Author: Denis Avetisyan
New research reveals that large language models possess surprisingly accurate numerical prediction capabilities encoded within their internal states, bypassing the need for traditional text generation.
This work demonstrates that LLMs can predict numerical values and quantify uncertainty without full autoregressive decoding, leveraging hidden state analysis and magnitude-factorized regression.
While Large Language Models (LLMs) excel at regression tasks through in-context learning, their reliance on autoregressive decoding presents computational bottlenecks for generating predictive distributions over continuous numerical outputs. This work, ‘Eliciting Numerical Predictive Distributions of LLMs Without Autoregression’, investigates whether distributional information can be recovered directly from LLM internal representations, bypassing the need for repeated sampling. The authors demonstrate that LLM embeddings contain informative signals about summary statistics-including uncertainty-of their predicted numerical values, achievable through trained regression probes. This raises the question of how LLMs inherently encode uncertainty in numerical tasks and whether lightweight alternatives to sampling-based approaches are viable for uncertainty-aware predictions.
Beyond Prediction: LLMs and the Illusion of Certainty
The versatility of Large Language Models (LLMs) is rapidly expanding beyond their origins in natural language processing, increasingly demonstrating efficacy in tasks involving structured data. Originally designed to understand and generate human language, these models are now being successfully applied to areas like tabular data regression, where they predict numerical values based on organized datasets. This shift signifies a broader potential for LLMs to analyze and interpret information presented in various formats, not just text. Researchers are discovering that the underlying architecture of LLMs, capable of recognizing complex patterns and relationships, translates surprisingly well to the domain of structured data, opening doors for innovative solutions in fields like finance, healthcare, and scientific modeling. The ability to leverage pre-trained LLMs for these non-linguistic tasks represents a significant advancement, reducing the need for task-specific model development and potentially unlocking new insights from existing datasets.
A critical hurdle in deploying Large Language Models (LLMs) for real-world applications involving structured data is the difficulty in reliably quantifying predictive uncertainty. While LLMs demonstrate proficiency in tasks like tabular data regression and time series forecasting, they often lack the ability to accurately express the confidence-or lack thereof-in their outputs. This poses significant risks, as decisions based on overconfident, yet incorrect, predictions can have substantial consequences in fields like finance, healthcare, and engineering. Establishing robust methods for uncertainty estimation-moving beyond simple point predictions-is therefore paramount to building trustworthy and dependable LLM-driven systems, enabling informed risk assessment and responsible deployment in critical applications.
Large Language Models (LLMs) are demonstrating a remarkable capacity for sequential prediction, extending their influence beyond text-based applications into areas like time series forecasting and autoregressive generation. These models, traditionally known for natural language processing, can effectively learn and extrapolate patterns from ordered data, predicting future values based on historical sequences. Unlike traditional statistical methods that often rely on predefined assumptions about data distribution, LLMs leverage their extensive pre-training to identify complex, non-linear relationships within the data. This capability allows them to model intricate temporal dependencies and generate plausible continuations of a given sequence, proving valuable in diverse applications such as financial forecasting, demand prediction, and even creative content generation, where maintaining coherence over time is crucial. The inherent ability of LLMs to capture long-range dependencies within sequences positions them as a powerful tool for tasks requiring an understanding of evolving patterns and future projections.
The performance of Large Language Models on structured data tasks, including numerical prediction, is fundamentally linked to their capacity to process information within a defined context window. Recent research indicates these models aren’t simply memorizing data, but rather effectively encoding sufficient information within this context to accurately predict numerical values. This is particularly noteworthy because it demonstrates a capacity for direct prediction, bypassing the need for computationally expensive autoregressive decoding methods commonly employed in sequential generation. The ability to predict values directly, rather than generating them step-by-step, significantly improves efficiency and opens new possibilities for real-time applications requiring swift and reliable numerical forecasting – effectively positioning LLMs as powerful tools for analyzing and interpreting structured datasets without the typical limitations of sequential processing.
Decoding the Black Box: Probing LLM Internals for Uncertainty
Probing models constitute a technique for analyzing the internal representations, or hidden states, of Large Language Models (LLMs). This involves training secondary models – the probes – to predict specific properties or aspects of the LLM’s input or output, directly from these hidden states. Successful probe training indicates that the LLM encodes the targeted information within its internal representations. The process doesn’t modify the LLM itself but instead provides a means to interpret the information stored within its layers, offering insight into the model’s reasoning process and the basis for its predictions. By analyzing which hidden states are most predictive of certain outcomes, researchers can gain a better understanding of how the LLM processes information and makes decisions.
Training probe models to interpret the hidden states of Large Language Models (LLMs) enables the extraction of information related to prediction confidence. These probe models are trained on the internal representations of the LLM – specifically, the activations at various layers – to predict quantities associated with uncertainty, such as prediction variance or the probability of incorrectness. By learning to map these internal states to quantifiable confidence metrics, researchers can analyze which aspects of the LLM’s processing contribute to high or low confidence predictions, and ultimately understand the basis for the model’s self-assessment of its own outputs. This allows for a decomposition of confidence, identifying whether it arises from the input data, the model’s internal knowledge, or inherent limitations in its reasoning capabilities.
