mirror of
https://github.com/hanzoai/papers.git
synced 2026-10-29 01:14:44 +00:00
zeekayandHanzo Dev
03c6289dfc
Design, prior art and a measurement protocol for a weighted inverted index over a mixed sparse basis and part-level routing before per-part HNSW in a ClickHouse-derived store. Each component is marked prior art or proposed. The protocol fits C(N) = aN^alpha to parts, granules and bytes touched per correct answer at a held recall. No numbers: every results cell is a placeholder read from results-data.tex until the baseline lane writes it. Co-authored-by: Hanzo Dev <[email protected]>
50 lines
2.7 KiB
TeX
50 lines
2.7 KiB
TeX
\section{Limitations}
|
|
\label{sec:limits}
|
|
|
|
\textbf{Nothing here is measured.} The design has not been built at the scale
|
|
it is argued for, and the protocol in \S\ref{sec:method} has produced no
|
|
numbers. Every statement about cost in this paper is a statement about what a
|
|
bound permits, not about what a machine did.
|
|
|
|
\textbf{The per-type calibration is unsolved.} A single score over a mixed
|
|
basis needs weights $w_t$ that put an entity linker's confidence and a lexical
|
|
impact on one scale. Learning them requires relevance judgements over the
|
|
mixture, which the lane does not yet have; until it does, any reported
|
|
effectiveness is the effectiveness of a hand-set combination, and should be
|
|
read as such.
|
|
|
|
\textbf{Bounds loosen with dimension, and that is not fixable by tuning.}
|
|
Covering radii stop separating regions in high intrinsic dimension, so the
|
|
exact routing rule can degenerate to a full visit; the approximate rule then
|
|
carries the load and converts a cost problem into a recall problem. The
|
|
protocol measures where that transition happens for a given corpus, but no
|
|
choice of region size avoids it.
|
|
|
|
\textbf{The routing metadata is itself a cost that grows.} The number of region
|
|
summaries is proportional to the number of regions, so a design that scanned
|
|
them all would be linear in the corpus with a small constant. The tree over
|
|
part summaries is what keeps that term sublinear, and its depth, fan-out and
|
|
maintenance cost during merges are unmeasured.
|
|
|
|
\textbf{Merge-time maintenance is a write-side cost we do not price.} Carrying
|
|
posting lists, block maxima and region summaries through a merge is work that
|
|
competes with ingestion. A design that makes reads cheap and merges expensive
|
|
can be a net loss for a table that is written more often than it is queried.
|
|
|
|
\textbf{The claim is about a query distribution.} An exponent fitted under one
|
|
distribution says nothing about another. The strata in \S\ref{sec:method} are
|
|
there so a reader can see which queries the average is made of, but the
|
|
protocol cannot certify that a deployment's queries resemble the set measured.
|
|
|
|
\textbf{Exactness is relative to the per-part search.} The routing rule is
|
|
exact given the region bounds, but the dense leg inside a part is an
|
|
approximate graph search, so the system's answer is exact only with respect to
|
|
what that search returns. Conflating the two would make a recall failure look
|
|
like a routing success.
|
|
|
|
\textbf{The largest sizes are not yet reachable.} A corpus of $10^9$ rows with
|
|
dense vectors and a mixed sparse basis needs hardware the lane has not yet been
|
|
given, the first pass stops two decades below it, and the collection it samples
|
|
holds $3.5 \times 10^7$ rows. A fit over the sizes actually run is a fit over
|
|
those sizes.
|