Tabular Numeric Stretch Transformation

2026-08-10

AI Summary

This work addresses the challenge of modeling tabular data with deep learning, where numerical features exhibit diverse distributions, scales, and statistical properties that hinder effective learning. To overcome this, the authors propose the Stretch transformation framework, which formulates feature preprocessing as an optimization problem aimed at enhancing feature learnability by explicitly improving the smoothness of the target objective function—a perspective not previously explored. The framework encompasses both unsupervised and supervised variants: the former employs a minimax optimization to redistribute feature densities, while the latter leverages Dirichlet energy minimization to induce target-aware transformations. Theoretical analysis establishes intrinsic connections between Stretch and established techniques such as piecewise linear encoding, empirical cumulative distribution functions, and target encoding. Extensive experiments across 38 datasets in the TALENT benchmark demonstrate that the supervised Stretch variant consistently outperforms all baseline methods, confirming its efficacy.

Abstract

Tabular data presents unique challenges for deep learning due to its heterogeneous nature, where numeric features exhibit diverse distributions, scales, and statistical properties. Although recent advances have improved how models learn from tabular data, how numeric data are transformed into model-friendly representations remains comparatively underexplored. We introduce the stretch transformation framework, which formulates numeric feature preprocessing as an optimization problem to make the target function smoother and thus more learnable. Our framework has two variants: (1) unsupervised stretch, which uniformly redistributes feature density via minimax optimization, and (2) supervised stretch, which optimizes target-aware numeric feature transformations from the perspective of target-function smoothness by minimizing the target function's Dirichlet energy in the transformed space. Our theoretical analysis further connects this framework to several popular transformations: unsupervised stretch is closely related to Piecewise Linear Encoding through a shared piecewise-linear geometry and approaches the empirical CDF transformation as the number of bins grows, while supervised stretch becomes closely related to target encoding in the fine-binning limit. Comprehensive experiments on 38 datasets from the TALENT benchmark demonstrate that supervised stretch consistently outperforms all baselines. These results show that explicitly optimizing for target function smoothness is a powerful and underexplored strategy for tabular deep learning.

Problem

• tabular data
• numeric features
• feature transformation
• deep learning
• target function smoothness

Innovation

• stretch transformation
• tabular deep learning
• Dirichlet energy
• target-function smoothness
• numeric feature preprocessing