per-channel quantizer instrument
| Definition | A quantizer that chooses a scale per coordinate. Chapter 11. Also per-channel. |
|---|---|
| Example | With per-coordinate steps of 0.5 and 0.1, the vector (1.3, 0.27) is stored as (1.5, 0.3). |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id per-channel-quantizer, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | turboquant-pro/docs/KV_KEYS_FINDING.md:1-49, lean/DataMiningAsObservation/Quantization.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A quantizer that chooses a step per coordinate. The squared error of a vector is at most the sum of the squared half steps, and a finer step on one coordinate lowers that coordinate’s bound alone, which is the allocation water-filling makes by sensitivity.
- At four bits the per-channel uniform quantizer held the perplexity at 14.91 against 12.24 uncompressed, where the direction-only quantizer at the same bits did not.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 11 section 11.2 of Data Mining as Observation, with
the per-channel rows of the quantizer table in
turboquant-pro/docs/KV_KEYS_FINDING.md:1-49.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 11 section 11.2 | fp16 12.24, values-only 13.12, PolarQuant K4 10643 and 0.095, per-channel uniform K4 14.91 and 0.062, per-channel NUQ K3 15.77 and 0.148, 2.4x and 670x, pre-rotary near 22000, 2 key heads serve 12 query heads | turboquant-pro/docs/KV_KEYS_FINDING.md:1-49 |
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, 3, 4, 11.
Related
quantization; direction-only quantizer; water-filling; KV cache.
See also
Book equations stated beside the entry’s terms, not defining it: 11.1, 0.13.
Ledger rows that cite the entry’s records without naming it: 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 11 section 11.1.
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.