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Random-Set Neural Networks
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Proposes Random-Set Neural Networks (RS-NN), which predict belief functions over a budgeted set of class subsets, trained with a BCE-plus-mass-regularization loss, giving pignistic predictions and credal-set-width uncertainty.
Problem
Standard softmax classifiers and Bayesian/ensemble uncertainty methods handle epistemic uncertainty from insufficient or unrepresentative training data poorly, leading to overconfident errors and weak OoD detection.
Approach
Replace softmax outputs with belief values over a budget of class subsets selected by GMM/ellipsoid overlap on t-SNE-reduced features; use the pignistic transform for predictions and the width of the induced credal set as an epistemic uncertainty measure.
Key results
- RS-NN reaches 93.53% test accuracy on CIFAR-10 versus 92.73% for DE and 92.08% for CNN, and 99.71% on MNIST.
- On ImageNet vs ImageNet-O, RS-NN achieves AUROC 60.38 versus 55.37 for DE and 54.28 for CNN.
- RS-NN has the lowest ECE on CIFAR-10 (0.0484) and the lowest on MNIST, with inference time 1.91 ms versus 13163 ms for DE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace softmax class probabilities with RS-NN belief-function predictions and pignistic probabilities | ResNet50 classifier · CIFAR-10 | test accuracy (%): 92.73 -> 93.53 | Helped |
| replace softmax class probabilities with RS-NN belief-function predictions and pignistic probabilities | ResNet50 classifier · MNIST | test accuracy (%): 99.58 -> 99.71 | Helped |
| use RS-NN belief-function predictions instead of the strongest listed baseline | ResNet50 classifier · ImageNet vs ImageNet-O | AUROC: 55.37 -> 60.38 | Helped |
| use RS-NN belief-function predictions instead of the strongest listed baseline | ResNet50 classifier · CIFAR-10 vs Intel Image | AUPRC: 79.36 -> 90.27 | Helped |
| use RS-NN belief-function predictions instead of DE | ResNet50 classifier · CIFAR-10 | ECE: 0.0482 -> 0.0484 | Hurt |
| use RS-NN belief-function predictions instead of LB-BNN | ResNet50 classifier · MNIST | ECE: 0.0032 -> 0.0029 | Helped |
| use RS-NN belief-function predictions instead of DE | ResNet50 classifier · ImageNet | ECE: 0.1940 -> 0.1416 | Helped |
| increase the number of non-singleton focal sets to the full power set rather than using a limited budget (ablation) | RS-NN · classification; CIFAR-10 reported for the K study | test accuracy | Hurt |
| set the focal-set budget to K=20 (ablation) | RS-NN · CIFAR-10 | test accuracy | Helped |
| set mass regularization hyperparameters alpha and beta to 1e-3 (ablation) | RS-NN · classification | test accuracy | Helped |
Surprising findings
- The pignistic entropy of RS-NN separates iD from OoD better than Bayesian predictive entropy.
- Standard CNN and DE have high entropy on both ImageNet and ImageNet-O, so they struggle to separate them.
Limitations
- The number of focal sets K must be set manually.
- Budgeting (t-SNE and GMM) adds one-time preprocessing cost that can be time consuming for large datasets.
- Conformal guarantees are only shown as an experiment, not a formal extension of the random-set representation.
Experimental setup
Datasets: MNIST CIFAR-10 Intel Image CIFAR-100 ImageNet SVHN F-MNIST K-MNIST ImageNet-O
Benchmarks: CIFAR-10 MNIST Intel Image CIFAR-100 ImageNet SVHN F-MNIST K-MNIST ImageNet-O
Metrics: test accuracy AUROC AUPRC entropy ECE inference time
Baselines: LB-BNN FSVI Deep Ensembles ENN standard CNN
Builds on: Deep Ensembles Laplace Bridge BNN Epistemic Neural Networks Dempster-Shafer theory conformal prediction
Closest papers by meaning
- SURE: SUrvey REcipes for building reliable and robust deep networks (CVPR 2024 · similarity 0.87)
- Random-Set Graph Neural Networks (NeurIPS 2026 · similarity 0.87)
- Uncertainty-Aware Deep Classifiers Using Generative Models (AAAI 2020 · similarity 0.86)
- Deep Evidential Regression (NeurIPS 2020 · similarity 0.86)
- Evidential Deep Learning to Quantify Classification Uncertainty (NeurIPS 2018 · similarity 0.86)
- Hyper Evidential Deep Learning to Quantify Composite Classification Uncertainty (ICLR 2024 · similarity 0.85)
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