Directly call ForwardDiff to compute the hessian
#1270
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Reverse mode over the Hessian julia> function f1(x, ps) # [edit: renamed not to clash]
hess = Zygote.hessian(x->sum(x.^3), x)
return hess * x .+ ps.bias
end
f1 (generic function with 1 method)
julia> x = rand(3);
julia> ps = (;bias = rand(3));
julia> Zygote.gradient(p -> sum(f1(x,p)), ps)
((bias = Fill(1.0, 3),),)Forward mode over the Hessian julia> using ComponentArrays, ForwardDiff
julia> ForwardDiff.gradient(p -> sum(f1(x,p)), ComponentArray(ps))
ComponentVector{Float64}(bias = [1.0, 1.0, 1.0]) |
YichengDWu
changed the title
ForwardDiff to compute the hessian
|
Looks like it wasn't a complicated fix after all! Could you add one of the examples from #1264 or elsewhere as a regression test? |
using ForwardDiff, Zygote, BenchmarkTools
f(x,W) = sum((W.^3)*x)
x = randn(30);
W = randn(128,30);
@benchmark Zygote.hessian(W->f($x,W), $W)
BenchmarkTools.Trial: 13 samples with 1 evaluation.
Range (min … max): 210.955 ms … 555.882 ms ┊ GC (min … max): 6.64% … 41.61%
Time (median): 312.789 ms ┊ GC (median): 13.30%
Time (mean ± σ): 386.835 ms ± 135.648 ms ┊ GC (mean ± σ): 30.41% ± 16.92%
▁ ▁█ ▁▁ ▁ ▁ ▁█ █
█▁▁▁▁▁▁▁██▁▁██▁▁▁▁█▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█▁▁▁▁██▁▁▁▁▁█ ▁
211 ms Histogram: frequency by time 556 ms <
Memory estimate: 851.09 MiB, allocs estimate: 8324.
hessian_dual(f, x::AbstractArray) = ForwardDiff.jacobian(x -> gradient(f, x)[1], x)
@benchmark hessian_dual(W->f($x,W),$W)
BenchmarkTools.Trial: 34 samples with 1 evaluation.
Range (min … max): 107.892 ms … 426.180 ms ┊ GC (min … max): 11.03% … 51.18%
Time (median): 133.778 ms ┊ GC (median): 12.17%
Time (mean ± σ): 149.663 ms ± 62.519 ms ┊ GC (mean ± σ): 19.00% ± 10.50%
▆██▄
▄▄▆████▄▁▄▁▁▁▁▁▁▁▁▁▁▄▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄ ▁
108 ms Histogram: frequency by time 426 ms <
Memory estimate: 607.80 MiB, allocs estimate: 9604. |
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Great acceleration! |
DhairyaLGandhi
approved these changes
Jul 23, 2022
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Sorry, I meant to add a test which fails on the current implementation but works on this PR. IIRC you had a couple, @MilkshakeForReal. |
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It's also possible that we might lose out on some code paths that worked
with Zygote via `forward_jacobian` since we could switch it out to using
Zygote without breaking API.
…On Sun, Jul 24, 2022, 08:01 Brian Chen ***@***.***> wrote:
Sorry, I meant to add a test which fails on the current implementation but
works on this PR. IIRC you had a couple, @MilkshakeForReal
<https://github.com/MilkshakeForReal>.
—
Reply to this email directly, view it on GitHub
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Related to #1070 edit: don't close it since julia> using CUDA
julia> CUDA.allowscalar(false)
julia> hessian(x -> sum(tanh.(x)), cu([1,2,3.4]))
ERROR: Scalar indexing is disallowed.
Invocation of getindex resulted in scalar indexing of a GPU array.
This is typically caused by calling an iterating implementation of a method.
Such implementations *do not* execute on the GPU, but very slowly on the CPU,
and therefore are only permitted from the REPL for prototyping purposes.
If you did intend to index this array, annotate the caller with @allowscalar.
