H-SPLID: HSIC-based Saliency Preserving Latent Information Decomposition

Claudia Plant (University of Vienna) · Lukas Miklautz (Max Planck Institute of Biochemistry) · Chengzhi Shi (Northeastern University) · Andrii Shkabrii (University of Vienna) · Theodoros Thirimachos Davarakis (Northeastern University) · Prudence Lam (Northeastern University) · Jennifer Dy (Northeastern University) · Stratis Ioannidis (Northeastern University)

dimensionality empirical evaluationsexplicit decompositionh-splidhilbert-schmidt independence criterion image classification information preservation input perturbationslatent representation compressionlow-dimensional featuresprediction deviationrobustnesssalient feature representationssensitivity to perturbationstask-relevant features

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.