Tensor models from the viewpoint of matrix models: the cases of loop models on random surfaces and of the Gaussian distribution
Bibliographic record
Abstract
Two direct connections between random tensors and random matrices are discussed in this article. In the rst part, we introduce U( \tau ) matrix models which generate fully packed, oriented loops on random surfaces. e latter are found to be in bijection with a set of regular edge-colored graphs. It is shown that the expansion in the number of loops is organized like the 1/ N expansion of rank-three tensor models. Recent results on tensor models are applied in this context. For example, congurations which maximize the number of loops are precisely the melonic graphs of tensor models and a scaling limit which projects onto themelonic sector is found. is approach is generalized to higher-rank tensor models, which generate loops with fugacity \tau on triangulations in dimension d–1 . In the second part, we introduce singular value decompositions to evaluate the expectations of polynomial observables of Gaussian random tensors. Performing the integrals over the unitary group leads to a notion of eective observables which expand onto regular trace invariants. We show that both asymptotic and exact new calculations of expectations can be performed this way.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".