When Will Gradient Methods Converge to Max-margin Classifier under ReLU Models?
This addresses the theoretical understanding of implicit bias in neural network training for researchers in machine learning, but it is incremental as it builds on existing work on max-margin classifiers.
The paper tackles the problem of understanding when gradient descent methods converge to max-margin classifiers for binary classification with ReLU models and exponential loss, showing that gradient descent can converge to global or local max-margin directions or diverge, while stochastic gradient descent converges in expectation to these directions if it converges.
We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show that there can exist spurious asymptotic local minima besides asymptotic global minima. We then show that gradient descent (GD) can converge to either a global or a local max-margin direction, or may diverge from the desired max-margin direction in a general context. For stochastic gradient descent (SGD), we show that it converges in expectation to either the global or the local max-margin direction if SGD converges. We further explore the implicit bias of these algorithms in learning a multi-neuron network under certain stationary conditions, and show that the learned classifier maximizes the margins of each sample pattern partition under the ReLU activation.