Self-Distillation for Gaussian Process Models
Bibliographic record
Abstract
Knowledge distillation has empirically proven to be an effective technique for training a student model to reproduce a teacher model. However, a theoretical understanding of why distillation techniques work is largely absent. In this paper, we aim to remedy this lack by theoretically analyzing self-distillation for Gaussian process regression (GPR) and classification (GPC). We propose two approaches to extend self-distillation to Gaussian processes, which we refer to as deterministic GPSD (d-GPSD) and probabilistic GPSD (ρ-GPSD). The d-GPSD approach resembles most current distillation techniques, and refits a model on deterministic predictions from the teacher, while the ρ-GPSD approach, re-uses the probabilistic posterior for the distillation. By analyzing the properties of these methods, we show that d-GPSD for GPR closely relates to known results for self-distillation and that ρ-GPSD for GPR corresponds to ordinary GPR with a particular choice of hyperparameters. We demonstrate that ρ-GPSD for GPC approximately corresponds to data duplication and a particular scaling of the covariance function and that d-GPSD for GPC requires replacing the Binomial likelihood with a continuous Bernoulli likelihood to be well-specified. We illustrate our theoretical results with empirical examples. To our knowledge, these are the first formulations of self-distillation specifically for GP models.
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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 | 0.005 | 0.018 |
| 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 | 0.001 | 0.004 |
| Open science | 0.002 | 0.003 |
| 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".