Gradient Flow Approximations in Temporal Difference Learning
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Bibliographic record
Abstract
We consider the continuous-time temporal difference (TD) learning dynamics with nonlinear value function approximations, where there is a slim understanding of the convergence properties in irreversible regimes. Motivated by Krener’s linearization idea ala Lie-brackets, we obtain conditions on the approximating value function and irreversibility coefficients under which the TD dynamics behaves close to a gradient flow. We show that our conditions lead to a set of partial differential equations, and study the existence of solutions using the algebraic invertibility of differential operators. Whenever a solution exists, using a perturbation analysis, we provide a stability result for nonlinear TD dynamics. As a by-product, we state the implications of the results for the classical case of linear approximations, where our conditions are algebraic, and easily verifiable.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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