def expand_dims_(x):
"""Implementation of `expand_dims`."""
with tf.name_scope(name or 'expand_dims'):
x = tf.convert_to_tensor(x, name='x')
new_axis = tf.convert_to_tensor(axis,
dtype_hint=tf.int32,
name='axis')
nx = prefer_static.rank(x)
na = prefer_static.size(new_axis)
is_neg_axis = new_axis < 0
k = prefer_static.reduce_sum(
prefer_static.cast(is_neg_axis, new_axis.dtype))
new_axis = prefer_static.where(is_neg_axis, new_axis + nx,
new_axis)
new_axis = prefer_static.sort(new_axis)
axis_neg, axis_pos = prefer_static.split(new_axis, [k, -1])
idx = prefer_static.argsort(prefer_static.concat([
axis_pos,
prefer_static.range(nx),
axis_neg,
],
axis=0),
stable=True)
shape = prefer_static.pad(prefer_static.shape(x),
paddings=[[na - k, k]],
constant_values=1)
shape = prefer_static.gather(shape, idx)
return tf.reshape(x, shape)
def _forward_event_shape_tensor(self, input_shape, is_inverse=False):
ndims = ps.size(input_shape)
indices = ps.reshape(ps.add(self.axis, ndims), shape=[-1, 1])
extra_sizes = ps.reduce_sum(self.paddings, axis=-1)
update_fn = (ps.tensor_scatter_nd_sub if is_inverse else
ps.tensor_scatter_nd_add)
return update_fn(ps.identity(input_shape), indices, extra_sizes)
def moments_of_masked_time_series(time_series_tensor, broadcast_mask):
"""Compute mean and variance, accounting for a mask.
Args:
time_series_tensor: float `Tensor` time series of shape
`concat([batch_shape, [num_timesteps]])`.
broadcast_mask: bool `Tensor` of the same shape as `time_series`.
Returns:
mean: float `Tensor` of shape `batch_shape`.
variance: float `Tensor` of shape `batch_shape`.
"""
num_unmasked_entries = ps.cast(
ps.reduce_sum(ps.cast(~broadcast_mask, np.int32), axis=-1),
time_series_tensor.dtype)
# Manually compute mean and variance, excluding masked entries.
mean = (tf.reduce_sum(tf.where(
broadcast_mask, tf.zeros([], dtype=time_series_tensor.dtype),
time_series_tensor),
axis=-1) / num_unmasked_entries)
variance = (tf.reduce_sum(tf.where(
broadcast_mask, tf.zeros([], dtype=time_series_tensor.dtype),
(time_series_tensor - mean[..., tf.newaxis])**2),
axis=-1) / num_unmasked_entries)
return mean, variance
def expand_dims(x, axis, name=None):
"""Like `tf.expand_dims` but accepts a vector of axes to expand."""
with tf.name_scope(name or 'expand_dims'):
x = tf.convert_to_tensor(x, name='x')
axis = tf.convert_to_tensor(axis, dtype_hint=tf.int32, name='axis')
nx = prefer_static.rank(x)
na = prefer_static.size(axis)
is_neg_axis = axis < 0
k = prefer_static.reduce_sum(
prefer_static.cast(is_neg_axis, axis.dtype))
axis = prefer_static.where(is_neg_axis, axis + nx, axis)
axis = prefer_static.sort(axis)
axis_neg, axis_pos = prefer_static.split(axis, [k, -1])
idx = prefer_static.argsort(prefer_static.concat([
axis_pos,
prefer_static.range(nx),
axis_neg,
],
axis=0),
stable=True)
shape = prefer_static.pad(prefer_static.shape(x),
paddings=[[na - k, k]],
constant_values=1)
shape = prefer_static.gather(shape, idx)
return tf.reshape(x, shape)
def _sample_bates(total_count, low, high, n, seed=None):
"""Vectorized production of `Bates` samples.
Args:
total_count: (Batches of) counts of `Uniform`s to take means of. Should
have integer dtype and already be broadcasted to the batch shape.
low: (Batches of) lower bounds of the `Uniform` variables to sample. Should
be the same floating dtype as `high` and broadcastable to the batch shape.
high: (Batches of) upper bounds of the `Uniform` variables to sample. Should
be the same floating dtype as `low` and broadcastable to the batch shape.
n: `int32` number of samples to generate.
seed: Random seed to pass to `Uniform` sampler.
