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Enhancing Noise-Robust Losses for Large-Scale Noisy Data Learning
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Proposes "logit bias," adding a class-count-dependent constant to the correct-class logit so bounded noise-robust losses (especially MAE) get non-vanishing gradients at initialization, and calculates loss hyperparameters without training.
Problem
Bounded noise-robust losses such as MAE underfit multi-class datasets because, at initialization, network logits barely overlap with the region where the loss derivative is non-vanishing, and this overlap shrinks as class count grows.
Approach
Analyze the average backpropagation error of the correct-class neuron against the initial logit distribution N(0,1); shift the correct-class logit by a class-count-dependent bias epsilon (MAE*) so that gradients are non-zero at init, and use the same error-matching criterion to set hyperparameters of genCE, NCE-AGCE and NF-MAE without training.
Key results
- On Cifar-10 with 0% noise, MAE* (epsilon=0.5) reaches 91.27% vs 84.90% for MAE and 91.30% for CE, with MAE* best at 20-40% symmetric noise.
- On WebVision (1000 classes), only MAE* among the noise-robust losses learns from scratch: genCE+ reaches 64.85% top-1 and MAE** reaches 81.11% top-5, while plain genCE, NF-MAE and NCE-AGCE stay near chance at 1-13% top-1.
- On Cifar-100 with 0% noise, MAE* (epsilon=3.0) reaches 76.49%, the best of all losses, versus 6.84% for MAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add logit bias ε=0.5 to MAE (ablation) | MAE on Cifar-10 · Cifar-10, symmetric noise 0% | accuracy: 84.90 $\pm$ 1.86 -> 91.27 $\pm$ 0.13 | Helped |
| Add logit bias ε=0.5 to MAE (ablation) | MAE on Cifar-10 · Cifar-10, symmetric noise 20% | accuracy: 80.45 $\pm$ 0.24 -> 89.95 $\pm$ 0.06 | Helped |
| Add logit bias ε=0.5 to MAE (ablation) | MAE on Cifar-10 · Cifar-10, asymmetric noise 40% | accuracy: 77.25 $\pm$ 6.32 -> 85.82 $\pm$ 5.68 | Helped |
| Add logit bias ε=3.0 to MAE (ablation) | MAE on Cifar-100 · Cifar-100, symmetric noise 0% | accuracy: 6.84 $\pm$ 0.66 -> 76.49 $\pm$ 0.09 | Helped |
| Use logit bias ε=3.0 rather than ε=1.5 (ablation) | MAE* on Cifar-100 · Cifar-100, symmetric noise 40% | accuracy: 55.71 $\pm$ 0.45 -> 44.20 $\pm$ 0.41 | Hurt |
| Vary logit bias from ε=1.3 to ε=1.7 around ε=1.5 (ablation) | MAE* on Cifar-100 · Cifar-100, symmetric noise 20% | accuracy: 67.9\%, 68.2\%, 68.3\%, 68.4\%, 68.2\% | No clear effect |
| Use class-count-adjusted loss parameters or logit bias (ablation) | Noise-robust losses on WebVision · WebVision validation | Top-1 accuracy: genCE 13.28 -> genCE+ 64.85 $\pm$ 0.04 | Helped |
| Use scheduled logit bias instead of the fixed bias (ablation) | MAE on WebVision · WebVision validation | Top-1 accuracy: 58.72 $\pm$ 0.11 | Helped |
Surprising findings
- Plain MAE fails on Cifar-100 (about 6.8% accuracy in the noise-free case), yet the logit bias alone lifts it to about 76%, the best result among the compared losses.
- Every noise-robust loss tested that works on Cifar-10 and Cifar-100 fails to learn WebVision without modification, except MAE*.
Limitations
- The logit bias formula tends to overestimate the required epsilon, which can compromise noise robustness at high noise levels (e.g., epsilon=3.0 overfits at 40-60% noise).
- Scope is limited to image classification.
- On WebVision, large epsilon makes test-time confidence low, requiring a hand-designed epsilon schedule that the authors consider a form of tuning.
Experimental setup
Datasets: Cifar-10 Cifar-100 Fashion-MNIST WebVision
Benchmarks: Cifar-10 Cifar-100 Fashion-MNIST WebVision
Metrics: test accuracy top-1 accuracy top-5 accuracy
Baselines: CE MAE genCE AGCE NF-MAE NCE-MAE NCE-AGCE biTemp symCE
Builds on: MAE loss generalized cross entropy normalized cross entropy active-passive losses bi-tempered logistic loss
Closest papers by meaning
- Normalized Loss Functions for Deep Learning with Noisy Labels (ICML 2020 · similarity 0.91)
- Asymmetric Loss Functions for Learning with Noisy Labels (ICML 2021 · similarity 0.91)
- Robust Loss Functions under Label Noise for Deep Neural Networks (AAAI 2017 · similarity 0.90)
- $\epsilon$-Softmax: Approximating One-Hot Vectors for Mitigating Label Noise (NeurIPS 2024 · similarity 0.89)
- Robust Loss Functions for Training Decision Trees with Noisy Labels (AAAI 2024 · similarity 0.87)
- Handling Label Noise via Instance-Level Difficulty Modeling and Dynamic Optimization (NeurIPS 2025 · similarity 0.87)
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