Bundling capacity: inside and outside a MAP bundle

A MAP hypervector bundle combines bound facts. This repository tests that bundle from two directions.

Throughout these docs, $h$ denotes a hypervector, $\otimes$ denotes binding, and $\oplus$ denotes bundling. Binding is implemented as element-wise multiplication in both studies. Bundling is the same in both: an arithmetic sum without a final sign threshold, so every bound fact can still be unbound. The regular plus sign ($+$) is reserved for ordinary arithmetic, such as adding scalar similarity contributions.

	Inside the bundle	Outside the bundle
Question	How many facts can one bundle hold before we can't read a fact back?	How many records fit before chance alone makes two unrelated records look like a match, for one search and for the whole dataset?
Pressure	Crowding within one vector: every added fact is noise for the others	Crowding among vectors: every added candidate is another chance to score high by accident
Workload	One person's scored answers to 5–50 IPIP questionnaire items	40,000 synthetic records with five categorical properties: region, education, occupation, interest cluster and employer
Encoder	$h_{\mathrm{item}} \otimes h_{\mathrm{answer}}$, then additive bundling ($\oplus$); five ordered answer levels	$h_{\mathrm{role}} \otimes h_{\mathrm{value}}$, then additive bundling ($\oplus$) of five facts; cosine between every pair of records
Measures	Answer cleanup, whole-profile geometry, similarity as bundles grow	False matches and missed matches against a match threshold, for one search and for the whole dataset, at D = 2,048, 4,096 and 8,192
Report	src/qa-encoding/REPORT.md	src/scale/REPORT.md
Code	src/qa-encoding	src/scale · methodology
Data	data/qa-encoding, 31 fixed synthetic profiles	data/scale, one fixed sequence of uniformly drawn records

The two studies use different encoders and workloads, so their numbers should not be compared as if one encoder produced both. Both datasets are synthetic. The original records stay the exact source of truth; bundle readout and similarity are measured properties of each encoder on its data, not general capacity limits of a hyperspace.

Each study has its own locked environment under src/<study>/. See each README for the reproduction commands.