def is_neg(var):
"""
Match a variable with the `-x` pattern.
:param var: The Variable to analyze.
:return: `x` if `var` is of the form `-x`, or None otherwise.
"""
apply = var.owner
if not apply:
return None
# First match against `tensor.neg`.
if apply.op == tensor.neg:
return apply.inputs[0]
# Then match against a multiplication by -1.
if apply.op == tensor.mul and len(apply.inputs) >= 2:
for idx, mul_input in enumerate(apply.inputs):
try:
constant = opt.get_scalar_constant_value(mul_input)
is_minus_1 = numpy.allclose(constant, -1)
except NotScalarConstantError:
is_minus_1 = False
if is_minus_1:
# Found a multiplication by -1.
if len(apply.inputs) == 2:
# Only return the other input.
return apply.inputs[1 - idx]
else:
# Return the multiplication of all other inputs.
return tensor.mul(*(apply.inputs[0:idx] +
apply.inputs[idx + 1:]))
# No match.
return None
def fibby_of_zero(node):
if node.op == fibby:
x = node.inputs[0]
try:
if numpy.all(0 == get_scalar_constant_value(x)):
return [x]
except NotScalarConstantError:
pass
def fibby_of_zero(node):
if node.op == fibby:
x = node.inputs[0]
try:
if numpy.all(0 == get_scalar_constant_value(x)):
return [x]
except NotScalarConstantError:
pass
def _is_1(expr):
"""rtype bool. True iff expr is a constant close to 1
"""
try:
v = opt.get_scalar_constant_value(expr)
return numpy.allclose(v, 1)
except tensor.NotScalarConstantError:
return False
def _is_1(expr):
"""
Returns
-------
bool
True iff expr is a constant close to 1.
"""
try:
v = opt.get_scalar_constant_value(expr)
return np.allclose(v, 1)
except tensor.NotScalarConstantError:
return False
def _is_1(expr):
"""
Returns
-------
bool
True iff expr is a constant close to 1.
"""
try:
v = opt.get_scalar_constant_value(expr)
return np.allclose(v, 1)
except tensor.NotScalarConstantError:
return False
def local_1msigmoid(node):
"""
1-sigm(x) -> sigm(-x)
"""
if node.op == tensor.sub:
sub_l, sub_r = node.inputs
if len(sub_r.clients) > 1:
return # graph is using both sigm and 1-sigm
if sub_r.owner and sub_r.owner.op == sigmoid:
try:
val_l = opt.get_scalar_constant_value(sub_l)
except Exception, e:
return
if numpy.allclose(numpy.sum(val_l), 1):
return [sigmoid(-sub_r.owner.inputs[0])]
def local_1msigmoid(node):
"""
1-sigm(x) -> sigm(-x)
"""
if node.op == tensor.sub:
sub_l, sub_r = node.inputs
if len(sub_r.clients) > 1:
return # graph is using both sigm and 1-sigm
if sub_r.owner and sub_r.owner.op == sigmoid:
try:
val_l = opt.get_scalar_constant_value(sub_l)
except tensor.NotScalarConstantError:
return
if np.allclose(np.sum(val_l), 1):
out = sigmoid(-sub_r.owner.inputs[0])
copy_stack_trace([sub_r, node.outputs[0]], out)
return [out]
def local_1msigmoid(node):
"""
1-sigm(x) -> sigm(-x)
"""
if node.op == tensor.sub:
sub_l, sub_r = node.inputs
if len(sub_r.clients) > 1:
return # graph is using both sigm and 1-sigm
if sub_r.owner and sub_r.owner.op == sigmoid:
try:
val_l = opt.get_scalar_constant_value(sub_l)
except tensor.NotScalarConstantError:
return
if np.allclose(np.sum(val_l), 1):
out = sigmoid(-sub_r.owner.inputs[0])
copy_stack_trace([sub_r, node.outputs[0]], out)
return [out]
def get_dummy_args(sequences=None,
outputs_info=None,
non_sequences=None,
n_steps=None,
truncate_gradient=-1,
go_backwards=False,
mode=None,
name=None,
profile=False,
allow_gc=None,
strict=False):
################################################################## P1>
# check if inputs are just single variables instead of lists
def wrap_into_list(x):
"""
Wrap the input into a list if it is not already a list.
"""
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(outputs_info)
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(non_sequences):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, integer_types)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if (hasattr(n_steps, 'dtype')
and str(n_steps.dtype)[:3] not in ('uin', 'int')):
raise ValueError(' n_steps must be an int. dtype provided '
'is %s' % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap sequences in a dictionary if they are not already dictionaries
for i in xrange(n_seqs):
if not isinstance(seqs[i], dict):
seqs[i] = OrderedDict([('input', seqs[i]), ('taps', [0])])
elif seqs[i].get('taps', None) is not None:
seqs[i]['taps'] = wrap_into_list(seqs[i]['taps'])
elif seqs[i].get('taps', None) is None:
# seqs dictionary does not have the ``taps`` key
seqs[i]['taps'] = [0]
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if isinstance(outs_info[i], dict):
# DEPRECATED :
if outs_info[i].get('return_steps', None) is not None:
raise ValueError(
"Using `return_steps` has been deprecated. "
"Simply select the entries you need using a "
"subtensor. Scan will optimize memory "
"consumption, so do not worry about that.")
# END
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = OrderedDict([('initial', outs_info[i]),
('taps', [-1])])
elif (outs_info[i].get('initial', None) is None
and outs_info[i].get('taps', None) is not None):
# ^ no initial state but taps provided
raise ValueError(('If you are using slices of an output '
'you need to provide a initial state '
'for it'), outs_info[i])
elif (outs_info[i].get('initial', None) is not None
and outs_info[i].get('taps', None) is None):
# ^ initial state but taps not provided
if 'taps' in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning(
'Output %s ( index %d) has a initial '
'state but taps is explicitly set to None ',
getattr(outs_info[i]['initial'], 'name', 'None'), i)
outs_info[i]['taps'] = [-1]
else:
# if a None is provided as the output info we replace it
# with an empty OrdereDict() to simplify handling
outs_info[i] = OrderedDict()
##
# Step 2. Generate inputs and outputs of the inner functions
# for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
# Note that you can have something like no taps for
# a sequence, though is highly unlikely in practice
if 'taps' in seq:
# go through the indicated slice
mintap = numpy.min(seq['taps'])
maxtap = numpy.max(seq['taps'])
for k in seq['taps']:
# create one slice of the input
# Later on, if we decide not to use scan because we are
# going for just one step, it makes things easier if we
# compute the correct outputs here. This way we can use
# the output of the lambda expression directly to replace
# the output of scan.
# If not we need to use copies, that will be replaced at
# each frame by the corresponding slice
actual_slice = seq['input'][k - mintap]
_seq_val = tensor.as_tensor_variable(seq['input'])
_seq_val_slice = _seq_val[k - mintap]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_seq_val_slice)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(
('Cannot compute test value for '
'the inner function of scan, input value '
'missing %s'), e)
# Add names to slices for debugging and pretty printing ..
# that is if the input already has a name
if getattr(seq['input'], 'name', None) is not None:
if k > 0:
nw_name = seq['input'].name + '[t+%d]' % k
elif k == 0:
nw_name = seq['input'].name + '[t]'
else:
nw_name = seq['input'].name + '[t%d]' % k
nw_slice.name = nw_name
# We cut the sequence such that seq[i] to correspond to
# seq[i-k]. For the purposes of cutting the sequences, we
# need to pretend tap 0 is used to avoid cutting the sequences
# too long if the taps are all lower or all higher than 0.
maxtap_proxy = max(maxtap, 0)
mintap_proxy = min(mintap, 0)
start = (k - mintap_proxy)
if k == maxtap_proxy:
nw_seq = seq['input'][start:]
else:
end = -(maxtap_proxy - k)
nw_seq = seq['input'][start:end]
if go_backwards:
nw_seq = nw_seq[::-1]
scan_seqs.append(nw_seq)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
# Since we've added all sequences now we need to level them up based on
# n_steps or their different shapes
lengths_vec = []
for seq in scan_seqs:
lengths_vec.append(seq.shape[0])
if not scan_utils.isNaN_or_Inf_or_None(n_steps):
# ^ N_steps should also be considered
lengths_vec.append(tensor.as_tensor(n_steps))
if len(lengths_vec) == 0:
# ^ No information about the number of steps
raise ValueError('No information about the number of steps '
'provided. Either provide a value for '
'n_steps argument of scan or provide an input '
'sequence')
# If the user has provided the number of steps, do that regardless ( and
# raise an error if the sequences are not long enough )
if scan_utils.isNaN_or_Inf_or_None(n_steps):
actual_n_steps = lengths_vec[0]
for contestant in lengths_vec[1:]:
actual_n_steps = tensor.minimum(actual_n_steps, contestant)
else:
actual_n_steps = tensor.as_tensor(n_steps)
# Add names -- it helps a lot when debugging
for (nw_seq, seq) in zip(scan_seqs, seqs):
if getattr(seq['input'], 'name', None) is not None:
nw_seq.name = seq['input'].name + '[%d:]' % k
scan_seqs = [seq[:actual_n_steps] for seq in scan_seqs]
# Conventions :
# mit_mot = multiple input taps, multiple output taps ( only provided
# by the gradient function )
# mit_sot = multiple input taps, single output tap (t + 0)
# sit_sot = single input tap, single output tap (t + 0)
# nit_sot = no input tap, single output tap (t + 0)
# MIT_MOT -- not provided by the user only by the grad function
n_mit_mot = 0
n_mit_mot_outs = 0
mit_mot_scan_inputs = []
mit_mot_inner_inputs = []
mit_mot_inner_outputs = []
mit_mot_out_slices = []
mit_mot_rightOrder = []
# SIT_SOT -- provided by the user
n_mit_sot = 0
mit_sot_scan_inputs = []
mit_sot_inner_inputs = []
mit_sot_inner_slices = []
mit_sot_inner_outputs = []
mit_sot_return_steps = OrderedDict()
mit_sot_tap_array = []
mit_sot_rightOrder = []
n_sit_sot = 0
sit_sot_scan_inputs = []
sit_sot_inner_inputs = []
sit_sot_inner_slices = []
sit_sot_inner_outputs = []
sit_sot_return_steps = OrderedDict()
sit_sot_rightOrder = []
# go through outputs picking up time slices as needed
for i, init_out in enumerate(outs_info):
