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A key challenge facing deep learning is that neural networks are often notrobust to shifts in the underlying data distribution. We study this problemfrom the perspective of the statistical concept of parameter identification.Generalization bounds from learning theory often assume that the testdistribution is close to the training distribution. In contrast, if we canidentify the "true" parameters, then the model generalizes to arbitrarydistribution shifts. However, neural networks typically have internalsymmetries that make parameter identification impossible. We show that we canidentify the function represented by a quadratic network even though we cannotidentify its parameters; we extend this result to neural networks with ReLUactivations. Thus, we can obtain robust generalization bounds for neuralnetworks. We leverage this result to obtain new bounds for contextual banditsand transfer learning with quadratic neural networks. Overall, our resultssuggest that we can improve robustness of neural networks by designing modelsthat can represent the true data generating process.

Robust Generalization of Quadratic Neural Networks via Function Identification