Deep Networks Favor Simple Data
Summary: arXiv:2604.00394v1 Announce Type: cross
Abstract: Estimated density is often interpreted as indicating how typical a sample is under a model. Yet deep models trained on one dataset can assign higher density to simpler out-of-distribution (OOD) data than to in-distribution test data. We refer to this behavior as the OOD anomaly. Prior work typically studies this phenomenon within a single architecture, detector, or benchmark, implicitly assuming certain canonical densities. We instead separate the trained network from the density estimator built from its representations or outputs. We introduce two estimators: Jacobian-based estimators and autoregressive self-estimators, making density analysis applicable to a wide range of models.
Key Findings
Applying this perspective to a range of models, including iGPT, PixelCNN++, Glow, score-based diffusion models, DINOv2, and I-JEPA, we find the same striking regularity that goes beyond the OOD anomaly:
- Lower-complexity samples receive higher estimated density, while higher-complexity samples receive lower estimated density.
- This ordering appears within a test set and across OOD pairs such as CIFAR-10 and SVHN.
- The results remain highly consistent across independently trained models.
Quantifying the Observations
To quantify these orderings, we introduce Spearman rank correlation and find striking agreement both across models and with external complexity metrics. Even when trained only on the lowest-density (most complex) samples or even a single such sample, the resulting models still rank simpler images as higher density.
Broader Implications
These observations lead us beyond the original OOD anomaly to a more general conclusion: deep networks consistently favor simple data. Our goal is not to close this question, but to define and visualize it more clearly. We broaden its empirical scope and show that it appears across architectures, objectives, and density estimators.
Conclusion
This research highlights the need for a deeper understanding of how deep neural networks interact with data complexity. The tendency of these networks to favor simpler data over more complex samples has significant implications for model training and evaluation. As we continue to explore this phenomenon, we aim to provide clearer definitions and visualizations that enhance our understanding of deep learning models and their behavior.