{"type":"ScholarlyArticle","title":"Cardinality-Minimal Explanations for Monotonic Neural Networks","authors":[{"name":"Ouns El Harzli","slug":"ouns-el-harzli","given":"Ouns","family":"El Harzli","affiliation":"Department of Computer Science , University of Oxford"},{"name":"Bernardo Cuenca Grau","slug":"bernardo-cuenca-grau","given":"Bernardo Cuenca","family":"Grau","affiliation":"Department of Computer Science , University of Oxford"},{"name":"Ian Horrocks","slug":"ian-horrocks","given":"Ian","family":"Horrocks","affiliation":"Department of Computer Science , University of Oxford"}],"abstract":"In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute  minimal subsets of input features that are sufficient for a given prediction to hold (respectively, to change a given prediction). The corresponding decision problems are, however, known to be intractable. In this paper, we investigate whether  tractability can be regained by focusing on neural models implementing a monotonic function. Although the relevant decision problems remain intractable, we can show that they become solvable in polynomial time by means of greedy algorithms if we additionally assume that the activation functions are continuous everywhere and differentiable almost everywhere. Our experiments suggest favourable performance of our algorithms.","doi":"10.24963/ijcai.2023/409","url":"https://ijcai.org/proceedings/2023/409","pdf":"https://ijcai.org/proceedings/2023/0409.pdf","markdown":"https://ijcai.org/proceedings/2023/409.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/409","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Machine Learning","track":"Main Track","number":409,"pages":{"first":3677,"last":3685},"keywords":["Machine Learning: ML: Theory of deep learning","Machine Learning: ML: Explainable/Interpretable machine learning","AI Ethics, Trust, Fairness: ETF: Explainability and interpretability"],"videos":[],"references":[{"position":1,"raw":"[Adebayo et al., 2018] J. 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