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Eliciting Numerical Predictive Distributions of LLMs Without Auto-Regression

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
mechanistic interpretabilityuncertainty estimationLLMstime seriesprobing
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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper investigates whether statistical functionals of LLM numerical output distributions can be recovered from internal representations without autoregressive sampling. It sits within the 'Predictive Distribution Elicitation from Embeddings' leaf, which contains only two papers total. This is a notably sparse research direction within the broader taxonomy of 50 papers across 36 topics, suggesting the specific approach of training regression probes on embeddings to extract distributional properties represents a relatively unexplored methodological niche compared to more populated branches like time series forecasting or confidence calibration.

The taxonomy reveals several neighboring research directions that provide context. The sibling leaf 'Future Token Anticipation and Prediction' examines whether hidden states encode information about future tokens, while the parent branch 'Internal State Analysis' also includes general representation probing methods. Adjacent branches pursue different strategies: 'Uncertainty Quantification and Calibration' focuses on post-hoc calibration of verbalized probabilities, while 'Direct Numerical Prediction' treats LLMs as end-to-end forecasters. The paper's approach diverges by targeting distributional recovery from embeddings rather than output-level calibration or direct prediction, positioning it at the intersection of representation analysis and uncertainty quantification.

Among 30 candidates examined, the contribution-level analysis shows mixed novelty signals. The magnitude-factorized regression probe examined 10 candidates with 1 appearing to provide overlapping prior work, suggesting some precedent for probe-based numerical extraction. The quantile regression probe and the demonstration that embeddings encode uncertainty each examined 10 candidates with 0 refutable matches, indicating these contributions may be more distinctive within the limited search scope. The analysis does not claim exhaustive coverage—only that among top-30 semantic matches and citation expansions, most contributions lack clear direct precedents.

Based on this limited literature search, the work appears to occupy a relatively novel position, particularly regarding quantile-based uncertainty extraction from embeddings. The sparse population of its taxonomy leaf and the low refutation rate across contributions suggest the specific combination of probing methods and distributional targets is not heavily explored. However, the search scope of 30 candidates means potentially relevant work in adjacent areas—such as general probing techniques or alternative uncertainty elicitation methods—may not have been fully captured.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: Eliciting numerical predictive distributions from language model representations. The field encompasses a diverse set of approaches for extracting quantitative predictions and uncertainty estimates from language models. At the highest level, the taxonomy divides into Direct Numerical Prediction and Forecasting (which includes time-series and domain-specific forecasting such as Zero-Shot Time Forecasters[5] and economic applications), Uncertainty Quantification and Calibration (focusing on methods like Conformal Language Modeling[9] and Calibrating Verbalized Probabilities[10]), Internal State Analysis and Representation Probing (examining how models encode predictive information in their hidden states), Probabilistic Reasoning and World Modeling (exploring how LLMs build internal models of dynamic systems, as in Chess World Models[41]), Specialized Prediction Applications (targeting domains from medical reasoning to energy forecasting), Model Behavior and Interpretability (investigating what models know and how they represent uncertainty), and Architectural and Training Innovations (developing new mechanisms for probabilistic outputs). These branches reflect both methodological diversity—ranging from probing existing representations to designing new training objectives—and application breadth across scientific, economic, and social domains. A particularly active line of work centers on whether and how to extract distributions directly from model internals versus relying on autoregressive token generation. Numerical Predictions Without Autoregression[0] sits squarely within the Internal State Analysis branch, specifically under Predictive Distribution Elicitation from Embeddings, where it shares conceptual ground with Innerthoughts[12], which also examines internal representations for extracting structured information. This contrasts with approaches in the Direct Numerical Prediction branch that treat LLMs as end-to-end forecasters (e.g., LLM Processes[1] or Soft Labeling Numerical[3]), and with Uncertainty Quantification methods that calibrate verbalized probabilities post-hoc. The central tension across these branches involves trade-offs between interpretability, computational efficiency, and the fidelity of elicited distributions: probing methods like Numerical Predictions Without Autoregression[0] aim to bypass token-level generation entirely, potentially offering faster inference and more direct access to latent beliefs, while calibration-focused work addresses whether models can reliably express uncertainty through natural language. Open questions remain about which representations best encode numerical knowledge and how architectural choices influence the quality of elicited distributions.

Claimed Contributions

Magnitude-factorised regression probe for numerical predictions

The authors propose a novel probing architecture that decomposes numerical prediction into magnitude classification and scaled value regression. This design addresses the challenge of training regression probes across widely varying orders of magnitude, enabling accurate recovery of point estimates (mean, median, greedy outputs) directly from LLM hidden states without autoregressive generation.

10 retrieved papers
Can Refute
Quantile regression probe for uncertainty estimation

The authors develop a magnitude-factorised quantile regression model that predicts multiple quantiles of the LLM's predictive distribution from internal representations. This approach recovers distributional uncertainty and produces well-calibrated confidence intervals without requiring repeated autoregressive sampling.

10 retrieved papers
Demonstration that LLM embeddings encode numerical predictions and uncertainty

The authors demonstrate empirically that LLM hidden states contain sufficient information to recover both point estimates and uncertainty of numerical predictions before autoregressive decoding begins. This finding suggests that numerical reasoning occurs during input processing rather than during token generation, opening possibilities for efficient single-pass prediction methods.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Magnitude-factorised regression probe for numerical predictions

The authors propose a novel probing architecture that decomposes numerical prediction into magnitude classification and scaled value regression. This design addresses the challenge of training regression probes across widely varying orders of magnitude, enabling accurate recovery of point estimates (mean, median, greedy outputs) directly from LLM hidden states without autoregressive generation.

Contribution

Quantile regression probe for uncertainty estimation

The authors develop a magnitude-factorised quantile regression model that predicts multiple quantiles of the LLM's predictive distribution from internal representations. This approach recovers distributional uncertainty and produces well-calibrated confidence intervals without requiring repeated autoregressive sampling.

Contribution

Demonstration that LLM embeddings encode numerical predictions and uncertainty

The authors demonstrate empirically that LLM hidden states contain sufficient information to recover both point estimates and uncertainty of numerical predictions before autoregressive decoding begins. This finding suggests that numerical reasoning occurs during input processing rather than during token generation, opening possibilities for efficient single-pass prediction methods.

Table of Contents