Compressed Computation is (probably) not Computation in Superposition
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Compressed Computation is (probably) not Computation in Superposition
Abstract:We study whether the Compressed Computation (CC) toy model (Braun et al., 2025) is an instance of computation in superposition. The CC model appears to compute 100 ReLU functions with just 50 neurons, achieving a better loss than expected from only representing 50 ReLU functions. We show that the model mixes inputs via its noisy residual stream, corresponding to an unintended mixing matrix in the labels. Splitting the training objective into the ReLU term and the mixing term, we find that performance gains scale with the magnitude of the mixing matrix and vanish when the matrix is removed. The learned neuron directions concentrate in the subspace associated with the top 50 eigenvalues of the mixing matrix, suggesting that the mixing term governs the solution. Finally, a semi-non-negative matrix factorization (SNMF) baseline derived solely from the mixing matrix reproduces the qualitative loss profile and improves on prior baselines, though it does not match the trained model. These results suggest CC is not a suitable toy model of computation in superposition.
| Comments: | Presented at the Mechanistic Interpretability Workshop at NeurIPS 2025 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.14673 [cs.LG] |
| (or arXiv:2606.14673v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.14673
arXiv-issued DOI via DataCite (pending registration)
|
Submission history
From: Stefan Heimersheim [view email][v1] Fri, 12 Jun 2026 17:39:31 UTC (1,379 KB)
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Representation as a Bottleneck for Mechanistic Interpretability: The Manifestation Unit Protocol
Jul 2
-
SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling
Jul 2
-
SemiScope: Disentangling Classifier Tuning and Joint Optimization in Semi-Supervised Security Classification
Jul 2
-
A Filtered Mixture-of-Generators for Fully Synthetic Survival Training
Jul 2
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.