Returns:
samples: Samples of (batches of) the `Bates` variable. Will have same dtype
as `low` and `high`. If the batch shape is `[B1,..., Bn]`, `samples` has
shape `[n, B1,..., Bn]`.
"""
# 1. Sample Uniform(0, 1)s, flattening the batch dimension into axis 0.
uniform_sample_shape = ps.concat([[ps.reduce_sum(total_count)], [n]], axis=0)
uniform_samples = samplers.uniform(
uniform_sample_shape, minval=0., maxval=1., dtype=low.dtype, seed=seed)
# 2. Produce segment means.
segment_lengths = tf.reshape(total_count, [-1])
segment_ids = tf.repeat(tf.range(tf.size(segment_lengths)), segment_lengths)
flatmeans = tf.math.segment_mean(uniform_samples, segment_ids)
# 3. Reshape and transpose segment means back to the original shape.
outshape = tf.concat([tf.shape(total_count), [n]], axis=0)
tmeans = tf.reshape(flatmeans, outshape)
axes = tf.range(tf.rank(tmeans))
means = tf.transpose(tmeans, tf.roll(axes, shift=1, axis=0))
# 4. Shift/scale from (0, 1) to (low, high).
return low + (high - low) * means
def _calculate_batch_shape(self):
"""Computes fully defined batch shape for the new distribution."""
all_batch_shapes = [d.batch_shape.as_list()
if tensorshape_util.is_fully_defined(d.batch_shape)
else d.batch_shape_tensor() for d in self.distributions]
original_shape = ps.stack(all_batch_shapes, axis=0)
index_mask = ps.cast(
ps.one_hot(self._axis, ps.shape(original_shape)[1]),
dtype=tf.bool)
new_concat_dim = ps.cast(
ps.reduce_sum(original_shape, axis=0)[self._axis], dtype=tf.int32)
return ps.where(index_mask, new_concat_dim,
ps.reduce_max(original_shape, axis=0))
def reduce_fn(operands, inits, axis=None, keepdims=False):
"""Applies `reducer` to the given operands along the given axes.
Args:
operands: tuple of tensors, all having the same shape.
inits: tuple of scalar tensors, with dtypes aligned to those of operands.
axis: The axis or axes to reduce. One of `None`, an `int` or a sequence of
`int`. `None` is taken to mean "reduce all axes".
keepdims: When `True`, we do not squeeze away the reduced dims, instead
returning values with singleton dims in those axes.
Returns:
reduced: A tuple of the reduced operands.
"""
# Static shape consistency checks.
args_shape = operands[0].shape
for arg in operands[1:]:
args_shape = tensorshape_util.merge_with(args_shape, arg.shape)
ndims = tensorshape_util.rank(args_shape)
if ndims is None:
raise ValueError(
'Rank of at least one of `operands` must be known statically.')
# Ensure the 'axis' arg is a tuple of non-negative ints.
axis = np.arange(ndims) if axis is None else np.array(axis)
if axis.ndim > 1:
raise ValueError(
'`axis` must be `None`, an `int`, or a sequence of '
'`int`, but got {}'.format(axis))
axis = np.reshape(axis, [-1])
axis = np.where(axis < 0, axis + ndims, axis)
axis = tuple(int(ax) for ax in axis)
axis_nhot = ps.reduce_sum(ps.one_hot(axis,
depth=ndims,
on_value=True,
off_value=False,
dtype=tf.bool),
axis=0)
in_shape = args_shape
if not tensorshape_util.is_fully_defined(in_shape):
in_shape = tf.shape(operands[0])
unsqueezed_shape = ps.where(axis_nhot, 1, in_shape)
result = _variadic_reduce_custom_grad(operands, inits, axis, reducer,
unsqueezed_shape)
if keepdims:
result = tf.nest.map_structure(
lambda t: tf.reshape(t, unsqueezed_shape), result)
return result
def preprocess_state(init_state):
"""Initial preprocessing at Stage 0."""
