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Reverse-mode automatic differentiation

The built-in vjp function computes the product of the Jacobian of a function at some point and a seed vector. This can be used to compute derivatives of functions.

def f x = f64.sqrt(x) * f64.sin(x)

def f' x = vjp f x 1
> f' 2f64

jvp corresponds to differentiation by reverse accumulation, and is most efficient for functions that have more inputs than outputs. A particularly important special case of these are loss functions that return just a single scalar. For these we can define a function for finding gradients:

def grad f x = vjp f x 1f64

def g (x,y) = f64.cos(x) * f64.sin(y)

def g' x y = grad g (x,y)
> g' 1f64 2f64
(-0.7651474012342926f64, -0.2248450953661529f64)

See also

Forward-mode automatic differentiation, Newton’s Method.