Wrong result when Zygote differentiate through update_coefficient and concretize #305
Description
Describe the bug 🐞
Gradients are inconsistent between matrix-based and operator-based formulations of the same LinearProblem. The primal solutions match, but the operator-based gradient is exactly twice the matrix-based one. This suggests ScalarOperator (or update_coefficients) is double-counting sensitivity in the pullback.
Expected behavior
Gradients of the operator-based and matrix-based formulations should agree.
Minimal Reproducible Example 👇
using LinearSolve, Zygote, SciMLOperators, Test
a1 = rand(3,3); a2 = rand(3,3)
func = p -> exp(1 - p)
a = p -> a1 + func(p) * a2
A1 = MatrixOperator(a1); A2 = MatrixOperator(a2)
Func = ScalarOperator(0.0, (A, u, p, t) -> func(p))
A = A1 + Func * A2
b = rand(3)
function sol1(p)
Ap = update_coefficients(A, 0, p, 0) |> concretize
prob = LinearProblem(Ap, b)
sol = solve(prob, KrylovJL_GMRES())
return sum(sol.u)
end
function sol2(p)
Ap = a(p)
prob = LinearProblem(Ap, b)
sol = solve(prob, KrylovJL_GMRES())
return sum(sol.u)
end
i = rand()
s1, s2 = sol1(i), sol2(i)
@test s1 == s2 # ✅ primal solutions agree
grad1 = Zygote.gradient(sol1, i)[1]
grad2 = Zygote.gradient(sol2, i)[1]
@test grad1 != grad2 # ❌ gradients unexpectedly differ
@test grad1 == 2 * grad2 # ❌ operator version gives exactly doubleError & Stacktrace
No runtime error — all tests pass — but the last two are logically unexpected.
Environment (please complete the following information):
using Pkg; Pkg.status()->
Status `/usr/local/julia-1.11.6/share/julia/environments/v1.11/Project.toml`
[47edcb42] ADTypes v1.17.0
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[14197337] GenericLinearAlgebra v0.3.18
⌃ [7073ff75] IJulia v1.30.1
[42fd0dbc] IterativeSolvers v0.9.4
[682c06a0] JSON v0.21.4
[ba0b0d4f] Krylov v0.10.1
[0b1a1467] KrylovKit v0.10.0
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[0bca4576] SciMLBase v2.113.0 `[https://github.com/SciML/SciMLBase.jl.git#v2.113.0`](https://github.com/SciML/SciMLBase.jl.git#v2.113.0%60)
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[e88e6eb3] Zygote v0.7.10
[37e2e46d] LinearAlgebra v1.11.0
[4607b0f0] SuiteSparse
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)->
Status `/usr/local/julia-1.11.6/share/julia/environments/v1.11/Manifest.toml`
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[62fd8b95] TensorCore v0.1.1
[5d786b92] TerminalLoggers v0.1.7
[b718987f] TextWrap v1.0.2
[8290d209] ThreadingUtilities v0.5.5
[731e570b] TiffImages v0.11.6
[a759f4b9] TimerOutputs v0.5.29
[9f7883ad] Tracker v0.2.38
[e689c965] Tracy v0.1.5
[3bb67fe8] TranscodingStreams v0.11.3
[981d1d27] TriplotBase v0.1.0
[781d530d] TruncatedStacktraces v1.4.0
[c3b1956e] TypeUtils v1.10.0
[5c2747f8] URIs v1.6.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.24.0
[013be700] UnsafeAtomics v0.3.0
[409d34a3] VectorInterface v0.5.0
⌃ [3d5dd08c] VectorizationBase v0.21.71
[81def892] VersionParsing v1.3.0
[e3aaa7dc] WebP v0.1.3
[efce3f68] WoodburyMatrices v1.0.0
[c2297ded] ZMQ v1.4.1
[e88e6eb3] Zygote v0.7.10
[700de1a5] ZygoteRules v0.2.7
[6e34b625] Bzip2_jll v1.0.9+0
[4e9b3aee] CRlibm_jll v1.0.1+0
⌅ [4ee394cb] CUDA_Driver_jll v0.13.1+0
