Superposition and Polysemanticity

Polysemanticity is the property of a neuron (or feature) responding to several unrelated inputs. The canonical example is an InceptionV1 neuron firing on both cat faces and car fronts; a one-layer language model studied by Anthropic had a single neuron responding to academic citations, English dialogue, HTTP requests, and Korean text. Polysemanticity is what blocks neuron-by-neuron reading of a network, and explaining where it comes from is the question this page tracks.¹

The superposition hypothesis is the leading explanation: a network represents more features than it has neurons by giving each feature a direction in activation space, with directions only almost-orthogonal to each other. High-dimensional geometry makes this cheap — exp(n) many almost-orthogonal vectors fit in n dimensions (Johnson–Lindenstrauss) — and sparse feature activations keep the interference cost down, with nonlinearities filtering the residual noise. In effect the small network noisily simulates a much larger sparse one.²

The demonstration: toy models

“Toy Models of Superposition” (Elhage, Hume, Olsson et al., Anthropic/Harvard, September 2022) gave the hypothesis its clean demonstration: small ReLU networks trained on synthetic sparse data store more features than they have dimensions — ground truth, not post-hoc interpretation. Key results include a phase diagram governing when superposition occurs (sparsity and feature importance decide it), computation while in superposition (absolute-value circuits), rich geometry (features organizing into digons, triangles, pentagons, tetrahedra), and learning dynamics with discrete “energy level” jumps. The paper’s strategic picture: real networks may be noisily simulating larger sparse networks, which would make decomposition (finding the overcomplete basis) the route to interpretability. It also reports preliminary evidence linking superposition to adversarial examples and grokking, and is careful that what generalizes from toy models to real networks is unclear.³

The decomposition program that followed — sparse autoencoders recovering monosemantic features — is covered on mechanistic-interpretability.

The misreading thesis (2026)

Nick Cammarata’s “Neural Networks Are Already Clean” (Goodfire, October 2026) argues that the canonical evidence for polysemanticity and superposition was misread, and that what looked like arbitrary packing is mostly a motif he calls recursive generalization: neurons cover coarse-grained concepts and differentiate as capacity allows (one car neuron covering many kinds of car, splitting into specific cars with more room), so a neuron grouping dogs and cars is ordinary generalization, not a knot to unfold. He revisits each canonical example:⁴

• The “cars in superposition” circuit (the Zoom In example introduced as a superposition phenomenon): Cammarata and Olah found it in 2019, read it as the network hiding a car in a high-dimensional combination — but, he now writes, nothing ever reads that combination; it was ordinary generalization and composition, and to his knowledge no second circuit with the claimed shape has ever been published.^{5 6}
• The cat-and-car neuron and other polysemanticity classics become coarse-grained generalization under this reading. The skeptical gloss is pareidolia: pattern-seeing by the observer (the numeral-network version of faces in clouds), which the essay works against by demanding explanations that could lose — tested predictions against the model, not just plausible stories.
• The mixed neuron from the Towards Monosemanticity introduction (citations, dialogue, HTTP, Korean) becomes a “don’t say a dot” motif: nearly all those examples fire on or near a dot, the Korean ones at unfinished syllables, and the negative logit weights support the same reading — “two small syntactic pushes” rather than arbitrary mixture.^{7 8}
• “Superposition of the gaps.” As tooling improved, superposition’s residual explanatory share shrank: audits of Qwen3-32B estimate ~90% of neuron poles with one main job, ~7% with two related jobs, ~2–4% unexplained — against ~1.7% interpretable found by a 2023 OpenAI project under its most generous measure. Recursive generalization also motivates the essay’s fractal-explanation view: explanations can be hierarchical, coarse first and zoomable, mirroring the generalization they describe.

The essay’s further claims (neurons as control flow rather than named nouns; the argument that recursive generalization is not “hard to vary”; whether scale helps or hurts superposition) are developed in its appendix, and the conclusion is stated as a working hypothesis with one step flagged highly speculative.⁹

Open questions and tensions

• Adversarial examples. The essay explains generalization through competing circuits (an exact-photo circuit losing to a general-dog circuit when data is thin), which sits uneasily next to adversarial fragility — a few changed pixels flipping confident classifications. Goodfellow, Shlens, and Szegedy (ICLR 2015) argue adversarial vulnerability follows from linearity in high dimensions: many individually-invisible perturbations align along a weight vector and sum. On that account, fragility needs no arbitrary-packing story and coexists with clean features. Toy Models, meanwhile, reported preliminary evidence linking superposition to adversarial examples. Which link holds is unresolved, and it is the sharpest empirical test the misreading thesis faces.^{10 11}
• Scale. The superposition argument is that arbitrarily large models can still hold a large fraction of features in superposition; the audit evidence says neurons at 32B and trillion-parameter scale are mostly monosemantic. Both may hold (different layers, different resolutions), and the essay’s own “Does Scale Help or Hurt Superposition?” section treats it as open.
• What counts as one job. Interpretability scores depend on the rubric and on automated-explanation models whose accuracy is itself unvalidated. The 90% figure is a single lab’s preliminary audit; the 4% tail is where the interesting fights will be.

Cross-domain connections

• mechanistic-interpretability — the field page: circuits program, sparse autoencoders, and the “already clean” turn.
• cold-fusion — instrument artifacts cutting both ways: Callisto traced apparent excess heat to apparatus and accounting errors (false positives), while the misreading thesis traces apparent polysemanticity to a poorly tuned microscope (false negatives). In both stories the surprising signal turned out to be a claim about the instrument.
• ai-as-normal-technology — networks proving legible under ordinary empirical methods is the “normal technology” reading of the arc.

Sources

• Nick Cammarata 2026 — Neural Networks Are Already Clean
• Nelson Elhage, Tristan Hume, Catherine Olsson, Nicholas Schiefer, et al. 2022 — Toy Models of Superposition
• Chris Olah, Nick Cammarata, Ludwig Schubert, Gabriel Goh, Michael Petrov, Shan Carter 2020 — Zoom In: An Introduction to Circuits
• Ian J. Goodfellow, Jonathon Shlens, Christian Szegedy 2015 — Explaining and Harnessing Adversarial Examples

Footnotes

1. Trenton Bricken, Adly Templeton, et al. 2023 — Towards Monosemanticity: Decomposing Language Models With Dictionary Learning ↩

2. Nelson Elhage, Tristan Hume, Catherine Olsson, Nicholas Schiefer, et al. 2022 — Toy Models of Superposition ↩

3. Nelson Elhage, Tristan Hume, Catherine Olsson, Nicholas Schiefer, et al. 2022 — Toy Models of Superposition ↩

4. Nick Cammarata 2026 — Neural Networks Are Already Clean ↩

5. Chris Olah, Nick Cammarata, Ludwig Schubert, Gabriel Goh, Michael Petrov, Shan Carter 2020 — Zoom In: An Introduction to Circuits ↩

6. Nick Cammarata 2026 — Neural Networks Are Already Clean ↩

7. Nick Cammarata 2026 — Neural Networks Are Already Clean ↩

8. Trenton Bricken, Adly Templeton, et al. 2023 — Towards Monosemanticity: Decomposing Language Models With Dictionary Learning ↩

9. Nick Cammarata 2026 — Neural Networks Are Already Clean ↩

10. Ian J. Goodfellow, Jonathon Shlens, Christian Szegedy 2015 — Explaining and Harnessing Adversarial Examples ↩

11. Nelson Elhage, Tristan Hume, Catherine Olsson, Nicholas Schiefer, et al. 2022 — Toy Models of Superposition ↩