Grotto: Screaming fast (2+1)-PC or ℤ2n via (2,2)-DPFs
Bibliographic record
Abstract
We introduce Grotto, a framework and C++ library for space- and time-efficient (2+1)-party piecewise polynomial (i.e., spline) evaluation on secrets additively shared over ℤ2n. Grotto improves on the state-of-the-art approaches based on distributed comparison functions (DCFs) in almost every metric, offering asymptotically superior communication and computation costs with the same or lower round complexity. At the heart of Grotto is a novel observation about the structure of the ''tree'' representation underlying the most efficient distributed point functions (DPFs) from the literature, alongside an efficient algorithm that leverages this structure to do with a lightweight DPF what state-of-the-art approaches require comparatively heavyweight DCFs to do. Our open-source Grotto implementation supports dozens of useful functions out of the box, including trigonometric and hyperbolic functions with their inverses; various logarithms; roots, reciprocals, and reciprocal roots; sign testing and bit counting; and over two dozen of the most common univariate activation functions from the deep-learning literature.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.030 | 0.008 |
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".