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Investigating Generalization by Controlling Normalized Margin
Alexander Farhang · Jeremy Bernstein · Kushal Tirumala · Yang Liu · Yisong Yue

Thu Jul 21 03:00 PM -- 05:00 PM (PDT) @ Hall E #319

Weight norm ‖W‖ and margin γ participate in learning theory via the normalized margin γ/‖W‖. Since standard neural net optimizers do not control normalized margin, it is hard to test whether this quantity causally relates to generalization. This paper designs a series of experimental studies that explicitly control normalized margin and thereby tackle two central questions. First: does normalized margin always have a causal effect on generalization? The paper finds that no—networks can be produced where normalized margin has seemingly no relationship with generalization, counter to the theory of Bartlett et al. (2017). Second: does normalized margin ever have a causal effect on generalization? The paper finds that yes—in a standard training setup, test performance closely tracks normalized margin. The paper suggests a Gaussian process model as a promising explanation for this behavior.

Author Information

Alexander Farhang (Caltech)
Jeremy Bernstein (Caltech)
Kushal Tirumala (FAIR/California Institute of Technology)
Yang Liu (Argo AI)
Yisong Yue (Caltech)
Yisong Yue

Yisong Yue is a Professor of Computing and Mathematical Sciences at Caltech and (via sabbatical) a Principal Scientist at Latitude AI. His research interests span both fundamental and applied pursuits, from novel learning-theoretic frameworks all the way to deep learning deployed in autonomous driving on public roads. His work has been recognized with multiple paper awards and nominations, including in robotics, computer vision, sports analytics, machine learning for health, and information retrieval. At Latitude AI, he is working on machine learning approaches to motion planning for autonomous driving.

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