Convex Potential Flows: Universal Probability Distributions with Optimal\n Transport and Convex Optimization
Bibliographic record
Abstract
Flow-based models are powerful tools for designing probabilistic models with\ntractable density. This paper introduces Convex Potential Flows (CP-Flow), a\nnatural and efficient parameterization of invertible models inspired by the\noptimal transport (OT) theory. CP-Flows are the gradient map of a strongly\nconvex neural potential function. The convexity implies invertibility and\nallows us to resort to convex optimization to solve the convex conjugate for\nefficient inversion. To enable maximum likelihood training, we derive a new\ngradient estimator of the log-determinant of the Jacobian, which involves\nsolving an inverse-Hessian vector product using the conjugate gradient method.\nThe gradient estimator has constant-memory cost, and can be made effectively\nunbiased by reducing the error tolerance level of the convex optimization\nroutine. Theoretically, we prove that CP-Flows are universal density\napproximators and are optimal in the OT sense. Our empirical results show that\nCP-Flow performs competitively on standard benchmarks of density estimation and\nvariational inference.\n
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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 | 0.003 | 0.017 |
| 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 | 0.003 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".