def adj_arr(shape, params):
"""Constructs a sliced weighted acyclic-digraph adjacency matrix.
Assigns weights from `params` to an acylic-digraph adjacency matrix
in row-major order. Nodes are assumed to be topologically sorted.
Args:
shape: Tuple containing number of nodes per type.
params: Sequence of weights.
Returns:
Weighted adjacency matrix where the rows and columns represent
source and target nodes respectively. Only arcs with non-output
source and non-input target are represented.
Raises:
AttributeError: If weighted adjacency matrix cannot be
completely initialized.
"""
inb, _, out = shape
Σ = np.sum(shape)
outbound = np.array([Σ - max(inb, n + 1) for n in range(Σ - out)])
arr = np.flip(np.arange(Σ - inb), 0) < outbound[:, None]
if np.count_nonzero(arr) != len(params):
msg = "{} weights required to initialize adj matrix of a {} network, got {}."
raise AttributeError(
msg.format(np.count_nonzero(arr), shape, len(params)))
return jo.index_update(arr.astype(float), arr, params)
def test_sparse_init(self):
"""Test that sparse_init produces sparse params."""
rng = jax.random.PRNGKey(0)
flax_module, params, input_shape, model_hps = _load_model(
'fully_connected')
non_zero_connection_weights = 3
init_hps = sparse_init.DEFAULT_HPARAMS
init_hps['non_zero_connection_weights'] = non_zero_connection_weights
init_hps.update(model_hps)
loss_name = 'cross_entropy'
loss_fn = losses.get_loss_fn(loss_name)
new_params = sparse_init.sparse_init(loss_fn=loss_fn,
flax_module=flax_module,
params=params,
hps=init_hps,
input_shape=input_shape[1:],
output_shape=OUTPUT_SHAPE,
rng_key=rng)
# Check new params are sparse
for key in new_params:
num_units = new_params[key]['kernel'].shape[0]
self.assertEqual(jnp.count_nonzero(new_params[key]['kernel']),
num_units * non_zero_connection_weights)
self.assertEqual(jnp.count_nonzero(new_params[key]['bias']), 0)
def test_shuffled_neuron_no_input_ablation_mask_sparsity_full(self):
"""Tests shuffled mask generation, for 100% sparsity."""
mask = masked.shuffled_neuron_no_input_ablation_mask(
self._masked_model, self._rng, 1.0)
with self.subTest(name='shuffled_full_mask'):
self.assertIn('MaskedModule_0', mask)
with self.subTest(name='shuffled_full_mask_values'):
self.assertEqual(
jnp.count_nonzero(mask['MaskedModule_0']['kernel']),
jnp.prod(jnp.array(self._input_dimensions)))
with self.subTest(name='shuffled_full_no_input_ablation'):
# Check no row (neurons are columns) is completely ablated.
self.assertTrue((jnp.count_nonzero(
mask['MaskedModule_0']['kernel'], axis=0) != 0).all())
with self.subTest(name='shuffled_full_mask_not_masked_values'):
self.assertIsNone(mask['MaskedModule_0']['bias'])
masked_output = self._masked_model(self._input, mask=mask)
with self.subTest(name='shuffled_full_mask_dense_shape'):
self.assertSequenceEqual(masked_output.shape,
self._unmasked_output.shape)
def logmarglike_lineargaussianmodel_twotransfers(
M_T, # (n_components, n_pix_y)
y, # (n_pix_y)
yinvvar, # (n_pix_y)
mu, # (n_components)
muinvvar, # (n_components)
logyinvvar=None,
logmuinvvar=None,
):
"""
Fit linear model to one Gaussian data sets, with Gaussian prior on linear components.