# Note that our convention dictates that if an output uses
# just the previous time step, as a initial state we will only
# provide a tensor of the same dimension as one time step; This
# makes code much cleaner for those who do not use taps. Otherwise
# they would always had to shape_padleft the initial state ..
# which is ugly
if init_out.get('taps', None) == [-1]:
actual_arg = init_out['initial']
if not isinstance(actual_arg, tensor.Variable):
actual_arg = tensor.as_tensor_variable(actual_arg)
arg = safe_new(actual_arg)
if isinstance(arg, tensor.Constant):
# safe new returns a clone of the constants, but that is not
# what we need for initial states
arg = arg.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
arg.tag.test_value = gof.Op._get_test_value(actual_arg)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(
('Cannot compute test value for the '
'inner function of scan, input value missing %s'),
e)
if getattr(init_out['initial'], 'name', None) is not None:
arg.name = init_out['initial'].name + '[t-1]'
# We need now to allocate space for storing the output and copy
# the initial state over. We do this using the expand function
# defined in scan utils
sit_sot_scan_inputs.append(
scan_utils.expand_empty(
tensor.unbroadcast(tensor.shape_padleft(actual_arg), 0),
actual_n_steps))
sit_sot_inner_slices.append(actual_arg)
if i in return_steps:
sit_sot_return_steps[n_sit_sot] = return_steps[i]
sit_sot_inner_inputs.append(arg)
sit_sot_rightOrder.append(i)
n_sit_sot += 1
elif init_out.get('taps', None):
if numpy.any(numpy.array(init_out.get('taps', [])) > 0):
# Make sure we do not have requests for future values of a
# sequence we can not provide such values
raise ValueError('Can not use future taps of outputs',
init_out)
# go through the taps
mintap = abs(numpy.min(init_out['taps']))
mit_sot_tap_array.append(init_out['taps'])
idx_offset = abs(numpy.min(init_out['taps']))
# Sequence
mit_sot_scan_inputs.append(
scan_utils.expand_empty(init_out['initial'][:mintap],
actual_n_steps))
if i in return_steps:
mit_sot_return_steps[n_mit_sot] = return_steps[i]
mit_sot_rightOrder.append(i)
n_mit_sot += 1
for k in init_out['taps']:
# create a new slice
actual_nw_slice = init_out['initial'][k + mintap]
_init_out_var = tensor.as_tensor_variable(init_out['initial'])
_init_out_var_slice = _init_out_var[k + mintap]
nw_slice = _init_out_var_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_init_out_var_slice)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(
('Cannot compute test value for '
'the inner function of scan, input value '
'missing. %s'), e)
# give it a name or debugging and pretty printing
if getattr(init_out['initial'], 'name', None) is not None:
if k > 0:
nw_slice.name = (init_out['initial'].name +
'[t+%d]' % k)
elif k == 0:
nw_slice.name = init_out['initial'].name + '[t]'
else:
nw_slice.name = (init_out['initial'].name +
'[t%d]' % k)
mit_sot_inner_inputs.append(nw_slice)
mit_sot_inner_slices.append(actual_nw_slice)
# NOTE: there is another case, in which we do not want to provide
# any previous value of the output to the inner function (i.e.
# a map); in that case we do not have to do anything ..
# Re-order args
max_mit_sot = numpy.max([-1] + mit_sot_rightOrder) + 1
max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
n_elems = numpy.max([max_mit_sot, max_sit_sot])
_ordered_args = [[] for x in xrange(n_elems)]
offset = 0
for idx in xrange(n_mit_sot):
n_inputs = len(mit_sot_tap_array[idx])
if n_fixed_steps in [1, -1]:
_ordered_args[mit_sot_rightOrder[idx]] = \
mit_sot_inner_slices[offset:offset + n_inputs]
else:
_ordered_args[mit_sot_rightOrder[idx]] = \
mit_sot_inner_inputs[offset:offset + n_inputs]
offset += n_inputs
for idx in xrange(n_sit_sot):
if n_fixed_steps in [1, -1]:
_ordered_args[sit_sot_rightOrder[idx]] = \
[sit_sot_inner_slices[idx]]
else:
_ordered_args[sit_sot_rightOrder[idx]] = \
[sit_sot_inner_inputs[idx]]
ordered_args = []
for ls in _ordered_args:
ordered_args += ls
if n_fixed_steps in [1, -1]:
args = (inner_slices + ordered_args + non_seqs)
else:
args = (inner_seqs + ordered_args + non_seqs)
# add only the non-shared variables and non-constants to the arguments of
# the dummy function [ a function should not get shared variables or
# constants as input ]
dummy_args = [
arg for arg in args if (not isinstance(arg, SharedVariable)
and not isinstance(arg, tensor.Constant))
]
################################################################## P1<
return dummy_args, locals()
def scan(fn,
sequences=None,
states=None,
params=None,
n_steps=None,
mode=None,
name=None,
profile=False,
allow_gc=None):
"""
Similar to Theano's official scan, this function gives the user more
control over the scan op, avoiding certain difficulties that arose from
missing optimizations.
:param fn: lambda function that describes one step of scan (see the
official Theano scan function)
:param sequences: similar to the official Theano's scan. This version
of scan does not support taps for the sequences (it can only be a
list of tensor). Scan assumes that sequences have the right length
and it does not check for this.
:param states: similar to outputs_info of the official scan function.
There is one crucial difference though, namely that the `initial`
key in the dictionary has been replace by 'membuf' key. This
reflects the change of meaning. Instead of passing to scan just
the initial steps misisng, one has now to pass a memory buffer in
which scan will try to store its output. In this memory buffer the
first entries should be set to the initial states of the
corresponding states.
Providing a memory buffer that has less entries then the number of
steps, mneans scan will only use that amount of memory. The user has
to match the memory buffer size with the number of steps, otherwise
scan will produce wrong results. Also if gradients are to be
computed through the scan, the memory buffer should have the same
length as the number of steps.
For states that do not require a initial state, one has to provide a
dictionary with a single key 'steps' that says how many intermediate
results to store. See examples below for more insight.
:param n_steps: This parameter is mandatory and it will represent the
number of steps scan will do (scan will not check sequences or any
other source of information to figure out how many steps it needs
to do).
:param mode: Same as for the official scan
:param name: Same as for the official scan
:param profile: Same as for the official scan
Note:
- there is no truncate / go_backwards anymore !
- the outputs returned by scan contain the initial states as well (i.e.
if I loop over k steps, with my smallest tap for an output -3 and keep
al intermediate results, my output will be of length k+3
Examples:
(a) if you do not want to store any intermediate results (just the
last one)
# The memory buffer can be the initial state, just that we need to
# add one extra dimension in front of it
state = TT.unbroadcast(TT.shape_padleft(x0),0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
# Once we got our result we need to remove the extra dimension
out = out[0]
(b) if you want to keep every intermediate results
state = TT.alloc(TT.constant(0), 6, x0.shape[0])
state = TT.set_subtensor(state[0], x0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
out = out[1:]
"""
def wrap_into_list(x):
'''
Wrap the input into a list if it is not already a list
'''
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(states)
if allow_gc is None:
allow_gc = config.scan.allow_gc
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(params):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if (hasattr(n_steps, 'dtype')
and str(n_steps.dtype)[:3] not in ('uin', 'int')):
raise ValueError(' n_steps must be an int. dtype provided '
'is %s' % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
elif (not outs_info[i].get('membuf', None)
and outs_info[i].get('taps', None)):
# ^ no initial state but taps provided
raise ValueError(('If you are using slices of an output '
'you need to provide a memory buffer for '
'the state '), outs_info[i])
elif (outs_info[i].get('membuf', None)
and not outs_info[i].get('taps', None)):
# ^ initial state but taps not provided
if 'taps' in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning(
'Output %s (index %d) has a memory '
'buffer but taps is explicitly set to None ',
getattr(outs_info[i]['membuf'], 'name', 'None'), i)
outs_info[i]['taps'] = [-1]
else:
# if a None is provided as the output info we replace it
# with an dict(steps=n_steps) to simplify handling
outs_info[i] = dict(steps=n_steps)
##
### Step 2. Generate inputs and outputs of the inner functions
### for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
if isinstance(seq, dict):
seq = seq['input']
actual_slice = seq[0]
_seq_val = tensor.as_tensor_variable(seq)
_seq_val_slice = _seq_val[0]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_seq_val_slice)
except AttributeError, e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing %s'), e)
if seq.name:
nw_slice.name = seq.name + '[t]'
scan_seqs.append(_seq_val)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
def scan(fn,
sequences=None,
states=None,
params=None,
n_steps=None,
mode=None,
name=None,
profile=False,
allow_gc=None):
"""
Similar to Theano's official scan, this function gives the user more
control over the scan op, avoiding certain difficulties that arose from
missing optimizations.
:param fn: lambda function that describes one step of scan (see the
official Theano scan function)
:param sequences: similar to the official Theano's scan. This version
of scan does not support taps for the sequences (it can only be a
list of tensor). Scan assumes that sequences have the right length
and it does not check for this.
:param states: similar to outputs_info of the official scan function.
There is one crucial difference though, namely that the `initial`
key in the dictionary has been replace by 'membuf' key. This
reflects the change of meaning. Instead of passing to scan just
the initial steps misisng, one has now to pass a memory buffer in
which scan will try to store its output. In this memory buffer the
first entries should be set to the initial states of the
corresponding states.
Providing a memory buffer that has less entries then the number of
steps, mneans scan will only use that amount of memory. The user has
to match the memory buffer size with the number of steps, otherwise
scan will produce wrong results. Also if gradients are to be
computed through the scan, the memory buffer should have the same
length as the number of steps.
For states that do not require a initial state, one has to provide a
dictionary with a single key 'steps' that says how many intermediate
results to store. See examples below for more insight.
:param n_steps: This parameter is mandatory and it will represent the
number of steps scan will do (scan will not check sequences or any
other source of information to figure out how many steps it needs
to do).
:param mode: Same as for the official scan
:param name: Same as for the official scan
:param profile: Same as for the official scan
Note:
- there is no truncate / go_backwards anymore !
