] add Zygote
Zygote provides source-to-source automatic differentiation (AD) in Julia, and is the next-gen AD system for the Flux differentiable programming framework. For more details and benchmarks of Zygote's technique, see our paper. You may want to check out Flux for more interesting examples of Zygote usage; the documentation here focuses on internals and advanced AD usage.
Zygote supports Julia 1.0 onwards, but we highly recommend using Julia 1.3 or later.
julia> using Zygote
julia> f(x) = 5x + 3
julia> f(10), f'(10)
(53, 5.0)
julia> @code_llvm f'(10)
define i64 @"julia_#625_38792"(i64) {
top:
ret i64 5
}"Source-to-source" means that Zygote hooks into Julia's compiler, and generates the backwards pass for you – as if you had written it by hand.
Zygote supports the full flexibility and dynamism of the Julia language, including control flow, recursion, closures, structs, dictionaries, and more.
julia> fs = Dict("sin" => sin, "cos" => cos, "tan" => tan);
julia> gradient(x -> fs[readline()](x), 1)
sin
0.5403023058681398Defining custom gradients is a cinch, and errors have good stacktraces.
julia> using Zygote: @adjoint
julia> add(a, b) = a + b
julia> @adjoint add(a, b) = add(a, b), Δ -> (Δ, Δ)To support large machine learning models with many parameters, Zygote can differentiate implicitly-used parameters, as opposed to just function arguments.
julia> W, b = rand(2, 3), rand(2);
julia> predict(x) = W*x .+ b;
julia> g = gradient(Params([W, b])) do
sum(predict([1,2,3]))
end
Grads(...)
julia> g[W], g[b]
([1.0 2.0 3.0; 1.0 2.0 3.0], [1.0, 1.0])