Omitted Variable Bias in Language Models Under Distribution Shift

Conformal prediction (CP) for language models is typically evaluated under a matched protocol, in which calibration and deployment use the same post-training inference configuration, such as quantization mode and inference temperature. In deployment, these choices often differ from those used at calibration to meet memory or throughput constraints or serving policies. We argue that this exposes a limitation in current CP evaluation protocols for language models. We formalize the underlying phenomenon as inference-time model shift: a change in the conformal score distribution induced by inference configuration rather than by the input--label distribution, and theoretically characterize how it breaks split-conformal exchangeability even when the task distribution and trained model are unchanged. We then evaluate its consequences across 8 language models, 4 finite-label benchmarks, and 12 inference configurations. We find that matched evaluation can substantially overstate deployment-time coverage, and that the effect is heterogeneous across models and datasets. We argue that inference configuration should be reported as a first-class experimental axis in CP evaluations for language-model systems.

Machine learning models for tabular prediction typically assume that training data are representative of the population on which they will be deployed. In practice, however, data are often collected based on convenience, availability, or cost, resulting in systematic sampling biases that can distort feature--target relationships and undermine real-world generalization. Existing tabular distribution-shift benchmarks primarily construct out-of-distribution (OOD) settings by partitioning observations across naturally occurring domains. While such partitions may induce changes in P(Y | X), the resulting shifts are neither explicitly controlled nor isolated, and the evaluation distributions themselves are often not representative of the broader target population. We introduce INCONVENIENT, a benchmark designed to study robustness to convenience-sample bias. Rather than relying on naturally occurring domain partitions, INCONVENIENT directly perturbs feature--target relationships in the training distribution while preserving the original population distribution as the deployment environment. This setting more closely reflects real-world scenarios in which models are developed from unrepresentative samples and subsequently deployed on a broader population. The distinction is particularly relevant for large language models (LLMs), whose pretraining may encode population-level knowledge that extends beyond the relationships observed in a biased training dataset. Unlike existing distribution-shift benchmarks, INCONVENIENT provides explicit control over both the direction and severity of relationship shifts, enabling a systematic assessment of robustness to convenience sampling. The benchmark comprises 200 tabular classification and regression datasets spanning diverse application domains and generates around 15,500 shifted training distributions which lead to substantial downstream degradation.

We introduce a simple yet powerful framework for training large language models. In contrast to the standard autoregressive next-token prediction based on an exact prefix, we propose a perturbation-based procedure that first transforms the prefix into a semantic neighbor and then conditions on this perturbed variant for next-token prediction. This yields a hierarchical model with a pre-post-additive noise structure. Within this framework, we develop a rigorous theory of extrapolability, namely, the capacity of a model class to make reliable predictions for token sequences that lie outside the empirical support of the training corpus. We evaluate the finite-sample performance of the proposed procedure using both synthetic and real-world language data. Results show that the proposed method consistently improves out-of-support prediction while maintaining competitive in-support performance, demonstrating that perturbation offers a practical route to language modeling.