mlsanityData to 7 Oct 2026

Mathematical Models of Computation in Superposition

arXiv 2408.05451 ↗First posted 10 Aug 2024cs.LG cs.AIcited by 34

Not on the map. Why?

Abstract (arXiv)

Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies representational superposition, where superposition is only used when passing information through bottlenecks. In this work, we present mathematical models of computation in superposition, where superposition is actively helpful for efficiently accomplishing the task. We first construct a task of efficiently emulating a circuit that takes the AND of the binomm2 pairs of each of m features. We construct a 1-layer MLP that uses superposition to perform this task up to varepsilon-error, where the network only requires tildeO(m^frac23) neurons, even when the input features are themselves in superposition. We generalize this construction to arbitrary sparse boolean circuits of low depth, and then construct ``error correction'' layers that allow deep fully-connected networks of width d to emulate circuits of width tildeO(d1.5) and any polynomial depth. We conclude by providing some potential applications of our work for interpreting neural networks that implement computation in superposition.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). Builds on 15 of its 38 references that are in the map. First posted on arXiv 10 Aug 2024.

Builds on

15 of 38 references.

References · 15

  1. 2020Transformer Feed-Forward Layers Are Key-Value Memoriescited by 1,307
  2. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,130
  3. 2022Toy Models of Superpositioncited by 928
  4. 2023Towards Automated Circuit Discovery for Mechanistic Interpretabilitycited by 700
  5. 2021Causal Abstractions of Neural Networkscited by 401
  6. 2023Finding Neurons in a Haystack: Case Studies with Sparse Probingcited by 328
  7. 2024Improving Dictionary Learning with Gated Sparse Autoencoderscited by 171
  8. 2016Linear Algebraic Structure of Word Senses, with Applications to Polysemycited by 165
  9. 2016Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networkscited by 106
  10. 2022Polysemanticity and Capacity in Neural Networkscited by 74
  11. 2024Identifying Functionally Important Features with End-to-End Sparse Dictionary Learningcited by 64
  12. 2023Codebook Features: Sparse and Discrete Interpretability for Neural Networkscited by 45
3 more
  1. 2023Randomized Numerical Linear Algebra : A Perspective on the Field With an Eye to Softwarecited by 38
  2. 2014On the Computational Intractability of Exact and Approximate Dictionary Learningcited by 14
  3. 2021Spiking Hyperdimensional Network: Neuromorphic Models Integrated with Memory-Inspired Frameworkcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 17; 2026: 13.

34 papers.

Sort:

By area:

  1. 2025From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuitcited by 45
  2. 2025Weight-sparse transformers have interpretable circuitscited by 40
  3. 2025Superposition Yields Robust Neural Scalingcited by 30
  4. 2024On the Complexity of Neural Computation in Superpositioncited by 21
  5. 2025Stochastic Parameter Decompositioncited by 14
  6. 2025On the Limits of Sparse Autoencoders: A Theoretical Framework and Reweighted Remedycited by 12
  7. 2025Towards Combinatorial Interpretability of Neural Computationcited by 9
  8. 2026AudioSAE: Towards Understanding of Audio-Processing Models with Sparse AutoEncoderscited by 8
  9. 2025Adversarial Attacks Leverage Interference Between Features in Superpositioncited by 7
  10. 2025Superposition as Lossy Compression: Measure with Sparse Autoencoders and Connect to Adversarial Vulnerabilitycited by 6
  11. 2025The Thin Line Between Comprehension and Persuasion in LLMscited by 5
  12. 2025Linear Spatial World Models Emerge in Large Language Modelscited by 4
22 more
  1. 2024Evaluating Synthetic Activations composed of SAE Latents in GPT-2cited by 3
  2. 2024Characterizing stable regions in the residual stream of LLMscited by 3
  3. 2026Putting a Face to Forgetting: Continual Learning meets Mechanistic Interpretabilitycited by 3
  4. 2024Investigating Sensitive Directions in GPT-2: An Improved Baseline and Comparative Analysis of SAEscited by 2
  5. 2025SAFR: Neuron Redistribution for Interpretabilitycited by 2
  6. 2025Expand Neurons, Not Parameterscited by 2
  7. 2025Compressed Computation: Dense Circuits in a Toy Model of the Universal-AND Problemcited by 1
  8. 2025Feature learning is decoupled from generalization in high capacity neural networkscited by 1
  9. 2025Binary Autoencoder for Mechanistic Interpretability of Large Language Modelscited by 1
  10. 2025Polysemy of Synthetic Neurons Towards a New Type of Explanatory Categorical Vector Spacescited by 0
  11. 2025Features Emerge as Discrete States: The First Application of SAEs to 3D Representationscited by 0
  12. 2026Similarity of Neural Network Representations in Superpositioncited by 0
  13. 2026Evidence for feature-specific error correction in LLMscited by 0
  14. 2026Discovering Millions of Interpretable Features with Sparse Autoencoderscited by 0
  15. 2026Compressed Computation under L4 Loss is likely Computation in Superpositioncited by 0
  16. 2026Training, Reading, and Editing Legible Transformerscited by 0
  17. 2026Scaling Interpretable Transformers with Parity Bottleneck Layerscited by 0
  18. 2026Weight-Space Mixture-of-Experts for Implicit Neural Representation Classificationcited by 0
  19. 2026Xeno-Interpretability: Investigating the Alien Minds of LLMscited by 0
  20. 2026Abstention and Noise Filtering: Two Missing Primitives of Softmax Attentioncited by 0
  21. 2026Interference Beyond Geometry in Concept Extractioncited by 0
  22. 2026The Ball and the Box: Two Geometries of Computation in Superpositioncited by 0