Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes

Uncertainty Weighted Gradients for Model Calibration

CVPR 2025 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Single-model predictive uncertainty · 6 citations (OpenAlex)

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Proposes applying a Brier-score-based uncertainty weight to the gradient of cross-entropy (BSCE-GRA) rather than to the loss, to improve neural network calibration without temperature scaling.

Problem

Deep networks are miscalibrated (over- or under-confident); existing focal-loss-style reweighting methods weight the loss itself, which misaligns gradient scale with sample uncertainty and uses single-logit uncertainty estimates.

Approach

Unifies focal and dual focal loss as uncertainty-weighted cross entropy, then detaches a generalized Brier Score uncertainty weight and multiplies it with the cross-entropy gradient (gradient weighting) so harder samples get larger updates while using all logits.

Key results

• BSCE-GRA achieves the lowest ECE in most dataset-model settings before temperature scaling, e.g. CIFAR-10 ResNet50 pre-TS ECE 0.74 vs 4.36 for cross-entropy.
• Most BSCE-GRA optimal temperatures are 1, indicating an inherently calibrated model without post-hoc scaling.
• On CIFAR-10 ResNet50, gradient weighting improved FLSD (uFL) from ECE 1.26 to 0.88 pre-TS and DFL from 1.00 to 0.93 pre-TS.

Measured effects reported in the paper

Surprising findings

• Applying a differentiable uncertainty weight to the loss can break the positive correlation between loss and gradient magnitude, so focal-style weighting may focus on moderately uncertain rather than most uncertain samples.
• Focal Loss produced better-calibrated models than BSCE-GRA during mid-training epochs (150-200) at moderate learning rate.

Limitations

• Results reported on small image classification benchmarks and ResNet/WideResNet/DenseNet only
• Ground-truth uncertainty unavailable on real data, so Brier-based proxy used; ECE-type group metrics cannot serve as per-sample weights
• Temperature scaling still needed in some settings (e.g., WideResNet on CIFAR-10 with BSCE-GRA post-TS results differ)

Experimental setup

Datasets: CIFAR-10 CIFAR-100 Tiny-ImageNet

Benchmarks: CIFAR-10 CIFAR-100 Tiny-ImageNet

Metrics: ECE AdaECE Classwise-ECE Brier Score accuracy

Baselines: Cross-Entropy Brier Loss MMCE FLSD Dual Focal Loss Temperature Scaling

Builds on: Focal Loss Dual Focal Loss FLSD Temperature Scaling

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