{"type":"ScholarlyArticle","title":"The Complexity of Verifying Feedforward Neural Networks in Quantised Settings","authors":[{"name":"Eric Alsmann","slug":"eric-alsmann","given":"Eric","family":"Alsmann","affiliation":""},{"name":"Martin Lange","slug":"martin-lange","given":"Martin","family":"Lange","affiliation":""},{"name":"Marco Sälzer","slug":"marco-salzer","given":"Marco","family":"Sälzer","affiliation":""}],"abstract":"We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights come from a finite-width arithmetic, and dynamically quantised FNNs in which rational networks are evaluated with respect to a given finite-width arithmetic. We consider two types of specifications used in the literature. Linear programming (LP) specifications are conjunctions of linear constraints, while bit-vector (BV) specifications allow reasoning at the bit level and can express non-linear constraints. Our results give a complexity landscape of these verification problems. For quantised FNNs with fixed arithmetic precision, we show that verification under both LP and BV specifications remains NP-complete, matching the complexity of the rational case. For dynamically quantised FNNs with BV specifications, we establish upper bounds, complementing a previously known PSPACE-hardness result.","doi":"10.24963/ijcai.2026/460","url":"https://ijcai.org/proceedings/2026/460","pdf":"https://ijcai.org/proceedings/2026/0460.pdf","markdown":"https://ijcai.org/proceedings/2026/460.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/460","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Machine Learning","track":"Main Track","number":460,"pages":{"first":4135,"last":4142},"keywords":["Machine Learning: Trustworthy machine learning","Machine Learning: Robustness","Machine Learning: Explainable/Interpretable machine learning"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}