On the Uncertainty Quantification Ability of Tabular Foundation Models

2026-05-31

AI Summary

This study investigates whether tabular foundation models can reliably quantify predictive uncertainty in regression tasks, particularly under data scarcity or high-dimensional complexity. Through a systematic empirical evaluation, the authors compare Tabular Prior-Data Fitted Networks (TabPFN v2.5) against Gaussian processes (GPs) across diverse regression benchmarks, assessing both predictive accuracy and uncertainty calibration. The findings reveal an inherent trade-off between explicit priors (GPs) and learned priors (TabPFN): GPs excel when data are scarce or when the assumed prior aligns well with the true data-generating process, whereas TabPFN demonstrates superior performance in high-dimensional, large-scale settings. The results are highly reproducible and delineate clear applicability boundaries for each approach.

Abstract

Foundation models (FMs) have achieved substantial success in generalizing across tasks without problemspecific training or fine-tuning. However, many critical applications in mechanics and computational science require not only accurate predictions but also reliable uncertainty quantification (UQ). Herein we investigate the UQ capabilities of tabular FMs in regression tasks through a comprehensive empirical study comparing Tabular Prior-Data Fitted Networks (TabPFN) against Gaussian processes (GPs). We systematically evaluate these two methods across a host of regression problems with varying complexity, dataset sizes, and input dimensionalities. We use a default setting to build all the GPs and for a fair comparison against TabPFN v2.5. Our findings highlight an important trade-off between explicit and learned priors: while TabPFN achieves highly competitive performance for complex, high-dimensional problems with sufficient data, GPs often provide superior predictive accuracy and UQ in data-scarce settings. Moreover, when the chosen kernel constitutes a good prior for the underlying function, GP performance can substantially exceed that of TabPFN. Our results can be reproduced from https://github.com/kianswarehouse/GPvsPFN.

Problem

• Uncertainty Quantification
• Tabular Foundation Models
• Gaussian Processes
• Regression Tasks
• Predictive Uncertainty

Innovation

• Uncertainty Quantification
• Tabular Foundation Models
• Gaussian Processes
• TabPFN
• Empirical Evaluation