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We study the implicit bias of gradient descent methods in solving a binaryclassification problem over a linearly separable dataset. The classifier isdescribed by a nonlinear ReLU model and the objective function adopts theexponential loss function. We first characterize the landscape of the lossfunction and show that there can exist spurious asymptotic local minima besidesasymptotic global minima. We then show that gradient descent (GD) can convergeto either a global or a local max-margin direction, or may diverge from thedesired max-margin direction in a general context. For stochastic gradientdescent (SGD), we show that it converges in expectation to either the global orthe local max-margin direction if SGD converges. We further explore theimplicit bias of these algorithms in learning a multi-neuron network undercertain stationary conditions, and show that the learned classifier maximizesthe margins of each sample pattern partition under the ReLU activation.

When Will Gradient Methods Converge to Max-margin Classifier under ReLU Models?