Conformal Language Modeling via Posterior Sampling

When language models lack relevant knowledge for a given query, they frequently generate plausible responses that can be hallucinations, rather than admitting being agnostic about the answer. Retraining models to reward admitting ignorance can lead to overly conservative behaviors and poor generalization due to scarce evaluation benchmarks. We propose a post hoc framework, Conformal Abstention (CA), adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. Importantly, the abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we improve selective answering significantly with 75 percent conditional correctness.

Language models are increasingly used in settings where outputs must satisfy user-specified randomness constraints, yet their generation probabilities are often poorly calibrated to those targets. We study whether this capability can be improved directly through fine-tuning. Concretely, we fine-tune language models on synthetic prompts that require sampling from mathematical distributions, and compare two Calibration Fine-Tuning variants: a soft-target method that converts the desired output distribution into trie-derived next-token targets, and a hard-target method that trains on sampled completions from the same target distribution. Across 12 models spanning four families, both methods substantially improve structured-sampling fidelity on held-out distribution families and unseen parameter settings, showing that probabilistic calibration is a trainable capability. Under our selected training configurations, the two methods exhibit different empirical profiles: hard-target fine-tuning is often strongest on structured numeric sampling, while soft-target fine-tuning performs better on broader stochastic generation benchmarks, including open-ended random generation, multiple-choice answer-position balancing, and NoveltyBench. The gains sometimes reduce downstream capability, especially arithmetic reasoning, with costs varying by model. Overall, our results show that probabilistic calibration can be improved through fine-tuning, with our hard-target configuration favoring exact numeric fidelity and our soft-target configuration favoring broader stochastic transfer. Code is available at https://github.com/chandar-lab/calibration-finetuning.

In open-ended generation, LLMs frequently fall into the "likelihood trap", characterized by repetitive degeneration and vocabulary dullness, resulting in a discrepancy between machine-generated and human-written text. While post-hoc tail truncation (e.g., Top-p, Min-p) avoids sampling from the unreliable tail, it can misalign generation with human lexical preferences by over-sampling from the uncalibrated head; fixed scalar repetition penalties, in turn, ignore how the scale of the logit distribution varies across inference steps, which can disrupt semantic coherence. To address both shortcomings, we propose Variance-Calibrated Modulation (VCM), a training-free pre-decoding intervention. VCM directly reshapes the probability distribution prior to truncation via two dynamic mechanisms: (1) Contextual Searchlight via PMI, which naturally suppresses global stopwords and elevates context-evoked tokens, and (2) Adaptive Self-Debiasing, which utilizes real-time logit standard deviation to provide scale-invariant penalization. In experiments across open-ended generation, factual QA, and mathematical reasoning, we show that VCM consistently mitigates the likelihood trap. With negligible computational overhead, VCM integrates with existing decoding strategies, improving diversity and coherence and, particularly at higher decoding temperatures, reasoning accuracy. Our code is publicly available on GitHub: https://github.com/AetherDing/VCM