LLM knowledge for improved Out-of-Distribution Tabular Prediction - A Cross-Validated Regularisation Approach

Prediction models degrade when the deployment population differs from the one used to train them, and training data cannot say which feature-response relationships will transfer. Expert elicitation is slow and unscalable. We ask whether coefficient priors elicited from large language models (LLMs) improve out-of-distribution (OOD) prediction as the shrinkage target of a regularised regression instead of zero, across five tabular datasets split on real covariates, selecting providers and prior structures by source-domain cross-validation alone. The priors help on four of five datasets, by up to 7.9% OOD mean squared error, and ten of twenty-four prior-informed results resolve the mean improvement at conventional confidence; single-deployment intervals are much wider. On classification the gain is in probabilistic accuracy, not ranking, and control tests with corrupted priors attribute the benefit to feature-specific content rather than scale. Two findings temper this. Variation across candidate priors exceeds the average benefit, yet cross-validation margins fall below their own noise, so selection avoids the worst prior rather than finding the best. On three datasets the prior improves in-domain accuracy as much as out-of-domain, making it better regularisation than shift correction. Only where the training data are large enough that the in-domain gain disappears does elicited knowledge demonstrably improve transfer. Code, priors and results: https://github.com/hugohammer/llm-priors-ood.