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:33
[2] assertscalar(op::String)
@ GPUArraysCore C:\Users\Luffy\.julia\packages\GPUArraysCore\rSIl2\src\GPUArraysCore.jl:78
[3] getindex
@ C:\Users\Luffy\.julia\packages\GPUArrays\gok9K\src\host\indexing.jl:9 [inlined]
[4] extract(xs::CuArray{ForwardDiff.Dual{Nothing, Float32, 3}, 1, CUDA.Mem.DeviceBuffer})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:23
[5] forward_jacobian(f::Zygote.var"#100#101"{var"#27#28"}, x::CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, #unused#::Val{3})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:29
[6] forward_jacobian(f::Function, x::CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}; chunk_threshold::Int64)
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:44
[7] forward_jacobian
@ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:43 [inlined]
[8] hessian_dual
@ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\grad.jl:76 [inlined]
[9] hessian(f::Function, x::CuArray{Float32, 1, CUDA.Mem.DeviceBuffer})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\grad.jl:74
[10] top-level scope
@ REPL[135]:1
[11] top-level scope
@ C:\Users\Luffy\.julia\packages\CUDA\DfvRa\src\initialization.jl:52
julia> hessian_dual(x -> sum(tanh.(x)), cu([1,2,3.4]))
3×3 CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
-0.6397 0.0 0.0
0.0 -0.136219 0.0
0.0 0.0 -0.00887072 |
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I'm digging into the issues and haven't found one case where |
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This issue #305 is closed but I'm still getting an error using Zygote
f(x) = [cos(x[1]) * sin(x[2]), sin(x[1]) * cos(x[2])]
jac(x) = last(Zygote.forward_jacobian(f, x))
g(x) = sum(jac(x))
x = [π/4, π/3]
Zygote.gradient(g, x)
julia> Zygote.gradient(g, x)
ERROR: Mutating arrays is not supported -- called setindex!(Matrix{Float64}, ...)
This error occurs when you ask Zygote to differentiate operations that change
the elements of arrays in place (e.g. setting values with x .= ...)
Possible fixes:
- avoid mutating operations (preferred)
- or read the documentation and solutions for this error
https://fluxml.ai/Zygote.jl/dev/limitations.html#Array-mutation-1
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:33
[2] _throw_mutation_error(f::Function, args::Matrix{Float64})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\array.jl:70
[3] (::Zygote.var"#444#445"{Matrix{Float64}})(#unused#::Nothing)
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\array.jl:82
[4] (::Zygote.var"#2496#back#446"{Zygote.var"#444#445"{Matrix{Float64}}})(Δ::Nothing)
@ Zygote C:\Users\Luffy\.julia\packages\ZygoteRules\AIbCs\src\adjoint.jl:67
[5] Pullback
@ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:31 [inlined]
[6] (::typeof(∂(forward_jacobian)))(Δ::Tuple{Nothing, FillArrays.Fill{Float64, 2, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
[7] Pullback
@ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:44 [inlined]
[8] Pullback
@ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\forward.jl:43 [inlined]
[9] (::typeof(∂(forward_jacobian)))(Δ::Tuple{Nothing, FillArrays.Fill{Float64, 2, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
[10] Pullback
@ .\REPL[190]:1 [inlined]
[11] (::typeof(∂(jac)))(Δ::FillArrays.Fill{Float64, 2, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
[12] Pullback
@ .\REPL[191]:1 [inlined]
[13] (::Zygote.var"#60#61"{typeof(∂(g))})(Δ::Float64)
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface.jl:41
[14] gradient(f::Function, args::Vector{Float64})
@ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface.jl:76
[15] top-level scope
@ REPL[193]:1
[16] top-level scope
@ C:\Users\Luffy\.julia\packages\CUDA\DfvRa\src\initialization.jl:52
Now try julia> jac(x) = last(ForwardDiff.jacobian(f, x))
jac (generic function with 1 method)
julia> Zygote.gradient(g, x)
([-0.6123724356957946, -0.3535533905932738],) |
mcabbott
reviewed
Jul 26, 2022
| @@ -73,8 +73,7 @@ julia> hessian(sin, pi/2) | |||
| """ | |||
| hessian(f, x) = hessian_dual(f, x) | |||
|
|
|||
| hessian_dual(f, x::AbstractArray) = forward_jacobian(x -> gradient(f, x)[1], x)[2] | |||
|
|
|||
| hessian_dual(f, x::AbstractArray) = ForwardDiff.jacobian(x -> gradient(f, x)[1], x) | |||
There was a problem hiding this comment.
