# The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Program

@article{Wang2021TheCG, title={The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Program}, author={Yifei Wang and Mert Pilanci}, journal={ArXiv}, year={2021}, volume={abs/2110.06488} }

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an equivalent convex model. We then show that the limit points of non-convex subgradient flows can be identified via primal-dual correspondence in this convex optimization problem. Moreover, we derive a sufficient condition on the dual variables which ensures that…

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