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Deep Neural Networks Tend To Extrapolate Predictably
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Shows that neural network predictions on high-dimensional OOD inputs tend to revert toward the optimal constant solution (OCS), gives a feature-norm/bias-accumulation explanation with theory for deep homogeneous ReLU nets, and uses reward-prediction models for risk-sensitive selective classification.
Problem
Conventional wisdom holds that neural networks extrapolate unpredictably and overconfidently on OOD inputs; the paper asks whether predictions on OOD inputs follow a predictable pattern.
Approach
Predictions on increasingly OOD high-dimensional inputs converge toward the optimal constant solution (the loss-minimizing prediction ignoring the input), explained by OOD features having small norms so outputs are dominated by accumulated bias/model constants, which approximate the OCS; this is leveraged by using a reward-prediction loss whose OCS is the cautious abstain action.
Key results
- Across 8 datasets, 3 losses and CNNs/transformers, distance between predictions and the OCS shrinks as the OOD score of the evaluation set rises.
- In the selective classification experiment on CIFAR10, the reward-prediction agent increasingly abstains with distribution shift and increasingly outperforms standard classification in reward on OOD inputs.
- Standard classification almost never selects abstain, whereas reward prediction and the oracle abstain more often as inputs become OOD.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase covariate distribution shift | Trained neural networks across the evaluated datasets · CIFAR10-C, ImageNet-R, ImageNet-Sketch, OfficeHome, BREEDS, WILDS Amazon, SkinLesionPixels, and UTKFace | distance to OCS | Helped |
| Use reward prediction with MSE so the OCS favors abstention | Selective classification · CIFAR10, OfficeHome, BREEDS living-17, and BREEDS non-living-26 | OOD reward | Helped |
| Evaluate on adversarially generated inputs | MNIST classifier trained with cross entropy · MNIST adversarial inputs | distance to OCS | Hurt |
| Increase impulse noise | Gaussian NLL model trained on UTKFace · UTKFace impulse-noise corruptions | distance to OCS | Hurt |
| Replace no normalization with batch normalization or layer normalization (ablation) | MNIST and CIFAR10 models · MNIST rotations and CIFAR10 noise | reversion-to-OCS trend | No clear effect |
Surprising findings
- Adversarial inputs (FGSM) and UTKFace with impulse noise violate reversion to the OCS: representation norms increase and predictions move away from the OCS.
Limitations
- Theory is limited to deep homogeneous ReLU networks with exponential loss in a binary setting and relies on gradient flow and max-margin results.
- Reversion to the OCS fails for some shifts (adversarial, impulse noise), and the conditions for when it holds are not characterized.
- OOD score and distance measures are only informative when evaluation sets have similar label distributions.
Experimental setup
Datasets: CIFAR10 ImageNet DomainBed OfficeHome BREEDS living-17 BREEDS non-living-26 WILDS Amazon SkinLesionPixels UTKFace MNIST
Benchmarks: CIFAR10-C ImageNet-R ImageNet-Sketch OfficeHome BREEDS WILDS Amazon SkinLesionPixels UTKFace
Metrics: OOD score KL divergence to OCS MSE to OCS abstain rate average reward
Baselines: standard cross-entropy classification oracle temperature-scaled risk-sensitive policy
Builds on: implicit bias of gradient flow on homogeneous networks OOD detection via maximum softmax probability
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