Differential-geometrical methods in statistics. Lecture notes in statistics - A. Shun-ichi.

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Revisiting Natural Gradient for Deep Networks (2013, background): “Natural gradient can be traced back to Amari’s work on information geometry (Amari, 1985) and its application to various neural networks (Amari et al. , 1992; Amari, 1997), though a more in depth introduction can be found in Amari (1998); Park et al. (2000); Arnold et al. (2011).”
Shrinkage priors for Bayesian prediction (2006, background): “∂lgij(θ))g kl(θ) are the coefficients of the Riemannian connection, Tijk(θ) := E[∂i log p(x|θ)∂j log p(x|θ)∂k log p(x|θ)|θ] is the skewness tensor, and gij denotes the (i, j)-component of the inverse matrix of (gij); see [2] for details.”
Neural Learning in Structured Parameter Spaces - Natural Riemannian Gradient (1996, background): “Information geometry (Amari, 1985) proves that the Fisher information G is the only invariant metric to be introduced in the space S = {1o} of the parameters of probability distributions.”
Wigner-Yanase skew information vs. quantum Fisher information (2003, background): “The notion of Fisher information plays a crucial role in the geometrical approach to statistics [1], and it is enjoying increasing popularity in the informational approach to physics [7].”