mlsanityData to 14 Oct 2026

On the Limits of Sparse Autoencoders: A Theoretical Framework and Reweighted Remedy

arXiv 2506.15963 ↗First posted 19 Jun 2025cs.LGcited by 14

On the map: Mechanistic interpretability → SAE features and their applications

Abstract (arXiv)

Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the features learned by large language models (LLMs). By reconstructing features with sparsely activated networks, SAEs aim to recover complex superposed polysemantic features into interpretable monosemantic ones. Despite their wide applications, it remains unclear under what conditions SAEs can fully recover the ground truth monosemantic features from the superposed polysemantic ones. In this paper, we provide the first theoretical analysis with a closed-form solution for SAEs, revealing that they generally fail to fully recover the ground truth monosemantic features unless the ground truth features are extremely sparse. To improve the feature recovery of SAEs in general cases, we propose a reweighting strategy targeting at enhancing the reconstruction of the ground truth monosemantic features instead of the observed polysemantic ones. We further establish a theoretical weight selection principle for our proposed weighted SAE (WSAE). Experiments across multiple settings validate our theoretical findings and demonstrate that our WSAE significantly improves feature monosemanticity and interpretability.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability. Builds on 26 of its 32 references that are in the map. First posted on arXiv 19 Jun 2025.

Builds on

26 of 32 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability12 Mar
  2. 2025Rethinking Evaluation of Sparse Autoencoders through the Representation of Polysemous Words9 Jan
  3. 2024Automatically Interpreting Millions of Features in Large Language Models17 Oct
  4. 2024Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders19 Jul
  5. 2024Scaling and evaluating sparse autoencoders6 Jun
  6. 2024Improving Dictionary Learning with Gated Sparse Autoencoders24 Apr
  7. 2023Sparse Autoencoders Find Highly Interpretable Features in Language Models15 Sep

Other references · 19

  1. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
  2. 2023Pythia: A Suite for Analyzing Large Language Models Across Training and Scalingcited by 1,786
  3. 2022Toy Models of Superpositioncited by 971
  4. 2024Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2cited by 394
  5. 2013k-Sparse Autoencoderscited by 215
  6. 2016Linear Algebraic Structure of Word Senses, with Applications to Polysemycited by 165
  7. 2025Learning Multi-Level Features with Matryoshka Sparse Autoencoderscited by 143
  8. 2024Do I Know This Entity? Knowledge Awareness and Hallucinations in Language Modelscited by 115
  9. 2022Polysemanticity and Capacity in Neural Networkscited by 77
  10. 2024Sparse autoencoders reveal selective remapping of visual concepts during adaptationcited by 68
  11. 2024Identifying Functionally Important Features with End-to-End Sparse Dictionary Learningcited by 67
  12. 2025Universal Sparse Autoencoders: Interpretable Cross-Model Concept Alignmentcited by 62
7 more
  1. 2024Mathematical Models of Computation in Superpositioncited by 35
  2. 2025SAE-V: Interpreting Multimodal Models for Enhanced Alignmentcited by 23
  3. 2023What Causes Polysemanticity? An Alternative Origin Story of Mixed Selectivity from Incidental Causescited by 19
  4. 2024Non-negative Contrastive Learningcited by 19
  5. 2023Identifiable Contrastive Learning with Automatic Feature Importance Discoverycited by 14
  6. 2024Beyond Interpretability: The Gains of Feature Monosemanticity on Model Robustnesscited by 13
  7. 2023Learning from Emergence: A Study on Proactively Inhibiting the Monosemantic Neurons of Artificial Neural Networkscited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 12.

14 papers.

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  1. 2025Exploratory Causal Inference in SAEncecited by 4
  2. 2025AlignSAE: Concept-Aligned Sparse Autoencoderscited by 4
  3. 2026SAE as a Crystal Ball: Interpretable Features Predict Cross-domain Transferability of LLMs without Trainingcited by 2
  4. 2026When Language Overwrites Vision: Over-Alignment and Geometric Debiasing in Vision-Language Modelscited by 1
  5. 2026Concept Modulation Models: A Unified Framework for Identifiability and Extrapolationcited by 1
  6. 2026Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effectscited by 1
  7. 2026Phase-Associative Memory: Sequence Modeling in Complex Hilbert Spacecited by 0
  8. 2026Sign-Aware Gated Sparse Autoencoders: Modeling Anticorrelated Features with Bi-Jump-ReLU Activationscited by 0
  9. 2026How Optimality Structures Sparse Dictionaries: Theory for Interpreting SAE Representationscited by 0
  10. 2026Same Concept, Different Directions: Cross-Modal Feature Heterogeneity in Sparse Autoencoderscited by 0
  11. 2026Escaping Low-Dimensional Overlap: Multi-Task Model Merging via High-Dimensional Sparse Disentanglementcited by 0
  12. 2026Interference Beyond Geometry in Concept Extractioncited by 0
2 more
  1. 2026Language Models Have Interpretable Narrative Mechanismscited by 0
  2. 2026Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utilitycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Taming Polysemanticity in LLMs: Provable Feature Recovery via Sparse Autoencoders
  2. 2025Sparse Autoencoders Can Capture Language-Specific Concepts Across Diverse Languages
  3. 2025Sparse Autoencoders Trained on the Same Data Learn Different Features
  4. 2025AbsTopK: Rethinking Sparse Autoencoders For Bidirectional Features
  5. 2025A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models
  6. 2025Evaluating Sparse Autoencoders for Monosemantic Representation
  7. 2026Are Sparse Autoencoder Benchmarks Reliable?
  8. 2026Discovering Millions of Interpretable Features with Sparse Autoencoders