Lost Domain Generalization Is a Natural Consequence of Lack of Training Domains
Bibliographic record
Abstract
We show a hardness result for the number of training domains required to achieve a small population error in the test domain. Although many domain generalization algorithms have been developed under various domain-invariance assumptions, there is significant evidence to indicate that out-of-distribution (o.o.d.) test accuracy of state-of-the-art o.o.d. algorithms is on par with empirical risk minimization and random guess on the domain generalization benchmarks such as DomainBed. In this work, we analyze its cause and attribute the lost domain generalization to the lack of training domains. We show that, in a minimax lower bound fashion, any learning algorithm that outputs a classifier with an ε excess error to the Bayes optimal classifier requires at least poly(1/ε) number of training domains, even though the number of training data sampled from each training domain is large. Experiments on the DomainBed benchmark demonstrate that o.o.d. test accuracy is monotonically increasing as the number of training domains increases. Our result sheds light on the intrinsic hardness of domain generalization and suggests benchmarking o.o.d. algorithms by the datasets with a sufficient number of training domains.
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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 | 0.001 | 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 | 0.000 |
| 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 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".