anisotropic concept
| Definition | Of a covariance, having different variances in different directions. Chapter 0. Also anisotrop. |
|---|---|
| Example | Covariance diag(0.3, 1.7) has variance 0.3 along the first axis and 1.7 along the second, so it is anisotropic. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id anisotropic, 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/Isotropy.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- Of a covariance, having different variances in different directions, which is to say unequal eigenvalues. Two readers at different angles to an anisotropic covariance read different variances, and the flip between two codes exists exactly when the covariance is anisotropic along the directions that separate them.
- Centring an embedding raised a ranker from 0.79 to 0.84 on the legal corpus, which is the condition under which a learned quotient and a variance quotient disagree most, and an isotropic control collapses the flip.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.4 of Data Mining as Observation, with
the program’s centring measurement in
geometric-observation/claims/LEDGER.md row GO-B-legal and
the anisotropy channel in lebse/README.md:40-75.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 11 section 11.8 | 0.765 to 0.971 with interval 0.190 to 0.223, 0.545 to 0.562 with interval 0.004 to 0.031, v1 0.340 with interval negative 0.214 to negative 0.081, anisotropy 0.570 to 0.259 | lebse/README.md:40-75;
lebse\PAPER.md:1-15,60-66;
lebse/MODEL_CARD.md:48-52 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Isotropy.lean,
theorems isotropic_reads_same,
isotropic_no_flip, anisotropic_readers_differ,
flip_iff_anisotropic, at observation-data-mining f3914f0;
what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 0, 3, 9, 11, 12.
Related
isotropic; covariance matrix; spectrum; whitening.
See also
Book equations stated beside the entry’s terms, not defining it: 0.5, 3.1, 4.6.
Ledger rows that cite the entry’s records without naming it: GO-2 (neg. half: not reconstruction), GO-B-legal (035→036).
Sources-table rows that share a record with the entry without naming it: chapter 12 section 12.3, chapter 12 section 12.4.
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.