embedding concept
| Definition | A vector assigned to an object, a word, a sentence, a node, a document, so that nearness in the vector space stands for a relation between the objects. Chapter 11. |
|---|---|
| Example | A sentence becomes a vector of 768 numbers, and two paraphrases become vectors with cosine near one. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id embedding, kind concept. |
| Status | measures [predicted]. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | geometric-observation/claims/LEDGER.md:119, lean/DataMiningAsObservation/Embedding.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A vector assigned to an object so that nearness in the vector space stands for a relation between the objects. Objects with the same embedding are indistinguishable to every consumer of the embedding, so the embedding is a quotient, and a cosine reader takes a further quotient in which the nearest neighbour is unchanged when the query is rescaled, where a dot-product reader does not.
- What an embedding is worth to a consumer is the consumer’s number. The keys that reconstructed at cosine 0.995 and raised the perplexity by three orders of magnitude are the case, and the rank certificate is the instrument that says which neighbour rankings a compressed embedding preserved.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
- measures. GO-B-legal (035→036)
[predicted]. Legal-citation retrieval (CourtListener), cosine-ranking consumer, LaBSE embeddings — real large corpus, non-physical consumergeometric-observation/claims/LEDGER.md:119.
First stated
Chapter 11 section 11.1 of Data Mining as Observation, with the program’s embeddings in the legal-citation flip, the GloVe corpus of readscope, and the attention keys of the KV finding.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Embedding.lean,
theorems quotient, cosine_scale_free,
nearest_scale_free, dot_not_scale_free, 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, 1, 3, 4, 8, 9, 10, 11, 12, 13, 14.
Related
encoder; dot product; rank certificate; hubness; the flip.
See also
Book equations stated beside the entry’s terms, not defining it: 11.1, 11.2.
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 4 section 4.5, chapter 8 section 8.2, 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.