dimension = ps.reduce_sum([
ps.reduce_prod(ps.shape(x)[1:]) for x in init_state])
likelihood_log_prob = likelihood_log_prob_fn(*init_state)
# Default to the optimal for normal distributed targets.
# TODO(b/152412213): Revisit this default parameter.
scale_start = (
tf.constant(2.38 ** 2, dtype=likelihood_log_prob.dtype) /
tf.constant(dimension, dtype=likelihood_log_prob.dtype))
# TODO(b/152412213): Enable batch of batches style by using non-scalar
# inverse_temperature
inverse_temperature = tf.zeros([], dtype=likelihood_log_prob.dtype)
scalings = ps.ones_like(likelihood_log_prob) * ps.minimum(scale_start, 1.)
kernel = make_kernel_fn(
_make_tempered_target_log_prob_fn(
prior_log_prob_fn,
likelihood_log_prob_fn,
inverse_temperature),
init_state,
scalings,
seed=seed_stream())
pkr = kernel.bootstrap_results(current_state)
_, kernel_target_log_prob = gather_mh_like_result(pkr)
particle_info = ParticleInfo(
log_accept_prob=ps.zeros_like(likelihood_log_prob),
log_scalings=tf.math.log(scalings),
tempered_log_prob=kernel_target_log_prob,
likelihood_log_prob=likelihood_log_prob,
)
return SMCResults(
num_steps=tf.convert_to_tensor(
max_num_steps, dtype=tf.int32, name='num_steps'),
inverse_temperature=inverse_temperature,
log_marginal_likelihood=tf.constant(
0., dtype=likelihood_log_prob.dtype),
particle_info=particle_info
)
def sample_sequential_monte_carlo(
prior_log_prob_fn,
likelihood_log_prob_fn,
current_state,
max_num_steps=25,
max_stage=100,
make_kernel_fn=make_rwmh_kernel_fn,
tuning_fn=simple_heuristic_tuning,
make_tempered_target_log_prob_fn=default_make_tempered_target_log_prob_fn,
ess_threshold_ratio=0.5,
parallel_iterations=10,
seed=None,
name=None):
"""Runs Sequential Monte Carlo to sample from the posterior distribution.
This function uses an MCMC transition operator (e.g., Hamiltonian Monte Carlo)
to sample from a series of distributions that slowly interpolates between
an initial 'prior' distribution:
`exp(prior_log_prob_fn(x))`
and the target 'posterior' distribution:
`exp(prior_log_prob_fn(x) + target_log_prob_fn(x))`,
by mutating a collection of MC samples (i.e., particles). The approach is also
known as Particle Filter in some literature. The current implemenetation is
largely based on Del Moral et al [1], which adapts the tempering sequence
adaptively (base on the effective sample size) and the scaling of the mutation
kernel (base on the sample covariance of the particles) at each stage.
Args:
prior_log_prob_fn: Python callable that returns the log density of the
prior distribution.
likelihood_log_prob_fn: Python callable which takes an argument like
`current_state` (or `*current_state` if it's a list) and returns its
(possibly unnormalized) log-density under the likelihood distribution.
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s). The first `r` dimensions index
independent chains, `r = tf.rank(target_log_prob_fn(*current_state))`.
max_num_steps: The maximum number of kernel transition steps in one mutation
of the MC samples. Note that the actual number of steps in one mutation is
tuned during sampling and likely lower than the max_num_step.
max_stage: Integer number of the stage for increasing the temperature
from 0 to 1.
make_kernel_fn: Python `callable` which returns a `TransitionKernel`-like
object. Must take one argument representing the `TransitionKernel`'s
`target_log_prob_fn`. The `target_log_prob_fn` argument represents the
`TransitionKernel`'s target log distribution. Note:
`sample_sequential_monte_carlo` creates a new `target_log_prob_fn`
which is an interpolation between the supplied `target_log_prob_fn` and
`proposal_log_prob_fn`; it is this interpolated function which is used as
an argument to `make_kernel_fn`.
tuning_fn: Python `callable` which takes the number of steps, the log
scaling, and the log acceptance ratio from the last mutation and output
the number of steps and log scaling for the next mutation.
make_tempered_target_log_prob_fn: Python `callable` that takes the
`prior_log_prob_fn`, `likelihood_log_prob_fn`, and `inverse_temperatures`
and creates a `target_log_prob_fn` `callable` that pass to
`make_kernel_fn`.
ess_threshold_ratio: Target ratio for effective sample size.
parallel_iterations: The number of iterations allowed to run in parallel.
