Near-Floor Geometry Is Generic: Leverage Dispersion in Trained Overcomplete Codes

תקציר מקורי באנגליתarXiv:2605.01192v2 Announce Type: replace Abstract: An overcomplete code packs $F$ features into $d<F$ dimensions, so linear readout of one feature picks up cross-talk from the others, bounded below by the rank-trace floor $W(F,d)=(F-d)/(d(F-1))$. Proximity to this floor is read as evidence of an efficient arrangement. It is not: an i.i.d. code of the same shape attains it at every shape and load we measure (1.0000-1.0005 over 7 matched controls), and the reason is exact. For the gain-calibrated pseudoinverse the attainment ratio is $\frac{d}{F(F-d)}(\sum_i h_i^{-1}-F)$ with $\sum_i h_i=d$, so it equals one precisely when the leverage $h_i$ is equalised across features: distance from the floor IS leverage dispersion. On 40 released decoder matrices - 24 sparse-autoencoder decoders plus 16