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

2025-10-23

AI Summary

This work addresses the problem that entanglement of salient and non-salient information in feature representations degrades model robustness and interpretability. To this end, we propose H-SPLID—a novel algorithm that, for the first time, integrates the Hilbert–Schmidt Independence Criterion (HSIC) with saliency-preserving latent variable decomposition to explicitly decompose input features into orthogonal salient and non-salient subspaces. We theoretically establish that prediction bias is jointly upper-bounded by the dimensionality of the salient subspace and the HSIC between inputs and representations, thereby quantitatively linking representation robustness to latent-space compression. Empirically, on image classification tasks, H-SPLID significantly improves robustness against background perturbations and yields decisions focused on semantically salient object regions—demonstrating the efficacy and generalization advantage of the learned low-dimensional salient representations.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Natural Language Processing: Safety and Robustness

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Decomposes salient and non-salient features into separate representation spaces
• Promotes learning low-dimensional task-relevant features for robustness
• Reduces sensitivity to perturbations in non-salient input components

Innovation

• Decomposes salient and non-salient features into separate spaces
• Uses HSIC to bound prediction deviation under input perturbations
• Promotes learning low-dimensional task-relevant salient features