It must be a positive integer. See `tf.while_loop` for more details.
seed: Python integer or TFP seedstream to seed the random number generator.
name: Python `str` name prefixed to Ops created by this function.
Default value: `None` (i.e., 'sample_sequential_monte_carlo').
Returns:
n_stage: Number of the mutation stage SMC ran.
final_state: `Tensor` or Python `list` of `Tensor`s representing the
final state(s) of the Markov chain(s). The output are the posterior
samples.
final_kernel_results: `collections.namedtuple` of internal calculations used
to advance the chain.
#### References
[1] Del Moral, Pierre, Arnaud Doucet, and Ajay Jasra. An adaptive sequential
Monte Carlo method for approximate Bayesian computation.
_Statistics and Computing_, 22.5(1009-1020), 2012.
"""
with tf.name_scope(name or 'sample_sequential_monte_carlo'):
seed_stream = SeedStream(seed, salt='smc_seed')
unwrap_state_list = not tf.nest.is_nested(current_state)
if unwrap_state_list:
current_state = [current_state]
current_state = [
tf.convert_to_tensor(s, dtype_hint=tf.float32)
for s in current_state
]
# Initial preprocessing at Stage 0
likelihood_log_prob = likelihood_log_prob_fn(*current_state)
likelihood_rank = ps.rank(likelihood_log_prob)
dimension = ps.reduce_sum([
ps.reduce_prod(ps.shape(x)[likelihood_rank:])
for x in current_state
])
# We infer the particle shapes from the resulting likelihood:
# [num_particles, b1, ..., bN]
particle_shape = ps.shape(likelihood_log_prob)
num_particles, batch_shape = particle_shape[0], particle_shape[1:]
effective_sample_size_threshold = tf.cast(
num_particles * ess_threshold_ratio, tf.int32)
# TODO(b/152412213): Revisit this default parameter.
# Default to the optimal scaling of a random walk kernel for a d-dimensional
# normal distributed targets: 2.38 ** 2 / d.
# For more detail see:
# Roberts GO, Gelman A, Gilks WR. Weak convergence and optimal scaling of
# random walk Metropolis algorithms. _The annals of applied probability_.
# 1997;7(1):110-20.
scale_start = (tf.constant(2.38**2, dtype=likelihood_log_prob.dtype) /
tf.constant(dimension, dtype=likelihood_log_prob.dtype))
inverse_temperature = tf.zeros(batch_shape,
dtype=likelihood_log_prob.dtype)
scalings = ps.ones_like(likelihood_log_prob) * ps.minimum(
scale_start, 1.)
kernel = make_kernel_fn(make_tempered_target_log_prob_fn(
prior_log_prob_fn, likelihood_log_prob_fn, inverse_temperature),
current_state,
scalings,
seed=seed_stream)
pkr = kernel.bootstrap_results(current_state)
_, kernel_target_log_prob = gather_mh_like_result(pkr)
particle_info = ParticleInfo(
log_accept_prob=ps.zeros_like(likelihood_log_prob),
log_scalings=tf.math.log(scalings),
tempered_log_prob=kernel_target_log_prob,
likelihood_log_prob=likelihood_log_prob,
)
current_pkr = SMCResults(
num_steps=tf.convert_to_tensor(max_num_steps,
dtype=tf.int32,
name='num_steps'),
inverse_temperature=inverse_temperature,
log_marginal_likelihood=tf.zeros_like(inverse_temperature),
particle_info=particle_info)
def update_weights_temperature(inverse_temperature,
likelihood_log_prob):
"""Calculate the next inverse temperature and update weights."""
likelihood_diff = likelihood_log_prob - tf.reduce_max(
likelihood_log_prob, axis=0)
def _body_fn(new_beta, upper_beta, lower_beta, eff_size,
log_weights):
"""One iteration of the temperature and weight update."""
