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Yingru Li Argues the Policy Gradient Is a Covariance and the Fisher a Variance

Yingru Li Argues the Policy Gradient Is a Covariance and the Fisher a Variance

Oct 16, 2026
Yingru Li

Yingru Li argues in Part 1 of a three-part theory series that the expected policy gradient is a covariance and the Fisher a variance, capping the gradient for any reward and explaining why post-training updates stay sparse. Li cites measurements that the top 1% of coordinates by Fisher hold 47.40% of the top 1% by gradient magnitude.

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