Automatic Differentiation: Theory and Practice
arXiv:2207.06114v1h-index: 4
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This provides a theoretical foundation for automatic differentiation, which is incremental as it builds on existing mathematical frameworks.
The paper presents a coordinate-free formalism for automatic differentiation in real and complex settings, deriving forward and backward formulae for matrix functions from basic principles.
We present the classical coordinate-free formalism for forward and backward mode ad in the real and complex setting. We show how to formally derive the forward and backward formulae for a number of matrix functions starting from basic principles.