`AD.jacobian` much slower than `Zygote.jacobian`

[gdalle]

Hi, and thanks for this amazing interface!

When computing jacobians, I recently noted a significant speed difference between standalone Zygote and Zygote used as an AD backend. The allocations also differ wildly. Do you happen to know where that comes from?

Here's a minimal working example:

julia> using AbstractDifferentiation, BenchmarkTools, Zygote

julia> f(x) = x .^ 2
f (generic function with 1 method)

julia> x = rand(100);

julia> ab = AD.ZygoteBackend()
AbstractDifferentiation.ReverseRuleConfigBackend{Zygote.ZygoteRuleConfig{Zygote.Context}}(Zygote.ZygoteRuleConfig{Zygote.Context}(Zygote.Context(nothing)))

julia> Zygote.jacobian(f, x)
([1.3044988022198039 0.0 … 0.0 0.0; 0.0 1.9710054432976252 … 0.0 0.0; … ; 0.0 0.0 … 1.9276513864536091 0.0; 0.0 0.0 … 0.0 1.6930015760093526],)

julia> AD.jacobian(ab, f, x)
([1.3044988022198039 0.0 … 0.0 0.0; 0.0 1.9710054432976252 … 0.0 0.0; … ; 0.0 0.0 … 1.9276513864536091 0.0; 0.0 0.0 … 0.0 1.6930015760093526],)

julia> @benchmark Zygote.jacobian(f, x)
BenchmarkTools.Trial: 7001 samples with 1 evaluation.
 Range (min … max):  629.524 μs …   5.403 ms  ┊ GC (min … max): 0.00% … 87.03%
 Time  (median):     681.270 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   712.290 μs ± 295.183 μs  ┊ GC (mean ± σ):  3.42% ±  6.90%

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  630 μs           Histogram: frequency by time          778 μs <

 Memory estimate: 427.06 KiB, allocs estimate: 4141.

julia> @benchmark AD.jacobian(ab, f, x)
BenchmarkTools.Trial: 1393 samples with 1 evaluation.
 Range (min … max):  2.673 ms … 64.564 ms  ┊ GC (min … max):  0.00% … 94.96%
 Time  (median):     2.999 ms              ┊ GC (median):     0.00%
 Time  (mean ± σ):   3.583 ms ±  4.786 ms  ┊ GC (mean ± σ):  11.42% ±  8.30%

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  2.67 ms      Histogram: log(frequency) by time      8.1 ms <

 Memory estimate: 1.26 MiB, allocs estimate: 28023.

[devmotion]

Possibly, recent changes have already reduced the performance gap. But I assume possibly the original benchmarks in this issues were not completely accurate - note that ab, f, and x are non-constant globals and not interpolated in the @benchmarking. Typically, this leads to incorrectly high number of allocations and incorrectly slow benchmark results (https://juliaci.github.io/BenchmarkTools.jl/stable/manual/#Interpolating-values-into-benchmark-expressions). On the master branch I get

julia> import AbstractDifferentiation as AD

julia> using BenchmarkTools, Zygote

julia> f(x) = x .^ 2
f (generic function with 1 method)

julia> x = rand(100);

julia> ab = AD.ZygoteBackend()
AbstractDifferentiation.ReverseRuleConfigBackend{Zygote.ZygoteRuleConfig{Zygote.Context{false}}}(Zygote.ZygoteRuleConfig{Zygote.Context{false}}(Zygote.Context{false}(nothing)))

julia> Zygote.jacobian(f, x)
([0.09722052175255036 0.0 … 0.0 0.0; 0.0 1.4127603956877295 … 0.0 0.0; … ; 0.0 0.0 … 1.4095040963600012 0.0; 0.0 0.0 … 0.0 0.864262095462434],)

julia> AD.jacobian(ab, f, x)
([0.09722052175255036 0.0 … 0.0 0.0; 0.0 1.4127603956877295 … 0.0 0.0; … ; 0.0 0.0 … 1.4095040963600012 0.0; 0.0 0.0 … 0.0 0.864262095462434],)

julia> @benchmark Zygote.jacobian($f, $x)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  365.542 μs …  2.172 ms  ┊ GC (min … max): 0.00% … 79.38%
 Time  (median):     375.958 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   384.061 μs ± 67.837 μs  ┊ GC (mean ± σ):  1.61% ±  5.99%

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  366 μs          Histogram: frequency by time          437 μs <

 Memory estimate: 416.30 KiB, allocs estimate: 3639.

julia> @benchmark AD.jacobian($ab, $f, $x)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  463.333 μs …  1.184 ms  ┊ GC (min … max): 0.00% … 55.33%
 Time  (median):     474.750 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   482.724 μs ± 58.422 μs  ┊ GC (mean ± σ):  1.46% ±  5.94%

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  463 μs        Histogram: log(frequency) by time       929 μs <

 Memory estimate: 701.36 KiB, allocs estimate: 15919.

[gdalle]

That's reassuring! Indeed I was still a newbie when I did these non-interpolated benchmarks

[devmotion]

IMO it's a bug nevertheless - I'd expect AD.jacobian to just call Zygote.jacobian.