Adopting opaque machine learning predictors, which achieve very high predictive performance, often necessitates incorporating symbolic knowledge-extraction techniques. These techniques aim to explain the opaque predictions, thus making them applicable in high-stakes scenarios. The development of symbolic knowledge-extraction procedures is evolving alongside the dynamic machine learning landscape. However, there are recurring drawbacks that tend to be overlooked or addressed in a suboptimum way. Common examples include the non-exhaustiveness of the global explanations generated for a black-box predictor or the unwanted discretisation introduced in the prediction of continuous variables. To tackle these challenges, in this work, we introduce the HEx algorithm, its formalisation and its properties. This algorithm aims to obtain a symbolic, hierarchical representation of the knowledge acquired by opaque machine learning classifiers and regressors, always ensuring knowledge exhaustiveness and avoiding any output discretisation. Experiments demonstrating the superior capabilities of HEx compared to state-of-the-art competitors in terms of predictive performance, completeness, and human readability are presented.
Among the different approaches for automated music composition, those based on neural sequence models like the transformer show particular promise. A critical aspect for such approaches is how given music data sets are represented, or tokenised, for serving as suitable inputs for such models, as the choice of representation influences the quality of the produced output. In this paper, we introduce seven novel tokenisation techniques for converting MIDI data into numeric sequences. We compare characteristics of our tokenisers based on sets of musical data translated using our approaches. Our results show that some of our techniques greatly outperform the approaches found in the literature with respect to different metrics such as sequence length, information density, or memory requirements. Moreover, to evaluate the influence of our tokenisation approaches on the quality of the output of a model, we trained an ensemble of transformer models on the sets of tokenised musical data and performed a user study to assess the quality of the generated music pieces. The result of the study shows that the quality of pieces produced using our most promising techniques is equal to or outperforms state-of-the-art approaches.
