ERROR SURFACES FOR MULTILAYER PERCEPTRONS

The paper explores the characteristics of error surfaces for the multilayer perceptron neural network. These characteristics help explain why learning techniques that use hill climbing methods are so slow in these networks. They also help provide insights into techniques that may help speed learning. Several important characteristics are revealed. First, the surface has a stair-step appearance with many very flat and very steep regions. In fact, when the number of training samples is small there is often a one-to-one correspondence between individual training samples and the steps on the surface. As the number of training samples is increased the surface becomes smoother. In addition the surface has flat regions that extend to infinity in all directions making it dangerous to apply learning algorithms that perform line searches. The magnitude of gradients on the surface is found to span several orders of magnitude, strongly supporting the need for floating point representations during learning. The consequences of various weight initialization techniques are also discussed.