Bibliographic record
Abstract
We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an implementation, momtrop , and apply it to a series of relevant integrals from the loop-tree duality framework. Compared to naive sampling methods, we observe convergence speedups by factors of more than 10 6 . Program Title: momtrop CPC Library link to program files: https://doi.org/10.17632/v9mxr9dw2z.1 Developer's repository link: https://github.com/alphal00p/momtrop Licensing provisions: MIT Programming language: Rust Nature of problem: Efficient numerical evaluation of Feynman-type integrals (e.g. phase space or loop-tree duality integrals). Solution method: Efficient sampling of loop momenta distributed as the Feynman measure (i.e. the integrand of a scalar Euclidean Feynman integral) using tropical sampling [1]. The input to the library is the graph associated to the Feynman measure. From the graph a sampler is produced that takes as input a set of uniformly distributed random numbers and returns a (weighted) set of loop momenta. Additional comments including restrictions and unusual features: Memory usage is exponential in the number of propagators of the Feynman integral. There can be numerical instabilities if the parameters are close to a divergent configuration. [1] M. Borinsky, Tropical Monte Carlo quadrature for Feynman integrals, Ann. Inst. H. Poincare D Comb. Phys. Interact. 10 (4) (2023) 635–685. arXiv:2008.12310 , https://doi.org/10.4171/aihpd/158 .
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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 | 0.002 | 0.010 |
| 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 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".