Parameters
----------
y, yinvvar : ndarray (n_pix_y)
data and data inverse variances
M_T : ndarray (n_components, n_pix_y)
design matrix of linear model
mu, muinvvar : ndarray (n_components)
data and data variances for y
Returns
-------
logfml : ndarray scalar
log likelihood values with parameters marginalised and at best fit
theta_map : ndarray (n_components)
Best fit MAP parameters
theta_cov : ndarray (n_components, n_components)
Parameter covariance
"""
log2pi = np.log(2.0 * np.pi)
nt = np.shape(M_T)[-2]
ny = np.count_nonzero(yinvvar)
nm = np.count_nonzero(muinvvar)
M = np.transpose(M_T) # (n_pix_y, n_components)
Myinv = M * yinvvar[:, None] # (n_pix_y, n_components)
Hbar = (np.matmul(M_T, Myinv) + np.eye(nt) * muinvvar[:, None]
) # (n_components, n_components)
etabar = np.sum(Myinv * y[:, None],
axis=0) + mu * muinvvar # (n_components)
theta_map = np.linalg.solve(Hbar, etabar) # (n_components)
theta_cov = np.linalg.inv(Hbar) # (n_components, n_components)
if logyinvvar is None:
logyinvvar = np.where(yinvvar == 0, 0, np.log(yinvvar))
if logmuinvvar is None:
logmuinvvar = np.where(muinvvar == 0, 0, np.log(muinvvar))
logdetH = +np.sum(logyinvvar) + np.sum(logmuinvvar) # scalar
xi1 = -0.5 * ((ny + nm) * log2pi - logdetH + np.sum(y * y * yinvvar) +
np.sum(mu * mu * muinvvar)) # scalar
sign, logdetHbar = np.linalg.slogdet(Hbar)
xi2 = -0.5 * (nt * log2pi - logdetHbar + np.sum(etabar * theta_map))
logfml = xi1 - xi2
print("my Cinv_X", np.sum(y * y * yinvvar) - np.sum(etabar * theta_map))
print("my logdet", -logdetH + logdetHbar)
print("my counts", (ny + nm - nt) * log2pi)
return logfml, theta_map, theta_cov
def logmarglike_lineargaussianmodel_onetransfer(M_T,
y,
yinvvar,
logyinvvar=None):
"""
Fit linear model to one Gaussian data set, with no (=uniform) prior on the linear components.
Parameters
----------
y, yinvvar, logyinvvar : ndarray (n_pix_y)
data and data inverse variances.
Zeros will be ignored.
M_T : ndarray (n_components, n_pix_y)
design matrix of linear model
Returns
-------
logfml : ndarray scalar
log likelihood values with parameters marginalised and at best fit
theta_map : ndarray (n_components)
Best fit MAP parameters
theta_cov : ndarray (n_components, n_components)
Parameter covariance
"""
# assert y.shape[-2] == yinvvar.shape[-2]
assert y.shape[-1] == yinvvar.shape[-1]
# assert y.shape[-1] == 1
assert M_T.shape[-1] == yinvvar.shape[-1]
assert np.all(np.isfinite(yinvvar)) # no negative elements
assert np.all(np.isfinite(y)) # all finite
assert np.all(np.isfinite(M_T)) # all finite
assert np.count_nonzero(
yinvvar) > 2 # at least two valid (non zero) pixels
log2pi = np.log(2.0 * np.pi)
nt = np.shape(M_T)[-2]
ny = np.count_nonzero(yinvvar)
M = np.transpose(M_T) # (n_pix_y, n_components)
Myinv = M * yinvvar[:, None] # (n_pix_y, n_components)
Hbar = np.matmul(M_T, Myinv) # (n_components, n_components)
etabar = np.sum(Myinv * y[:, None], axis=0) # (n_components)
theta_map = np.linalg.solve(Hbar, etabar) # (n_components)
theta_cov = np.linalg.inv(Hbar) # (n_components, n_components)
if logyinvvar is None:
logyinvvar = np.where(yinvvar == 0, 0, np.log(yinvvar))
logdetH = np.sum(logyinvvar) # scalar
xi1 = -0.5 * (ny * log2pi - logdetH + np.sum(y * y * yinvvar)) # scalar
sign, logdetHbar = np.linalg.slogdet(Hbar)
xi2 = -0.5 * (nt * log2pi - logdetHbar + np.sum(etabar * theta_map))
logfml = xi1 - xi2
return logfml, theta_map, theta_cov
def testCountNonzero(self, shape, dtype, axis): rng = jtu.rand_some_zero() onp_fun = lambda x: onp.count_nonzero(x, axis) lnp_fun = lambda x: lnp.count_nonzero(x, axis) args_maker = lambda: [rng(shape, dtype)] self._CheckAgainstNumpy(onp_fun, lnp_fun, args_maker, check_dtypes=True) self._CompileAndCheck(lnp_fun, args_maker, check_dtypes=True)
def test_shuffled_neuron_no_input_ablation_mask_sparsity_full_twolayer(
self):
"""Tests shuffled mask generation for two layers, and 100% sparsity."""
