mlsanityData to 14 Oct 2026

Sparsification and Reconstruction from the Perspective of Representation Geometry

arXiv 2505.22506 ↗First posted 28 May 2025cs.LGcited by 0

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

Abstract (arXiv)

Sparse Autoencoders (SAEs) have emerged as a predominant tool in mechanistic interpretability, aiming to identify interpretable monosemantic features. However, how does sparse encoding organize the representations of activation vector from language models? What is the relationship between this organizational paradigm and feature disentanglement as well as reconstruction performance? To address these questions, we propose the SAEMA, which validates the stratified structure of the representation by observing the variability of the rank of the symmetric semipositive definite (SSPD) matrix corresponding to the modal tensor unfolded along the latent tensor with the level of noise added to the residual stream. To systematically investigate how sparse encoding alters representational structures, we define local and global representations, demonstrating that they amplify inter-feature distinctions by merging similar semantic features and introducing additional dimensionality. Furthermore, we intervene the global representation from an optimization perspective, proving a significant causal relationship between their separability and the reconstruction performance. This study explains the principles of sparsity from the perspective of representational geometry and demonstrates the impact of changes in representational structure on reconstruction performance. Particularly emphasizes the necessity of understanding representations and incorporating representational constraints, providing empirical references for developing new interpretable tools and improving SAEs. The code is available at hyperlinkhttps://github.com/wenjie1835/SAERepGeohttps://github.com/wenjie1835/SAERepGeo.

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 34 of its 46 references that are in the map. First posted on arXiv 28 May 2025.

Builds on

34 of 46 references.

Closest ancestors · 6

Same direction, newest first

  1. 2025Superposition Yields Robust Neural Scaling15 May
  2. 2024Adaptive Sparse Allocation with Mutual Choice & Feature Choice Sparse Autoencoders4 Nov
  3. 2024The Geometry of Concepts: Sparse Autoencoder Feature Structure10 Oct
  4. 2024Efficient Dictionary Learning with Switch Sparse Autoencoders10 Oct
  5. 2024Interpreting Attention Layer Outputs with Sparse Autoencoders25 Jun
  6. 2022Toy Models of Superposition21 Sep

Other references · 28

  1. 2024Gemma 2: Improving Open Language Models at a Practical Sizecited by 1,998
  2. 2023Pythia: A Suite for Analyzing Large Language Models Across Training and Scalingcited by 1,786
  3. 2019How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddingscited by 784
  4. 2023Towards Automated Circuit Discovery for Mechanistic Interpretabilitycited by 724
  5. 2023The Linear Representation Hypothesis and the Geometry of Large Language Modelscited by 716
  6. 2024Mechanistic Interpretability for AI Safety -- A Reviewcited by 422
  7. 2024Not All Language Model Features Are One-Dimensionally Linearcited by 212
  8. 2024Improving Dictionary Learning with Gated Sparse Autoencoderscited by 179
  9. 2025Open Problems in Mechanistic Interpretabilitycited by 179
  10. 2024BatchTopK Sparse Autoencoderscited by 130
  11. 2022Disentangled Representation Learningcited by 112
  12. 2022The Geometry of Multilingual Language Model Representationscited by 95
16 more
  1. 2024On the Origins of Linear Representations in Large Language Modelscited by 79
  2. 2024Transformers represent belief state geometry in their residual streamcited by 77
  3. 2025A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Modelscited by 76
  4. 2024Steering Knowledge Selection Behaviours in LLMs via SAE-Based Representation Engineeringcited by 63
  5. 2020Guided Variational Autoencoder for Disentanglement Learningcited by 57
  6. 2021Multi-VAE: Learning Disentangled View-common and View-peculiar Visual Representations for Multi-view Clusteringcited by 51
  7. 2024Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Modelscited by 51
  8. 2021Diagonal Attention and Style-based GAN for Content-Style Disentanglement in Image Generation and Translationcited by 35
  9. 2019OOGAN: Disentangling GAN with One-Hot Sampling and Orthogonal Regularizationcited by 17
  10. 2019JumpReLU: A Retrofit Defense Strategy for Adversarial Attackscited by 14
  11. 2024Group-SAE: Efficient Training of Sparse Autoencoders for Large Language Models via Layer Groupscited by 11
  12. 2021Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clusteringcited by 9
  13. 2022Gromov-Wasserstein Autoencoderscited by 7
  14. 2025Geometry-Preserving Encoder/Decoder in Latent Generative Modelscited by 6
  15. 2023Disentanglement in a GAN for Unconditional Speech Synthesiscited by 4
  16. 2024Latent Space Characterization of Autoencoder Variantscited by 2

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