Convex Potential Flows: Universal Probability Distributions with Optimal\n Transport and Convex Optimization
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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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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it