mask = masked.shuffled_neuron_no_input_ablation_mask(
self._masked_model_twolayer, self._rng, 1.0)
with self.subTest(name='shuffled_full_mask_layer1'):
self.assertIn('MaskedModule_0', mask)
with self.subTest(name='shuffled_full_mask_values_layer1'):
self.assertEqual(
jnp.count_nonzero(mask['MaskedModule_0']['kernel']),
jnp.prod(jnp.array(self._input_dimensions)))
with self.subTest(name='shuffled_full_mask_not_masked_values_layer1'):
self.assertIsNone(mask['MaskedModule_0']['bias'])
with self.subTest(name='shuffled_full_no_input_ablation_layer1'):
# Check no row (neurons are columns) is completely ablated.
self.assertTrue((jnp.count_nonzero(
mask['MaskedModule_0']['kernel'], axis=0) != 0).all())
with self.subTest(name='shuffled_full_mask_layer2'):
self.assertIn('MaskedModule_1', mask)
with self.subTest(name='shuffled_full_mask_values_layer2'):
self.assertEqual(
jnp.count_nonzero(mask['MaskedModule_1']['kernel']),
jnp.prod(MaskedTwoLayerDense.NUM_FEATURES[0]))
with self.subTest(name='shuffled_full_mask_not_masked_values_layer2'):
self.assertIsNone(mask['MaskedModule_1']['bias'])
with self.subTest(name='shuffled_full_no_input_ablation_layer2'):
# Note: check no *inputs* are ablated, and inputs < num_neurons.
self.assertEqual(
jnp.sum(
jnp.count_nonzero(mask['MaskedModule_1']['kernel'],
axis=0)),
MaskedTwoLayerDense.NUM_FEATURES[0])
masked_output = self._masked_model_twolayer(self._input, mask=mask)
with self.subTest(name='shuffled_full_mask_dense_shape'):
self.assertSequenceEqual(masked_output.shape,
self._unmasked_output_twolayer.shape)
def add_eos_token(indices, eos_token):
"""Add EOS token to sequence."""
batch_size = indices.shape[0]
lengths = jnp.count_nonzero(indices, axis=1)
indices = jnp.pad(indices, pad_width=[(0, 0), (0, 1)], mode='constant')
# Add EOS token.
indices = indices.at[jnp.arange(batch_size), lengths].set(eos_token)
return indices.astype(jnp.int32)
def example_helper(model, padded_example_and_rng):
"""Run the model on one example."""
# Compute the same estimates as in training, for ease of comparison.
# Instead of aggregating with nanmean per-batch, we aggregate over the full
# validation set.
if use_sampling_model:
(output_logits, targets, valid_mask, loss,
batch_metrics) = sample_loss_fn(model, padded_example_and_rng,
target_edge_index, num_edge_types)
else:
(output_logits, targets, valid_mask, num_nodes,
captured) = extract_outputs_and_targets(model,
padded_example_and_rng,
target_edge_index,
num_edge_types)
loss, batch_metrics = loss_fn(output_logits, targets, valid_mask,
num_nodes, captured)
batch_metrics_non_nan = jax.tree_map(jnp.nan_to_num, batch_metrics)
batch_metrics_non_nan_counts = jax.tree_map(
lambda x: jnp.count_nonzero(~jnp.isnan(x)), batch_metrics)
# Compute additional metrics by counting how many predictions cross our
# thresholds.
output_probs = jax.scipy.special.expit(output_logits)
preds = (output_probs[None, :, :] > candidate_thresholds[:, None,
None])
# Count true/false target/pred pairs.
valid = valid_mask.astype(bool)
count_t_target_t_pred = jnp.count_nonzero(valid & targets & preds,
axis=(1, 2))
count_t_target_f_pred = jnp.count_nonzero(valid & targets & (~preds),
axis=(1, 2))
count_f_target_t_pred = jnp.count_nonzero(valid & (~targets) & preds,
axis=(1, 2))
count_f_target_f_pred = jnp.count_nonzero(valid & (~targets) &
(~preds),
axis=(1, 2))
counts = (count_t_target_t_pred, count_t_target_f_pred,
count_f_target_t_pred, count_f_target_f_pred)
return loss, 1, batch_metrics_non_nan, batch_metrics_non_nan_counts, counts
def test_shuffled_neuron_no_input_ablation_mask_sparsity_half_full(self):
"""Tests shuffled mask generation, for a half-full mask."""
