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Neural network models are widely used in a variety of domains, often asblack-box solutions, since they are not directly interpretable for humans. Thefield of explainable artificial intelligence aims at developing explanationmethods to address this challenge, and several approaches have been developedover the recent years, including methods for investigating what type ofknowledge these models internalise during the training process. Among these,the method of concept detection, investigates which \emph{concepts} neuralnetwork models learn to represent in order to complete their tasks. In thiswork, we present an extension to the method of concept detection, named\emph{concept backpropagation}, which provides a way of analysing how theinformation representing a given concept is internalised in a given neuralnetwork model. In this approach, the model input is perturbed in a mannerguided by a trained concept probe for the described model, such that theconcept of interest is maximised. This allows for the visualisation of thedetected concept directly in the input space of the model, which in turn makesit possible to see what information the model depends on for representing thedescribed concept. We present results for this method applied to a various setof input modalities, and discuss how our proposed method can be used tovisualise what information trained concept probes use, and the degree as towhich the representation of the probed concept is entangled within the neuralnetwork model itself.

Concept backpropagation: An Explainable AI approach for visualising learned concepts in neural network models