- the outputs returned by scan contain the initial states as well (i.e.
if I loop over k steps, with my smallest tap for an output -3 and keep
al intermediate results, my output will be of length k+3
Examples:
(a) if you do not want to store any intermediate results (just the
last one)
# The memory buffer can be the initial state, just that we need to
# add one extra dimension in front of it
state = TT.unbroadcast(TT.shape_padleft(x0),0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
# Once we got our result we need to remove the extra dimension
out = out[0]
(b) if you want to keep every intermediate results
state = TT.alloc(TT.constant(0), 6, x0.shape[0])
state = TT.set_subtensor(state[0], x0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
out = out[1:]
"""
def wrap_into_list(x):
'''
Wrap the input into a list if it is not already a list
'''
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(states)
if allow_gc is None:
allow_gc = config.scan.allow_gc
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(params):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if (hasattr(n_steps, 'dtype') and
str(n_steps.dtype)[:3] not in ('uin', 'int')):
raise ValueError(' n_steps must be an int. dtype provided '
'is %s' % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
elif (not outs_info[i].get('membuf', None) and
outs_info[i].get('taps', None)):
# ^ no initial state but taps provided
raise ValueError(('If you are using slices of an output '
'you need to provide a memory buffer for '
'the state '), outs_info[i])
elif (outs_info[i].get('membuf', None) and
not outs_info[i].get('taps', None)):
# ^ initial state but taps not provided
if 'taps' in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning(
'Output %s (index %d) has a memory '
'buffer but taps is explicitly set to None ',
getattr(outs_info[i]['membuf'], 'name', 'None'),
i)
outs_info[i]['taps'] = [-1]
else:
# if a None is provided as the output info we replace it
# with an dict(steps=n_steps) to simplify handling
outs_info[i] = dict(steps=n_steps)
##
# Step 2. Generate inputs and outputs of the inner functions
# for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
if isinstance(seq, dict):
seq = seq['input']
actual_slice = seq[0]
_seq_val = tensor.as_tensor_variable(seq)
_seq_val_slice = _seq_val[0]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_seq_val_slice)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing %s'), e)
if seq.name:
nw_slice.name = seq.name + '[t]'
scan_seqs.append(_seq_val)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
actual_n_steps = tensor.as_tensor(n_steps)
# Conventions :
# mit_mot = multiple input taps, multiple output taps ( only provided
# by the gradient function )
# mit_sot = multiple input taps, single output tap (t + 0)
# sit_sot = single input tap, single output tap (t + 0)
# nit_sot = no input tap, single output tap (t + 0)
# MIT_MOT -- not provided by the user only by the grad function
n_mit_mot = 0
n_mit_mot_outs = 0
mit_mot_scan_inputs = []
mit_mot_inner_inputs = []
mit_mot_inner_outputs = []
mit_mot_out_slices = []
mit_mot_rightOrder = []
# SIT_SOT -- provided by the user
n_mit_sot = 0
mit_sot_scan_inputs = []
mit_sot_inner_inputs = []
mit_sot_inner_slices = []
mit_sot_inner_outputs = []
mit_sot_return_steps = OrderedDict()
mit_sot_tap_array = []
mit_sot_rightOrder = []
n_sit_sot = 0
sit_sot_scan_inputs = []
sit_sot_inner_inputs = []
sit_sot_inner_slices = []
sit_sot_inner_outputs = []
sit_sot_return_steps = OrderedDict()
sit_sot_rightOrder = []
nit_sot_steps = []
# go through outputs picking up time slices as needed
for i, init_out in enumerate(outs_info):
# Note that our convention dictates that if an output uses
# just the previous time step, as a initial state we will only
# provide a tensor of the same dimension as one time step; This
# makes code much cleaner for those who do not use taps. Otherwise
# they would always had to shape_padleft the initial state ..
# which is ugly
# Note, 'taps' might not be in the dictionary
if 'taps' in init_out and init_out['taps'] == [-1]:
actual_arg = init_out['membuf']
arg = safe_new(init_out['membuf'][0])
if isinstance(arg, tensor.Constant):
# safe new returns a clone of the constants, but that is not
# what we need for initial states
arg = arg.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
arg.tag.test_value = gof.Op._get_test_value(actual_arg)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for the '
'inner function of scan, input value missing %s'),
e)
if getattr(init_out['membuf'], 'name', None) is not None:
arg.name = init_out['membuf'].name + '[t-1]'
# We need now to allocate space for storing the output and copy
# the initial state over. We do this using the expand function
# defined in scan utils
sit_sot_scan_inputs.append(actual_arg)
sit_sot_inner_slices.append(actual_arg[0])
if i in return_steps:
sit_sot_return_steps[n_sit_sot] = return_steps[i]
sit_sot_inner_inputs.append(arg)
sit_sot_rightOrder.append(i)
n_sit_sot += 1
elif init_out.get('taps', None):
if numpy.any(numpy.array(init_out.get('taps', [])) > 0):
# Make sure we do not have requests for future values of a
# sequence we can not provide such values
raise ValueError('Can not use future taps of outputs',
init_out)
# go through the taps
mintap = abs(numpy.min(init_out['taps']))
mit_sot_tap_array.append(init_out['taps'])
idx_offset = abs(numpy.min(init_out['taps']))
# Sequence
mit_sot_scan_inputs.append(init_out['membuf'])
if i in return_steps:
mit_sot_return_steps[n_mit_sot] = return_steps[i]
mit_sot_rightOrder.append(i)
n_mit_sot += 1
for k in init_out['taps']:
# create a new slice
actual_nw_slice = init_out['membuf'][k + mintap]
_init_out_var = tensor.as_tensor_variable(init_out['membuf'])
_init_out_var_slice = _init_out_var[k + mintap]
nw_slice = _init_out_var_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_init_out_var_slice)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing. %s'), e)
# give it a name or debugging and pretty printing
if getattr(init_out['membuf'], 'name', None) is not None:
if k > 0:
nw_slice.name = (init_out['membuf'].name +
'[t+%d]' % k)
elif k == 0:
nw_slice.name = init_out['membuf'].name + '[t]'
else:
nw_slice.name = (init_out['membuf'].name +
'[t%d]' % k)
mit_sot_inner_inputs.append(nw_slice)
mit_sot_inner_slices.append(actual_nw_slice)
else:
pass
# Re-order args
max_mit_sot = numpy.max([-1] + mit_sot_rightOrder) + 1
max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
n_elems = numpy.max([max_mit_sot, max_sit_sot])
_ordered_args = [[] for x in xrange(n_elems)]
offset = 0
for idx in xrange(n_mit_sot):
n_inputs = len(mit_sot_tap_array[idx])
if n_fixed_steps == 1:
_ordered_args[mit_sot_rightOrder[idx]] = \
mit_sot_inner_slices[offset:offset + n_inputs]
else:
_ordered_args[mit_sot_rightOrder[idx]] = \
mit_sot_inner_inputs[offset:offset + n_inputs]
offset += n_inputs
for idx in xrange(n_sit_sot):
if n_fixed_steps == 1:
_ordered_args[sit_sot_rightOrder[idx]] = \
[sit_sot_inner_slices[idx]]
else:
_ordered_args[sit_sot_rightOrder[idx]] = \
[sit_sot_inner_inputs[idx]]
ordered_args = []
for ls in _ordered_args:
ordered_args += ls
if n_fixed_steps == 1:
args = (inner_slices +
ordered_args +
non_seqs)
else:
args = (inner_seqs +
ordered_args +
non_seqs)
# add only the non-shared variables and non-constants to the arguments of
# the dummy function [ a function should not get shared variables or
# constants as input ]
dummy_args = [arg for arg in args
if (not isinstance(arg, SharedVariable) and
not isinstance(arg, tensor.Constant))]
# when we apply the lambda expression we get a mixture of update rules
# and outputs that needs to be separated
lambda_result = fn(*args)
condition, outputs, updates = scan_utils.get_updates_and_outputs(
lambda_result)
if condition is not None:
as_while = True
else:
as_while = False
##
# Step 3. Check if we actually need scan and remove it if we don't
##
if n_fixed_steps == 1:
# We do not need to use the scan op anymore, so we can just return
# the outputs and updates we have
if condition is not None:
_logger.warning(('When the number of steps is fixed and equal '
'to 1, the provided stopping condition, ',
str(condition), ' is ignored'))
for pos, inner_out in enumerate(outputs):
# we need to see if we need to pad our sequences with an
# unbroadcastable dimension; case example : we return an
# output for which we want all intermediate. If n_steps is 1
# then, if we return the output as given by the innner function
# this will represent only a slice and it will have one
# dimension less.
if (isinstance(inner_out.type, tensor.TensorType) and
return_steps.get(pos, 0) != 1):
outputs[pos] = tensor.unbroadcast(
tensor.shape_padleft(inner_out), 0)
if len(outputs) == 1:
outputs = outputs[0]
return (outputs, updates)
##
# Step 4. Compile the dummy function
##
# We can now compile a dummy function just to see what shared variable
# we have and what are their update rules (note that the user has
# the option not to pass the shared variable to scan, so we need to
# pick them manually and add them to scan)
# make the compilation as fast as possible by not applying any
# optimization or conversion to C [ note this region is not important
# for performance so we can do stuff as unoptimal as we wish ]
# extract still missing inputs (there still might be so) and add them
# as non sequences at the end of our args
fake_nonseqs = [x.type() for x in non_seqs]
fake_outputs = scan_utils.clone(outputs + updates.values(),
replace=dict(zip(non_seqs,
fake_nonseqs)))
all_inputs = itertools.ifilter(
lambda x: (isinstance(x, gof.Variable) and
not isinstance(x, SharedVariable) and
not isinstance(x, gof.Constant)),
gof.graph.inputs(fake_outputs))
extra_inputs = filter(lambda x: x not in args + fake_nonseqs,
all_inputs)
non_seqs += extra_inputs
# Note we do not use all_inputs directly since the order of variables
# in args is quite important
dummy_args += extra_inputs
dummy_outs = outputs
if condition is not None:
dummy_outs.append(condition)
# If we use a regular dict here, the results are non-deterministic
if not isinstance(updates, (list, tuple)):
if isinstance(updates, dict) and \
not isinstance(updates, OrderedDict):
warnings.warn("Using non-deterministic dictionary.")
