A study of the learnability of relational properties: model counting meets machine learning (MCML)

This paper introduces the MCML approach for empirically studying the learnability of relational properties that can be expressed in the well-known software design language Alloy. A key novelty of MCML is quantification of the performance of and semantic differences among trained machine learning (ML) models, specifically decision trees, with respect to entire (bounded) input spaces, and not just for given training and test datasets (as is the common practice). MCML reduces the quantification problems to the classic complexity theory problem of model counting, and employs state-of-the-art model counters. The results show that relatively simple ML models can achieve surprisingly high performance (accuracy and F1-score) when evaluated in the common setting of using training and test datasets -- even when the training dataset is much smaller than the test dataset -- indicating the seeming simplicity of learning relational properties. However, MCML metrics based on model counting show that the performance can degrade substantially when tested against the entire (bounded) input space, indicating the high complexity of precisely learning these properties, and the usefulness of model counting in quantifying the true performance.