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Learning with Noisy Labels Using Hyperspherical Margin Weighting
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Proposes Integrated Area Margin (IAM) metric and Hyperspherical Margin Weighting (HMW), a sample-weighting method for learning with noisy labels that better separates clean hard-to-learn examples from mislabeled ones than the small-loss trick.
Problem
Learning with noisy labels: the small-loss trick misidentifies clean but hard-to-learn examples as mislabeled because they also produce large losses.
Approach
Combines the Area Under the Margin ranking with a new Top-K Under the Margin (TKUM) ranking into an IAM metric with cosine-annealed temporal weighting, then maps it to hyperspherical (cosine) space to produce per-example weights that are plugged into CCE, SCE, or UNICON.
Key results
- On CIFAR-10 with 0.8 symmetric noise, CCE+HMW reaches 65.8% vs 26.1% for CCE; UNICON+HMW reaches 90.7% at 0.9 symmetric noise on CIFAR-100-level settings (vs 89.4% UNICON).
- On ANIMAL-10N, CCE+HMW achieves 86.5% test accuracy versus 79.4% for CCE and 84.6% for the best prior method (InstanceGM).
- On WebVision, CCE+HMW reaches 78.04% top-1 vs 77.78% for ELR+; on ILSVRC12 top-1 it reaches 71.88%, below ELR+ at 70.29% ... above it, with CCE at 58.88%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add HMW to CCE | CCE · ANIMAL-10N | accuracy (%): 79.4 -> 86.5 | Helped |
| Add HMW to CCE | CCE · ILSVRC12 | top-1 accuracy (%): 58.88 -> 71.88; ProtoMix: 73.3 | Mixed |
| Add HMW to UNICON | UNICON · CIFAR-10 symmetric noise 0.9 | accuracy (%): 89.4 -> 90.7 | Helped |
| Add HMW to UNICON | UNICON · CIFAR-100 symmetric noise 0.9 | accuracy (%): 40.3 -> 43.4 | Helped |
| Add HMW to UNICON | UNICON · CIFAR-10 symmetric noise 0.2 | accuracy (%): 94.2 -> 93.5 | Hurt |
| Add the CA strategy to AUM-only weighting (ablation) | HMW · CIFAR-10 symmetric noise 0.5 | accuracy (%): 67.9 -> 82.1 | Helped |
| Add the full HMW weighting instead of AUM + CA (ablation) | AUM + CA · CIFAR-10 symmetric noise 0.5 | accuracy (%): 82.1 -> 89.8 | Helped |
| Use AUM only, without CA or the full HMW (ablation) | HMW · CIFAR-10 symmetric noise 0.5 | accuracy (%): 89.8 -> 67.9 | Hurt |
Surprising findings
- Improvements of HMW when applied to already-robust methods (SCE, UNICON) are smaller than when applied to plain CCE, which the authors attribute to overlap between the methods' mechanisms.
Limitations
- Improvements on robust baselines (SCE, UNICON) are smaller, and optimal hyperparameters of the original methods may not transfer.
- Hyperparameters alpha and beta must be tuned per noise level and per base method (e.g., 100 vs 1 vs 0.1 across settings).
- Asymmetric-noise gains are smaller than symmetric-noise gains.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ANIMAL-10N WebVision ILSVRC12
Benchmarks: CIFAR-10 CIFAR-100 ANIMAL-10N WebVision ILSVRC12
Metrics: test accuracy top-1 accuracy top-5 accuracy
Baselines: CCE Forward SCE P-correction DivideMix ELR MOIT+ UNICON CED SELFIE PLC InstanceGM
Builds on: Area Under the Margin (AUM) UNICON Symmetric cross entropy Co-teaching
Closest papers by meaning
- Forming Auxiliary High-confident Instance-level Loss to Promote Learning from Label Proportions (CVPR 2025 · similarity 0.86)
- Dirichlet-based Per-Sample Weighting by Transition Matrix for Noisy Label Learning (ICLR 2024 · similarity 0.85)
- Hyperspherical Classification with Dynamic Label-to-Prototype Assignment (CVPR 2024 · similarity 0.85)
- Learning with Open-world Noisy Data via Class-independent Margin in Dual Representation Space (AAAI 2025 · similarity 0.85)
- Regroup Median Loss for Combating Label Noise (AAAI 2024 · similarity 0.85)
- Semi-supervised Multi-label Learning with Balanced Binary Angular Margin Loss (NeurIPS 2024 · similarity 0.84)
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