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Add forward mode differentiation for torch.linalg.cholesky and transpose #62159

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Add forward mode differentiation for torch.linalg.cholesky and transpose #62159

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72b08ba
Add cholesky forward mode differentiation
IvanYashchuk Jul 25, 2021
4344fa5
Use const Tensor&
IvanYashchuk Jul 25, 2021
9478095
Merge remote-tracking branch 'upstream/master' into cholesky-jvp
IvanYashchuk Jul 28, 2021
0e17d8b
Merge remote-tracking branch 'upstream/master' into cholesky-jvp
IvanYashchuk Sep 6, 2021
14dcdec
Add upper kwarg support to forward ad rule
IvanYashchuk Sep 6, 2021
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1 change: 1 addition & 0 deletions tools/autograd/derivatives.yaml
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Original file line number Diff line number Diff line change
Expand Up @@ -339,6 +339,7 @@

- name: linalg_cholesky_ex(Tensor self, *, bool upper=False, bool check_errors=False) -> (Tensor L, Tensor info)
self: cholesky_backward(grad, upper, L)
L: cholesky_jvp(self_t, L, upper)

- name: cholesky_solve(Tensor self, Tensor input2, bool upper=False) -> Tensor
self, input2: cholesky_solve_backward(grad, self, input2, result, upper)
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14 changes: 14 additions & 0 deletions torch/csrc/autograd/FunctionsManual.cpp
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Expand Up @@ -1006,6 +1006,20 @@ Tensor masked_scatter_backward(const Tensor & grad, const Tensor & mask, IntArra
return mask_selected.view(sizes);
}

Tensor cholesky_jvp(const Tensor& input_tangent, const Tensor& L, bool upper) {
// Differentiation of the Cholesky decomposition, Iain Murray
// https://arxiv.org/abs/1602.07527
// equation 8
auto input_tangent_ = upper ? input_tangent.transpose(-1, -2).conj() : input_tangent;
auto L_ = upper ? L.transpose(-1, -2).conj() : L;

auto L_inverse = std::get<0>(at::triangular_solve(at::eye(L.size(-1), L.options()), L_, /*upper=*/false));
auto phi = at::matmul(at::matmul(L_inverse, input_tangent_), L_inverse.transpose(-2, -1).conj());
phi.tril_().diagonal(/*offset=*/0, /*dim1=*/-2, /*dim2=*/-1).mul_(0.5);
auto L_tangent = L_.matmul(phi);
return upper ? L_tangent.transpose(-1, -2).conj() : L_tangent;
}

Tensor cholesky_backward(Tensor grad, bool upper, Tensor L) {
// cf. Iain Murray (2016); arXiv 1602.07527
// This gradient is symmetric, and not triangular.
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1 change: 1 addition & 0 deletions torch/csrc/autograd/FunctionsManual.h
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Expand Up @@ -101,6 +101,7 @@ at::Tensor mean_backward(at::Tensor grad, const at::IntArrayRef sizes, int64_t n
at::Tensor var_std_mean_backward(const variable_list& grads, const at::Tensor& self, const at::Tensor& r1, const at::Tensor& r2, c10::optional<IntArrayRef> dim, c10::optional<int64_t> correction, bool keepdim, bool is_std);
at::Tensor masked_scatter_backward(const at::Tensor & grad, const at::Tensor & mask, at::IntArrayRef sizes);
at::Tensor cholesky_backward(at::Tensor grad, bool upper, at::Tensor L);
at::Tensor cholesky_jvp(const at::Tensor& input_tangent, const at::Tensor& L, bool upper);
at::Tensor cholesky_inverse_backward(at::Tensor grad, at::Tensor L, bool upper, at::Tensor inverse);
at::Tensor split_with_sizes_backward(const std::vector<torch::autograd::Variable> &grads,
IntArrayRef split_sizes, int64_t dim, IntArrayRef sizes, const at::TensorOptions &options);
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12 changes: 9 additions & 3 deletions torch/testing/_internal/common_methods_invocations.py
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Expand Up @@ -3494,10 +3494,10 @@ def sample_inputs_linalg_cholesky(op_info, device, dtype, requires_grad=False, *
batches = [(), (0, ), (2, ), (1, 1)]
ns = [5, 0]
out = []
for batch, n in product(batches, ns):
for batch, n, upper in product(batches, ns, [True, False]):
a = random_hermitian_pd_matrix(n, *batch, dtype=dtype, device=device)
a.requires_grad = requires_grad
out.append(SampleInput(a))
out.append(SampleInput(a, kwargs={"upper": upper}))
return out

def sample_inputs_symeig(op_info, device, dtype, requires_grad=False):
Expand Down Expand Up @@ -6804,6 +6804,7 @@ def gradcheck_wrapper_triangular_input(op, input, *args, upper=False, **kwargs):
# got: vmap: Calling Tensor.as_strided is not supported
# unless the batch dims being vmapped over are at the front of the tensor (in memory layout).
check_batched_gradgrad=False,
supports_forward_ad=True,
sample_inputs_func=sample_inputs_linalg_cholesky,
gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
Expand All @@ -6817,9 +6818,14 @@ def gradcheck_wrapper_triangular_input(op, input, *args, upper=False, **kwargs):
aten_name='linalg_cholesky_ex',
dtypes=floating_and_complex_types(),
check_batched_gradgrad=False,
supports_forward_ad=True,
sample_inputs_func=sample_inputs_linalg_cholesky,
gradcheck_wrapper=gradcheck_wrapper_hermitian_input,
decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack]),
decorators=[skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfRocm, skipCPUIfNoLapack],
skips=(
# Gradcheck for complex generates invalid inputs for this function
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@lezcano lezcano Jul 26, 2021

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Might this be because it does not create Hermitian inputs? It's not clear whether we can assume that the inputs are Hermitian or not. See #62163 (comment)

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@albanD albanD Jul 26, 2021

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Ho yes, I encountered that one but forgot to fix it.
We should update

pytorch/torch/autograd/gradcheck.py

Line 925 in b73d759

return apply_to_c_inps(fn, lambda x: x + 0 * 1j), apply_to_c_inps(fn, lambda x: x * 1j)
to make it keep the original imag/real respectively instead of setting them to 0s.

SkipInfo('TestGradients', 'test_forward_mode_AD', dtypes=complex_types()),),
),
OpInfo('linalg.cond',
aten_name='linalg_cond',
dtypes=floating_and_complex_types(),
Expand Down