  A key challenge facing deep learning is that neural networks are often not
robust to shifts in the underlying data distribution. We study this problem
from the perspective of the statistical concept of parameter identification.
Generalization bounds from learning theory often assume that the test
distribution is close to the training distribution. In contrast, if we can
identify the "true" parameters, then the model generalizes to arbitrary
distribution shifts. However, neural networks typically have internal
symmetries that make parameter identification impossible. We show that we can
identify the function represented by a quadratic network even though we cannot
identify its parameters; we extend this result to neural networks with ReLU
activations. Thus, we can obtain robust generalization bounds for neural
networks. We leverage this result to obtain new bounds for contextual bandits
and transfer learning with quadratic neural networks. Overall, our results
suggest that we can improve robustness of neural networks by designing models
that can represent the true data generating process.