dummy_f = function(dummy_args,
dummy_outs,
updates=updates,
mode=compile.mode.Mode(linker='py',
optimizer=None),
on_unused_input='ignore')
##
# Step 5. Re-arange inputs of scan into a more strict order
##
# Step 5.0 Check the outputs of the dummy function to see if they
# match with user provided data
# if the number of outputs to the function does not match the number of
# assumed outputs until now (provided by the user) there can be
# only one explanation: No information is provided for any of the
# outputs (i.e. we are dealing with a map)
tmp_dummy_f_outs = len(dummy_f.maker.outputs)
if as_while:
tmp_dummy_f_outs -= 1
if not (tmp_dummy_f_outs == n_outs or outs_info == []):
raise ValueError('Please provide None as output_info for '
'any output that does not feed back into '
'scan (i.e. it behaves like a map) ')
if outs_info == []:
n_outs = len(dummy_f.maker.outputs)
if as_while:
n_outs = n_outs - 1
outs_info = [dict(steps=n_steps) for x in xrange(n_outs)]
# Step 5.1 Outputs with taps different then -1
for i, out in enumerate(outs_info):
if 'taps' in out and out['taps'] != [-1]:
mit_sot_inner_outputs.append(outputs[i])
# Step 5.2 Outputs with tap equal to -1
for i, out in enumerate(outs_info):
if 'taps' in out and out['taps'] == [-1]:
sit_sot_inner_outputs.append(outputs[i])
# Step 5.3 Outputs that correspond to update rules of shared variables
givens = OrderedDict()
n_shared_outs = 0
shared_scan_inputs = []
shared_inner_inputs = []
shared_inner_outputs = []
for input in dummy_f.maker.expanded_inputs:
if isinstance(input.variable, SharedVariable) and input.update:
new_var = safe_new(input.variable)
if getattr(input.variable, 'name', None) is not None:
new_var.name = input.variable.name + '_copy'
shared_inner_inputs.append(new_var)
shared_scan_inputs.append(input.variable)
shared_inner_outputs.append(input.update)
givens[input.variable] = new_var
n_shared_outs += 1
# Step 5.4 Outputs with no taps used in the input
n_nit_sot = 0
nit_sot_inner_outputs = []
nit_sot_return_steps = OrderedDict()
nit_sot_rightOrder = []
for i, out in enumerate(outs_info):
if not 'taps' in out:
nit_sot_inner_outputs.append(outputs[i])
if i in return_steps:
nit_sot_return_steps[n_nit_sot] = return_steps[i]
nit_sot_rightOrder.append(i)
nit_sot_steps.append(out['steps'])
n_nit_sot += 1
# Step 5.5 all other arguments including extra inputs
other_scan_args = []
other_inner_args = []
other_scan_args += [arg for arg in non_seqs
if (not isinstance(arg, SharedVariable) and
not isinstance(arg, tensor.Constant))]
# Step 5.6 all shared variables with no update rules
other_inner_args += [safe_new(arg, '_copy') for arg in non_seqs
if (not isinstance(arg, SharedVariable) and
not isinstance(arg, tensor.Constant))]
givens.update(dict(zip(other_scan_args, other_inner_args)))
other_shared_scan_args = [arg.variable for arg
in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and
not arg.update)]
other_shared_inner_args = [safe_new(arg.variable, '_copy') for arg
in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and
not arg.update)]
givens.update(dict(zip(other_shared_scan_args,
other_shared_inner_args)))
##
# Step 6. Re-order the outputs and clone them replacing things
# using the givens
##
inner_inputs = (inner_seqs +
mit_mot_inner_inputs +
mit_sot_inner_inputs +
sit_sot_inner_inputs +
shared_inner_inputs +
other_shared_inner_args +
other_inner_args)
inner_outs = (mit_mot_inner_outputs +
mit_sot_inner_outputs +
sit_sot_inner_outputs +
nit_sot_inner_outputs +
shared_inner_outputs)
if condition is not None:
inner_outs.append(condition)
new_givens = OrderedDict()
for w, w_copy in givens.iteritems():
new_givens[w] = w.type.filter_variable(w_copy)
new_outs = scan_utils.clone(inner_outs, replace=new_givens)
##
# Step 7. Create the Scan Op
##
tap_array = mit_sot_tap_array + [[-1] for x in xrange(n_sit_sot)]
info = OrderedDict()
info['tap_array'] = tap_array
info['n_seqs'] = n_seqs
info['n_mit_mot'] = n_mit_mot
info['n_mit_mot_outs'] = n_mit_mot_outs
info['mit_mot_out_slices'] = mit_mot_out_slices
info['n_mit_sot'] = n_mit_sot
info['n_sit_sot'] = n_sit_sot
info['n_shared_outs'] = n_shared_outs
info['n_nit_sot'] = n_nit_sot
info['truncate_gradient'] = -1
info['name'] = name
info['mode'] = mode
info['destroy_map'] = OrderedDict()
info['inplace'] = False
info['gpu'] = False
info['as_while'] = as_while
info['profile'] = profile
info['_scan_savemem_visited'] = True
info['allow_gc'] = allow_gc
local_op = scan_op.Scan(inner_inputs, new_outs, info)
##
# Step 8. Compute the outputs using the scan op
##
_scan_inputs = (scan_seqs +
mit_mot_scan_inputs +
mit_sot_scan_inputs +
sit_sot_scan_inputs +
shared_scan_inputs +
nit_sot_steps +
other_shared_scan_args +
other_scan_args)
scan_inputs = []
for arg in [actual_n_steps] + _scan_inputs:
if not isinstance(arg, gof.Variable):
arg = tensor.as_tensor_variable(arg)
scan_inputs += [arg]
scan_outs = local_op(*scan_inputs)
if type(scan_outs) not in (list, tuple):
scan_outs = [scan_outs]
##
# Step 9. Figure out which outs are update rules for shared variables
# and so on ...
##
update_map = OrderedUpdates()
offset = n_mit_mot
offsets = [abs(numpy.min(x)) for x in mit_sot_tap_array]
mit_sot_outs = scan_outs[offset:offset + n_mit_sot]
offset += n_mit_sot
offsets = [1 for x in xrange(n_sit_sot)]
sit_sot_outs = scan_outs[offset:offset + n_sit_sot]
offset += n_sit_sot
nit_sot_outs = scan_outs[offset:offset + n_nit_sot]
offset += n_nit_sot
for idx, update_rule in enumerate(
scan_outs[offset:offset + n_shared_outs]):
update_map[shared_scan_inputs[idx]] = update_rule
_scan_out_list = (mit_sot_outs +
sit_sot_outs +
nit_sot_outs)
# Step 10. I need to reorder the outputs to be in the order expected by
# the user
rightOrder = (mit_sot_rightOrder +
sit_sot_rightOrder +
nit_sot_rightOrder)
scan_out_list = [None] * len(rightOrder)
for idx, pos in enumerate(rightOrder):
scan_out_list[pos] = _scan_out_list[idx]
if len(scan_out_list) == 1:
scan_out_list = scan_out_list[0]
elif len(scan_out_list) == 0:
scan_out_list = None
assert isinstance(update_map, OrderedDict)
return (scan_out_list, update_map)
def scan(fn,
sequences=None,
outputs_info=None,
non_sequences=None,
n_steps=None,
truncate_gradient=-1,
go_backwards=False,
mode=None,
name=None,
profile=False,
allow_gc=None,
strict=False):
"""
This function constructs and applies a Scan op to the provided
arguments.
:param fn:
``fn`` is a function that describes the operations involved in one
step of ``scan``. ``fn`` should construct variables describing the
output of one iteration step. It should expect as input theano
variables representing all the slices of the input sequences
and previous values of the outputs, as well as all other arguments
given to scan as ``non_sequences``. The order in which scan passes
these variables to ``fn`` is the following :
* all time slices of the first sequence
* all time slices of the second sequence
* ...
* all time slices of the last sequence
* all past slices of the first output
* all past slices of the second otuput
* ...
* all past slices of the last output
* all other arguments (the list given as `non_sequences` to
scan)
The order of the sequences is the same as the one in the list
`sequences` given to scan. The order of the outputs is the same
as the order of ``outputs_info``. For any sequence or output the
order of the time slices is the same as the one in which they have
been given as taps. For example if one writes the following :
.. code-block:: python
scan(fn, sequences = [ dict(input= Sequence1, taps = [-3,2,-1])
, Sequence2
, dict(input = Sequence3, taps = 3) ]
, outputs_info = [ dict(initial = Output1, taps = [-3,-5])
, dict(initial = Output2, taps = None)
, Output3 ]
, non_sequences = [ Argument1, Argument2])
``fn`` should expect the following arguments in this given order:
#. ``Sequence1[t-3]``
#. ``Sequence1[t+2]``
#. ``Sequence1[t-1]``
#. ``Sequence2[t]``
#. ``Sequence3[t+3]``
#. ``Output1[t-3]``
#. ``Output1[t-5]``
#. ``Output3[t-1]``
#. ``Argument1``
#. ``Argument2``
The list of ``non_sequences`` can also contain shared variables
used in the function, though ``scan`` is able to figure those
out on its own so they can be skipped. For the clarity of the
code we recommend though to provide them to scan. To some extend
``scan`` can also figure out other ``non sequences`` (not shared)
even if not passed to scan (but used by `fn`). A simple example of
this would be :
.. code-block:: python
import theano.tensor as TT
W = TT.matrix()
W_2 = W**2
def f(x):
return TT.dot(x,W_2)
The function is expected to return two things. One is a list of
outputs ordered in the same order as ``outputs_info``, with the
difference that there should be only one output variable per
output initial state (even if no tap value is used). Secondly
`fn` should return an update dictionary (that tells how to
update any shared variable after each iteration step). The
dictionary can optionally be given as a list of tuples. There is
no constraint on the order of these two list, ``fn`` can return
either ``(outputs_list, update_dictionary)`` or
``(update_dictionary, outputs_list)`` or just one of the two (in
case the other is empty).
To use ``scan`` as a while loop, the user needs to change the
function ``fn`` such that also a stopping condition is returned.
To do so, he/she needs to wrap the condition in an ``until`` class.
