Extended Learning Graphs for Triangle Finding
Bibliographic record
Abstract
We present new quantum algorithms for Triangle Finding improving its best\npreviously known quantum query complexities for both dense and spare\ninstances.For dense graphs on $n$ vertices, we get a query complexity of\n$O(n^{5/4})$ without any of the extra logarithmic factors present in the\nprevious algorithm of Le Gall [FOCS'14]. For sparse graphs with $m\\geq n^{5/4}$\nedges, we get a query complexity of $O(n^{11/12}m^{1/6}\\sqrt{\\log n})$, which\nis better than the one obtained by Le Gall and Nakajima [ISAAC'15] when $m \\geq\nn^{3/2}$. We also obtain an algorithm with query complexity ${O}(n^{5/6}(m\\log\nn)^{1/6}+d_2\\sqrt{n})$ where $d_2$ is the variance of the degree distribution.\nOur algorithms are designed and analyzed in a new model of learning graphs that\nwe call extended learning graphs. In addition, we present a framework in order\nto easily combine and analyze them. As a consequence we get much simpler\nalgorithms and analyses than previous algorithms of Le Gall {\\it et al} based\non the MNRS quantum walk framework [SICOMP'11].\n
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".