mask = masked.shuffled_neuron_no_input_ablation_mask(
self._masked_model, self._rng, 0.5)
param_shape = self._masked_model.params['MaskedModule_0']['unmasked'][
'kernel'].shape
with self.subTest(name='shuffled_mask_values'):
self.assertEqual(jnp.sum(mask['MaskedModule_0']['kernel']),
param_shape[0] // 2 * param_shape[1])
with self.subTest(name='shuffled_half_no_input_ablation'):
# Check no row (neurons are columns) is completely ablated.
self.assertTrue((jnp.count_nonzero(
mask['MaskedModule_0']['kernel'], axis=0) != 0).all())
def get_largest_component_indices(
graph: JAXSparse,
dtype: jnp.dtype = jnp.int32,
directed: bool = True,
connection="weak",
) -> jnp.ndarray:
ncomponents, labels = get_component_indices(graph,
dtype=dtype,
directed=directed,
connection=connection)
if ncomponents == 1:
return jnp.arange(graph.shape[0], dtype=dtype)
sizes = jnp.asarray(
[jnp.count_nonzero(labels == i) for i in range(ncomponents)])
i = jnp.argmax(sizes)
(indices, ) = jnp.where(labels == i)
return jnp.asarray(indices, dtype)
def __call__(self, param_name, param):
"""Shuffles the weight matrix/mask for a given parameter, per-neuron.
This is to be used with mask_map, and accepts the standard mask_map
function parameters.
Args:
param_name: The parameter's name.
param: The parameter's weight or mask matrix.
Returns:
A shuffled weight/mask matrix, with each neuron shuffled independently.
"""
del param_name # Unused.
incoming_connections = jnp.prod(jnp.array(param.shape[:-1]))
num_neurons = param.shape[-1]
# Ensure each input neuron has at least one connection unmasked.
mask = _fill_diagonal_wrap((incoming_connections, num_neurons),
1,
dtype=jnp.uint8)
# Randomly shuffle which of the neurons have these connections.
mask = jax.random.shuffle(self._get_rng(), mask, axis=0)
# Add extra required random connections to mask to satisfy sparsity.
mask_cols = []
for col in range(mask.shape[-1]):
neuron_mask = mask[:, col]
off_diagonal_count = max(
round((1 - self._sparsity) * incoming_connections) -
jnp.count_nonzero(neuron_mask), 0)
zero_indices = jnp.flatnonzero(neuron_mask == 0)
random_entries = _random_neuron_mask(len(zero_indices),
off_diagonal_count,
self._get_rng())
neuron_mask = neuron_mask.at[zero_indices].set(random_entries)
mask_cols.append(neuron_mask)
return jnp.column_stack(mask_cols).reshape(param.shape)
def logmarglike_scalingmodel_flatprior_jit(
ymod, # (n_components, n_pix_y)
y, # (n_components, n_pix_y)
yinvvar, # (n_components, n_pix_y)
logyinvvar, # (n_components, n_pix_y)
):
"""
Fit model to one Gaussian data set, with Gaussian prior on scaling.
Parameters
----------
y, yinvvar, logyinvvar : ndarray (n_components, n_pix_y)
data and data inverse variances
ymod : ndarray (n_components, n_pix_y)
design matrix of linear model
mu, muinvvar : ndarray (n_components)
priors
Returns
-------
logfml : ndarray (n_components)
log likelihood values with parameters marginalised and at best fit
theta_map : ndarray (n_components)
Best fit MAP parameters
theta_cov : ndarray (n_components)
Parameter covariance
"""
log2pi = np.log(2.0 * np.pi)
ny = np.count_nonzero(yinvvar)
# n_components
FOT = np.sum(ymod * y * yinvvar, axis=-1)
FTT = np.sum(ymod**2 * yinvvar, axis=-1)
FOO = np.sum(ymod**2 * yinvvar, axis=-1)
logSigma_det = np.sum(logyinvvar, axis=-1)
ellML = FOT / FTT
chi2 = FOO - (FOT / FTT) * FOT
logfml = -0.5 * (chi2 + np.log(FTT) - logSigma_det + ny * log2pi)
theta_map = FOT / FTT
theta_cov = FTT**-1
return logfml, theta_map, theta_cov
def mean_and_var(
x: Optional[np.ndarray],
axis: Optional[Axes] = None,
dtype: Optional[np.dtype] = None,
out: Optional[None] = None,
ddof: int = 0,
keepdims: bool = False,
mask: Optional[np.ndarray] = None,
get_var: bool = False
) -> Tuple[Optional[np.ndarray], Optional[np.ndarray]]:
"""`np.mean` and `np.var` taking the `mask` information into account."""
var = None
if x is None:
return x, var
if mask is None:
mean = np.mean(x, axis, dtype, out, keepdims)
if get_var:
var = np.var(x, axis, dtype, out, ddof, keepdims)
else:
axis = tuple(utils.canonicalize_axis(axis, x))
size = utils.size_at(x, axis)
mask = np.broadcast_to(mask, x.shape)
mask_size = np.count_nonzero(mask, axis)
for i in axis:
mask_size = np.expand_dims(mask_size, i)
size -= mask_size
size = np.maximum(size, 1)
mean = np.sum(x, axis=axis, keepdims=True) / size
if not keepdims:
mean = np.squeeze(mean, axis)
if get_var:
var = np.sum(
(x - mean)**2, axis=axis, keepdims=True) / (size - ddof)
if not keepdims:
var = np.squeeze(var, axis)
return mean, var
def smooth_and_normalize(vec, normalize=True):
"""
Parameters:
* vec : np.array of shape (n,)
* normalize : bool
Returns:
out : np.array of shape (n,).