The example you test relies on the gradient rule for ForwardDiff.jacobian, which assumes its f is pure. This is true here.
It would be worth trying to look at some examples where this isn't true, i.e. f closes over some parameters (either arrays or numbers). In this case their gradients are not traced. I believe you should get a warning from ForwardDiff.jacobian's rule.
Are there any further surprises? Anything which could be tested?
There was a problem hiding this comment.
Did you mean nn layers from Flux? I will dig in a bit tomorrow.
The scalar indexing in the above comment can be added to testing as well.
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is this still active? |
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@YichengDWu did this solve the GPU issue? |
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@vpuri3 I'm no longer active in the Julia community. However, the "fix" in this PR is simple, you can surely test it out. |
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Thanks for letting me know @YichengDWu. The change works with Lux.jl, but I'm still getting scalar indexing errors on the GPU. |
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with the change in this PR, this code is working: using Random
using Lux, CUDA, LuxCUDA, ComponentArrays
using Zygote, ForwardDiff
CUDA.allowscalar(false)
#==========================#
function testhessian(
NN::Lux.AbstractExplicitLayer,
data::Tuple;
device = cpu_device(),
)
p, st = Lux.setup(Random.default_rng(), NN)
st = Lux.testmode(st)
p = ComponentArray(p)
xdata, ydata = data |> device
p, st = (p, st) |> device
function loss(optx)
ypred, _ = NN(xdata, optx, st)
sum(abs2, ydata - ypred)
end
g(p) = Zygote.gradient(loss, p)[1]
H(p) = ForwardDiff.jacobian(g, p)
Zygote.hessian(loss, p)
end
#==========================#
NN = Chain(Dense(1, 3), Dense(3, 1))
data = ntuple(_ -> rand(1, 10), 2)
device = Lux.gpu_device()
H = testhessian(NN, data; device)julia> include("hess.jl")
10×10 CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
0.236781 -0.075257 -1.20583 0.31846 -0.101217 -1.62179 -0.713834 0.503548 -1.14138 1.98508
-0.075257 0.0239192 0.383253 -0.101217 0.0321702 0.515458 0.0296168 -0.780695 0.362769 -0.630924
-1.20583 0.383253 6.1408 -1.62179 0.515458 8.2591 0.474545 -2.56436 5.19194 -10.1092
0.318461 -0.101217 -1.62179 0.514738 -0.163601 -2.62135 -2.09317 0.677249 -1.53511 3.20854
-0.101217 0.0321702 0.515458 -0.163601 0.0519977 0.833151 0.0398333 -2.18309 0.487909 -1.01978
-1.62179 0.515458 8.2591 -2.62135 0.833151 13.3494 0.638242 -3.44895 5.84984 -16.3398
-0.713834 0.0296168 0.474545 -2.09317 0.0398333 0.638242 0.0366717 -0.198167 0.449183 -0.781213
0.503548 -0.780695 -2.56436 0.677249 -2.18309 -3.44895 -0.198167 1.07086 -2.4273 4.22154
-1.14138 0.362769 5.19194 -1.53511 0.487909 5.84984 0.449183 -2.4273 5.50193 -9.56889
1.98508 -0.630924 -10.1092 3.20854 -1.01978 -16.3398 -0.781213 4.22154 -9.56889 20.0(hess) pkg> st
Status `~/.julia/dev/GeometryLearning.jl/hess/Project.toml`
[052768ef] CUDA v5.0.0
[b0b7db55] ComponentArrays v0.15.4
[f6369f11] ForwardDiff v0.10.36
[b2108857] Lux v0.5.8
[d0bbae9a] LuxCUDA v0.3.1
