quantization concept
| Definition | Replacing each number with one of a small set of allowed values so that it can be stored in a few bits. Chapter 0 section 0.11. Also quantiz. |
|---|---|
| Example | Rounding 1.37 to a step of 0.5 gives 1.5, an error of 0.13. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id quantization, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 11.1. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Quantization.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 11.1.
\[\cos\big(k,\hat k\big)=0.995\qquad\text{while}\qquad \mathrm{PPL}:\ 12.24\ \to\ 10643.\]
Conditions
- Replacing each number with one of a small set of allowed values so that it can be stored in a few bits. A uniform quantizer with a given step has error at most half the step and zero error on a level, and halving the step halves the bound.
- Those are the identity reader’s bounds. What a quantizer does to a consumer is the flip’s question, and the key quantizer table of chapter 11 is the case in which the smaller reconstruction error was the worse code.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.11 and chapter 11 section 11.2 of Data Mining
as Observation, with the program’s quantizer table in
turboquant-pro/docs/KV_KEYS_FINDING.md:1-49.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Quantization.lean,
theorems error_le_half_step, quantize_level,
half_step_bound, sq_error_le,
finer_step, 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, 2, 3, 4, 7, 8, 10, 11.
Related
bit; codebook; per-channel quantizer; direction-only quantizer; the flip.
See also
Book equations stated beside the entry’s terms, not defining it: 0.13.
Ledger rows that cite the entry’s records without naming it: GO-2 (neg. half: not reconstruction), NEG-2.
Sources-table rows that share a record with the entry without naming it: chapter 1 section 1.4, chapter 2 section 2.5, chapter 3 section 3.2, chapter 8 section 8.2, chapter 8 section 8.9, chapter 11 section 11.1, chapter 11 section 11.2.
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.