The condition should be returned as a third element, for example:
.. code-block:: python
...
return [y1_t, y2_t], {x:x+1}, theano.scan_module.until(x < 50)
Note that a number of steps (considered in here as the maximum
number of steps ) is still required even though a condition is
passed (and it is used to allocate memory if needed). = {}):
:param sequences:
``sequences`` is the list of Theano variables or dictionaries
describing the sequences ``scan`` has to iterate over. If a
sequence is given as wrapped in a dictionary, then a set of optional
information can be provided about the sequence. The dictionary
should have the following keys:
* ``input`` (*mandatory*) -- Theano variable representing the
sequence.
* ``taps`` -- Temporal taps of the sequence required by ``fn``.
They are provided as a list of integers, where a value ``k``
impiles that at iteration step ``t`` scan will pass to ``fn``
the slice ``t+k``. Default value is ``[0]``
Any Theano variable in the list ``sequences`` is automatically
wrapped into a dictionary where ``taps`` is set to ``[0]``
:param outputs_info:
``outputs_info`` is the list of Theano variables or dictionaries
describing the initial state of the outputs computed
recurrently. When this initial states are given as dictionary
optional information can be provided about the output corresponding
to these initial states. The dictionary should have the following
keys:
* ``initial`` -- Theano variable that represents the initial
state of a given output. In case the output is not computed
recursively (think of a map) and does not require an initial
state this field can be skipped. Given that (only) the previous
time step of the output is used by ``fn``, the initial state
**should have the same shape** as the output and **should not
involve a downcast** of the data type of the output. If multiple
time taps are used, the initial state should have one extra
dimension that should cover all the possible taps. For example
if we use ``-5``, ``-2`` and ``-1`` as past taps, at step 0,
``fn`` will require (by an abuse of notation) ``output[-5]``,
``output[-2]`` and ``output[-1]``. This will be given by
the initial state, which in this case should have the shape
(5,)+output.shape. If this variable containing the initial
state is called ``init_y`` then ``init_y[0]`` *corresponds to*
``output[-5]``. ``init_y[1]`` *correponds to* ``output[-4]``,
``init_y[2]`` corresponds to ``output[-3]``, ``init_y[3]``
coresponds to ``output[-2]``, ``init_y[4]`` corresponds to
``output[-1]``. While this order might seem strange, it comes
natural from splitting an array at a given point. Assume that
we have a array ``x``, and we choose ``k`` to be time step
``0``. Then our initial state would be ``x[:k]``, while the
output will be ``x[k:]``. Looking at this split, elements in
``x[:k]`` are ordered exactly like those in ``init_y``.
* ``taps`` -- Temporal taps of the output that will be pass to
``fn``. They are provided as a list of *negative* integers,
where a value ``k`` implies that at iteration step ``t`` scan
will pass to ``fn`` the slice ``t+k``.
``scan`` will follow this logic if partial information is given:
* If an output is not wrapped in a dictionary, ``scan`` will wrap
it in one assuming that you use only the last step of the output
(i.e. it makes your tap value list equal to [-1]).
* If you wrap an output in a dictionary and you do not provide any
taps but you provide an initial state it will assume that you are
using only a tap value of -1.
* If you wrap an output in a dictionary but you do not provide any
initial state, it assumes that you are not using any form of
taps.
* If you provide a ``None`` instead of a variable or a empty
dictionary ``scan`` assumes that you will not use any taps for
this output (like for example in case of a map)
If ``outputs_info`` is an empty list or None, ``scan`` assumes
that no tap is used for any of the outputs. If information is
provided just for a subset of the outputs an exception is
raised (because there is no convention on how scan should map
the provided information to the outputs of ``fn``)
:param non_sequences:
``non_sequences`` is the list of arguments that are passed to
``fn`` at each steps. One can opt to exclude variable
used in ``fn`` from this list as long as they are part of the
computational graph, though for clarity we encourage not to do so.
:param n_steps:
``n_steps`` is the number of steps to iterate given as an int
or Theano scalar. If any of the input sequences do not have
enough elements, scan will raise an error. If the *value is 0* the
outputs will have *0 rows*. If the value is negative, ``scan``
will run backwards in time. If the ``go_backwards`` flag is already
set and also ``n_steps`` is negative, ``scan`` will run forward
in time. If n_steps is not provided, ``scan`` will figure
out the amount of steps it should run given its input sequences.
:param truncate_gradient:
``truncate_gradient`` is the number of steps to use in truncated
BPTT. If you compute gradients through a scan op, they are
computed using backpropagation through time. By providing a
different value then -1, you choose to use truncated BPTT instead
of classical BPTT, where you go for only ``truncate_gradient``
number of steps back in time.
:param go_backwards:
``go_backwards`` is a flag indicating if ``scan`` should go
backwards through the sequences. If you think of each sequence
as indexed by time, making this flag True would mean that
``scan`` goes back in time, namely that for any sequence it
starts from the end and goes towards 0.
:param name:
When profiling ``scan``, it is crucial to provide a name for any
instance of ``scan``. The profiler will produce an overall
profile of your code as well as profiles for the computation of
one step of each instance of ``scan``. The ``name`` of the instance
appears in those profiles and can greatly help to disambiguate
information.
:param mode:
It is recommended to leave this argument to None, especially
when profiling ``scan`` (otherwise the results are not going to
be accurate). If you prefer the computations of one step of
``scan`` to be done differently then the entire function, you
can use this parameter to describe how the computations in this
loop are done (see ``theano.function`` for details about
possible values and their meaning).
:param profile:
Flag or string. If true, or different from the empty string, a
profile object will be created and attached to the inner graph of
scan. In case ``profile`` is True, the profile object will have the
name of the scan instance, otherwise it will have the passed string.
Profile object collect (and print) information only when running the
inner graph with the new cvm linker ( with default modes,
other linkers this argument is useless)
:param allow_gc:
Set the value of allow gc for the internal graph of scan. If
set to None, this will use the value of config.scan.allow_gc.
:param strict:
If true, all the shared variables used in ``fn`` must be provided as a
part of ``non_sequences`` or ``sequences``.
:rtype: tuple
:return: tuple of the form (outputs, updates); ``outputs`` is either a
Theano variable or a list of Theano variables representing the
outputs of ``scan`` (in the same order as in
``outputs_info``). ``updates`` is a subclass of dictionary
specifying the
update rules for all shared variables used in scan
This dictionary should be passed to ``theano.function`` when
you compile your function. The change compared to a normal
dictionary is that we validate that keys are SharedVariable
and addition of those dictionary are validated to be consistent.
"""
# General observation : this code is executed only once, at creation
# of the computational graph, so we don't yet need to be smart about
# anything (to speed things up)
##
# Step 1. Wrap all inputs in dictionaries and add default values
##
# check if inputs are just single variables instead of lists
def wrap_into_list(x):
'''
Wrap the input into a list if it is not already a list
'''
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(outputs_info)
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(non_sequences):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if (hasattr(n_steps, 'dtype') and
str(n_steps.dtype)[:3] not in ('uin', 'int')):
raise ValueError(' n_steps must be an int. dtype provided '
'is %s' % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap sequences in a dictionary if they are not already dictionaries
for i in xrange(n_seqs):
if not isinstance(seqs[i], dict):
seqs[i] = OrderedDict([('input', seqs[i]), ('taps', [0])])
elif seqs[i].get('taps', None) is not None:
seqs[i]['taps'] = wrap_into_list(seqs[i]['taps'])
elif seqs[i].get('taps', None) is None:
# seqs dictionary does not have the ``taps`` key
seqs[i]['taps'] = [0]
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if isinstance(outs_info[i], dict):
# DEPRECATED :
if outs_info[i].get('return_steps', None) is not None:
raise ValueError(
"Using `return_steps` has been deprecated. "
"Simply select the entries you need using a "
"subtensor. Scan will optimize memory "
"consumption, so do not worry about that.")
# END
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = OrderedDict([('initial', outs_info[i]), ('taps', [-1])])
elif (outs_info[i].get('initial', None) is None and
outs_info[i].get('taps', None) is not None):
# ^ no initial state but taps provided
raise ValueError(('If you are using slices of an output '
'you need to provide a initial state '
'for it'), outs_info[i])
elif (outs_info[i].get('initial', None) is not None and
outs_info[i].get('taps', None) is None):
# ^ initial state but taps not provided
if 'taps' in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning('Output %s ( index %d) has a initial '
'state but taps is explicitly set to None ',
getattr(outs_info[i]['initial'], 'name', 'None'),
i)
outs_info[i]['taps'] = [-1]
else:
# if a None is provided as the output info we replace it
# with an empty OrdereDict() to simplify handling
outs_info[i] = OrderedDict()
##
# Step 2. Generate inputs and outputs of the inner functions
# for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
# Note that you can have something like no taps for
# a sequence, though is highly unlikely in practice
if 'taps' in seq:
# go through the indicated slice
mintap = numpy.min(seq['taps'])
maxtap = numpy.max(seq['taps'])
for k in seq['taps']:
# create one slice of the input
# Later on, if we decide not to use scan because we are
# going for just one step, it makes things easier if we
# compute the correct outputs here. This way we can use
# the output of the lambda expression directly to replace
# the output of scan.
# If not we need to use copies, that will be replaced at
# each frame by the corresponding slice
actual_slice = seq['input'][k - mintap]
_seq_val = tensor.as_tensor_variable(seq['input'])
_seq_val_slice = _seq_val[k - mintap]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_seq_val_slice)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing %s'), e)
