capacity concept
| Definition | The number of distinctions a model class can draw, the model-side half of the budget. Chapter 6. |
|---|---|
| Example | A formula of depth three over 18 operations can draw far fewer boundaries than a forest of 500 trees. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id capacity, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/ProbeCliff.lean, lean/DataMiningAsObservation/Rank.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The number of distinctions a model class can draw, the budget’s model-side half. A read operator’s rank is at most the dimension, and a probe with fewer directions than the dimension cannot resolve the operator, which is the cliff.
- A formula of depth three over eighteen operations has a capacity the ensemble exceeds, and the ensemble wins exactly when the boundary needs that excess.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 6 section 6.1 of Data Mining as Observation, with
the budget inversion in
geometric-observation/claims/LEDGER.md row GO-4.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/ProbeCliff.lean,
theorems centralDiff_affine,
centralDiff_basis, exists_blind_direction,
indistinguishable, budget_cliff, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
lean/DataMiningAsObservation/Rank.lean,
theorems rank_le_width, rank_le_height,
rank_outer_le_one, rank_mul_le,
rank_zero, rank_transpose, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation chapters 6, 7.
Related
budget; budget cliff; rank; ensemble.
See also
Book equations stated beside the entry’s terms, not defining it: 1.1, 6.1, 11.4.
Ledger rows that cite the entry’s records without naming it: GO-4.
Sources-table rows that share a record with the entry without naming it: chapter 4 section 4.4, chapter 6 section 6.3.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.