Do We Always Need Sampling? Eliciting Numerical Predictive Distributions of LLMs Without Auto-Regression

Julianna Piskorz, Kasia Kobalczyk, Mihaela van der Schaar

Keywords: Probing, Automated interpretability

Other Keywords: Numerical predictions, time series data

TL;DR: We showcase that simple probing models can accurately recover the statistics of the numerical predictive distributions of LLMs, without the need for auto-regressive decoding and repeated sampling.

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 is ill-suited to continuous-valued outputs, and obtaining predictive distributions over numerical targets typically requires repeated sampling, leading to high computational cost. 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 numerical uncertainty, and that summary statistics of their predictive distributions can be approximated with reduced computational overhead. 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.

Submission Number: 126