In traditional pattern recognition tasks, neural networks are trained to recognise human-defined patterns (e.g. audio categories) in model inputs (e.g. audio). Meanwhile, some Explainable AI (XAI) methods explain latent patterns characterising the network's recognition of inputs as human-defined patterns; this work calls these latent patterns second-order patterns and proposes to discover them. Accordingly, we apply a hierarchical clustering algorithm to analyse whether our speaker recognition network's representations learned from known utterances naturally form hierarchical clusters. Each resulting cluster is a second-order pattern that characterises a context in our network's recognition of the known utterances as speaker identities. All discovered second-order patterns are then interpreted using the Hierarchical Cluster-Class Matching (HCCM) method. Moreover, we propose a new task, second-order pattern recognition, to identify which of the discovered second-order patterns characterising the recognition of known utterances also apply to unseen utterances, thereby characterising the recognition of unseen utterances. Accordingly, we design the Hierarchical Cluster Navigation and Assignment (HCNA) method. HCNA recognises a second-order pattern as applying to an unseen utterance when the utterance's network representation lies within the extrapolation space of the cluster regarded as that second-order pattern. Experimental results demonstrate that the extrapolation space introduced in HCNA substantially improves task performance.

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