ora-0101
7.6 The cost of categorical learning
Classical sample complexity is only one coordinate of UOCL complexity. A useful accounting vector is
\[ \mathbf C_{\mathrm{UOCL}}= (N_{\mathrm{base}},N_{\mathrm{tan}},N_{\mathrm{revision}}, N_{\mathrm{doctrine}},C_{\mathrm{update}},C_{\mathrm{memory}}). \]
It records base probes, tangent-sensitive probes, ordinary accommodation, doctrinal accommodation, computational update cost, and the size of persistent warrants. Two learners with identical predictive error can differ radically: one may reconstruct a stable reusable theory, while the other repeatedly relearns answers after destructive revision.
This vector also clarifies the role of a categorical prior. A stronger prior may reduce probe and revision complexity while increasing the risk of doctrinal obstruction. The gain must therefore be evaluated together with the cost and correctness of accommodation.