# Add names to slices for debugging and pretty printing ..
# that is if the input already has a name
if getattr(seq['input'], 'name', None) is not None:
if k > 0:
nw_name = seq['input'].name + '[t+%d]' % k
elif k == 0:
nw_name = seq['input'].name + '[t]'
else:
nw_name = seq['input'].name + '[t%d]' % k
nw_slice.name = nw_name
# We cut the sequence such that seq[i] to correspond to
# seq[i-k]
if maxtap < 0:
offset = abs(maxtap)
else:
offset = 0
if maxtap == mintap and maxtap != 0:
if maxtap < 0:
nw_seq = seq['input'][:maxtap]
else:
nw_seq = seq['input'][maxtap:]
elif maxtap - k != 0:
nw_seq = seq['input'][offset + k - mintap: -(maxtap - k)]
else:
nw_seq = seq['input'][offset + k - mintap:]
if go_backwards:
nw_seq = nw_seq[::-1]
scan_seqs.append(nw_seq)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
# Since we've added all sequences now we need to level them up based on
# n_steps or their different shapes
lengths_vec = []
for seq in scan_seqs:
lengths_vec.append(seq.shape[0])
if not scan_utils.isNaN_or_Inf_or_None(n_steps):
# ^ N_steps should also be considered
lengths_vec.append(tensor.as_tensor(n_steps))
if len(lengths_vec) == 0:
# ^ No information about the number of steps
raise ValueError(' No information about the number of steps '
'provided. Either provide a value for '
'n_steps argument of scan or provide an input '
'sequence')
# If the user has provided the number of steps, do that regardless ( and
# raise an error if the sequences are not long enough )
if scan_utils.isNaN_or_Inf_or_None(n_steps):
actual_n_steps = lengths_vec[0]
for contestant in lengths_vec[1:]:
actual_n_steps = tensor.minimum(actual_n_steps, contestant)
else:
actual_n_steps = tensor.as_tensor(n_steps)
# Add names -- it helps a lot when debugging
for (nw_seq, seq) in zip(scan_seqs, seqs):
if getattr(seq['input'], 'name', None) is not None:
nw_seq.name = seq['input'].name + '[%d:]' % k
scan_seqs = [seq[:actual_n_steps] for seq in scan_seqs]
# Conventions :
# mit_mot = multiple input taps, multiple output taps ( only provided
# by the gradient function )
# mit_sot = multiple input taps, single output tap (t + 0)
# sit_sot = single input tap, single output tap (t + 0)
# nit_sot = no input tap, single output tap (t + 0)
# MIT_MOT -- not provided by the user only by the grad function
n_mit_mot = 0
n_mit_mot_outs = 0
mit_mot_scan_inputs = []
mit_mot_inner_inputs = []
mit_mot_inner_outputs = []
mit_mot_out_slices = []
mit_mot_rightOrder = []
# SIT_SOT -- provided by the user
n_mit_sot = 0
mit_sot_scan_inputs = []
mit_sot_inner_inputs = []
mit_sot_inner_slices = []
mit_sot_inner_outputs = []
mit_sot_return_steps = OrderedDict()
mit_sot_tap_array = []
mit_sot_rightOrder = []
n_sit_sot = 0
sit_sot_scan_inputs = []
sit_sot_inner_inputs = []
sit_sot_inner_slices = []
sit_sot_inner_outputs = []
sit_sot_return_steps = OrderedDict()
sit_sot_rightOrder = []
# go through outputs picking up time slices as needed
for i, init_out in enumerate(outs_info):
# Note that our convention dictates that if an output uses
# just the previous time step, as a initial state we will only
# provide a tensor of the same dimension as one time step; This
# makes code much cleaner for those who do not use taps. Otherwise
# they would always had to shape_padleft the initial state ..
# which is ugly
if init_out.get('taps', None) == [-1]:
actual_arg = init_out['initial']
if not isinstance(actual_arg, tensor.Variable):
actual_arg = tensor.as_tensor_variable(actual_arg)
arg = safe_new(actual_arg)
if isinstance(arg, tensor.Constant):
# safe new returns a clone of the constants, but that is not
# what we need for initial states
arg = arg.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
arg.tag.test_value = gof.Op._get_test_value(actual_arg)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for the '
'inner function of scan, input value missing %s'),
e)
if getattr(init_out['initial'], 'name', None) is not None:
arg.name = init_out['initial'].name + '[t-1]'
# We need now to allocate space for storing the output and copy
# the initial state over. We do this using the expand function
# defined in scan utils
sit_sot_scan_inputs.append(
scan_utils.expand(
tensor.unbroadcast(
tensor.shape_padleft(actual_arg), 0),
actual_n_steps
))
sit_sot_inner_slices.append(actual_arg)
if i in return_steps:
sit_sot_return_steps[n_sit_sot] = return_steps[i]
sit_sot_inner_inputs.append(arg)
sit_sot_rightOrder.append(i)
n_sit_sot += 1
elif init_out.get('taps', None):
if numpy.any(numpy.array(init_out.get('taps', [])) > 0):
# Make sure we do not have requests for future values of a
# sequence we can not provide such values
raise ValueError('Can not use future taps of outputs',
init_out)
# go through the taps
mintap = abs(numpy.min(init_out['taps']))
mit_sot_tap_array.append(init_out['taps'])
idx_offset = abs(numpy.min(init_out['taps']))
# Sequence
mit_sot_scan_inputs.append(
scan_utils.expand(init_out['initial'][:mintap],
actual_n_steps))
if i in return_steps:
mit_sot_return_steps[n_mit_sot] = return_steps[i]
mit_sot_rightOrder.append(i)
n_mit_sot += 1
for k in init_out['taps']:
# create a new slice
actual_nw_slice = init_out['initial'][k + mintap]
_init_out_var = tensor.as_tensor_variable(init_out['initial'])
_init_out_var_slice = _init_out_var[k + mintap]
nw_slice = _init_out_var_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_init_out_var_slice)
except AttributeError as e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing. %s'), e)
# give it a name or debugging and pretty printing
if getattr(init_out['initial'], 'name', None) is not None:
if k > 0:
nw_slice.name = (init_out['initial'].name +
'[t+%d]' % k)
elif k == 0:
nw_slice.name = init_out['initial'].name + '[t]'
else:
nw_slice.name = (init_out['initial'].name +
'[t%d]' % k)
mit_sot_inner_inputs.append(nw_slice)
mit_sot_inner_slices.append(actual_nw_slice)
# NOTE: there is another case, in which we do not want to provide
# any previous value of the output to the inner function (i.e.
# a map); in that case we do not have to do anything ..
# Re-order args
max_mit_sot = numpy.max([-1] + mit_sot_rightOrder) + 1
max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
n_elems = numpy.max([max_mit_sot, max_sit_sot])
_ordered_args = [[] for x in xrange(n_elems)]
offset = 0
for idx in xrange(n_mit_sot):
n_inputs = len(mit_sot_tap_array[idx])
if n_fixed_steps in [1, -1]:
_ordered_args[mit_sot_rightOrder[idx]] = \
mit_sot_inner_slices[offset:offset + n_inputs]
else:
_ordered_args[mit_sot_rightOrder[idx]] = \
mit_sot_inner_inputs[offset:offset + n_inputs]
offset += n_inputs
for idx in xrange(n_sit_sot):
if n_fixed_steps in [1, -1]:
_ordered_args[sit_sot_rightOrder[idx]] = \
[sit_sot_inner_slices[idx]]
else:
_ordered_args[sit_sot_rightOrder[idx]] = \
[sit_sot_inner_inputs[idx]]
ordered_args = []
for ls in _ordered_args:
ordered_args += ls
if n_fixed_steps in [1, -1]:
args = (inner_slices +
ordered_args +
non_seqs)
else:
args = (inner_seqs +
ordered_args +
non_seqs)
# add only the non-shared variables and non-constants to the arguments of
# the dummy function [ a function should not get shared variables or
# constants as input ]
dummy_args = [arg for arg in args
if (not isinstance(arg, SharedVariable) and
not isinstance(arg, tensor.Constant))]
# when we apply the lambda expression we get a mixture of update rules
# and outputs that needs to be separated
condition, outputs, updates = scan_utils.get_updates_and_outputs(fn(*args))
if condition is not None:
as_while = True
else:
as_while = False
##
# Step 3. Check if we actually need scan and remove it if we don't
##
if n_fixed_steps in [1, -1]:
# We do not need to use the scan op anymore, so we can just return
# the outputs and updates we have
if condition is not None:
_logger.warning(('When the number of steps is fixed and equal '
'to 1, the provided stopping condition, ',
str(condition), ' is ignored'))
for pos, inner_out in enumerate(outputs):
# we need to see if we need to pad our sequences with an
# unbroadcastable dimension; case example : we return an
# output for which we want all intermediate. If n_steps is 1
# then, if we return the output as given by the innner function
# this will represent only a slice and it will have one
# dimension less.
if (isinstance(inner_out.type, tensor.TensorType) and
return_steps.get(pos, 0) != 1):
outputs[pos] = tensor.unbroadcast(
tensor.shape_padleft(inner_out), 0)
if len(outputs) == 1:
outputs = outputs[0]
return (outputs, updates)
##
# Step 4. Compile the dummy function
##
# We can now compile a dummy function just to see what shared variable
# we have and what are their update rules (note that the user has
# the option not to pass the shared variable to scan, so we need to
# pick them manually and add them to scan)
# make the compilation as fast as possible by not applying any
# optimization or conversion to C [ note this region is not important
# for performance so we can do stuff as unoptimal as we wish ]
# extract still missing inputs (there still might be so) and add them
# as non sequences at the end of our args
fake_nonseqs = [x.type() for x in non_seqs]
fake_outputs = scan_utils.clone(outputs,
replace=OrderedDict(zip(non_seqs,
fake_nonseqs)))
all_inputs = itertools.ifilter(
lambda x: (isinstance(x, gof.Variable) and
not isinstance(x, SharedVariable) and
not isinstance(x, gof.Constant)),
gof.graph.inputs(fake_outputs))
extra_inputs = [x for x in all_inputs if x not in args + fake_nonseqs]
non_seqs += extra_inputs
# Note we do not use all_inputs directly since the order of variables
# in args is quite important
dummy_args += extra_inputs
dummy_outs = outputs
if condition is not None:
dummy_outs.append(condition)
dummy_f = function(dummy_args,
dummy_outs,
updates=updates,
mode=compile.mode.Mode(linker='py',
optimizer=None),
on_unused_input='ignore',
profile=False)
##
# Step 5. Re-arange inputs of scan into a more strict order
##
# Step 5.0 Check the outputs of the dummy function to see if they
# match with user provided data
# if the number of outputs to the function does not match the number of
# assumed outputs until now (provided by the user) there can be
# only one explanation: No information is provided for any of the
# outputs (i.e. we are dealing with a map)
tmp_dummy_f_outs = len(dummy_f.maker.outputs)
if as_while:
tmp_dummy_f_outs -= 1
if not (tmp_dummy_f_outs == n_outs or outs_info == []):
raise ValueError('Please provide None as outputs_info for '
'any output that does not feed back into '
'scan (i.e. it behaves like a map) ')
if outs_info == []:
n_outs = len(dummy_f.maker.outputs)
if as_while:
n_outs = n_outs - 1
outs_info = [OrderedDict() for x in xrange(n_outs)]
# Step 5.1 Outputs with taps different then -1
for i, out in enumerate(outs_info):
if 'taps' in out and out['taps'] != [-1]:
mit_sot_inner_outputs.append(outputs[i])
# Step 5.2 Outputs with tap equal to -1
for i, out in enumerate(outs_info):
if 'taps' in out and out['taps'] == [-1]:
sit_sot_inner_outputs.append(outputs[i])
# Step 5.3 Outputs that correspond to update rules of shared variables
givens = OrderedDict()
n_shared_outs = 0
shared_scan_inputs = []
shared_inner_inputs = []
shared_inner_outputs = []
sit_sot_shared = []
for input in dummy_f.maker.expanded_inputs:
if isinstance(input.variable, SharedVariable) and input.update:
new_var = safe_new(input.variable)
if getattr(input.variable, 'name', None) is not None:
new_var.name = input.variable.name + '_copy'
if isinstance(new_var.type, ops.expandable_types):
sit_sot_inner_inputs.append(new_var)
sit_sot_scan_inputs.append(
scan_utils.expand(
tensor.unbroadcast(
tensor.shape_padleft(input.variable), 0),
actual_n_steps))
tensor_update = tensor.as_tensor_variable(input.update)
sit_sot_inner_outputs.append(tensor_update)