⌅ [76a88914] CUDA_Runtime_jll v0.17.1+0
⌅ [4889d778] CUDSS_jll v0.4.0+0
[83423d85] Cairo_jll v1.18.5+0
[5ae413db] EarCut_jll v2.2.4+0
[7cc45869] Enzyme_jll v0.0.194+0
[2e619515] Expat_jll v2.7.1+0
⌅ [b22a6f82] FFMPEG_jll v6.1.3+0
[f5851436] FFTW_jll v3.3.11+0
[a3f928ae] Fontconfig_jll v2.17.1+0
[d7e528f0] FreeType2_jll v2.13.4+0
[559328eb] FriBidi_jll v1.0.17+0
[b0724c58] GettextRuntime_jll v0.22.4+0
[59f7168a] Giflib_jll v5.2.3+0
[020c3dae] Git_LFS_jll v3.7.0+0
[f8c6e375] Git_jll v2.51.0+0
[7746bdde] Glib_jll v2.84.3+0
[3b182d85] Graphite2_jll v1.3.15+0
[528830af] Gumbo_jll v0.10.2+0
[2e76f6c2] HarfBuzz_jll v8.5.1+0
[905a6f67] Imath_jll v3.1.11+0
[1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
[aacddb02] JpegTurbo_jll v3.1.2+0
[9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
[c1c5ebd0] LAME_jll v3.100.3+0
[88015f11] LERC_jll v4.0.1+0
[dad2f222] LLVMExtra_jll v0.0.37+2
[1d63c593] LLVMOpenMP_jll v18.1.8+0
[dd4b983a] LZO_jll v2.10.3+0
[81d17ec3] L_BFGS_B_jll v3.0.1+0
[ad6e5548] LibTracyClient_jll v0.9.1+6
[e9f186c6] Libffi_jll v3.4.7+0
[7e76a0d4] Libglvnd_jll v1.7.1+1
[94ce4f54] Libiconv_jll v1.18.0+0
[4b2f31a3] Libmount_jll v2.41.1+0
[89763e89] Libtiff_jll v4.7.1+0
[38a345b3] Libuuid_jll v2.41.1+0
[856f044c] MKL_jll v2025.2.0+0
[e98f9f5b] NVTX_jll v3.2.2+0
[e7412a2a] Ogg_jll v1.3.6+0
[6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.29+0
[18a262bb] OpenEXR_jll v3.2.4+0
⌅ [9bd350c2] OpenSSH_jll v9.9.2+0
[458c3c95] OpenSSL_jll v3.5.2+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[91d4177d] Opus_jll v1.5.2+0
[eead6e0c] PRIMA_jll v0.7.1+0
[36c8627f] Pango_jll v1.56.3+0
⌅ [30392449] Pixman_jll v0.44.2+0
[f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.3+0
[ffd25f8a] XZ_jll v5.8.1+0
[4f6342f7] Xorg_libX11_jll v1.8.12+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+0
[a3789734] Xorg_libXdmcp_jll v1.1.6+0
[1082639a] Xorg_libXext_jll v1.3.7+0
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[8f1865be] ZeroMQ_jll v4.3.6+0
[3161d3a3] Zstd_jll v1.5.7+1
[1e29f10c] demumble_jll v1.3.0+0
[9a68df92] isoband_jll v0.2.3+0
[a4ae2306] libaom_jll v3.12.1+0
[0ac62f75] libass_jll v0.17.4+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[b53b4c65] libpng_jll v1.6.50+0
[47bcb7c8] libsass_jll v3.6.6+0
[075b6546] libsixel_jll v1.10.5+0
[a9144af2] libsodium_jll v1.0.21+0
[f27f6e37] libvorbis_jll v1.3.8+0
[c5f90fcd] libwebp_jll v1.6.0+0
[1317d2d5] oneTBB_jll v2022.0.0+0
[1270edf5] x264_jll v10164.0.1+0
[dfaa095f] x265_jll v4.1.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[8bf52ea8] CRC32c v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.11.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.5+0
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
versioninfo()->
Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 144 × Intel(R) Xeon(R) Gold 6240L CPU @ 2.60GHz
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, cascadelake)
Threads: 1 default, 0 interactive, 1 GC (on 144 virtual cores)
Additional context
This seems related to the AD rules for ScalarOperator or update_coefficients. Zygote handles the plain matrix case correctly, so the inconsistency likely originates in SciMLOperators’ ChainRules definitions.