Neuro-symbolic learning has gained tremendous attention in the last few years [1, 2, 3, 4] as such integration has the potential of leading to a new era of intelligent solutions, enabling the integration of deep learning and reasoning strategies (e.g., logic-based or expert systems). While a lot of efort has been devoted to devising neuro-symbolic methods in the discriminative setting [5, 6, 7], less attention has been paid to the generative counterpart. An ideal generative neuro-symbolic framework should be able to encode the available small amount of training data into an expressive symbolic representation and to exploit complex forms of high level reasoning on such representation to generate new data samples. This is far from the actual state-of-the-art, where neuro-symbolic methods [8, 9, 10] have been mostly applied on generative tasks requiring only spatial-reasoning. As a motivation for this work, consider a task where a single image of multiple handwritten numbers is labeled with their sum. Suppose that we want to generate new images not only given their addition, but also given their multiplication, power, etc. Common generative approaches, like VAE-based models, have a strong connection between the latent representation and the label of the training task (i.e., the addition) [11, 12]. Consequently, when considering new generation tasks that go beyond the simple addition, they have to be retrained on new data.
Italy GM is funded by the Research Foundation-Flanders (FWO-Vlaanderen, GA No 1239422N). This research is funded by TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No 952215. ES is partially funded by the KU Leuven Research Fund (C14/18/062) and the Flemish Government (AI Research Program).