This appendix explains how TensorFlow’s autodiff feature works, and how it compares to other solutions.
Suppose you define a function f(x,y) = x^{2}y + y + 2, and you need its partial derivatives and , typically to perform Gradient Descent (or some other optimization algorithm). Your main options are manual differentiation, symbolic differentiation, numerical differentiation, forward-mode autodiff, and finally reverse-mode autodiff. TensorFlow implements this last option. Let’s go through each of these options.
The first approach is to pick up a pencil and a piece of paper and use your calculus knowledge to derive the partial derivatives manually. For the function f(x,y) just defined, it is not too hard; you just need to use five rules:
The derivative of a constant is 0.
The derivative of λx is λ (where λ is a constant).
The derivative of x^{λ} is λx^{λ – 1}, so the derivative of x^{2} is 2x.
The derivative of a sum of functions is the sum of these functions’ derivatives.
The derivative of λ times a function is λ times its derivative.
From these rules, you can derive Equation D-1:
This approach ...
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