new_beta = (lower_beta + upper_beta) / 2.0
log_weights = (new_beta -
inverse_temperature) * likelihood_diff
log_weights_norm = tf.math.log_softmax(log_weights, axis=0)
eff_size = tf.cast(
tf.exp(-tf.math.reduce_logsumexp(2 * log_weights_norm,
axis=0)), tf.int32)
upper_beta = tf.where(
eff_size < effective_sample_size_threshold, new_beta,
upper_beta)
lower_beta = tf.where(
eff_size < effective_sample_size_threshold, lower_beta,
new_beta)
return new_beta, upper_beta, lower_beta, eff_size, log_weights
def _cond_fn(new_beta, upper_beta, lower_beta, eff_size, *_): # pylint: disable=unused-argument
# TODO(junpenglao): revisit threshold below to be dtype specific.
threshold = 1e-6
return (tf.math.reduce_any(upper_beta - lower_beta > threshold)
& tf.math.reduce_any(
eff_size != effective_sample_size_threshold))
(new_beta, upper_beta, lower_beta, eff_size,
log_weights) = tf.while_loop( # pylint: disable=unused-variable
cond=_cond_fn,
body=_body_fn,
loop_vars=(tf.zeros_like(inverse_temperature),
tf.fill(ps.shape(inverse_temperature),
tf.constant(2, inverse_temperature.dtype)),
inverse_temperature,
tf.zeros_like(inverse_temperature, dtype=tf.int32),
tf.zeros_like(likelihood_diff)),
parallel_iterations=parallel_iterations)
log_weights = tf.where(new_beta < 1., log_weights,
(1. - inverse_temperature) *
likelihood_diff)
marginal_loglike_ = reduce_logmeanexp(
(new_beta - inverse_temperature) * likelihood_log_prob, axis=0)
new_inverse_temperature = tf.clip_by_value(new_beta, 0., 1.)
return marginal_loglike_, new_inverse_temperature, log_weights
def mutate(current_state, log_scalings, num_steps,
inverse_temperature):
"""Mutate the state using a Transition kernel."""
with tf.name_scope('mutate_states'):
scalings = tf.exp(log_scalings)
kernel = make_kernel_fn(make_tempered_target_log_prob_fn(
prior_log_prob_fn, likelihood_log_prob_fn,
inverse_temperature),
current_state,
scalings,
seed=seed_stream)
pkr = kernel.bootstrap_results(current_state)
kernel_log_accept_ratio, _ = gather_mh_like_result(pkr)
def mutate_onestep(i, state, pkr, log_accept_prob_sum):
next_state, next_kernel_results = kernel.one_step(
state, pkr)
kernel_log_accept_ratio, _ = gather_mh_like_result(pkr)
log_accept_prob = tf.minimum(kernel_log_accept_ratio, 0.)
log_accept_prob_sum = log_add_exp(log_accept_prob_sum,
log_accept_prob)
return i + 1, next_state, next_kernel_results, log_accept_prob_sum
(
_, next_state, next_kernel_results, log_accept_prob_sum
) = tf.while_loop(
cond=lambda i, *args: i < num_steps,
body=mutate_onestep,
loop_vars=(
tf.zeros([], dtype=tf.int32),
current_state,
pkr,
# we accumulate the acceptance probability in log space.
tf.fill(
ps.shape(kernel_log_accept_ratio),
tf.constant(-np.inf,
kernel_log_accept_ratio.dtype))),
parallel_iterations=parallel_iterations)
_, kernel_target_log_prob = gather_mh_like_result(
next_kernel_results)
avg_log_accept_prob_per_particle = log_accept_prob_sum - tf.math.log(
tf.cast(num_steps + 1, log_accept_prob_sum.dtype))
return (next_state, avg_log_accept_prob_per_particle,
kernel_target_log_prob)
# One SMC steps.
def smc_body_fn(stage, state, smc_kernel_result):
"""Run one stage of SMC with constant temperature."""
(new_marginal, new_inv_temperature,
log_weights) = update_weights_temperature(
smc_kernel_result.inverse_temperature,
smc_kernel_result.particle_info.likelihood_log_prob)
# TODO(b/152412213) Use a tf.scan to better collect debug info.
if PRINT_DEBUG:
tf.print(
'Stage:', stage, 'Beta:', new_inv_temperature, 'n_steps:',
smc_kernel_result.num_steps, 'accept:',
tf.exp(
reduce_logmeanexp(
smc_kernel_result.particle_info.log_accept_prob,
axis=0)), 'scaling:',
tf.exp(
reduce_logmeanexp(
smc_kernel_result.particle_info.log_scalings,
axis=0)))
(resampled_state,
resampled_particle_info), _ = resample_particle_and_info(
(state, smc_kernel_result.particle_info),
log_weights,
seed=seed_stream)
next_num_steps, next_log_scalings = tuning_fn(
smc_kernel_result.num_steps,
resampled_particle_info.log_scalings,
resampled_particle_info.log_accept_prob)
