Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus

By Michael Spivak. 2019

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Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions (2016, background): “As long as I − α∇2f(x) is invertible, from Inverse Function Theorem (see [26]) follows that g is a local diffeomorphism.”
On the Spectral Bias of Neural Networks (2018, methodology): “So by Stokes’ theorem (see e.g Spivak (2018)), the integral of its divergence is a pure boundary term.”
Optimality of Matched-Pair Designs in Randomized Controlled Trials (2022, background): “Bugni, F. A., I. A. Canay, and A. M. Shaikh (2018, October). Inference Under Covariate-Adaptive Randomization. Journal of the American Statistical Association 113 (524), 1784–1796. Publisher: Taylor & Francis eprint: https://doi.org/10.1080/01621459.2017.1375934. Bugni, F. A., I. A. Canay, and A. M.”
Normalizing Flows: An Introduction and Review of Current Methods (2020, background): “One can also use differential structure to deﬁne measures on manifolds [86].”