Title: CNNs are Globally Optimal Given Multi-Layer Support,
Abstract: Stochastic Gradient Descent (SGD) is the central workhorse for training
modern CNNs. Although giving impressive empirical performance it can be slow to
converge. In this paper we explore a novel strategy for training a CNN using an
alternation strategy that offers substantial speedups during training. We make
the following contributions: (i) replace the ReLU non-linearity within a CNN
with positive hard-thresholding, (ii) reinterpret this non-linearity as a
binary state vector making the entire CNN linear if the multi-layer support is
known, and (iii) demonstrate that under certain conditions a global optima to
the CNN can be found through local descent. We then employ a novel alternation
strategy (between weights and support) for CNN training that leads to
substantially faster convergence rates, nice theoretical properties, and
achieving state of the art results across large scale datasets (e.g. ImageNet)
as well as other standard benchmarks.