Gluing Local Contexts into Global Meaning: A Sheaf-Theoretic Decomposition of Transformer Representations
Existing interpretability tools do not test whether a representation keeps the same content when only the phrasing changes. We treat each paraphrase pair as a local witness that two activations should agree and build a cellular sheaf over the paraphrase graph; its Laplacian $L_\mathcal{F}$ answers the question on a frozen model with no training. The kernel $H^0$ is a content subspace: at 20 dimensions it beats the preserved subspace of the concept eraser LEACE on held-out CounterFact fact retrieval across eight architectures by a mean $+17.1$\,pp, and constraining all paraphrases of a fact jointly adds a further $+6.5$\,pp. The spectral complement concentrates causal influence: ablating t...
| Authors | Bryce Grant, Peng Wang |
|---|---|
| Primary category | cs.CL |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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