faster default gradient performance

src/tracker/Tracker.jl

@@ -5,7 +5,8 @@ using MacroTools: @q, @forward
 
 import Base: ==
 
-export TrackedArray, TrackedVector, TrackedMatrix, Params, param, back!
+export TrackedArray, TrackedVector, TrackedMatrix, Params, gradient,
+  param, back!
 
 tracker(x) = nothing
 
@@ -99,7 +100,8 @@ end
 
 nobacksies(f, x) = track(nobacksies, f, x)
 nobacksies(f, xs::Tuple) = map(x -> nobacksies(f, x), xs)
-@grad nobacksies(f, x) = data(x), Δ -> error("Nested AD not defined for $f")
+@grad nobacksies(f::Symbol, x) = data(x), Δ -> error("Nested AD not defined for $f")
+@grad nobacksies(f::String, x) = data(x), Δ -> error(f)
 
 param(x::Number) = TrackedReal(float(x))
 param(xs::AbstractArray) = TrackedArray(float.(xs))

src/tracker/back.jl

@@ -66,6 +66,15 @@ function back!(x, Δ; once = true)
   return
 end
 
+function gradient_(f, xs...)
+  xs = param.(xs)
+  l = f(xs...)
+  losscheck(l)
+  back!(l)
+  nobacksies("Use `gradient(...; nest = true)` for nested derivatives",
+             grad.(xs))
+end
+
 # Out-of-place gradients
 
 struct Params
@@ -162,20 +171,11 @@ function losscheck(x)
   isnan(x) && error("Loss is NaN")
 end
 
-function gradient(f, args...)
+function gradient_nested(f, args...)
   y, back = forward(f, args...)
   losscheck(y)
   return back(1)
 end
 
-derivative(f, x) = gradient(f, x)[1]
+gradient(f, xs...; nest = false) =
-
+  nest ? gradient_nested(f, xs...) : gradient_(f, xs...)
-# Non-nesting versions
-
-function gradient_(f, xs...)
-  xs = param.(xs)
-  l = f(xs...)
-  losscheck(l)
-  back!(l)
-  grad.(xs)
-end

test/tracker.jl

@@ -1,6 +1,6 @@
 using Flux
 using Flux.Tracker, Test, NNlib
-using Flux.Tracker: TrackedReal, gradcheck, grad, derivative, checkpoint
+using Flux.Tracker: TrackedReal, gradcheck, grad, checkpoint
 using NNlib: conv, depthwiseconv
 using Printf: @sprintf
 using LinearAlgebra: diagm, dot, LowerTriangular, norm
@@ -285,9 +285,9 @@ end
     count += 1
     a * b
   end
-  @test derivative(x -> mul(5, x), 3) == 5
+  @test gradient(x -> mul(5, x), 3)[1] == 5
   @test count == 1
-  @test derivative(x -> checkpoint(mul, 5, x), 3) == 5
+  @test gradient(x -> checkpoint(mul, 5, x), 3)[1] == 5
   @test count == 3
 end