Robust Generalization of Quadratic Neural Networks via Function Identification
This addresses robustness issues in deep learning for applications like bandits and transfer learning, though it is incremental as it builds on existing identification theory.
The paper tackles the problem of neural networks lacking robustness to distribution shifts by showing that the function represented by quadratic networks can be identified even when parameters cannot, enabling robust generalization bounds for arbitrary shifts. It extends this to ReLU networks and applies it to contextual bandits and transfer learning.
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.