Causal Dimensionality of Transformer Representations: Measurement, Scaling, and Layer Structure
Sparse autoencoders (SAEs) decompose transformer residual streams into interpretable feature dictionaries, yet the relationship between SAE width and causal influence on model output has not been systematically characterised. We introduce causal dimensionality kappa(L, M, T), defined as the effective rank of the expected Jacobian outer product at layer L, and show it can be estimated via the SAE width sweep paired with attribution patching. Across seven SAE widths from 16,384 to 1,048,576 features on Gemma-2-2B layer 12, representational capacity grows 15.6x while causal capacity grows only 4.35x: a robust separation we term the representational-causal wedge. A saturating fit yields kappa...
| Authors | Nilesh Sarkar, Dawar Jyoti Deka |
|---|---|
| Primary category | cs.LG |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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