Oblivious string embeddings and edit distance approximations
Bibliographic record
Abstract
We introduce an oblivious embedding that maps strings of length n under edit distance to strings of length at most n/r under edit distance for any value of parameter r. For any given r, our embedding provides a distortion of Õ(r1+μ) for some μ = o(1), which we prove to be (almost) optimal. The embedding can be computed in Õ(21/μn) time.We also show how to use the main ideas behind the construction of our embedding to obtain an efficient algorithm for approximating the edit distance between two strings. More specifically, for any 1 > ε ≥ 0, we describe an algorithm to compute the edit distance D(S, R) between two strings S and R of length n in time Õ(n1+ε), within an approximation factor of min{n1-ε/3+o(1), (D(S, R/nε)1/2+o(1)}. For the case of ε = 0, we get a Õ(n)-time algorithm that approximates the edit distance within a factor of min{n1/3+o(1), D(S, R)1/2+o(1)}, improving the recent result of Bar-Yossef et al. [2].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.010 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".