On the Computability of Robust PAC Learning
Bibliographic record
Abstract
We initiate the study of computability requirements for adversarially robust learning. Adversarially robust PAC-type learnability is by now an established field of research. However, the effects of computability requirements in PAC-type frameworks are only just starting to emerge. We introduce the problem of robust computable PAC (robust CPAC) learning and provide some simple sufficient conditions for this. We then show that learnability in this setup is not implied by the combination of its components: classes that are both CPAC and robustly PAC learnable are not necessarily robustly CPAC learnable. Furthermore, we show that the novel framework exhibits some surprising effects: for robust CPAC learnability it is not required that the robust loss is computably evaluable! Towards understanding characterizing properties, we introduce a novel dimension, the computable robust shattering dimension. We prove that its finiteness is necessary, but not sufficient for robust CPAC learnability. This might yield novel insights for the corresponding phenomenon in the context of robust PAC learnability, where insufficiency of the robust shattering dimension for learnability has been conjectured, but so far a resolution has remained elusive.
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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 | 0.006 | 0.041 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.010 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.002 | 0.009 |
| Insufficient payload (model declined to judge) | 0.006 | 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".