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By comparing with formula {{EquationNote|tow_terms}}, it is not difficult to find that when [math]\pi_i=\frac{1}{n}[/math], [math]JSD_{\pi}[/math] degenerates into EI.
By comparing with formula {{EquationNote|tow_terms}}, it is not difficult to find that when [math]\pi_i=\frac{1}{n}[/math], [math]JSD_{\pi}[/math] degenerates into EI.
In the literature <ref name="GJSD">{{cite conference|author1=Erik Englesson|author2=Hossein Azizpour|title=Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels|conference=35th Conference on Neural Information Processing Systems (NeurIPS 2021)|year=2021}}</ref>, the authors discussed the application of generalized JS divergence in measuring classification diversity. Therefore, EI can also be understood as a measure of the diversity of row vectors.
Furthermore, if we consider [[Shannon Entropy]][math]H(P_i)[/math] as a function, it is not difficult to verify that H is a [[Concave Function]], and formula {{EquationNote|GJSD}} is actually the [[Jensen Gap]] of the H function. There are numerous papers discussing the mathematical properties of this gap, including its upper and lower bound estimates.<ref name="Gao et al.">{{cite journal | last1 = Gao | first1 = Xiang | last2 = Sitharam | first2 = Meera | last3 = Roitberg | first3 = Adrian | year = 2019 | title = Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions | journal=The Australian Journal of Mathematical Analysis and Applications | arxiv = 1712.05267 | url = https://ajmaa.org/searchroot/files/pdf/v16n2/v16i2p14.pdf | volume = 16 | issue = 2 }}</ref>
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===因果涌现读书会===
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*[https://pattern.swarma.org/study_group_issue/490 因果涌现读书会第三季第一期：涌现、因果与人工智能]