Constrained Sequential Inference in Machine Learning Using Constraint Programming
Bibliographic record
Abstract
Sequence models in machine learning often struggle to exhibit long-term structure. We consider this problem at inference time in the context of enforcing constraints that are not necessarily featured in the dataset on which the generative model was trained. The difficulty lies in imposing previously-unseen structure while staying close to the training dataset. It is particularly hard for long-term structure, which requires balancing foresight over many yet-to-be generated tokens and the immediacy of next-token predictions from the sequence model. We address this problem by introducing our neurosymbolic framework GeAI-BLAnC. The learned probabilities of the sequence model are mixed in with the marginal probabilities computed from a constraint programming / belief propagation framework applied to a constraint programming model expressing the desired structure. The next predicted token is then selected from the resulting probability distribution. Experiments in the context of molecule and music generation show that we can achieve the structure imposed post-training without straying too much from the structure of the dataset learned during training.
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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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".