Iterative Erasure Count Is Not an Affine-Invariant Concept Dimension
How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank. We show that both quantities can change under an information-preserving invertible reparameterization, so neither is intrinsically a concept dimension. We distinguish model-defined population quantities (generating dimension, sufficient linear dimension, and minimum guarding rank) from procedure-defined quantities such as stopping count and cumulative edit rank. In a population Gaussian construction, an invertible shear preserves the prediction problem and all three quantities, yet changes the cumulative Euc...
| Authors | Tingan Jin, Shuhang Dong, Haosong Li et al. |
|---|---|
| Primary category | stat.ML |
| Published | 11 August 2026 |
| Last updated at source | 11 August 2026 |
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