What makes an artificial neural network easier to train and more likely to produce desirable solutions than other comparable networks? In this paper, we provide a new angle to study such issues under the setting of a fixed number of model parameters which in general is the most dominant cost factor. We introduce a notion of variability and show that it correlates positively to the activation ratio and negatively to a phenomenon called {Collapse to Constants} (or C2C), which is closely related but not identical to the phenomenon commonly known as vanishing gradient. Experiments on a styled model problem empirically verify that variability is indeed a key performance indicator for fully connected neural networks. The insights gained from this variability study will help the design of new and effective neural network architectures.
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