# Not that pos is not a negative index. The sign of pos is used
# as a flag to indicate if this output should be part of the
# update rules or part of the standard outputs of scan.
# If `pos` is positive than it corresponds to the standard
# outputs of scan and it refers to output of index `pos`. If `pos`
# is negative that it corresponds to update rules of scan and it
# refers to update rule of index -1 - `pos`.
sit_sot_rightOrder.append(-1 - len(sit_sot_shared))
sit_sot_shared.append(input.variable)
givens[input.variable] = new_var
else:
shared_inner_inputs.append(new_var)
shared_scan_inputs.append(input.variable)
shared_inner_outputs.append(input.update)
givens[input.variable] = new_var
n_shared_outs += 1
n_sit_sot = len(sit_sot_inner_inputs)
# Step 5.4 Outputs with no taps used in the input
n_nit_sot = 0
nit_sot_inner_outputs = []
nit_sot_return_steps = OrderedDict()
nit_sot_rightOrder = []
for i, out in enumerate(outs_info):
if not 'taps' in out:
nit_sot_inner_outputs.append(outputs[i])
if i in return_steps:
nit_sot_return_steps[n_nit_sot] = return_steps[i]
nit_sot_rightOrder.append(i)
n_nit_sot += 1
# Step 5.5 all other arguments including extra inputs
other_scan_args = []
other_inner_args = []
other_scan_args += [arg for arg in non_seqs
if (not isinstance(arg, SharedVariable) and
not isinstance(arg, tensor.Constant))]
# Step 5.6 all shared variables with no update rules
other_inner_args += [safe_new(arg, '_copy') for arg in non_seqs
if (not isinstance(arg, SharedVariable) and
not isinstance(arg, tensor.Constant))]
givens.update(OrderedDict(zip(other_scan_args, other_inner_args)))
if strict:
non_seqs_set = set(non_sequences if non_sequences != None else [])
other_shared_scan_args = [arg.variable for arg
in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and
not arg.update and
arg.variable in non_seqs_set)]
other_shared_inner_args = [safe_new(arg.variable, '_copy') for arg
in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and
not arg.update and
arg.variable in non_seqs_set)]
else:
other_shared_scan_args = [arg.variable for arg
in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and
not arg.update)]
other_shared_inner_args = [safe_new(arg.variable, '_copy') for arg
in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and
not arg.update)]
givens.update(OrderedDict(zip(other_shared_scan_args,
other_shared_inner_args)))
##
# Step 6. Re-order the outputs and clone them replacing things
# using the givens
##
inner_inputs = (inner_seqs +
mit_mot_inner_inputs +
mit_sot_inner_inputs +
sit_sot_inner_inputs +
shared_inner_inputs +
other_shared_inner_args +
other_inner_args)
inner_outs = (mit_mot_inner_outputs +
mit_sot_inner_outputs +
sit_sot_inner_outputs +
nit_sot_inner_outputs +
shared_inner_outputs)
if condition is not None:
inner_outs.append(condition)
# Cuda is imported here, instead of being imported on top of the file
# because forces on the user some dependencies that we might do not want
# to. Currently we are working on removing the dependencies on sandbox
# code completeley.
from theano.sandbox import cuda
if cuda.cuda_available:
# very often we end up in this situation when we want to
# replace w with w_copy, where w is CudaNdarray
# and w_copy is TensorType. This is caused because shared
# variables are put on GPU right aways >:| ,
new_givens = OrderedDict()
for w, w_copy in givens.iteritems():
if (isinstance(w.type, cuda.CudaNdarrayType)
and isinstance(w_copy.type, tensor.TensorType)):
for o in inner_outs:
new_givens = traverse(o, w, w_copy, new_givens)
else:
new_givens[w] = w_copy
else:
new_givens = givens
new_outs = scan_utils.clone(inner_outs, replace=new_givens)
##
# Step 7. Create the Scan Op
##
tap_array = mit_sot_tap_array + [[-1] for x in xrange(n_sit_sot)]
if allow_gc is None:
allow_gc = config.scan.allow_gc
info = OrderedDict()
info['tap_array'] = tap_array
info['n_seqs'] = n_seqs
info['n_mit_mot'] = n_mit_mot
info['n_mit_mot_outs'] = n_mit_mot_outs
info['mit_mot_out_slices'] = mit_mot_out_slices
info['n_mit_sot'] = n_mit_sot
info['n_sit_sot'] = n_sit_sot
info['n_shared_outs'] = n_shared_outs
info['n_nit_sot'] = n_nit_sot
info['truncate_gradient'] = truncate_gradient
info['name'] = name
info['mode'] = mode
info['destroy_map'] = OrderedDict()
info['gpu'] = False
info['as_while'] = as_while
info['profile'] = profile
info['allow_gc'] = allow_gc
info['strict'] = strict
if strict:
warnings.warn('In the strict mode, all neccessary shared variables '
'must be passed as a part of non_sequences', Warning)
local_op = scan_op.Scan(inner_inputs, new_outs, info)
##
# Step 8. Compute the outputs using the scan op
##
_scan_inputs = (scan_seqs +
mit_mot_scan_inputs +
mit_sot_scan_inputs +
sit_sot_scan_inputs +
shared_scan_inputs +
[actual_n_steps for x in xrange(n_nit_sot)] +
other_shared_scan_args +
other_scan_args)
scan_inputs = []
for arg in [actual_n_steps] + _scan_inputs:
try:
arg = tensor.as_tensor_variable(arg)
except TypeError:
# This happens for Random States for e.g. but it is a good way
# to make sure no input is a cuda ndarrays
pass
scan_inputs += [arg]
scan_outs = local_op(*scan_inputs)
if type(scan_outs) not in (list, tuple):
scan_outs = [scan_outs]
##
# Step 9. Figure out which outs are update rules for shared variables
# and so on ...
##
update_map = OrderedUpdates()
def remove_dimensions(outs, steps_return, offsets=None):
out_ls = []
for idx, out in enumerate(outs):
if idx in steps_return:
if steps_return[idx] > 1:
out_ls.append(out[-steps_return[idx]:])
else:
out_ls.append(out[-1])
else:
if offsets is None:
out_ls.append(out)
else:
out_ls.append(out[offsets[idx]:])
return out_ls
offset = n_mit_mot
offsets = [abs(numpy.min(x)) for x in mit_sot_tap_array]
mit_sot_outs = remove_dimensions(
scan_outs[offset:offset + n_mit_sot],
mit_sot_return_steps,
offsets)
offset += n_mit_sot
offsets = [1 for x in xrange(n_sit_sot)]
sit_sot_outs = remove_dimensions(
scan_outs[offset:offset + n_sit_sot],
sit_sot_return_steps,
offsets)
offset += n_sit_sot
nit_sot_outs = remove_dimensions(
scan_outs[offset:offset + n_nit_sot],
nit_sot_return_steps)
offset += n_nit_sot
for idx, update_rule in enumerate(
scan_outs[offset:offset + n_shared_outs]):
update_map[shared_scan_inputs[idx]] = update_rule
_scan_out_list = (mit_sot_outs +
sit_sot_outs +
nit_sot_outs)
# Step 10. I need to reorder the outputs to be in the order expected by
# the user
rightOrder = (mit_sot_rightOrder +
sit_sot_rightOrder +
nit_sot_rightOrder)
scan_out_list = [None] * len(rightOrder)
for idx, pos in enumerate(rightOrder):
if pos >= 0:
scan_out_list[pos] = _scan_out_list[idx]
else:
# Not that pos is not a negative index. The sign of pos is used
# as a flag to indicate if this output should be part of the
# update rules or part of the standard outputs of scan.
# If `pos` is positive than it corresponds to the standard
# outputs of scan and it refers to output of index `pos`. If `pos`
# is negative that it corresponds to update rules of scan and it
# refers to update rule of index -1 - `pos`.
update_map[sit_sot_shared[abs(pos) - 1]] = _scan_out_list[idx][-1]
scan_out_list = [x for x in scan_out_list if x is not None]
if len(scan_out_list) == 1:
scan_out_list = scan_out_list[0]
elif len(scan_out_list) == 0:
scan_out_list = None
return (scan_out_list, update_map)
def scan(fn,
sequences=None,
states=None,
params=None,
n_steps=None,
mode=None,
name=None,
profile=False):
"""
Similar to Theano's official scan, this function gives the user more
control over the scan op, avoiding certain difficulties that arose from
missing optimizations.
:param fn: lambda function that describes one step of scan (see the
official Theano scan function)
:param sequences: similar to the official Theano's scan. This version
of scan does not support taps for the sequences (it can only be a
list of tensor). Scan assumes that sequences have the right length
and it does not check for this.
:param states: similar to outputs_info of the official scan function.
There is one crucial difference though, namely that the `initial`
key in the dictionary has been replace by 'membuf' key. This
reflects the change of meaning. Instead of passing to scan just
the initial steps misisng, one has now to pass a memory buffer in
which scan will try to store its output. In this memory buffer the
first entries should be set to the initial states of the
corresponding states.