If vec_i = 0, then out_i = epsilon. If vec_i !=0, then out_i = vec_i - c.
c is chosen such that sum(vec) == 1.
"""
vec = np.asarray(vec, dtype=np.float32)
if normalize:
vec = vec / vec.sum()
n = len(vec)
epsilon = 0.0001
num_nonzero = np.count_nonzero(vec)
c = epsilon * (n - num_nonzero) / num_nonzero
perturbation = (vec == 0) * epsilon - (vec != 0) * c
return vec + perturbation
def validation_function(model):
with contextlib.ExitStack() as exit_stack:
valid_iterator = valid_iterator_factory()
if prefetch:
valid_iterator = exit_stack.enter_context(
data_loading.ThreadedPrefetcher(valid_iterator, 4))
accumulated = None
example_count = 0
for batch in valid_iterator:
results = parallel_metrics_batch(model, batch.example,
batch.mask,
batch.static_metadata)
metrics = jax.tree_map(float,
flax.jax_utils.unreplicate(results))
metrics["epoch"] = np.sum(batch.epoch)
if accumulated is None:
accumulated = metrics
else:
accumulated = jax.tree_multimap(operator.add, accumulated,
metrics)
example_count += jnp.count_nonzero(batch.mask)
assert example_count > 0, "Validation iterator must be nonempty"
accumulated = typing.cast(Dict[str, Any], accumulated)
final_metrics = {}
for k, v in accumulated.items():
if isinstance(v, RatioMetric):
final_metrics[k] = v.numerator / v.denominator
if include_total_counts:
final_metrics[k + "_numerator"] = v.numerator
final_metrics[k + "_denominator"] = v.denominator
else:
final_metrics[k] = v / example_count
objective = final_metrics[objective_metric_name]
if include_total_counts:
final_metrics["validation_total_example_count"] = example_count
return (objective, final_metrics)
def logmarglike_lineargaussianmodel_onetransfer_jit(M_T, y, yinvvar,
logyinvvar):
"""
Fit linear model to one Gaussian data set, with no (=uniform) prior on the linear components.
Parameters
----------
y, yinvvar, logyinvvar : ndarray (n_pix_y)
data and data inverse variances.
Zeros will be ignored.
M_T : ndarray (n_components, n_pix_y)
design matrix of linear model
Returns
-------
logfml : ndarray scalar
log likelihood values with parameters marginalised and at best fit
theta_map : ndarray (n_components)
Best fit MAP parameters
theta_cov : ndarray (n_components, n_components)
Parameter covariance
"""
log2pi = np.log(2.0 * np.pi)
nt = np.shape(M_T)[-2]
ny = np.count_nonzero(yinvvar)
M = np.transpose(M_T) # (n_pix_y, n_components)
Myinv = M * yinvvar[:, None] # (n_pix_y, n_components)
Hbar = np.matmul(M_T, Myinv) # (n_components, n_components)
etabar = np.sum(Myinv * y[:, None], axis=0) # (n_components)
theta_map = np.linalg.solve(Hbar, etabar) # (n_components)
theta_cov = np.linalg.inv(Hbar) # (n_components, n_components)
logdetH = np.sum(logyinvvar) # scalar
xi1 = -0.5 * (ny * log2pi - logdetH + np.sum(y * y * yinvvar)) # scalar
sign, logdetHbar = np.linalg.slogdet(Hbar)
xi2 = -0.5 * (nt * log2pi - logdetHbar + np.sum(etabar * theta_map))
logfml = xi1 - xi2
return logfml, theta_map, theta_cov
def unique(rng, binary_vectors: np.ndarray) -> int:
"""Computes the number of unique binary columns."""
alpha = jax.random.normal(rng, shape=((1, binary_vectors.shape[1])))
return 1 + np.count_nonzero(
np.diff(np.sort(np.sum(binary_vectors * alpha, axis=-1))))
def count_permutations_mask_layer(mask_layer,
next_mask_layer=None,
parameter_key='kernel'):
"""Calculates the number of permutations for a layer, given binary masks.
