تقرير
Conditioning the complexity of random landscapes on marginal optima
العنوان: | Conditioning the complexity of random landscapes on marginal optima |
---|---|
المؤلفون: | Kent-Dobias, Jaron |
سنة النشر: | 2024 |
المجموعة: | Condensed Matter |
مصطلحات موضوعية: | Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics |
الوصف: | Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors are a vanishing minority compared with nonmarginal optima and other unstable stationary points. We introduce a generic technique for conditioning the statistics of stationary points in random landscapes on their marginality, and apply it in three isotropic settings with qualitatively different structure: in the spherical spin-glasses, where the energy is Gaussian and its Hessian is GOE; in multispherical spin glasses, which are Gaussian but non-GOE; and in sums of squared spherical random functions, which are non-Gaussian. In these problems we are able to fully characterize the distribution of marginal optima in the landscape, including when they are in the minority. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2407.02082 |
رقم الأكسشن: | edsarx.2407.02082 |
قاعدة البيانات: | arXiv |
كن أول من يترك تعليقا!