Computer Science > Machine Learning
[Submitted on 22 Sep 2021 (v1), last revised 16 Feb 2022 (this version, v3)]
Title:Robust Generalization of Quadratic Neural Networks via Function Identification
View PDFAbstract: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.
Submission history
From: Kan Xu [view email][v1] Wed, 22 Sep 2021 18:02:00 UTC (35 KB)
[v2] Mon, 31 Jan 2022 22:12:20 UTC (63 KB)
[v3] Wed, 16 Feb 2022 23:22:34 UTC (38 KB)
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