### Automatic differentiation in  C++ ###

Day 8: Forward mode implementation part 1

I've figured out how to implement the forward mode for the simple cases: 
Case 1: input x is a vector and output y is a real number.
The second case is just a generalization of the output (y is also a vector).

I had some cool small examples of the manual execution and values of the gradients trace, but it got deleted somehow 🥲 I'll do it again and share it the next day!

In forward mode, it seems that each forward pass can compute the gradient of the output with respect to only one input at a time. So if the input is a vector, would that be considered as 1 input or would each value in that vector be considered as 1 input (so x has n inputs basically)?

When treating the input as a single input vector, forward mode would compute dy/dx in one pass, and if you treat it as multiple inputs, the forward mode will compute it dy/dx_i for each value in that input, thus requiring multiple forward passing. Implementation wise, I'll have to think which way is better.

Make sense, thank you for the clarification!
4390 $degen