Position: Adopt Constraints Over Fixed Penalties in Deep Learning
Bibliographic record
Abstract
Recent efforts to develop trustworthy AI systems have increased interest in learning problems with explicit requirements, or constraints. In deep learning, however, such problems are often handled through fixed weighted-sum penalization: the constraints are added to the task loss with fixed coefficients, and the resulting scalarized objective is minimized. This position paper argues that fixed penalization is often ill-suited for deep learning problems with non-negotiable requirements for several reasons. First, in non-convex settings, the penalized and constrained problems are generally not equivalent, so solving the former need not solve the latter. Second, fixed penalization weakens hard requirements into soft penalties to be traded off against task performance. Third, choosing penalty coefficients to indirectly solve the constrained problem often involves costly trial and error, because changing them alters the penalized objective itself, and hence can mean solving the wrong problem altogether. We therefore argue that, when a deep learning problem specifies non-negotiable requirements, the constrained formulation itself should be the starting point, not the surrogate problem defined by fixed penalization. The appropriate solution strategy should then be chosen based on the problem's structure and scale.
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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 | 0.007 | 0.027 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".