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Adaptive Hierarchical Certification for Segmentation using Randomized Smoothing
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Proposes AdaptiveCertify, which certifies segmentation pixels at adaptively chosen coarser levels of a class hierarchy instead of abstaining, and a Certified Information Gain metric to evaluate it.
Problem
Randomized-smoothing certification for semantic segmentation over a flat set of fine-grained classes yields high abstain rates because the model fluctuates among many classes at unstable pixels.
Approach
Use a class hierarchy DAG and assign each pixel a hierarchy level based on the posterior gap between its top two classes (estimated from independent samples); unstable pixels are certified at a coarser parent label via adaptive sampling over the flat model treated as a black box, with Bonferroni-corrected binomial tests. A new CIG metric weights certified labels by their granularity.
Key results
- On COCO-Stuff-10K (sigma=0.25, n=100, tau=0.75), AdaptiveCertify raises CIG from 0.58 to 0.60 and reduces abstain rate from 20% to 13%.
- On Cityscapes at sigma=0.50 (n=100), CIG improves from 0.41 to 0.44 and abstain drops from 26% to 15%.
- AdaptiveCertify has CIG at least 1.1% higher and abstain rate never above SegCertify across all reported settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · Cityscapes (n=100, τ=0.75, σ=0.25) | CIG: 0.89 -> 0.90 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · Cityscapes (n=100, τ=0.75, σ=0.25) | abstain rate (%): 7 -> 5 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · ACDC (n=100, τ=0.75, σ=0.25) | CIG: 0.67 -> 0.68 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · ACDC (n=100, τ=0.75, σ=0.25) | abstain rate (%): 21 -> 16 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · PASCAL-Context (n=100, τ=0.75, σ=0.25) | CIG: 0.57 -> 0.58 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · PASCAL-Context (n=100, τ=0.75, σ=0.25) | abstain rate (%): 20 -> 16 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · COCO-Stuff-10K (n=100, τ=0.75, σ=0.25) | CIG: 0.58 -> 0.60 | Helped |
| Use adaptive hierarchical certification instead of flat SegCertify | HrNetV2 segmentation certification · COCO-Stuff-10K (n=100, τ=0.75, σ=0.25) | abstain rate (%): 20 -> 13 | Helped |
Limitations
- Hierarchy and threshold parameters must be hand-designed and grid-searched per dataset.
- Gains in CIG are modest on Cityscapes and ACDC at low noise.
- Adaptive level assignment depends on a separate sample set, adding sampling cost.
Experimental setup
Datasets: Cityscapes ACDC PASCAL-Context COCO-Stuff-10K
Benchmarks: Cityscapes ACDC PASCAL-Context COCO-Stuff-10K
Metrics: Certified Information Gain (CIG) class-average CIG (cCIG) % abstain class-average % abstain mIoU
Baselines: SegCertify Uncertified HrNet
Builds on: SegCertify randomized smoothing Bonferroni correction
Closest papers by meaning
- Pixel-level Certified Explanations via Randomized Smoothing (ICML 2025 · similarity 0.86)
- Incremental Randomized Smoothing Certification (ICLR 2024 · similarity 0.86)
- Halt Fast! Early Stopping for Certified Robustness (NeurIPS 2026 · similarity 0.84)
- Mitigating the Curse of Dimensionality for Certified Robustness via Dual Randomized Smoothing (ICLR 2024 · similarity 0.84)
- The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing (ICLR 2024 · similarity 0.83)
- Certified Robustness for Deep Equilibrium Models via Serialized Random Smoothing (NeurIPS 2024 · similarity 0.83)
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