当前位置: X-MOL 学术J. Phys. A: Math. Theor. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Replica symmetry breaking in neural networks: a few steps toward rigorous results
Journal of Physics A: Mathematical and Theoretical ( IF 2.1 ) Pub Date : 2020-09-17 , DOI: 10.1088/1751-8121/abaf2c
Elena Agliari 1, 2 , Linda Albanese 3 , Adriano Barra 2, 3, 4 , Gabriele Ottaviani 5
Affiliation  

In this paper we adapt the broken replica interpolation technique (developed by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian variables) in order to work also with the Hopfield model (i.e. a pairwise mean-field neural-network whose couplings are drawn according to Hebb’s learning rule): this is accomplished by grafting Guerra’s telescopic averages on the transport equation technique, recently developed by some of the authors. As an overture, we apply the technique to solve the Sherrington-Kirkpatrick model with i.i.d. Gaussian couplings centered at J 0 and with finite variance J ; the mean J 0 provides a ferromagnetic contribution to be detected in a noisy environment tuned by J , hence making this model a natural test-case to be investigated before addressing the Hopfield model. For both the models, an explicit expression...

中文翻译:

神经网络中的副本对称性破坏:迈向严格结果的几步

在本文中,我们采用了破碎副本插值技术(由Francesco Guerra开发,用于处理Sherrington-Kirkpatrick模型,即成对的均值场自旋玻璃,其耦合是iid标准高斯变量),以便与Hopfield模型一起使用(即成对的平均场神经网络,其耦合根据Hebb的学习规则绘制):这是通过将Guerra的伸缩平均值嫁接到某些作者最近开发的输运方程技术上来实现的。作为序言,我们应用该技术求解以i 0为中心的艾德·高斯耦合和有限方差为J的Sherrington-Kirkpatrick模型。平均值J 0提供了在由J调谐的嘈杂环境中要检测的铁磁贡献,因此,在处理Hopfield模型之前,使该模型成为要研究的自然测试案例。对于这两个模型,一个显式表达式...
更新日期:2020-09-20
down
wechat
bug