Yötä

Reverse-mode automatic differentiation for static and dynamic graphs.

Migration to Yota v0.5

If you have previously used Yota < v0.5, pay attention to the following changes:

• grad() now returns (value, (fn-grad, arg-grads...)), where fn-grad is the gradient w.r.t. the function object fields (if any). Previous versions of Yota only returned gradients w.r.t. function arguments, which are now shifted by one. That is, must use g[i + 1] to refer to the gradient w.r.t. to the ith argument.
• Struct gradients are now represented by ChainRulesCore.Tangent type.
• Function tracing has been reworked and moved to Ghost.jl.

Usage

mutable struct Linear{T}
    W::AbstractArray{T,2}
    b::AbstractArray{T}
end

forward(m::Linear, X) = m.W * X

loss(m::Linear, X) = sum(forward(m, X))

m = Linear(rand(3,4), rand(3))
X = rand(4,5)

val, g = grad(loss, m, X)

g is a tuple of gradients of the loss function w.r.t. to the function object itself and its 2 arguments.

These gradients can then be used in the update!() function to modify tensors and fields of (mutable) structs:

for i=1:100
    val, g = grad(loss, m, X)
    println("Loss value in $(i)th epoch: $val")
    update!(m, g[2], (x, gx) -> x .- 0.01gx)
end

ChainRules

The primary method for extending the set of supported derivatives is using ChainRules.jl.

Some functions are handled by Yota's own rules ("d-rules") instead, but at the moment this mechanism is purely internal and should not be used outside of the package.

How it works

Yota is built on top of the code tracer in Ghost.jl. Essentially, differentiation boils down to the following steps:

1. Trace function execution using Ghost.trace() producing a computational graph as a Tape.
2. Run Yota.gradtape!() to add derivative operations to that tape.
3. Compile the tape back to a Julia function.

One function useful for debugging is Yota.gradtape(f, args...) (without exclamation sign) which skips the compilation and instead returns the computed tape.