[2604.05635] From Uniform to Learned Knots: A Study of Spline-Based Numerical Encodings for Tabular Deep Learning

Computer Science > Machine Learning arXiv:2604.05635 (cs) [Submitted on 7 Apr 2026] Title:From Uniform to Learned Knots: A Study of Spline-Based Numerical Encodings for Tabular Deep Learning Authors:Manish Kumar, Anton Frederik Thielmann, Christoph Weisser, Benjamin Säfken View a PDF of the paper titled From Uniform to Learned Knots: A Study of Spline-Based Numerical Encodings for Tabular Deep Learning, by Manish Kumar and 3 other authors View PDF HTML (experimental) Abstract:Numerical preprocessing remains an important component of tabular deep learning, where the representation of continuous features can strongly affect downstream performance. Although its importance is well established for classical statistical and machine learning models, the role of explicit numerical preprocessing in tabular deep learning remains less well understood. In this work, we study this question with a focus on spline-based numerical encodings. We investigate three spline families for encoding numerical features, namely B-splines, M-splines, and integrated splines (I-splines), under uniform, quantile-based, target-aware, and learnable-knot placement. For the learnable-knot variants, we use a differentiable knot parameterization that enables stable end-to-end optimization of knot locations jointly with the backbone. We evaluate these encodings on a diverse collection of public regression and classification datasets using MLP, ResNet, and FT-Transformer backbones, and compare them against comm...