Quantile Regression, when applied to Large Language Model (LLM) probing, moves beyond predicting a single expected value and instead models the complete conditional distribution of potential outputs. This is achieved by training probe models to predict specific quantiles – values below which a certain percentage of the distribution falls – allowing for the estimation of prediction intervals. Unlike methods that rely on single point estimates or approximations of variance, Quantile Regression directly learns the relationship between LLM internal states and various points within the output distribution. This provides a more nuanced understanding of predictive uncertainty, capturing both the central tendency and the spread of potential outcomes, and enables the calculation of statistical measures like interquartile range (IQR) and confidence intervals without requiring repeated sampling from the LLM.
Methods for estimating prediction uncertainty beyond simple point estimates, specifically utilizing Empirical Quantiles, Interquartile Range (IQR), and Confidence Intervals, offer substantial computational efficiency. Compared to autoregressive sampling, which generates a single LLM sample sequentially, these probing-based approaches achieve a 47x speedup in inference time. Validation demonstrates a strong correlation between predicted and sampled IQR values, as measured by Pearson R, indicating the reliability of these methods for quantifying predictive uncertainty without the cost of repeated sampling.
Beyond the Test Set: Validating Generalization and Robustness
Evaluating the generalisation ability of probing models is a critical step in determining the reliability of their uncertainty estimations when deployed in real-world applications. A model’s capacity to accurately assess its own uncertainty is directly linked to its performance on data distributions differing from the training set; poor generalisation leads to miscalibrated confidence scores. Consequently, rigorous validation using datasets independent of the training set is essential to quantify the model’s robustness and ensure that predicted uncertainties reflect the true likelihood of error. This process identifies potential failure modes and allows for refinement of the model or its associated uncertainty estimation techniques before practical deployment, particularly in safety-critical scenarios where reliable uncertainty quantification is paramount.
Validation of model generalisation and robustness necessitates evaluation across a range of data distributions, achievable through the use of both real-world datasets and synthetically generated data. Real-world data provides assessment of performance on naturally occurring variations, while synthetic data allows for controlled experimentation and targeted testing of specific edge cases or distributional shifts not readily available in existing datasets. Utilizing a combination of both ensures a comprehensive evaluation, identifying potential failure modes and quantifying performance degradation when the model encounters data differing from its training distribution. This dual approach provides a more reliable measure of a model’s ability to generalize to unseen scenarios and maintain consistent performance across diverse inputs.
Magnitude-Factorised Regression improves the calibration of uncertainty estimates by decoupling the magnitude and scale of predictions during regression. Evaluations demonstrate a significant reduction in Mean Squared Error (MSE) compared to a standard Multi-Layer Perceptron (MLP) probe; specifically, a 41% reduction was observed for greedy predictions, 33% for mean predictions, and 42% for median predictions. This separation allows for more accurate quantification of predictive uncertainty, as the model can independently learn the overall magnitude of the target variable and the associated scale of uncertainty without conflating the two.
Integrating validation with both real-world and synthetic datasets, alongside advanced regression techniques such as Magnitude-Factorised Regression, demonstrably improves predictive reliability in challenging conditions. Magnitude-Factorised Regression specifically decouples magnitude and scale in uncertainty estimation, resulting in significant performance gains-a 41% Mean Squared Error (MSE) reduction for greedy prediction, 33% for mean prediction, and 42% for median prediction-when compared to a standard Multi-Layer Perceptron (MLP) probe. This combination of diverse validation datasets and refined regression methods yields more robust predictions by addressing potential biases and improving calibration across varying data distributions, crucial for deployment in complex, real-world scenarios.
The pursuit of extracting numerical predictions directly from an LLM’s hidden states, as detailed in the paper, feels less like innovation and more like a predictable escalation. It’s a shift from generating sequences to probing for pre-existing values – essentially admitting the model already ‘knows’ the answer, it just packages it inefficiently. This aligns with a fundamental truth: elegant architectures inevitably succumb to the realities of production. As Barbara Liskov once said, “It’s one thing to design an elegant system, but quite another to get it to work reliably.” The paper’s magnitude-factorized regression, while clever, is merely a sophisticated workaround for the inherent limitations of forcing language models into numerical tasks. It’s another layer of abstraction built on top of assumptions that will, inevitably, fail to hold in unforeseen circumstances.
What’s Next?
The demonstrated ability to extract numerical predictions directly from hidden states is… convenient. It neatly sidesteps the computational cost of full autoregressive decoding, which, let’s be honest, was always a brute-force solution masquerading as elegance. The real question isn’t whether this ‘magnitude-factorized regression’ works – it demonstrably does – but how robust it is. Production systems have a knack for finding the exact input that breaks everything, and one suspects that edge cases involving extrapolation, or, heaven forbid, actual time series with meaningful seasonality, will prove challenging. If a system crashes consistently, at least it’s predictable.
The current work feels like a clever hack, and that’s not necessarily a criticism. Most progress is simply rearranging existing problems. But it highlights a deeper issue: are these models actually ‘understanding’ numerical relationships, or are they just very good at memorizing correlations? Probing hidden states is fascinating, but it’s akin to reverse-engineering a black box with a multimeter. It tells one what is happening, not why.
Future work will inevitably focus on scaling this approach – more data, larger models, and the inevitable marketing buzzword: ‘cloud-native numerical prediction.’ It’s the same mess, just more expensive. A more interesting direction might be exploring the limitations. What types of numerical predictions cannot be extracted this way? And what does that tell one about the fundamental capabilities – or, more likely, the fundamental incapabilities – of these increasingly complex systems? Ultimately, one suspects this is another step toward building systems that are impressive, but whose inner workings will remain opaque to the digital archaeologists of the future. We don’t write code – we leave notes for them.
Original article: https://arxiv.org/pdf/2603.02913.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2026-03-04 16:40