def rotated_gradient(self, basis, sample):
r"""Computes the gradients rotated into the measurement basis
:param basis: The bases in which the measurement is made
:type basis: numpy.ndarray
:param sample: The measurement (either 0 or 1)
:type sample: torch.Tensor
:returns: A list of two tensors, representing the rotated gradients
of the amplitude and phase RBMs
:rtype: list[torch.Tensor, torch.Tensor]
"""
UrhoU, UrhoU_v, v = unitaries.rotate_rho_probs(self,
basis,
sample,
include_extras=True)
inv_UrhoU = 1 / (UrhoU + 1e-8) # avoid dividing by zero
raw_grads = [self.am_grads(v), self.ph_grads(v)]
rotated_grad = [
-cplx.einsum("ijb,ijbg->bg", UrhoU_v, g, imag_part=False)
for g in raw_grads
]
return [torch.einsum("b,bg->g", inv_UrhoU, g) for g in rotated_grad]
def test_rotate_rho_probs(num_visible, state_type, precompute_rho):
nn_state = state_type(num_visible, gpu=False)
basis = "X" * num_visible
unitary_dict = create_dict()
space = nn_state.generate_hilbert_space()
rho = nn_state.rho(space, expand=True) if precompute_rho else None
rho_r = rotate_rho(nn_state, basis, space, unitary_dict, rho=rho)
rho_r_probs = torch.diagonal(cplx.real(rho_r))
rho_r_probs_fast = rotate_rho_probs(nn_state,
basis,
space,
unitary_dict,
rho=rho)
# use different tolerance as this sometimes just barely breaks through the
# smaller TOL value from test_grads.py
assertAlmostEqual(
rho_r_probs,
rho_r_probs_fast,
tol=(TOL * 10),
msg="Fast rho probs rotation failed!",
)
def NLL(nn_state, samples, space=None, sample_bases=None, **kwargs):
r"""A function for calculating the negative log-likelihood (NLL).
:param nn_state: The neural network state.
:type nn_state: qucumber.nn_states.NeuralStateBase
:param samples: Samples to compute the NLL on.
:type samples: torch.Tensor
:param space: The basis elements of the Hilbert space of the system :math:`\mathcal{H}`.
If `None`, will generate them using the provided `nn_state`.
:type space: torch.Tensor
:param sample_bases: An array of bases where measurements were taken.
:type sample_bases: numpy.ndarray
:param \**kwargs: Extra keyword arguments that may be passed. Will be ignored.
:returns: The Negative Log-Likelihood.
:rtype: float
"""
space = space if space is not None else nn_state.generate_hilbert_space()
Z = nn_state.normalization(space)
if sample_bases is None:
nn_probs = nn_state.probability(samples, Z)
NLL_ = -torch.mean(probs_to_logits(nn_probs)).item()
return NLL_
else:
NLL_ = 0.0
unique_bases, indices = np.unique(sample_bases,
axis=0,
return_inverse=True)
indices = torch.Tensor(indices).to(samples)
for i in range(unique_bases.shape[0]):
basis = unique_bases[i, :]
rot_sites = np.where(basis != "Z")[0]
if rot_sites.size != 0:
if isinstance(nn_state, WaveFunctionBase):
Upsi = rotate_psi_inner_prod(nn_state, basis,
samples[indices == i, :])
nn_probs = (cplx.absolute_value(Upsi)**2) / Z
else:
nn_probs = (rotate_rho_probs(nn_state, basis,
samples[indices == i, :]) / Z)
else:
nn_probs = nn_state.probability(samples[indices == i, :], Z)
NLL_ -= torch.sum(probs_to_logits(nn_probs))
return NLL_ / float(len(samples))
def algorithmic_gradKL(self, target, space, all_bases, **kwargs):
grad_KL = [
torch.zeros(
self.nn_state.rbm_am.num_pars,
dtype=torch.double,
device=self.nn_state.device,
),
torch.zeros(
self.nn_state.rbm_ph.num_pars,
dtype=torch.double,
device=self.nn_state.device,
),
]
Z = self.nn_state.normalization(space)
for b in range(len(all_bases)):
if isinstance(target, dict):
target_r = target[all_bases[b]]
target_r = torch.diagonal(cplx.real(target_r))
else:
target_r = rotate_rho_probs(
self.nn_state, all_bases[b], space, rho=target
)
for i in range(len(space)):
rotated_grad = self.nn_state.gradient(space[i], all_bases[b])
grad_KL[0] += target_r[i] * rotated_grad[0] / float(len(all_bases))
grad_KL[1] += target_r[i] * rotated_grad[1] / float(len(all_bases))
probs = self.nn_state.probability(space, Z)
all_grads = self.nn_state.rbm_am.effective_energy_gradient(space, reduce=False)
grad_KL[0] -= torch.mv(
all_grads.t(), probs
) # average the gradients, weighted by probs
return grad_KL
def KL(nn_state, target, space=None, bases=None, **kwargs):
r"""A function for calculating the KL divergence averaged over every given
basis.
