Distributional Generalization: A New Kind of Generalization

2020/09/17 by Preetum Nakkiran, Yamini Bansal, Nakkiran, Preetum +1 · 3 citations
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine Learning and Data Classification #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2009.08092

openalex publication_date 2020/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new notion of generalization -- Distributional Generalization -- which roughly states that outputs of a classifier at train and test time are close *as distributions*, as opposed to close in just their average error. For example, if we mislabel 30% of dogs as cats in the train set of CIFAR-10, then a ResNet trained to interpolation will in fact mislabel roughly 30% of dogs as cats on the *test set* as well, while leaving other classes unaffected. This behavior is not captured by classical generalization, which would only consider the average error and not the distribution of errors over the input domain. Our formal conjectures, which are much more general than this example, characterize the form of distributional generalization that can be expected in terms of problem parameters: model architecture, training procedure, number of samples, and data distribution. We give empirical evidence for these conjectures across a variety of domains in machine learning, including neural networks, kernel machines, and decision trees. Our results thus advance our empirical understanding of interpolating classifiers.

Citations

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• RFCDE: Random Forests for Conditional Density Estimation
• Making Sense of Random Forest Probabilities: a Kernel Perspective
• Physical Attribute Prediction Using Deep Residual Neural Networks
• Stiffness: A New Perspective on Generalization in Neural Networks
• The generalization error of random features regression: Precise asymptotics and double descent curve
• Array programming with NumPy
• Learning Multiple Layers of Features from Tiny Images

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