  Artificial Neural Networks have shown impressive success in very different
application cases. Choosing a proper network architecture is a critical
decision for a network's success, usually done in a manual manner. As a
straightforward strategy, large, mostly fully connected architectures are
selected, thereby relying on a good optimization strategy to find proper
weights while at the same time avoiding overfitting. However, large parts of
the final network are redundant. In the best case, large parts of the network
become simply irrelevant for later inferencing. In the worst case, highly
parameterized architectures hinder proper optimization and allow the easy
creation of adverserial examples fooling the network. A first step in removing
irrelevant architectural parts lies in identifying those parts, which requires
measuring the contribution of individual components such as neurons. In
previous work, heuristics based on using the weight distribution of a neuron as
contribution measure have shown some success, but do not provide a proper
theoretical understanding. Therefore, in our work we investigate game theoretic
measures, namely the Shapley value (SV), in order to separate relevant from
irrelevant parts of an artificial neural network. We begin by designing a
coalitional game for an artificial neural network, where neurons form
coalitions and the average contributions of neurons to coalitions yield to the
Shapley value. In order to measure how well the Shapley value measures the
contribution of individual neurons, we remove low-contributing neurons and
measure its impact on the network performance. In our experiments we show that
the Shapley value outperforms other heuristics for measuring the contribution
of neurons.
