A Compositional Kernel Model for Feature Learning
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Abstract (arXiv)
We study a compositional variant of kernel ridge regression in which the predictor is applied to a coordinate-wise reweighting of the inputs. Formulated as a variational problem, this model provides a tractable setting for studying feature learning in compositional architectures. From the perspective of variable selection, we show how relevant variables are recovered while noise variables are eliminated. We prove that both global minimizers and stationary points discard noise coordinates when the noise variables are Gaussian distributed. A central finding is that ℓ1-type kernels, such as the Laplace kernel, succeed in recovering features contributing to nonlinear effects at stationary points, whereas Gaussian kernels recover only linear ones.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 9 of its 36 references that are in the map. First posted on arXiv 17 Sep 2025.
Builds on
9 of 36 references.
References · 9
- 2016Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selectioncited by 121
- 2017Kernel Feature Selection via Conditional Covariance Minimizationcited by 20
- 2025xRFM: Accurate, scalable, and interpretable feature learning models for tabular datacited by 16
- 2025Position: A Theory of Deep Learning Must Include Compositional Sparsitycited by 14
- 2025Iteratively reweighted kernel machines efficiently learn sparse functionscited by 10
- 2024Enhanced Feature Learning via Regularisation: Integrating Neural Networks and Kernel Methodscited by 5
- 2021On the Self-Penalization Phenomenon in Feature Selectioncited by 4
- 2021Taming Nonconvexity in Kernel Feature Selection -- Favorable Properties of the Laplace Kernelcited by 3
- 2025Gradient flow in the kernel learning problemcited by 1
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Citing papers per year: 2026: 1.
1 paper.