Spectral regularization dynamics: a continuous-time framework for non-convex optimization
International Journal of Machine Learning and Cybernetics, cilt.17, sa.7, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 17 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s13042-026-03164-8
- Dergi Adı: International Journal of Machine Learning and Cybernetics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Continuous-time dynamics, Dynamical systems, Non-convex optimization, Saddle-point avoidance, Second-order methods
- Eskişehir Osmangazi Üniversitesi Adresli: Evet
Özet
We propose Spectral Regularization Dynamics (SRD), a continuous-time system for unconstrained non-convex optimization. Unlike discrete iterations that solve regularized subproblems, SRD employs an autonomous feedback control mechanism coupled to the Hessian’s minimum eigenvalue. This mechanism guarantees a descent direction by driving the regularization parameter strictly positive in regions of negative curvature. We prove global convergence to the set of critical points via LaSalle’s invariance principle. Furthermore, using the stable manifold theorem, we establish that the system dynamics almost surely avoid strict saddle points. In local neighborhoods of strict minima, the regularization vanishes asymptotically, recovering the convergence rate of the continuous Newton flow. Numerical benchmarks illustrate the saddle-avoidance mechanism and local convergence properties.