Cunnington, DanielLaw, MarkLobo, JorgeRusso, Alessandra2023-03-132023-03-132023Cunnington D, Law M, Lobo J, Russo A. FFNSL: Feed-Forward Neural-Symbolic Learner. Mach Learn. 2023 Feb;112(2):515-69. DOI: 10.1007/s10994-022-06278-60885-6125http://hdl.handle.net/10230/56179Logic-based machine learning aims to learn general, interpretable knowledge in a data-efficient manner. However, labelled data must be specified in a structured logical form. To address this limitation, we propose a neural-symbolic learning framework, called Feed-Forward Neural-Symbolic Learner (FFNSL), that integrates a logic-based machine learning system capable of learning from noisy examples, with neural networks, in order to learn interpretable knowledge from labelled unstructured data. We demonstrate the generality of FFNSL on four neural-symbolic classification problems, where different pre-trained neural network models and logic-based machine learning systems are integrated to learn interpretable knowledge from sequences of images. We evaluate the robustness of our framework by using images subject to distributional shifts, for which the pre-trained neural networks may predict incorrectly and with high confidence. We analyse the impact that these shifts have on the accuracy of the learned knowledge and run-time performance, comparing FFNSL to tree-based and pure neural approaches. Our experimental results show that FFNSL outperforms the baselines by learning more accurate and interpretable knowledge with fewer examples.application/pdfengThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s10994-022-06278-6Neural-symbolic learningInductive logic programmingLogic-based machine learningDistributional shiftinfo:eu-repo/semantics/openAccess