Why `d f : S -> (S -o T)` and not `d f : (S -> T) -> (S -o T)`? After all `d` takes a function and returns a linear map. The notation says it takes an `S` and returns a linear map. huh? Edit: Ah, because the linear map is a different one depending on where on the domain of `f` the derivative is evaluated. But how does that match the definition of the derivative as a limit?
@kanchankumar15193 жыл бұрын
'df' itself is the function being defined here, (d is an operator and isn't defined here). Also, the notion of limit leads us to a linear function as derivative. In 1d for example, the derivative is the tangent line, which is simply a linear function. In 2-d, it would be a plane -- again a linear map
@sapito1695 жыл бұрын
this is not for dummies
@JSimba944 жыл бұрын
I felt like a dummy watching. But a great watch regardless!
@guzh2 жыл бұрын
@@JSimba94 confusing lecture. NG.
@haps3000 Жыл бұрын
Also, congrats to the audience for supressing their inner rage towards the guy that created Haskell.
@undisclosedmusic49693 жыл бұрын
After 1 hour and 5 minutes of pretentious programming language and notation BS, turns out this magical implementation is still just plain, old reverse-mode AD. Still gotta define the local gradients, still gotta backpropagate…
@vtrandal2 жыл бұрын
Thank you! Seriously, thank you for sorting this mess for me. To make matters worse the speaker is chummy and on a first name basis with Conal Elliot.