Eliciting Numerical Predictive Distributions of LLMs Without Autoregression

TL;DR

This paper explores methods to extract numerical predictive distributions from Large Language Models without autoregressive sampling, by analyzing internal representations to estimate distributional statistics efficiently.

Contribution

It introduces regression probes that predict statistical functionals from LLM embeddings, revealing that models encode useful uncertainty information internally.

Findings

LLM embeddings contain signals about predictive distribution statistics

Probes can estimate means, medians, and quantiles without sampling

Potential for more efficient uncertainty estimation in LLMs

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.