An SQLite virtual table is implemented by a set of functions (methods) described here https://sqlite.org/vtab.html

The CROSS JOIN is explained in section 7.3 of https://sqlite.org/optoverview.html

Lets assume you have a table of text documents:

CREATE TABLE docs (Id INTEGER PRIMARY KEY, content TEXT);

You then need a virtual table module to generate a vector from a text.

CREATE VIRTUAL TABLE text2vec4 USING vector(4);

which pretends to be a table declared as (v1 float, v2 float, v3 float, v4 float, content text hidden). 

You can then SELECT * from text2vec4 where content = 'sample text'; to return a vector representation of the content. Syntactic sugar allows you to SELECT text2vec4('sample text'); instead

Then another virtual table to store and retrieve vectors.

CREATE VIRTUAL TABLE docs_index USING dense(4);

which pretends to be a table declared as (v1 float hidden, v2 float hidden, v3 float hidden, v4 float hidden, docid integer);

You can then load your data using

INSERT INTO docs_index(docid,v1,v2,v3,v4) SELECT Id,text2vec4(content) FROM docs;

And you can retrieve documents matching a search phrase using

SELECT content FROM docs_index CROSS JOIN docs ON docs_index.docid = docs.Id WHERE (v1,v2,v3,v4) = text2vec4('search phrase');

or shorter

SELECT content FROM docs WHERE Id = docs_index(text2vec4('search phrase'));