.. math:: KL(P_{target} \vert P_{RBM}) = -\sum_{x \in \mathcal{H}} P_{target}(x)\log(\frac{P_{RBM}(x)}{P_{target}(x)})
:param nn_state: The neural network state.
:type nn_state: qucumber.nn_states.NeuralStateBase
:param target: The true state (wavefunction or density matrix) of the system.
Can be a dictionary with each value being the state
represented in a different basis, and the key identifying the basis.
:type target: torch.Tensor or dict(str, torch.Tensor)
:param space: The basis elements of the Hilbert space of the system :math:`\mathcal{H}`.
The ordering of the basis elements must match with the ordering of the
coefficients given in `target`. If `None`, will generate them using
the provided `nn_state`.
:type space: torch.Tensor
:param bases: An array of unique bases. If given, the KL divergence will be
computed for each basis and the average will be returned.
:type bases: numpy.ndarray
:param \**kwargs: Extra keyword arguments that may be passed. Will be ignored.
:returns: The KL divergence.
:rtype: float
"""
space = space if space is not None else nn_state.generate_hilbert_space()
Z = nn_state.normalization(space)
if isinstance(target, dict):
target = {k: v.to(nn_state.device) for k, v in target.items()}
if bases is None:
bases = list(target.keys())
else:
assert set(bases) == set(target.keys(
)), "Given bases must match the keys of the target_psi dictionary."
else:
target = target.to(nn_state.device)
KL = 0.0
if bases is None:
target_probs = cplx.absolute_value(target)**2
nn_probs = nn_state.probability(space, Z)
KL += _single_basis_KL(target_probs, nn_probs)
elif isinstance(nn_state, WaveFunctionBase):
for basis in bases:
if isinstance(target, dict):
target_psi_r = target[basis]
assert target_psi_r.dim(
) == 2, "target must be a complex vector!"
else:
assert target.dim() == 2, "target must be a complex vector!"
target_psi_r = rotate_psi(nn_state, basis, space, psi=target)
psi_r = rotate_psi(nn_state, basis, space)
nn_probs_r = (cplx.absolute_value(psi_r)**2) / Z
target_probs_r = cplx.absolute_value(target_psi_r)**2
KL += _single_basis_KL(target_probs_r, nn_probs_r)
KL /= float(len(bases))
else:
for basis in bases:
if isinstance(target, dict):
target_rho_r = target[basis]
assert target_rho_r.dim(
) == 3, "target must be a complex matrix!"
target_probs_r = torch.diagonal(cplx.real(target_rho_r))
else:
assert target.dim() == 3, "target must be a complex matrix!"
target_probs_r = rotate_rho_probs(nn_state,
basis,
space,
rho=target)
rho_r = rotate_rho_probs(nn_state, basis, space)
nn_probs_r = rho_r / Z
KL += _single_basis_KL(target_probs_r, nn_probs_r)
KL /= float(len(bases))
return KL.item()