Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser s...Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser six cognitive functions and provide new perspectives on which a lot of extensions and particularlly flexible Lmser are proposed.Interestingly,either or two of these dualities actually takes an important role in recent models such as U-net,ResNet,and Dense Net.The second thread is about bidirectional learning principles unified by best yIng-yAng(IA)harmony in BYY system.After getting insights on deep bidirectional learning from a bird-viewing on existing typical learning principles from one or both of the inward and outward directions,maximum likelihood,variational principle,and several other learning principles are summarised as exemplars of the BYY learning,with new perspectives on advanced topics.The third thread further proceeds to deep bidirectional intelligence,driven by long term dynamics(LTD)for parameter learning and short term dynamics(STD)for image thinking and rational thinking in harmony.Image thinking deals with information flow of continuously valued arrays and especially image sequence,as if thinking was displayed in the real world,exemplified by the flow from inward encoding/cognition to outward reconstruction/transformation performed in Lmser learning and BYY learning.In contrast,rational thinking handles symbolic strings or discretely valued vectors,performing uncertainty reasoning and problem solving.In particular,a general thesis is proposed for bidirectional intelligence,featured by BYY intelligence potential theory(BYY-IPT)and nine essential dualities in architecture,fundamentals,and implementation,respectively.Then,problems of combinatorial solving and uncertainty reasoning are investigated from this BYY IPT perspective.First,variants and extensions are suggested for AlphaGoZero like searching tasks,such as traveling salesman problem(TSP)and attributed graph matching(AGM)that ar展开更多
By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent ...By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.展开更多
基金supported by the Zhi-Yuan Chair Professorship Start-up Grant (WF220103010) from Shanghai Jiao Tong University
文摘Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser six cognitive functions and provide new perspectives on which a lot of extensions and particularlly flexible Lmser are proposed.Interestingly,either or two of these dualities actually takes an important role in recent models such as U-net,ResNet,and Dense Net.The second thread is about bidirectional learning principles unified by best yIng-yAng(IA)harmony in BYY system.After getting insights on deep bidirectional learning from a bird-viewing on existing typical learning principles from one or both of the inward and outward directions,maximum likelihood,variational principle,and several other learning principles are summarised as exemplars of the BYY learning,with new perspectives on advanced topics.The third thread further proceeds to deep bidirectional intelligence,driven by long term dynamics(LTD)for parameter learning and short term dynamics(STD)for image thinking and rational thinking in harmony.Image thinking deals with information flow of continuously valued arrays and especially image sequence,as if thinking was displayed in the real world,exemplified by the flow from inward encoding/cognition to outward reconstruction/transformation performed in Lmser learning and BYY learning.In contrast,rational thinking handles symbolic strings or discretely valued vectors,performing uncertainty reasoning and problem solving.In particular,a general thesis is proposed for bidirectional intelligence,featured by BYY intelligence potential theory(BYY-IPT)and nine essential dualities in architecture,fundamentals,and implementation,respectively.Then,problems of combinatorial solving and uncertainty reasoning are investigated from this BYY IPT perspective.First,variants and extensions are suggested for AlphaGoZero like searching tasks,such as traveling salesman problem(TSP)and attributed graph matching(AGM)that ar
基金Supported by National Natural Science Foundation of China(Grant No.12071491)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.
