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第1,050行：
第1,050行： − 而[[矩阵的秩]]衡量的是矩阵P非退化（也就是可逆）的程度，与Degeneracy有着类似的效果。+ − − 而当[math]\alpha\rightarrow 2[/math]，则[math]\Gamma_{\alpha}[/math]就退化成了矩阵P的[[Frobinius范数]]的平方，即： + − + + + − 所以，当[math]\alpha\in(0,2)[/math]连续变化的时候，[math]\Gamma_{\alpha}[/math]就可以在简并性与确定性二者之间切换了。通常情况下，我们取[math]\alpha=1[/math]，这可以让[math]\Gamma_{\alpha}[/math]能够在确定性与简并性之间达到一种平衡。+ − 在文献<ref name="zhang_reversibility" />中，作者们证明了EI与动力学可逆性[math]\Gamma_{\alpha}[/math]之间存在着一种近似的关系： 第1,088行：
第1,088行： − 通过与公式{{EquationNote|tow_terms}}比较，不难发现，当[math]\pi_i=\frac{1}{n}[/math]，则[math]JSD_{\pi}[/math]就退化为EI了。+
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</math>
</math>
The [[Rank of a Matrix]] measures the degree to which matrix P is non degenerate (i.e. reversible), similar to the effect of degeneracy.
And when [math]\alpha\rightarrow 2[/math], then [math]\Gamma_{\alpha}[/math] degenerates into the square of the [[Frobinius Norm]] of matrix P, that is:
<math>
<math>
||P||_F^2=\sum_{i=1}^N\sigma_i^{2}
||P||_F^2=\sum_{i=1}^N\sigma_i^{2}
</math> 这一指标衡量的是矩阵P的确定性的程度，这是因为只有当矩阵P中的所有行向量都是[[独热向量]]（one-hot）的时候，[math]||P||_F[/math]才会最大，因此它与Determinism有着类似的衡量效果。
</math> This indicator measures the degree of certainty of matrix P, because only when all row vectors in matrix P are [[One-hot Vectors]], [math]||P||_F[/math] will be maximized. Therefore, it has a similar measurement effect to Determinism.
So, when [math]\alpha\in(0,2)[/math] changes continuously, [math]\Gamma_{\alpha}[/math] can switch between degeneracy and determinacy. Normally, we take [math]\alpha=1[/math], which allows [math]\Gamma_{\alpha}[/math] to achieve a balance between determinacy and degeneracy.
In reference <ref name="zhang_reversibility" />, the authors demonstrated an approximate relationship between EI and dynamic reversibility [math]\Gamma_{\alpha}[/math]：
<math>
<math>
|{{EquationRef|GJSD}}}}Among them, [math]P_i,i\in[1,m][/math]is a set of probability distribution vectors, m is their dimension, and [math]\pi=(\pi_1,\pi_2,\cdots,\pi_n)[/math] is a set of weights that satisfy:[math]\pi_i\in[0,1],\forall i\in[1,n][/math]和[math]\sum_{i=1}^n\pi_i=1[/math].
|{{EquationRef|GJSD}}}}Among them, [math]P_i,i\in[1,m][/math]is a set of probability distribution vectors, m is their dimension, and [math]\pi=(\pi_1,\pi_2,\cdots,\pi_n)[/math] is a set of weights that satisfy:[math]\pi_i\in[0,1],\forall i\in[1,n][/math]和[math]\sum_{i=1}^n\pi_i=1[/math].
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.
在文献<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>中，作者们讨论了广义JS散度在分类多样性度量方面的应用。因此，EI也可以理解为是对行向量多样化程度的一种度量。
在文献<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>中，作者们讨论了广义JS散度在分类多样性度量方面的应用。因此，EI也可以理解为是对行向量多样化程度的一种度量。