Convolutional neural networks (CNNs) are commonplace in high-performing solutions to many real-world problems, such as audio classification. CNNs have many parameters and filters, with some having a larger impact on the performance than others. This means that networks may contain many unnecessary filters, increasing a CNN's computation and memory requirements while providing limited performance benefits. To make CNNs more efficient, we propose a pruning framework that eliminates filters with the highest "commonality". We measure this commonality using the graph-theoretic concept of "centrality". We hypothesise that a filter with a high centrality should be eliminated as it represents commonality and can be replaced by other filters without affecting the performance of a network much. An experimental evaluation of the proposed framework is performed on acoustic scene classification and audio tagging. On the DCASE 2021 Task 1A baseline network, our proposed method reduces computations per inference by 71\% with 50\% fewer parameters at less than a two percentage point drop in accuracy compared to the original network. For large-scale CNNs such as PANNs designed for audio tagging, our method reduces 24\% computations per inference with 41\% fewer parameters at a slight improvement in performance.

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