title: SGD Learns Over-parameterized Networks that Provably Generalize on Linearly Separable Data
abstract: Neural networks exhibit good generalization behavior in the
  over-parameterized regime, where the number of network parameters
  exceeds the number of observations. Nonetheless,
  current generalization bounds for neural networks fail to explain this
  phenomenon. In an attempt to bridge this gap, we study the problem of
  learning a two-layer over-parameterized neural network, when the data is generated by a linearly separable function. In the case where the network has Leaky
  ReLU activations, we provide both optimization and generalization guarantees for over-parameterized networks.
  Specifically, we prove convergence rates of SGD to a global
  minimum and provide generalization guarantees for this global minimum
  that are independent of the network size. 
  Therefore, our result clearly shows that the use of SGD for optimization both finds a global minimum, and avoids overfitting despite the high capacity of the model. This is the first theoretical demonstration that SGD can avoid overfitting, when learning over-specified neural network classifiers.
authors: Alon Brutzkus Amir Globerson Eran Malach Shai Shalev-Shwartz
hIndex: Shai Shalev-Shwartz 54