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[WIP] Attempt at adjusting SVD pullback tolerance to make its accuracy independent of the normalization #285

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[WIP] Attempt at adjusting SVD pullback tolerance to make its accuracy independent of the normalization #285

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2 changes: 1 addition & 1 deletion src/Defaults.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -98,7 +98,7 @@ const svd_rrule_tol = ctmrg_tol
const svd_rrule_min_krylovdim = 48
const svd_rrule_verbosity = -1
const svd_rrule_alg = :full # ∈ {:full, :gmres, :bicgstab, :arnoldi}
const svd_rrule_broadening = 1.0e-13
const svd_rrule_broadening = 1.0e-10
const krylovdim_factor = 1.4

# Projectors
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12 changes: 7 additions & 5 deletions src/utility/svd.jl
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Expand Up @@ -346,9 +346,11 @@ function ChainRulesCore.rrule(
U, S, V⁺ = info.U_full, info.S_full, info.V_full # untruncated SVD decomposition

smallest_sval = minimum(((_, b),) -> minimum(diag(b)), blocks(S̃))
tol_scale = norm(S, Inf)
pullback_tol = clamp(
smallest_sval, eps(scalartype(S̃))^(3 / 4), eps(scalartype(S̃))^(1 / 2)
1.0e-2 * smallest_sval, tol_scale * eps(scalartype(S̃))^(3 / 4), tol_scale * eps(scalartype(S̃))^(1 / 2)
)
broadening = tol_scale * alg.rrule_alg.broadening

function svd_trunc!_full_pullback(ΔUSVi)
ΔU, ΔS, ΔV⁺, = unthunk.(ΔUSVi)
Expand All @@ -367,7 +369,7 @@ function ChainRulesCore.rrule(
ΔSdc,
ΔV⁺c;
tol = pullback_tol,
broadening = alg.rrule_alg.broadening,
broadening = broadening,
verbosity = alg.rrule_alg.verbosity,
)
end
Expand All @@ -392,7 +394,7 @@ function ChainRulesCore.rrule(
# update rrule_alg tolerance to be compatible with smallest singular value
rrule_alg = alg.rrule_alg
smallest_sval = minimum(((_, b),) -> minimum(diag(b)), blocks(S))
proper_tol = clamp(rrule_alg.tol, eps(scalartype(S))^(3 / 4), 1.0e-2 * smallest_sval)
proper_tol = clamp(rrule_alg.tol, _default_pullback_gaugetol(S), 1.0e-2 * smallest_sval)
rrule_alg = @set rrule_alg.tol = proper_tol

function svd_trunc!_itersvd_pullback(ΔUSVi)
Expand Down Expand Up @@ -470,12 +472,12 @@ end
# Lorentzian broadening for divergent term in SVD rrule, see
# https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013237
function _lorentz_broaden(x, ε = eps(real(scalartype(x)))^(3 / 4))
return x / (x^2 + ε)
return x / (x^2 + ε^2)
end

function _default_pullback_gaugetol(x)
n = norm(x, Inf)
return eps(eltype(n))^(3 / 4) * max(n, one(n))
return eps(eltype(n))^(3 / 4) * n
end

# SVD_pullback: pullback implementation for general (possibly truncated) SVD
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4 changes: 2 additions & 2 deletions test/utility/svd_wrapper.jl
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Expand Up @@ -47,7 +47,7 @@ end
r_degen = u * s * v

no_broadening_no_cutoff_alg = @set full_alg.rrule_alg.broadening = 1.0e-30
small_broadening_alg = @set full_alg.rrule_alg.broadening = 1.0e-13
small_broadening_alg = @set full_alg.rrule_alg.broadening = 1.0e-10

l_only_cutoff, g_only_cutoff = withgradient(
A -> lossfun(A, full_alg, R, trunc), r_degen
Expand Down Expand Up @@ -101,7 +101,7 @@ end
symm_r_degen = u * s * v

no_broadening_no_cutoff_alg = @set full_alg.rrule_alg.broadening = 1.0e-30
small_broadening_alg = @set full_alg.rrule_alg.broadening = 1.0e-13
small_broadening_alg = @set full_alg.rrule_alg.broadening = 1.0e-10

l_only_cutoff, g_only_cutoff = withgradient(
A -> lossfun(A, full_alg, symm_R, symm_trspace), symm_r_degen
Expand Down