[e88e6eb3] Zygote v0.6.67 `~/.julia/dev/Zygote` |
|
But using Random
using Lux, CUDA, LuxCUDA, ComponentArrays
using Zygote, ForwardDiff
CUDA.allowscalar(false)
#==========================#
function testhessian(
NN::Lux.AbstractExplicitLayer,
data::Tuple;
device = cpu_device(),
)
p, st = Lux.setup(Random.default_rng(), NN)
st = Lux.testmode(st)
p = ComponentArray(p)
xdata, ydata = data |> device
p, st = (p, st) |> device
function loss(optx)
ypred, _ = NN(xdata, optx, st)
sum(abs2, ydata - ypred)
end
g(p) = Zygote.gradient(loss, p)[1]
H(p) = ForwardDiff.jacobian(g, p)
Zygote.hessian(loss, p)
end
#==========================#
NN = Chain(Dense(1, 3), Dense(3, 1))
E, K = 1, 10
NN = Chain(Embedding(E => 3), Dense(3, 1))
data = (ones(Int32, K), rand(1, K))
H = testhessian(NN, data; device)
julia> include("hess.jl")
ERROR: LoadError: InvalidIRError: compiling MethodInstance for NNlibCUDAExt.scatter_kernel!(::typeof(+), ::CuDeviceMatrix{…}, ::CuDeviceMatrix{…}, ::CuDeviceVector{…},
::Int64, ::Int64, ::Tuple{…}) resulted in invalid LLVM IR
Reason: unsupported call to an unknown function (call to julia.new_gc_frame)
Reason: unsupported call to an unknown function (call to julia.push_gc_frame)
Reason: unsupported call to an unknown function (call to julia.pop_gc_frame)
Reason: unsupported call to an unknown function (call to julia.get_gc_frame_slot)
Reason: unsupported dynamic function invocation (call to atomic_cas!)
Stacktrace:
[1] atomic_op!
@ ~/.julia/packages/CUDA/nbRJk/src/device/intrinsics/atomics.jl:228
[2] atomic_arrayset
@ ~/.julia/packages/CUDA/nbRJk/src/device/intrinsics/atomics.jl:468
[3] atomic_arrayset
@ ~/.julia/packages/CUDA/nbRJk/src/device/intrinsics/atomics.jl:440
[4] macro expansion
@ ~/.julia/packages/CUDA/nbRJk/src/device/intrinsics/atomics.jl:435
[5] scatter_kernel!
@ ~/.julia/packages/NNlib/5iRSB/ext/NNlibCUDAExt/scatter.jl:28
Hint: catch this exception as `err` and call `code_typed(err; interactive = true)` to introspect the erronous code with Cthulhu.jl
Stacktrace:
[1] check_ir(job::GPUCompiler.CompilerJob{GPUCompiler.PTXCompilerTarget, CUDA.CUDACompilerParams}, args::LLVM.Module)
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/validation.jl:147
[2] macro expansion
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:440 [inlined]
[3] macro expansion
@ GPUCompiler ~/.julia/packages/TimerOutputs/RsWnF/src/TimerOutput.jl:253 [inlined]
[4] macro expansion
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:439 [inlined]
[5] emit_llvm(job::GPUCompiler.CompilerJob; libraries::Bool, toplevel::Bool, optimize::Bool, cleanup::Bool, only_entry::Bool, validate::Bool)
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/utils.jl:92
[6] emit_llvm
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/utils.jl:86 [inlined]
[7]
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:129
[8] codegen
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:110 [inlined]
[9] compile(target::Symbol, job::GPUCompiler.CompilerJob; libraries::Bool, toplevel::Bool, optimize::Bool, cleanup::Bool, strip::Bool, validate::Bool, only_entry::Boo
l)
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:106
[10] compile
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:98 [inlined]
