparse Autoencoders
  4. 2025AbsTopK: Rethinking Sparse Autoencoders For Bidirectional Features
  5. 2025Concept-SAE: A Controllable and Invertible Concept Interface for Sparse Autoencoders
  6. 2026Inference and learning in sparse autoencoders as natural gradient flow
  7. 2026Expander Sparse Autoencoders: Parameter-Efficient Dictionaries for Mechanistic Interpretability
  8. 2025Sparse Autoencoders Trained on the Same Data Learn Different Features