Args:
mask_layer: The binary weight mask of a dense/conv layer, where last
dimension is number of neurons/filters.
next_mask_layer: The binary weight mask of the following a dense/conv layer,
or None if this is the last layer.
parameter_key: The name of the parameter to count the permutations of in each
layer.
Returns:
A dictionary with stats on the permutation structure of a mask, including
the number of symmetric permutations of the mask, number of unique mask
columns, count of the zeroed out (structurally pruned) neurons, and total
number of neurons/filters.
"""
# Have to check 'is None' since mask_layer[parameter_key] is jnp.array.
if not mask_layer or parameter_key not in mask_layer or mask_layer[
parameter_key] is None:
return {
'permutations': 1,
'zeroed_neurons': 0,
'total_neurons': 0,
'unique_neurons': 0,
}
mask = mask_layer[parameter_key]
num_neurons = mask.shape[-1]
# Initialize with stats for an empty mask.
mask_stats = {
'permutations': 0,
'zeroed_neurons': num_neurons,
'total_neurons': num_neurons,
'unique_neurons': 0,
}
# Re-shape masks as 1D, in case they are 2D (e.g. convolutional).
connection_mask = mask.reshape(-1, num_neurons)
# Only consider non-zero columns (in JAX neurons/filters are last index).
non_zero_neurons = ~jnp.all(connection_mask == 0, axis=0)
# Count only zeroed neurons in the current layer.
zeroed_count = num_neurons - jnp.count_nonzero(non_zero_neurons)
# Special case where all neurons in current layer are ablated.
if zeroed_count == num_neurons:
return mask_stats
# Have to check is None since next_mask_layer[parameter_key] is jnp.array.
if next_mask_layer and parameter_key in next_mask_layer and next_mask_layer[
parameter_key] is not None:
next_mask = next_mask_layer[parameter_key]
# Re-shape masks as 1D, in case they are 2D (e.g. convolutional).
next_connection_mask = next_mask.T.reshape(-1, num_neurons)
# Update with neurons that are non-zero in outgoing connections too.
non_zero_neurons &= ~jnp.all(next_connection_mask == 0, axis=0)
# Remove rows corresponding to neurons that are ablated.
next_connection_mask = next_connection_mask[:, non_zero_neurons]
connection_mask = connection_mask[:, non_zero_neurons]
# Combine the outgoing and incoming masks in one vector per-neuron.
connection_mask = jnp.concatenate(
(connection_mask, next_connection_mask), axis=0)
else:
connection_mask = connection_mask[:, non_zero_neurons]
# Effectively no connections between these two layers.
if not connection_mask.size:
return mask_stats
# Note: np.unique not implemented in JAX numpy yet.
_, unique_counts = np.unique(connection_mask, axis=-1, return_counts=True)
# Convert from device array.
mask_stats['zeroed_neurons'] = int(zeroed_count)
mask_stats['permutations'] = functools.reduce(operator.mul,
(np.math.factorial(t)
for t in unique_counts))
mask_stats['unique_neurons'] = len(unique_counts)
return mask_stats
flax.serialization.to_state_dict(
replicated_optimizer),
"batch":
batch,
"metrics":
metrics,
"agg_grads":
flax.serialization.to_state_dict(agg_grads),
}
pickle.dump(postmortem,
fp,
protocol=pickle.HIGHEST_PROTOCOL)
bad_grads = jax.tree_map(
lambda x: float(
jnp.count_nonzero(~jnp.isfinite(x)) / x.size),
flax.serialization.to_state_dict(agg_grads))
bad_grads_str = json.dumps(bad_grads, indent=2)
raise RuntimeError(f"Non-finite gradients at step {step}!\n\n"
f"Bad fraction:\n{bad_grads_str}")
elapsed_sec = time.time() - start_time
metrics["elapsed_hours"] = elapsed_sec / 3600
if max_seconds is not None and elapsed_sec > max_seconds:
logging.info("Hit max train timeout at step %d", step)
shutdown_after_this_iteration = True
# Do a validation step.
if validation_fn and step % steps_per_validate == 0:
logging.info("Running validation at step %d", step)
objective, valid_metrics = validation_fn(
def evaluate_batch(self, images, labels):
logits = self.model(images, training=False)
num_correct = jn.count_nonzero(
jn.equal(jn.argmax(logits, axis=1), labels))
return num_correct
def logmarglike_lineargaussianmodel_threetransfers_jit(
ell, # scalar
M_T, # (n_components, n_pix_y)
R_T, # (n_components, n_pix_z)
y, # (n_pix_y)
yinvvar, # (n_pix_y),
logyinvvar, # (n_pix_y),
z, # (n_pix_z)
zinvvar, # (n_pix_z)
logzinvvar, # (n_pix_z)
mu, # (n_components)
muinvvar, # (n_components)
logmuinvvar, # (n_components)
):
"""
Fit linear model to two Gaussian data sets, with Gaussian prior on components.
