mlsanityData to 14 Oct 2026

Understanding sparse autoencoder scaling in the presence of feature manifolds

arXiv 2509.02565 ↗First posted 2 Sep 2025cs.LGcited by 11

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

Abstract (arXiv)

Sparse autoencoders (SAEs) model the activations of a neural network as linear combinations of sparsely occurring directions of variation (latents). The ability of SAEs to reconstruct activations follows scaling laws w.r.t. the number of latents. In this work, we adapt a capacity-allocation model from the neural scaling literature (Brill, 2024) to understand SAE scaling, and in particular, to understand how "feature manifolds" (multi-dimensional features) influence scaling behavior. Consistent with prior work, the model recovers distinct scaling regimes. Notably, in one regime, feature manifolds have the pathological effect of causing SAEs to learn far fewer features in data than there are latents in the SAE. We provide some preliminary discussion on whether or not SAEs are in this pathological regime in the wild.

Key facts. Cited by 11 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 21 of its 30 references that are in the map. First posted on arXiv 2 Sep 2025.

Builds on

21 of 30 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit3 Jun
  2. 2025The Origins of Representation Manifolds in Large Language Models23 May
  3. 2025Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry3 Mar
  4. 2025Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models18 Feb
  5. 2024Group Crosscoders for Mechanistic Analysis of Symmetry31 Oct
  6. 2024Decomposing The Dark Matter of Sparse Autoencoders18 Oct
  7. 2024Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 29 Aug
  8. 2022Toy Models of Superposition21 Sep

Other references · 13

  1. 2020Scaling Laws for Neural Language Modelscited by 6,586
  2. 2022Training Compute-Optimal Large Language Modelscited by 3,019
  3. 2023Sparse Autoencoders Find Highly Interpretable Features in Language Modelscited by 1,420
  4. 2024Scaling and evaluating sparse autoencoderscited by 553
  5. 2024Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoderscited by 300
  6. 2024Not All Language Model Features Are One-Dimensionally Linearcited by 212
  7. 2024Transcoders Find Interpretable LLM Feature Circuitscited by 200
  8. 2024A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoderscited by 160
  9. 2023The Quantization Model of Neural Scalingcited by 138
  10. 2024BatchTopK Sparse Autoencoderscited by 130
  11. 2024Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representationscited by 47
  12. 2024Neural Scaling Laws Rooted in the Data Distributioncited by 15
1 more
  1. 2025Incorporating Hierarchical Semantics in Sparse Autoencoder Architecturescited by 14

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 11.

11 papers.

  1. 2026When Models Manipulate Manifolds: The Geometry of a Counting Taskcited by 46
  2. 2026Do Sparse Autoencoders Capture Concept Manifolds?cited by 31
  3. 2026SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Datacited by 11
  4. 2026Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retentioncited by 10
  5. 2026Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifoldscited by 5
  6. 2026Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretabilitycited by 4
  7. 2026SMIXAE: Towards Unsupervised Manifold Discovery in Language Modelscited by 1
  8. 2026The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Lawscited by 1
  9. 2026A Geometric View for Understanding Concept Learning and Neuron Interpretation in Sparse Autoencoderscited by 1
  10. 2026Critical Percolation as a Synthetic Data Model for Interpretabilitycited by 0
  11. 2026Geometry of Ordinal Representations in Language Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Sparse Autoencoders, Again?
  2. 2026Sanity Checks for Sparse Autoencoders: Do SAEs Beat Random Baselines?
  3. 2026Sparse Autoencoders Encode Both Concepts and Functions: The Downstream Geometry of Feature Effects
  4. 2024Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning
  5. 2025Sparse Autoencoders Trained on the Same Data Learn Different Features
  6. 2025SAEs Are Good for Steering -- If You Select the Right Features
  7. 2024Interpreting Attention Layer Outputs with Sparse Autoencoders
  8. 2026Feature Starvation as Geometric Instability in Sparse Autoencoders