Vector Space & the HAG

Vector Space, and the Three Graphs It Holds

An interactive engineering walkthrough of embeddings, similarity, retrieval, and the dependency edges that do work geometry cannot — built from the live LearningNuggets corpus.

Ordinary search matches characters. Meaning search turns text into numbers so a tutor can find the right memory even when a learner words the question differently from how the answer was written. This lab shows that translation end to end.

You start with a ground-up primer: three dials, a space you can rotate, and the idea that “close” is cosine similarity. From there the page opens the real map — 56 anonymized production hag_entries with real 1,536-dimensional embeddings, a 29-node crypto graph, and a similarity matrix computed by pgvector over stored vectors.

Retrieval, anchors, and the three graphs (geometry, typed dependency edges, and lifecycle) show where pure similarity lies and where curated edges carry prerequisites, warnings, and teaching order that distance alone cannot encode.

Every threshold on the page is a live hag_settings dial. The walkthrough is a primary source for the orchestration claims in The Oracle and the Collaborator: memory, context assembly, and continuous learning as the layer around the model.