Bibliographic record
Abstract
Abstract. We analyze the complexity of the Walk on Spheres algorithm for simulating Brownian Motion in a domain Ω ⊂ Rd. The algorithm produces samples from the hitting probability distribu-tion on ∂Ω within an error of ε. We introduce energy functions using Newton potentials to obtain an O(log2 1/ε) upper bound on the convergence of the algorithm for a very rich class of domains Ω. In particular, we show this rate of convergence for all 3-dimensional domains with connected exterior. We show that, in general, the convergence rate of the algorithm may be polynomial in 1/ε, and give a tight worst-case bound of O(ε4/d−2) on the convergence of the algorithm in d ≥ 3 dimensions. For d = 3, this gives an optimal upper bound of O(ε−2/3), improving on the previously known bound of O(ε−1). 1.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 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".