We introduce H-SPLID, a novel algorithm for learning salient feature representations through the explicit decomposition of salient and non-salient features into separate spaces. We show that H-SPLID promotes learning low-dimensional, task-relevant features. We prove that the expected prediction deviation under input perturbations is upper-bounded by the dimension of the salient subspace and the Hilbert-Schmidt Independence Criterion (HSIC) between inputs and representations. This establishes a link between robustness and latent representation compression in terms of the dimensionality and information preserved. Empirical evaluations on image classification tasks show that models trained with H-SPLID primarily rely on salient input components, as indicated by reduced sensitivity to perturbations affecting non-salient features, such as image backgrounds. Our code is available at https://github.com/neu-spiral/H-SPLID.
@article{arxiv.2510.20627,
title = {H-SPLID: HSIC-based Saliency Preserving Latent Information Decomposition},
author = {Lukas Miklautz and Chengzhi Shi and Andrii Shkabrii and Theodoros Thirimachos Davarakis and Prudence Lam and Claudia Plant and Jennifer Dy and Stratis Ioannidis},
journal= {arXiv preprint arXiv:2510.20627},
year = {2026}
}