Andrew Fribush
fig. 2.2.2 · the score matrix of 100,000 arXiv titles, and the pairs the bound clears.
The bound clears 99.9% of pairs; all 1,487 above 0.9 sit in what is left100,000 arXiv title embeddings, ordered so similar titles sit together · rank-64 screen, threshold0.9One cell is ~256 × 256 titles, darker = higher mean cosine; washed grey = the bound rejects everypair in it; dot = one pair ≥ 0.9rows and columns: the same 100,000 titles, in similarity order1,487 pairs ≥ 0.9Every one inside a cell the boundkept. Most hug the diagonal:near-duplicate titles.35% of cells greyThe other 65% each keep at least onesurvivor, so the rejection works pairby pair, not block by block.4,369,607 survivorsof 4,999,950,000 pairs (0.087%) passthe bound and get a full 768-d dot.

source: gpu-threshold-join benchmarks/data/arxiv/arxiv-100000.npy, all 4,999,950,000 pairs scored on the CPU; bound per kernels/screen_bounds.cu, emulated in numpy · scoreMatrix.data.ts

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Andrew Fribush, software and computer engineer in Austin. I build consequential systems where software meets institutions: finance, healthcare, commerce, government data, and the mechanisms that govern AI agents. Taking new engagements: hello@andrewfribush.com.