Paper
Eliciting Numerical Predictive Distributions of LLMs Without Autoregression
Authors
Julianna Piskorz, Katarzyna Kobalczyk, Mihaela van der Schaar
Abstract
Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.
Metadata
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.02913v1</id>\n <title>Eliciting Numerical Predictive Distributions of LLMs Without Autoregression</title>\n <updated>2026-03-03T12:13:40Z</updated>\n <link href='https://arxiv.org/abs/2603.02913v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.02913v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding process may be ill-suited to continuous-valued outputs, where obtaining predictive distributions over numerical targets requires repeated sampling, leading to high computational cost and inference time. In this work, we investigate whether distributional properties of LLM predictions can be recovered without explicit autoregressive generation. To this end, we study a set of regression probes trained to predict statistical functionals (e.g., mean, median, quantiles) of the LLM's numerical output distribution directly from its internal representations. Our results suggest that LLM embeddings carry informative signals about summary statistics of their predictive distributions, including the numerical uncertainty. This investigation opens up new questions about how LLMs internally encode uncertainty in numerical tasks, and about the feasibility of lightweight alternatives to sampling-based approaches for uncertainty-aware numerical predictions.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-03-03T12:13:40Z</published>\n <arxiv:comment>First two authors contributed equally. Published as a conference paper at ICLR2026</arxiv:comment>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Julianna Piskorz</name>\n </author>\n <author>\n <name>Katarzyna Kobalczyk</name>\n </author>\n <author>\n <name>Mihaela van der Schaar</name>\n </author>\n </entry>"
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