Parameters
----------
ell : ndarray scalar
scaling between the data: y = ell * z
y, yinvvar, logyinvvar : ndarray (n_pix_y)
data and data inverse variances
M_T : ndarray (n_components, n_pix_y)
design matrix of linear model
z, zinvvar, logzinvvar : ndarray (n_pix_z)
data and data variances for y
R_T : ndarray (n_components, n_pix_z)
design matrix of linear model for z
mu, muinvvar, logmuinvvar : ndarray (n_components)
data and data variances for y
Returns
-------
logfml : ndarray scalar
log likelihood values with parameters marginalised and at best fit
theta_map : ndarray (n_components)
Best fit MAP parameters
theta_cov : ndarray (n_components, n_components)
Parameter covariance
"""
log2pi = np.log(2.0 * np.pi)
nt = np.shape(M_T)[-2]
ny = np.count_nonzero(yinvvar)
nz = np.count_nonzero(zinvvar)
nm = np.count_nonzero(muinvvar)
M = np.transpose(M_T) # (n_pix_y, n_components)
R = np.transpose(R_T) # (n_pix_z, n_components)
Myinv = M * yinvvar[:, None] # (n_pix_y, n_components)
Rzinv = R * zinvvar[:, None] # (n_pix_z, n_components)
Hbar = (ell**2 * np.matmul(R_T, Rzinv) + np.matmul(M_T, Myinv) +
np.eye(nt) * muinvvar[:, None]) # (n_components, n_components)
etabar = (ell * np.sum(Rzinv * z[:, None], axis=0) +
np.sum(Myinv * y[:, None], axis=0) + mu * muinvvar
) # (n_components)
theta_map = np.linalg.solve(Hbar, etabar) # (n_components)
theta_cov = np.linalg.inv(Hbar) # (n_components, n_components)
logdetH = np.sum(logyinvvar) + np.sum(logzinvvar) + np.sum(
logmuinvvar) # scalar
xi1 = -0.5 * (
(ny + nz + nm) * log2pi - logdetH + np.sum(y * y * yinvvar) +
np.sum(z * z * zinvvar) + np.sum(mu * mu * muinvvar)) # scalar
sign, logdetHbar = np.linalg.slogdet(Hbar)
xi2 = -0.5 * (nt * log2pi - logdetHbar + np.sum(etabar * theta_map))
logfml = xi1 - xi2
return logfml, theta_map, theta_cov
# confusion_matrix = utils.copy_docstring(
# tf.math.confusion_matrix,
# lambda labels, predictions, num_classes=None, weights=None,
# dtype=tf.int32, name=None: ...)
conj = utils.copy_docstring(tf.math.conj, lambda x, name=None: np.conj(x))
cos = utils.copy_docstring(tf.math.cos, lambda x, name=None: np.cos(x))
cosh = utils.copy_docstring(tf.math.cosh, lambda x, name=None: np.cosh(x))
count_nonzero = utils.copy_docstring(
tf.math.count_nonzero,
lambda input, axis=None, keepdims=None, dtype=tf.int64, name=None: ( # pylint: disable=g-long-lambda
utils.numpy_dtype(dtype)(np.count_nonzero(input, axis))))
cumprod = utils.copy_docstring(tf.math.cumprod, _cumprod)
cumsum = utils.copy_docstring(tf.math.cumsum, _cumsum)
digamma = utils.copy_docstring(tf.math.digamma,
lambda x, name=None: scipy_special.digamma(x))
divide = utils.copy_docstring(tf.math.divide,
lambda x, y, name=None: np.divide(x, y))
divide_no_nan = utils.copy_docstring(
tf.math.divide_no_nan,
lambda x, y, name=None: np.where( # pylint: disable=g-long-lambda
onp.broadcast_to(np.equal(y, 0.),
for i in range(args.max_iter):
# update parameters
model.step()
loss = model.objective()
if not args.silent:
print(
"step: {:3d}, loss: {:7.4f}, ||Ax* - b||_2^2: {:6.4f}".format(
i + 1, loss, model.feval(model.x)))
prox_optval.append(loss)
if i > 1 and np.abs(prox_optval[-1] - prox_optval[-2]) < args.tol:
break
print("-" * 40)
print('Parameters: gamma={}, solver={}'.format(args.gamma, args.opt))
print('||Ax* - b||_2^2: {:6.3f}, Obj: {:6.3f}'.format(
model.feval(model.x), prox_optval[-1]))
if args.opt == 'ADMM':
print("nnz of x*: ", jnp.count_nonzero(model.z))
else:
print("nnz of x*: ", jnp.count_nonzero(model.x))
print('Writing the results...')
