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H-SPLID: HSIC-based Saliency Preserving Latent Information Decomposition
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Proposes H-SPLID, which splits an encoder's latent space into salient and non-salient subspaces via learned masks with cluster and HSIC penalties, and proves a bound on expected prediction deviation under input perturbations by salient dimension and HSIC.
Problem
Neural networks rely on entangled latent features that include task-irrelevant (non-salient) information, making them sensitive to perturbations of non-salient input regions such as backgrounds.
Approach
Learn a binary/continuous diagonal mask splitting the latent space into salient (used for classification, clustered per class, HSIC-compressed against inputs) and non-salient (globally aligned, HSIC-tied to labels) parts, optimized by alternating SGD and a closed-form mask update; theory bounds output deviation by salient dimension and HSIC(x, z_s).
Key results
- On COCO background PGD attack at eps=3/255, H-SPLID reaches 57.5% accuracy vs 43.0% for the best competitor (weight decay/HBaR range) and 34.2%-ish for vanilla under full PGD at 2/255 (58.9% vs 41.9% best competitor).
- On ISIC-2017 under brightness, defocus, and occlusion corruptions, H-SPLID achieves 70.00%, 68.38%, 69.50% vs HBaR's 68.70%, 65.62%, 66.18%.
- On ImageNet-9 MixedRand, H-SPLID achieves 59.5% vs 56.4% for the strongest baseline; on CA-Counter it reaches 60.6% vs 58.5% for HBaR.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use H-SPLID instead of the strongest listed baseline | ResNet-18 on COCO · PGD background attack ε=3/255 | accuracy: 43.0±0.1 -> 57.5±0.2 | Helped |
| Use H-SPLID instead of the vanilla model | ResNet-18 on COCO · PGD full attack ε=2/255 | accuracy: 34.2±0.3 -> 58.9±0.4 | Helped |
| Use H-SPLID instead of the best competing method | ResNet-50 on ISIC-2017 · brightness, defocus, and occlusion corruptions | accuracy | Helped |
| Use H-SPLID instead of the vanilla baseline | ResNet-50 on ImageNet-9 · ImageNet-9 | accuracy: 74.0 -> 76.7 | Helped |
| Use H-SPLID instead of L1 Sparse Activations | ResNet-50 on CounterAnimal · Common | accuracy: 80.7 -> 80.3 | Hurt |
| Use H-SPLID instead of HBaR | ResNet-50 on CounterAnimal · Counter | accuracy: 58.5 -> 60.6 | Helped |
| Add salient and non-salient clustering losses (ablation) | H-SPLID on COCO · PGD background attack ε=3/255 | accuracy: 33.75±0.1 -> 43.69±0.2 | Helped |
| Add HSIC penalties (ablation) | H-SPLID on COCO · PGD background attack ε=3/255 | accuracy: 33.75±0.1 -> 42.71±0.3 | Helped |
| Add clustering losses and HSIC penalties together (ablation) | H-SPLID on COCO · PGD background attack ε=3/255 | accuracy: 33.75±0.1 -> 57.12±0.3 | Helped |
| Add clustering losses and HSIC penalties together (ablation) | H-SPLID on COCO · PGD full attack ε=2/255 | accuracy: 35.29±0.5 -> 58.44±0.2 | Helped |
Surprising findings
- Vanilla cross-entropy with clean accuracy 98.1% on COCO drops to 33.75% under background PGD attack, showing strong reliance on non-salient features.
Limitations
- Assumes irrelevant information varies independently of class-specific features; features always co-occurring with the same context cannot be separated.
- Analysis restricted to image data.
- Theorem is first-order (o(r) terms) and relies on kernel universality and truncated-Gaussian input assumptions.
Experimental setup
Datasets: C-MNIST COCO (bear, elephant, giraffe, zebra subset) ISIC-2017 ImageNet-1K ImageNet-9 CounterAnimal
Benchmarks: C-MNIST PGD COCO subset PGD/AutoAttack ISIC-2017 corruptions ImageNet-9 CounterAnimal
Metrics: clean accuracy robust accuracy
Baselines: Vanilla cross-entropy Weight Decay L1 sparse activations L1 sparse weights Group-Lasso activations Group-Lasso weights HBaR
Builds on: HSIC bottleneck HBaR Group-Lasso Contrastive Analysis
Closest papers by meaning
- Energy-Based Generative Cooperative Saliency Prediction (AAAI 2022 · similarity 0.85)
- Understanding and Visualizing Deep Visual Saliency Models (CVPR 2019 · similarity 0.84)
- Image Saliency Prediction in Transformed Domain: A Deep Complex Neural Network Method (AAAI 2019 · similarity 0.84)
- No Pains, More Gains: Recycling Sub-Salient Patches for Efficient High-Resolution Image Recognition (CVPR 2025 · similarity 0.84)
- SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation (ICLR 2024 · similarity 0.83)
- Task-Adaptive Saliency Guidance for Exemplar-free Class Incremental Learning (CVPR 2024 · similarity 0.83)
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