{"type":"ScholarlyArticle","title":"Differentiable Spectral Normalization for Large-Scale Ising Optimization","authors":[{"name":"Thinh Nguyen-Cong","slug":"thinh-nguyen-cong","given":"Thinh","family":"Nguyen-Cong","affiliation":""},{"name":"Thang N. Dinh","slug":"thang-n-dinh","given":"Thang","family":"N. Dinh","affiliation":""}],"abstract":"Spectral relaxation is widely used for large-scale combinatorial optimization due to its computational efficiency. Yet its effectiveness depends critically on the choice of graph normalization, a design decision typically made heuristically. Here, we show that normalization can be treated as a continuous optimization variable rather than a fixed preprocessing choice. Our method, Differentiable Spectral Normalization (DSN), parameterizes the spectral relaxation through a diagonal metric and maximizes the resulting lower bound via projected gradient ascent. Exact gradients are obtained through the Hellmann-Feynman theorem using only the principal eigenpair, maintaining linear complexity per iteration. On benchmark instances ranging from 10^3 to 8.4 x 10^6 nodes, DSN improves solution quality by 3-15% over static spectral methods. Its performance comes within 1-3% of state-of-the-art metaheuristics, such as simulated annealing, at up to 190x lower computational cost on large-scale instances. These results suggest that learning problem-specific relaxation geometry can substantially close the gap between spectral scalability and metaheuristic solution quality.","doi":"10.24963/ijcai.2026/258","url":"https://ijcai.org/proceedings/2026/258","pdf":"https://ijcai.org/proceedings/2026/0258.pdf","markdown":"https://ijcai.org/proceedings/2026/258.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/258","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":"Constraint Satisfaction and Optimization","track":"Main Track","number":258,"pages":{"first":2319,"last":2327},"keywords":["Search: Combinatorial search and optimisation","Constraint Satisfaction and Optimization: Constraint optimization problems","Machine Learning: Optimization","Machine Learning: Matrix/tensor methods","Constraint Satisfaction and Optimization: Mixed discrete and continuous optimization"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}