# Skip tuning at stage 0.
next_num_steps = tf.where(stage == 0, smc_kernel_result.num_steps,
next_num_steps)
next_log_scalings = tf.where(stage == 0,
resampled_particle_info.log_scalings,
next_log_scalings)
next_num_steps = tf.clip_by_value(next_num_steps, 2, max_num_steps)
next_state, log_accept_prob, tempered_log_prob = mutate(
resampled_state, next_log_scalings, next_num_steps,
new_inv_temperature)
next_pkr = SMCResults(
num_steps=next_num_steps,
inverse_temperature=new_inv_temperature,
log_marginal_likelihood=(
new_marginal + smc_kernel_result.log_marginal_likelihood),
particle_info=ParticleInfo(
log_accept_prob=log_accept_prob,
log_scalings=next_log_scalings,
tempered_log_prob=tempered_log_prob,
likelihood_log_prob=likelihood_log_prob_fn(*next_state),
))
return stage + 1, next_state, next_pkr
(n_stage, final_state, final_kernel_results) = tf.while_loop(
cond=lambda i, state, pkr: ( # pylint: disable=g-long-lambda
(i < max_stage) & tf.reduce_any(pkr.inverse_temperature < 1.)),
body=smc_body_fn,
loop_vars=(tf.zeros([],
dtype=tf.int32), current_state, current_pkr),
parallel_iterations=parallel_iterations)
if unwrap_state_list:
final_state = final_state[0]
return n_stage, final_state, final_kernel_results
def _inverse_event_shape_tensor(self, output_shape):
input_size = ps.reduce_sum(self.block_sizes)
return ps.concat([output_shape[:-1], input_size[tf.newaxis]], -1)
def _forward_event_shape_tensor(self, input_shape):
output_size = ps.reduce_sum(self._output_block_sizes())
return ps.concat([input_shape[:-1], output_size[tf.newaxis]], -1)
def reduce_fn(operands, inits, axis=None, keepdims=False):
"""Applies `reducer` to the given operands along the given axes.
Args:
operands: tuple of tensors, all having the same shape.
inits: tuple of scalar tensors, with dtypes aligned to those of operands.
axis: The axis or axes to reduce. One of `None`, an `int` or a sequence of
`int`. `None` is taken to mean "reduce all axes".
keepdims: When `True`, we do not squeeze away the reduced dims, instead
returning values with singleton dims in those axes.
Returns:
reduced: A tuple of the reduced operands.
"""
# Static shape consistency checks.
args_shape = operands[0].shape
for arg in operands[1:]:
args_shape = tensorshape_util.merge_with(args_shape, arg.shape)
ndims = tensorshape_util.rank(args_shape)
if ndims is None:
raise ValueError(
'Rank of at least one of `operands` must be known statically.')
# Ensure the 'axis' arg is a tuple of non-negative ints.
axis = np.arange(ndims) if axis is None else np.array(axis)
if axis.ndim > 1:
raise ValueError(
'`axis` must be `None`, an `int`, or a sequence of '
'`int`, but got {}'.format(axis))
axis = np.reshape(axis, [-1])
axis = np.where(axis < 0, axis + ndims, axis)
axis = tuple(int(ax) for ax in axis)
if JAX_MODE:
from jax import lax # pylint: disable=g-import-not-at-top
result = lax.reduce(operands,
init_values=inits,
dimensions=axis,
computation=reducer)
elif (tf.executing_eagerly()
or not control_flow_util.GraphOrParentsInXlaContext(
tf1.get_default_graph())):
result = _variadic_reduce(operands,
init=inits,
axis=axis,
reducer=reducer)
else:
result = _xla_reduce(operands, inits, axis)
if keepdims:
axis_nhot = ps.reduce_sum(ps.one_hot(axis,
depth=ndims,
on_value=True,
off_value=False,
dtype=tf.bool),
axis=0)
in_shape = args_shape
if not tensorshape_util.is_fully_defined(in_shape):
in_shape = tf.shape(operands[0])
final_shape = ps.where(axis_nhot, 1, in_shape)
result = tf.nest.map_structure(
lambda t: tf.reshape(t, final_shape), result)
return result