Basis Function Discovery Using Spectral Clustering and Bisimulation Metrics
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Bibliographic record
Abstract
We study the problem of automatically generating features for function approximation in reinforcement learning. We build on the work of Mahadevan and his colleagues, who pioneered the use of spectral clustering methods for basis function construction. Their methods work on top of a graph that captures state adjacency. Instead, we use bisimulation metrics in order to provide state distances for spectral clustering. The advantage of these metrics is that they incorporate reward information in a natural way, in addition to the state transition information. We provide theoretical bounds on the quality of the obtained approximation, which justify the importance of incorporating reward information. We also demonstrate empirically that the approximation quality improves when bisimulation metrics are used instead of the state adjacency graph in the basis function construction process.
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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 | 0.000 |
| 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