[11] #1042
@ GPUCompiler ~/.julia/packages/CUDA/nbRJk/src/compiler/compilation.jl:166 [inlined]
[12] JuliaContext(f::CUDA.var"#1042#1045"{GPUCompiler.CompilerJob{GPUCompiler.PTXCompilerTarget, CUDA.CUDACompilerParams}})
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/driver.jl:47
[13] compile(job::GPUCompiler.CompilerJob)
@ CUDA ~/.julia/packages/CUDA/nbRJk/src/compiler/compilation.jl:165
[14] actual_compilation(cache::Dict{…}, src::Core.MethodInstance, world::UInt64, cfg::GPUCompiler.CompilerConfig{…}, compiler::typeof(CUDA.compile), linker::typeof(CUD
A.link)) @ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/execution.jl:125
[15] cached_compilation(cache::Dict{…}, src::Core.MethodInstance, cfg::GPUCompiler.CompilerConfig{…}, compiler::Function, linker::Function)
@ GPUCompiler ~/.julia/packages/GPUCompiler/2mJjc/src/execution.jl:103
[16] macro expansion
@ CUDA ~/.julia/packages/CUDA/nbRJk/src/compiler/execution.jl:323 [inlined]
[17] macro expansion
@ CUDA ./lock.jl:267 [inlined]
[18] cufunction(f::typeof(NNlibCUDAExt.scatter_kernel!), tt::Type{Tuple{…}}; kwargs::@Kwargs{})
@ CUDA ~/.julia/packages/CUDA/nbRJk/src/compiler/execution.jl:318
[19] cufunction
@ NNlibCUDAExt ~/.julia/packages/CUDA/nbRJk/src/compiler/execution.jl:315 [inlined]
[20] macro expansion
@ NNlibCUDAExt ~/.julia/packages/CUDA/nbRJk/src/compiler/execution.jl:104 [inlined]
[21] scatter!(op::typeof(+), dst::CuArray{…}, src::CuArray{…}, idx::CuArray{…})
@ NNlibCUDAExt ~/.julia/packages/NNlib/5iRSB/ext/NNlibCUDAExt/scatter.jl:58
[22] ∇gather_src @ Zygote ~/.julia/packages/NNlib/5iRSB/src/gather.jl:131 [inlined]
[23] gather!_pullback
@ Zygote ~/.julia/packages/NNlib/5iRSB/src/gather.jl:136 [inlined]
[24] ZBack
@ Zygote ~/.julia/dev/Zygote/src/compiler/chainrules.jl:211 [inlined] [25] gather
@ Zygote ~/.julia/packages/NNlib/5iRSB/src/gather.jl:46 [inlined]
[26] Embedding
@ Zygote ~/.julia/packages/Lux/Al3Ab/src/layers/basic.jl:490 [inlined]
[27] apply
@ Zygote ~/.julia/packages/LuxCore/aumFq/src/LuxCore.jl:115 [inlined] [28] macro expansion
@ Zygote ~/.julia/packages/Lux/Al3Ab/src/layers/containers.jl:0 [inlined]
[29] applychain
@ Zygote ~/.julia/packages/Lux/Al3Ab/src/layers/containers.jl:480 [inlined]
[30] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Tuple{CuArray{…}, Nothing})
@ Zygote ~/.julia/dev/Zygote/src/compiler/interface2.jl:0
[31] Chain
@ Zygote ~/.julia/packages/Lux/Al3Ab/src/layers/containers.jl:478 [inlined]
[32] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Tuple{CuArray{…}, Nothing}) @ Zygote ~/.julia/dev/Zygote/src/compiler/interface2.jl:0
[33] loss
@ Zygote ~/.julia/dev/GeometryLearning.jl/hess/hess.jl:23 [inlined]
[34] (::Zygote.Pullback{Tuple{var"#loss#34"{…}, ComponentVector{…}}, Any})(Δ::ForwardDiff.Dual{ForwardDiff.Tag{Zygote.var"#125#126"{…}, Float32}, Float32, 7})
@ Zygote ~/.julia/dev/Zygote/src/compiler/interface2.jl:0 |
|
I narrowed the error in the above case to the MWE in FluxML/NNlib.jl#547. That doesn't seem related to this PR. |
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Closes #1264
Zygote.forward_jacobianis not well maintained and the motivation for using it is not clear.