On distance to monotonicity and longest increasing subsequence of a data stream
Why this work is in the frame
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Bibliographic record
Abstract
In this paper we consider problems related to the sortedness of a data stream. First we investigate the problem of estimating the distance to monotonicity; given a sequence of length n, we give a deterministic (2 + e)-approximation algorithm for estimating its distance to monotonicity in space O(1/e2 log2 (en)). This improves over the randomized (4 + e)-approximation, algorithm of [3]. We then consider the problem of approximating the length of the longest increasing subsequence of an input stream of length n. We use techniques from multi-party communication complexity combined with a fooling set approach to prove that any O(1)-pass deterministic streaming algorithm that approximates the length of the longest increasing subsequence within 1 + e requires Ω(√n) space. This proves the conjecture in [3] and matches the current upper bound.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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 it