Implicit Bias of Gradient Descent on Linear Convolutional Networks

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Suriya Gunasekar, Jason D. Lee, Daniel Soudry, Nati Srebro


We show that gradient descent on full-width linear convolutional networks of depth $L$ converges to a linear predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to linearly fully connected networks, where gradient descent converges to the hard margin linear SVM solution, regardless of depth.