Higher-order mutual information reveals synergistic sub-networks for multi-neuron importance
This work addresses the need for understanding neural network inner workings by providing a method for multi-neuron importance analysis, which is incremental as it builds on prior single-neuron attribution methods.
The authors tackled the problem of quantifying neuron importance in neural networks by analyzing synergistic and redundant information in neuron groups using O-information, revealing that first layers are redundant for general features and last layers are synergistic for class-specific features, and demonstrated that re-training synergistic sub-networks leads to minimal performance changes.
Quantifying which neurons are important with respect to the classification decision of a trained neural network is essential for understanding their inner workings. Previous work primarily attributed importance to individual neurons. In this work, we study which groups of neurons contain synergistic or redundant information using a multivariate mutual information method called the O-information. We observe the first layer is dominated by redundancy suggesting general shared features (i.e. detecting edges) while the last layer is dominated by synergy indicating local class-specific features (i.e. concepts). Finally, we show the O-information can be used for multi-neuron importance. This can be demonstrated by re-training a synergistic sub-network, which results in a minimal change in performance. These results suggest our method can be used for pruning and unsupervised representation learning.