Grotto: Screaming fast (2+1)-PC or ℤ2n via (2,2)-DPFs
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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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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 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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