Understanding deep learning is increasingly emergent as it penetrates more and more into industry and science.In recent years,a research line from Fourier analysis sheds light on this magical“black box”by showing a ...Understanding deep learning is increasingly emergent as it penetrates more and more into industry and science.In recent years,a research line from Fourier analysis sheds light on this magical“black box”by showing a Frequency principle(F-Principle or spectral bias)of the training behavior of deep neural networks(DNNs)—DNNs often fit functions from low to high frequencies during the training.The F-Principle is first demonstrated by one-dimensional(1D)synthetic data followed by the verification in high-dimensional real datasets.A series of works subsequently enhance the validity of the F-Principle.This low-frequency implicit bias reveals the strength of neural networks in learning low-frequency functions as well as its deficiency in learning high-frequency functions.Such understanding inspires the design of DNN-based algorithms in practical problems,explains experimental phenomena emerging in various scenarios,and further advances the study of deep learning from the frequency perspective.Although incomplete,we provide an overview of the F-Principle and propose some open problems for future research.展开更多
This paper addresses new trends in quantitative geography research. Modern social science research--including economic and social geography--has in the past decades shown an increasing interest in micro-oriented behav...This paper addresses new trends in quantitative geography research. Modern social science research--including economic and social geography--has in the past decades shown an increasing interest in micro-oriented behaviour of actors. This is inter alia clearly reflected in SIMs （spatial interaction models）, where discrete choice approaches have assumed a powerful position. This paper aims to provide in particular a concise review of micro-based research, with the aim to review the potential--but also the caveats---of micro models to map out human behaviour. In particular, attention will be devoted to interactive learning principles that shape individual decisions. Lessons from cognitive sciences will be put forward and illustrated, amongst others on the basis of computational neural networks or spatial econometric approaches. Particular attention will be paid to non-linear dynamic spatial models, amongst others, in the context of chaos theory and complexity science. The methodology of deductive reasoning under conditions of large data bases in studying human mobility will be questioned as well. In this context more extensive attention is given to ceteris paribus conditions and evolutionary thinking. The relevance of the paper will be illustrated by referring to various spatial applications in different disciplines and different application areas, e.g. in geography, regional science or urban economics.展开更多
This study investigated the instructional preferences of full time adult credential students after they took a live course called Principles of Adult Education at California State University, Long Beach (CSULB) in the...This study investigated the instructional preferences of full time adult credential students after they took a live course called Principles of Adult Education at California State University, Long Beach (CSULB) in the fall semester of 2002. These full time adult credential students had been working on their adult teaching credentials to meet the competencies specified by the California Commission on Teacher Credentialing. The course introduced students to Andragogy developed by Malcolm Knowles out of the andragogical model developed by Lindeman (1926). The study used Principles of Adult Learning Scales (PALS), advanced by Gary Conti in 1983 to measure instructional preferences. Data were collected from 30 (100% of 30) full time adult credential students enrolled in a live course to determine their instructional preferences of helping adults learn. The results of the study showed in most cases these adult learning professionals taught adult students andragogically; in some cases they taught adult students pedagogically.展开更多
基金sponsored by the National Key R&D Program of China Grant No.2022YFA1008200(Z.X.,Y.Z.,T.L.)the National Natural Science Foundation of China Grant Nos.92270001(Z.X.),12371511(Z.X.),12101402(Y.Z.),12101401(T.L.)+2 种基金the Lingang Laboratory Grant No.LG-QS-202202-08(Y.Z.)the Shanghai Municipal Science and Technology Key Project No.22JC1401500(T.L.)the Shanghai Municipal of Science and Technology Major Project No.2021SHZDZX0102,and the HPC of School of Mathematical Sciences and the Student Innovation Center,and the Siyuan-1 cluster supported by the Center for High Performance Computing at Shanghai Jiao Tong University.
文摘Understanding deep learning is increasingly emergent as it penetrates more and more into industry and science.In recent years,a research line from Fourier analysis sheds light on this magical“black box”by showing a Frequency principle(F-Principle or spectral bias)of the training behavior of deep neural networks(DNNs)—DNNs often fit functions from low to high frequencies during the training.The F-Principle is first demonstrated by one-dimensional(1D)synthetic data followed by the verification in high-dimensional real datasets.A series of works subsequently enhance the validity of the F-Principle.This low-frequency implicit bias reveals the strength of neural networks in learning low-frequency functions as well as its deficiency in learning high-frequency functions.Such understanding inspires the design of DNN-based algorithms in practical problems,explains experimental phenomena emerging in various scenarios,and further advances the study of deep learning from the frequency perspective.Although incomplete,we provide an overview of the F-Principle and propose some open problems for future research.
文摘This paper addresses new trends in quantitative geography research. Modern social science research--including economic and social geography--has in the past decades shown an increasing interest in micro-oriented behaviour of actors. This is inter alia clearly reflected in SIMs （spatial interaction models）, where discrete choice approaches have assumed a powerful position. This paper aims to provide in particular a concise review of micro-based research, with the aim to review the potential--but also the caveats---of micro models to map out human behaviour. In particular, attention will be devoted to interactive learning principles that shape individual decisions. Lessons from cognitive sciences will be put forward and illustrated, amongst others on the basis of computational neural networks or spatial econometric approaches. Particular attention will be paid to non-linear dynamic spatial models, amongst others, in the context of chaos theory and complexity science. The methodology of deductive reasoning under conditions of large data bases in studying human mobility will be questioned as well. In this context more extensive attention is given to ceteris paribus conditions and evolutionary thinking. The relevance of the paper will be illustrated by referring to various spatial applications in different disciplines and different application areas, e.g. in geography, regional science or urban economics.
文摘This study investigated the instructional preferences of full time adult credential students after they took a live course called Principles of Adult Education at California State University, Long Beach (CSULB) in the fall semester of 2002. These full time adult credential students had been working on their adult teaching credentials to meet the competencies specified by the California Commission on Teacher Credentialing. The course introduced students to Andragogy developed by Malcolm Knowles out of the andragogical model developed by Lindeman (1926). The study used Principles of Adult Learning Scales (PALS), advanced by Gary Conti in 1983 to measure instructional preferences. Data were collected from 30 (100% of 30) full time adult credential students enrolled in a live course to determine their instructional preferences of helping adults learn. The results of the study showed in most cases these adult learning professionals taught adult students andragogically; in some cases they taught adult students pedagogically.
