Reverse Mode Automatic Differentiation for Julia
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ReverseDiff is a fast and compile-able tape-based reverse mode automatic differentiation (AD) that implements methods to take gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really).
While performance can vary depending on the functions you evaluate, the algorithms implemented by ReverseDiff generally outperform non-AD algorithms in both speed and accuracy.
To install ReverseDiff, simply use Julia's package manager:
Other Julia packages may provide some of these features, but only ReverseDiff provides all of them (as far as I know at the time of this writing):
@skip(with more to come!)
Dualnumbers (e.g. SIMD, zero-overhead arithmetic)
...and, simply put, it's fast (for gradients, at least). Using the code from
julia> using BenchmarkTools, Pkg
this script defines f and ∇f!
julia> include(joinpath(Pkg.dir("ReverseDiff"), "examples/gradient.jl"));
julia> a, b = rand(100, 100), rand(100, 100);
julia> inputs = (a, b);
julia> results = (similar(a), similar(b));
Benchmark the original objective function, sum(a' * b + a * b')
julia> @benchmark f($a, $b) BenchmarkTools.Trial: memory estimate: 234.61 kb allocs estimate: 6
minimum time: 110.000 μs (0.00% GC) median time: 137.416 μs (0.00% GC) mean time: 173.085 μs (11.63% GC) maximum time: 3.613 ms (91.47% GC)
Benchmark ∇f! at the same inputs (this is executing the function,
getting the gradient w.r.t.
a, and getting the gradient w.r.t
bsimultaneously). Notice that the whole thing is
julia> @benchmark ∇f!($results, $inputs) BenchmarkTools.Trial: memory estimate: 0.00 bytes allocs estimate: 0
minimum time: 429.650 μs (0.00% GC) median time: 431.460 μs (0.00% GC) mean time: 469.916 μs (0.00% GC) maximum time: 937.512 μs (0.00% GC)
I've used this benchmark (and others) to pit ReverseDiff against every other native Julia reverse-mode AD package that I know of (including source-to-source packages), and have found ReverseDiff to be faster and use less memory in most cases.
ForwardDiff is algorithmically more efficient for differentiating functions where the input dimension is less than the output dimension, while ReverseDiff is algorithmically more efficient for differentiating functions where the output dimension is less than the input dimension.
Thus, ReverseDiff is generally a better choice for gradients, but Jacobians and Hessians are trickier to determine. For example, optimized methods for computing nested derivatives might use a combination of forward-mode and reverse-mode AD.
ForwardDiff is often faster than ReverseDiff for lower dimensional gradients (
length(input) < 100), or gradients of functions where the number of input parameters is small compared to the number of operations performed on them. ReverseDiff is often faster if your code is expressed as a series of array operations, e.g. a composition of Julia's Base linear algebra methods.
In general, your choice of algorithms will depend on the function being differentiated, and you should benchmark different methods to see how they fare.