Vicinal Gaussian Transform: Rethinking Source-Free Domain Adaptation Through Source-Informed Label Consistency
Bibliographic record
Abstract
A central challenge in source-free domain adaptation (SFDA) is the lack of a theoretical framework for explicitly analyzing domain shifts, as the absence of source data prevents direct domain comparisons. In this paper, we introduce the Vicinal Gaussian Transform (VGT), an analytical operator that models source-informed latent vicinities as Gaussians and shows that vicinal prediction divergence is bounded by their covariance. By this formulation, SFDA can be reframed as shrinking covariance to reinforce label consistency. To operationalize this idea, we introduce the Energy-based VGT (EBVGT), a novel SDE that realizes the Gaussian transform by contracting covariance through a denoising mechanism. A recovery-likelihood with a Schrödinger-Bridge smoothness penalty denoises perturbed states, while a BYOL-derived energy function, directly obtained from model predictions, provides the score to guide label-consistent trajectories within the vicinity. This design not only yields noise-suppressed vicinal features for adaptation without source data, but also eliminates the need for additional learnable parameters for score estimation, in contrast to conventional deep SDEs. Our EBVGT is model- and modality-agnostic, efficient for classification, and improves state-of-the-art SFDA methods by 1.3-3.0% (2.0% on average) across both 2D image and 3D point cloud benchmarks.
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How this classification was reachedexpand
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 | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".