On Local Entropy, Stochastic Control, and Deep Neural Networks

被引:2
作者
Pavon, Michele [1 ]
机构
[1] Univ Padua, Dipartimento Matemat, I-35122 Padua, Italy
来源
IEEE CONTROL SYSTEMS LETTERS | 2023年 / 7卷
关键词
Entropy; Stochastic processes; Q measurement; Bridges; Volume measurement; Neural networks; Particle measurements; Stochastic optimal control; machine learning; neural networks; OPTIMAL TRANSPORT; REVERSAL;
D O I
10.1109/LCSYS.2022.3189927
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this letter, we connect some recent papers on smoothing of energy landscapes and scored-based generative models of machine learning to classical work in stochastic control. We clarify these connections providing rigorous statements and representations which may serve as guidelines for further learning models.
引用
收藏
页码:437 / 441
页数:5
相关论文
共 44 条
[1]   CLUSTERING AND CLASSIFICATION THROUGH NORMALIZING FLOWS IN FEATURE SPACE [J].
Agnelli, J. P. ;
Cadeiras, M. ;
Tabak, E. G. ;
Turner, C. V. ;
Vanden-Eijnden, E. .
MULTISCALE MODELING & SIMULATION, 2010, 8 (05) :1784-1802
[2]  
[Anonymous], 2003, GRAD STUD MATH
[3]   Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete Synapses [J].
Baldassi, Carlo ;
Ingrosso, Alessandro ;
Lucibello, Carlo ;
Saglietti, Luca ;
Zecchina, Riccardo .
PHYSICAL REVIEW LETTERS, 2015, 115 (12)
[4]  
Boltzmann L., 1877, Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Classe. Abt. II, V76, P373
[5]  
Chaudhari P., 2017, INT C LEARN REPR
[6]  
Chaudhari P, 2018, 2018 INFORMATION THEORY AND APPLICATIONS WORKSHOP (ITA)
[7]   Deep relaxation: partial differential equations for optimizing deep neural networks [J].
Chaudhari, Pratik ;
Oberman, Adam ;
Osher, Stanley ;
Soatto, Stefano ;
Carlier, Guillaume .
RESEARCH IN THE MATHEMATICAL SCIENCES, 2018, 5 :1-30
[8]  
Chen Ting, 2021, ARXIV
[9]   Optimal Transport in Systems and Control [J].
Chen, Yongxin ;
Georgiou, Tryphon T. ;
Pavon, Michele .
ANNUAL REVIEW OF CONTROL, ROBOTICS, AND AUTONOMOUS SYSTEMS, VOL 4, 2021, 2021, 4 :89-113
[10]   Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Scodinger Bridge [J].
Chen, Yongxin ;
Georgiou, Tryphon T. ;
Pavon, Michele .
SIAM REVIEW, 2021, 63 (02) :249-313