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This research demonstrates that probabilistic calibration in language models can be directly enhanced through fine-tuning on synthetic mathematical distributions, significantly improving fidelity for stochastic generation tasks. While the approach successfully transfers to natural language settings and broadens token support, it introduces trade-offs that sometimes degrade downstream capabilities like arithmetic reasoning. The findings highlight a critical balance between enhancing generative randomness and preserving core model performance across different families.
Probabilistic Calibration Is a Trainable Capability in Language Models
arXiv:2605.11845v2 Announce Type: replace Abstract: Language models are increasingly used in settings where outputs should follow an intended distribution, yet their generation probabilities are often poorly calibrated to it. In many such requests the distribution is implicit and the valid outputs cannot be listed in advance, so the task cannot be passed to an external random number generator. 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 training on cheap synthetic mathematical distributions improves sampling on unseen distributions, even in natural language. The gains also transfer to broader stochastic generation benchmarks, including open-ended random generation, where fine-tuned models broaden their first-token support by one to two orders of magnitude, 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 either objective, and that calibration learned on mathematical distributions transfers to natural-language stochastic generation. Code is available at https://github.com/chandar-lab/calibration-finetuning.
Abstract:Language models are increasingly used in settings where outputs should follow an intended distribution, yet their generation probabilities are often poorly calibrated to it. In many such requests the distribution is implicit and the valid outputs cannot be listed in advance, so the task cannot be passed to an external random number generator. 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 training on cheap synthetic mathematical distributions improves sampling on unseen distributions, even in natural language. The gains also transfer to broader stochastic generation benchmarks, including open-ended random generation, where fine-tuned models broaden their first-token support by one to two orders of magnitude, 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 either objective, and that calibration learned on mathematical distributions transfers to natural-language stochastic generation. Code is available at this https URL.
Computation and Language (cs.CL)
arXiv:2605.11845 [cs.CL]
(or arXiv:2605.11845v2 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2605.11845 Focus to learn more arXiv-issued DOI via DataCite
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