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

arXiv: https://arxiv.org/abs/2510.20627 · HTML: https://mlsanity.com/paper/2510.20627/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 65 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Score-CAM: Score-Weighted Visual Explanations for Convolutional Neural Networks](https://mlsanity.com/paper/1910.01279/) (2019)
- [Skin Lesion Analysis Toward Melanoma Detection: A Challenge at the 2017 International Symposium on Biomedical Imaging (ISBI), Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1710.05006/) (2017)
- [Noise or Signal: The Role of Image Backgrounds in Object Recognition](https://mlsanity.com/paper/2006.09994/) (2020)
- [Improving the Adversarial Robustness and Interpretability of Deep Neural Networks by Regularizing their Input Gradients](https://mlsanity.com/paper/1711.09404/) (2017)
- [Torchattacks: A PyTorch Repository for Adversarial Attacks](https://mlsanity.com/paper/2010.01950/) (2020)
- [SaliencyMix: A Saliency Guided Data Augmentation Strategy for Better Regularization](https://mlsanity.com/paper/2006.01791/) (2020)
- [On the Connection Between Adversarial Robustness and Saliency Map Interpretability](https://mlsanity.com/paper/1905.04172/) (2019)
- [The HSIC Bottleneck: Deep Learning without Back-Propagation](https://mlsanity.com/paper/1908.01580/) (2019)
- [The Conditional Entropy Bottleneck](https://mlsanity.com/paper/2002.05379/) (2020)
- [Improving Deep Learning Interpretability by Saliency Guided Training](https://mlsanity.com/paper/2111.14338/) (2021)
- [A Sober Look at the Robustness of CLIPs to Spurious Features](https://mlsanity.com/paper/2403.11497/) (2024)
- [Robust Learning with the Hilbert-Schmidt Independence Criterion](https://mlsanity.com/paper/1910.00270/) (2019)
- [Contrastive Variational Autoencoder Enhances Salient Features](https://mlsanity.com/paper/1902.04601/) (2019)
- [Revisiting Hilbert-Schmidt Information Bottleneck for Adversarial Robustness](https://mlsanity.com/paper/2106.02734/) (2021)
- [Moment Matching Deep Contrastive Latent Variable Models](https://mlsanity.com/paper/2202.10560/) (2022)

## Built on by (most cited first, 2 of 2)

- [ActQuant: Sub-4-bit Action-Guided Quantization for Vision-Language-Action Models](https://mlsanity.com/paper/2605.24011/) (2026)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)

## Abstract (arXiv)

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.