if not os.path.exists(args.output_dir):
os.mkdir(args.output_dir)
output_file = os.path.join(args.output_dir,
'{}_{}.npy'.format(args.opt, args.gamma))
jnp.save(output_file, jnp.array(prox_optval))
print('Done')
def loss_fn(
output_logits,
targets,
valid_mask,
num_nodes,
captured,
negative_example_weight=1,
focal_loss_gamma=0.0,
):
"""Compute loss and single-batch metrics for some outputs.
Args:
output_logits: Binary logits produced by the model.
targets: Model targets.
valid_mask: Mask determining which outputs are valid.
num_nodes: How many nodes there are in each example.
captured: Ignored
negative_example_weight: Weight to assign to a negative example when
computing the loss. Positive examples always get weight 1.
focal_loss_gamma: Focusing parameter for the focal loss, as described in Lin
et al. (2018). If zero, uses standard cross-entropy loss.
Returns:
Tuple (loss, metrics_dict).
"""
del captured
num_targets = jnp.count_nonzero(targets)
# Compute cross entropy.
unmasked_nll = model_util.binary_logit_cross_entropy(
output_logits, targets)
if focal_loss_gamma:
# (1-p_correct)**gamma = (-(p-1))**gamma = (-expm1(log(p)))**gamma
focus_term = jnp.power(-jnp.expm1(-unmasked_nll), focal_loss_gamma)
unmasked_nll = unmasked_nll * focus_term
# Mask the results so that they only count nodes that exist.
masked_nll = unmasked_nll * valid_mask
# Primary loss: Sum of nll over all nodes. We use sum because most of the
# edges are easy negatives.
positive_nll = jnp.sum(
jnp.where(targets, masked_nll, jnp.zeros_like(masked_nll)))
negative_nll = jnp.sum(
jnp.where(targets, jnp.zeros_like(masked_nll), masked_nll))
reweighted_nll = positive_nll + negative_example_weight * negative_nll
binary_nll = jnp.sum(reweighted_nll)
# Compute additional metrics to track learning progress.
# Average NLL of target edges:
avg_nll_per_target = positive_nll / num_targets
# Average NLL of non-target edges:
num_non_targets = num_nodes**2 - num_targets
avg_nll_per_non_target = negative_nll / num_non_targets
# Max error for any edge prediction:
worst_nll = jnp.max(masked_nll)
loss = binary_nll
# Ratio of positive to negative targets. If this is equal to
# negative_example_weight, the positive and negative examples will have the
# same total weight.
positive_per_negative = num_targets / num_non_targets
# Precision and recall at 0.1 threshold
thresholded_preds = output_logits > jax.scipy.special.logit(0.1)
count_target_pred = jnp.count_nonzero(thresholded_preds & targets)
count_pred = jnp.count_nonzero(thresholded_preds & valid_mask.astype(bool))
precision = count_target_pred / count_pred
recall = count_target_pred / num_targets
return loss, {
"avg_per_target":
avg_nll_per_target,
"avg_per_non_target":
avg_nll_per_non_target,
"worst":
worst_nll,
"positive_per_negative":
positive_per_negative,
"effective_p_model_given_target":
jnp.exp(-avg_nll_per_target),
"effective_p_model_given_nontarget":
1 - jnp.exp(-avg_nll_per_non_target),
"batch_clf_thresh_at_0.1/precision":
precision,
"batch_clf_thresh_at_0.1/recall":
recall,
"batch_clf_thresh_at_0.1/f1":
2 * (precision * recall) / (precision + recall),
}
def count_nonzero(a, axis=None, keepdims=False): if isinstance(a, JaxArray): a = a.value return jnp.count_nonzero(a, axis=axis, keepdims=keepdims)
def cond_fun(s: _BasicState):
rerr = compute_residual_error(s.R, s.eig_vals, s.X)
num_converged = jnp.count_nonzero(rerr < tol)
return jnp.logical_and(s.iteration < max_iters, num_converged < k)
