Wilsonian renormalization of neural network Gaussian processes<sup>*</sup>
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Bibliographic record
Abstract
Abstract Separating relevant and irrelevant information is key to any modeling process or scientific inquiry. Theoretical physics offers a powerful tool for achieving this in the form of the renormalization group (RG). Here we demonstrate a practical approach to performing Wilsonian RG in the context of Gaussian Process (GP) Regression. We systematically integrate out the unlearnable modes of the GP kernel, thereby obtaining an RG flow of the GP in which the data sets the IR scale. In simple cases, this results in a universal flow of the ridge parameter, which becomes input-dependent in the richer scenario in which non-Gaussianities are included. In addition to being analytically tractable, this approach goes beyond structural analogies between RG and neural networks by providing a natural connection between RG flow and learnable vs. unlearnable modes. Studying such flows may improve our understanding of feature learning in deep neural networks, and enable us to identify potential universality classes in these models.
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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 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| 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