Mildly Overparameterized ReLU Networks Have a Favorable Loss Landscape

We study the loss landscape of both shallow and deep, mildly overparameterized ReLU neural networks on a generic finite input dataset for the squared error loss. We show both by count and volume that most activation patterns correspond to parameter regions with no bad local minima. Furthermore, for one-dimensional input data, we show most activation regions realizable by the network contain a high dimensional set of global minima and no bad local minima. We experimentally confirm these results by finding …

count cs.lg data dataset error landscape loss math.co networks neural networks patterns relu show stat.ml study