Providing a memory buffer that has less entries then the number of
steps, mneans scan will only use that amount of memory. The user has
to match the memory buffer size with the number of steps, otherwise
scan will produce wrong results. Also if gradients are to be
computed through the scan, the memory buffer should have the same
length as the number of steps.
For states that do not require a initial state, one has to provide a
dictionary with a single key 'steps' that says how many intermediate
results to store. See examples below for more insight.
:param n_steps: This parameter is mandatory and it will represent the
number of steps scan will do (scan will not check sequences or any
other source of information to figure out how many steps it needs
to do).
:param mode: Same as for the official scan
:param name: Same as for the official scan
:param profile: Same as for the official scan
Note:
- there is no truncate / go_backwards anymore !
- the outputs returned by scan contain the initial states as well (i.e.
if I loop over k steps, with my smallest tap for an output -3 and keep
al intermediate results, my output will be of length k+3
Examples:
(a) if you do not want to store any intermediate results (just the
last one)
# The memory buffer can be the initial state, just that we need to
# add one extra dimension in front of it
state = TT.unbroadcast(TT.shape_padleft(x0),0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
# Once we got our result we need to remove the extra dimension
out = out[0]
(b) if you want to keep every intermediate results
state = TT.alloc(TT.constant(0), 6, x0.shape[0])
state = TT.set_subtensor(state[0], x0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
out = out[1:]
"""
def wrap_into_list(x):
'''
Wrap the input into a list if it is not already a list
'''
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(states)
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(params):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if (hasattr(n_steps, 'dtype') and
str(n_steps.dtype)[:3] not in ('uin', 'int')):
raise ValueError(' n_steps must be an int. dtype provided '
'is %s' % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
elif (not outs_info[i].get('membuf', None) and
outs_info[i].get('taps', None)):
# ^ no initial state but taps provided
raise ValueError(('If you are using slices of an output '
'you need to provide a memory buffer for '
'the state '), outs_info[i])
elif (outs_info[i].get('membuf', None) and
not outs_info[i].get('taps', None)):
# ^ initial state but taps not provided
if 'taps' in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning(
'Output %s (index %d) has a memory '
'buffer but taps is explicitly set to None ',
getattr(outs_info[i]['membuf'], 'name', 'None'),
i)
outs_info[i]['taps'] = [-1]
else:
# if a None is provided as the output info we replace it
# with an dict(steps=n_steps) to simplify handling
outs_info[i] = dict(steps=n_steps)
##
### Step 2. Generate inputs and outputs of the inner functions
### for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
actual_slice = seq[0]
_seq_val = tensor.as_tensor_variable(seq)
_seq_val_slice = _seq_val[0]
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_seq_val_slice)
except AttributeError, e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing %s'), e)
nw_slice = _seq_val_slice.type()
if seq.name:
nw_slice.name = seq.name + '[t]'
scan_seqs.append(_seq_val)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
def scan(fn,
sequences=None,
outputs_info=None,
non_sequences=None,
n_steps=None,
truncate_gradient=-1,
go_backwards=False,
mode=None,
name=None,
profile=False,
allow_gc=None,
strict=False):
"""
This function constructs and applies a Scan op to the provided
arguments.
:param fn:
``fn`` is a function that describes the operations involved in one
step of ``scan``. ``fn`` should construct variables describing the
output of one iteration step. It should expect as input theano
variables representing all the slices of the input sequences
and previous values of the outputs, as well as all other arguments
given to scan as ``non_sequences``. The order in which scan passes
these variables to ``fn`` is the following :
* all time slices of the first sequence
* all time slices of the second sequence
* ...
* all time slices of the last sequence
* all past slices of the first output
* all past slices of the second otuput
* ...
* all past slices of the last output
* all other arguments (the list given as `non_sequences` to
scan)
The order of the sequences is the same as the one in the list
`sequences` given to scan. The order of the outputs is the same
as the order of ``outputs_info``. For any sequence or output the
order of the time slices is the same as the one in which they have
been given as taps. For example if one writes the following :
.. code-block:: python
scan(fn, sequences = [ dict(input= Sequence1, taps = [-3,2,-1])
, Sequence2
, dict(input = Sequence3, taps = 3) ]
, outputs_info = [ dict(initial = Output1, taps = [-3,-5])
, dict(initial = Output2, taps = None)
, Output3 ]
, non_sequences = [ Argument1, Argument2])
``fn`` should expect the following arguments in this given order:
#. ``Sequence1[t-3]``
#. ``Sequence1[t+2]``
#. ``Sequence1[t-1]``
#. ``Sequence2[t]``
#. ``Sequence3[t+3]``
#. ``Output1[t-3]``
#. ``Output1[t-5]``
#. ``Output3[t-1]``
#. ``Argument1``
#. ``Argument2``
The list of ``non_sequences`` can also contain shared variables
used in the function, though ``scan`` is able to figure those
out on its own so they can be skipped. For the clarity of the
code we recommend though to provide them to scan. To some extend
``scan`` can also figure out other ``non sequences`` (not shared)
even if not passed to scan (but used by `fn`). A simple example of
this would be :
.. code-block:: python
import theano.tensor as TT
W = TT.matrix()
W_2 = W**2
def f(x):
return TT.dot(x,W_2)
The function is expected to return two things. One is a list of
outputs ordered in the same order as ``outputs_info``, with the
difference that there should be only one output variable per
output initial state (even if no tap value is used). Secondly
`fn` should return an update dictionary (that tells how to
update any shared variable after each iteration step). The
dictionary can optionally be given as a list of tuples. There is
no constraint on the order of these two list, ``fn`` can return
either ``(outputs_list, update_dictionary)`` or
``(update_dictionary, outputs_list)`` or just one of the two (in
case the other is empty).
To use ``scan`` as a while loop, the user needs to change the
function ``fn`` such that also a stopping condition is returned.
To do so, he/she needs to wrap the condition in an ``until`` class.
The condition should be returned as a third element, for example:
.. code-block:: python
...
return [y1_t, y2_t], {x:x+1}, theano.scan_module.until(x < 50)
Note that a number of steps (considered in here as the maximum
number of steps ) is still required even though a condition is
passed (and it is used to allocate memory if needed). = {}):
:param sequences:
``sequences`` is the list of Theano variables or dictionaries
describing the sequences ``scan`` has to iterate over. If a
sequence is given as wrapped in a dictionary, then a set of optional
information can be provided about the sequence. The dictionary
should have the following keys:
* ``input`` (*mandatory*) -- Theano variable representing the
sequence.
* ``taps`` -- Temporal taps of the sequence required by ``fn``.
They are provided as a list of integers, where a value ``k``
impiles that at iteration step ``t`` scan will pass to ``fn``
the slice ``t+k``. Default value is ``[0]``
Any Theano variable in the list ``sequences`` is automatically
wrapped into a dictionary where ``taps`` is set to ``[0]``
:param outputs_info:
``outputs_info`` is the list of Theano variables or dictionaries
describing the initial state of the outputs computed
recurrently. When this initial states are given as dictionary
optional information can be provided about the output corresponding
to these initial states. The dictionary should have the following
keys:
* ``initial`` -- Theano variable that represents the initial
state of a given output. In case the output is not computed
recursively (think of a map) and does not require an initial
state this field can be skipped. Given that (only) the previous
time step of the output is used by ``fn``, the initial state
**should have the same shape** as the output and **should not
involve a downcast** of the data type of the output. If multiple
time taps are used, the initial state should have one extra
dimension that should cover all the possible taps. For example
if we use ``-5``, ``-2`` and ``-1`` as past taps, at step 0,
``fn`` will require (by an abuse of notation) ``output[-5]``,
``output[-2]`` and ``output[-1]``. This will be given by
the initial state, which in this case should have the shape
(5,)+output.shape. If this variable containing the initial
state is called ``init_y`` then ``init_y[0]`` *corresponds to*
``output[-5]``. ``init_y[1]`` *correponds to* ``output[-4]``,
``init_y[2]`` corresponds to ``output[-3]``, ``init_y[3]``
coresponds to ``output[-2]``, ``init_y[4]`` corresponds to
``output[-1]``. While this order might seem strange, it comes
natural from splitting an array at a given point. Assume that
we have a array ``x``, and we choose ``k`` to be time step
``0``. Then our initial state would be ``x[:k]``, while the
output will be ``x[k:]``. Looking at this split, elements in
``x[:k]`` are ordered exactly like those in ``init_y``.
* ``taps`` -- Temporal taps of the output that will be pass to
``fn``. They are provided as a list of *negative* integers,
where a value ``k`` implies that at iteration step ``t`` scan
will pass to ``fn`` the slice ``t+k``.
``scan`` will follow this logic if partial information is given:
* If an output is not wrapped in a dictionary, ``scan`` will wrap
it in one assuming that you use only the last step of the output
(i.e. it makes your tap value list equal to [-1]).
* If you wrap an output in a dictionary and you do not provide any
taps but you provide an initial state it will assume that you are
using only a tap value of -1.
* If you wrap an output in a dictionary but you do not provide any
initial state, it assumes that you are not using any form of
taps.
* If you provide a ``None`` instead of a variable or a empty
dictionary ``scan`` assumes that you will not use any taps for
this output (like for example in case of a map)
If ``outputs_info`` is an empty list or None, ``scan`` assumes
that no tap is used for any of the outputs. If information is
provided just for a subset of the outputs an exception is
raised (because there is no convention on how scan should map
the provided information to the outputs of ``fn``)
:param non_sequences:
``non_sequences`` is the list of arguments that are passed to
``fn`` at each steps. One can opt to exclude variable
used in ``fn`` from this list as long as they are part of the
computational graph, though for clarity we encourage not to do so.
:param n_steps:
``n_steps`` is the number of steps to iterate given as an int
or Theano scalar. If any of the input sequences do not have
enough elements, scan will raise an error. If the *value is 0* the
outputs will have *0 rows*. If the value is negative, ``scan``
will run backwards in time. If the ``go_backwards`` flag is already
set and also ``n_steps`` is negative, ``scan`` will run forward
in time. If n_steps is not provided, ``scan`` will figure
out the amount of steps it should run given its input sequences.
:param truncate_gradient:
``truncate_gradient`` is the number of steps to use in truncated
BPTT. If you compute gradients through a scan op, they are
computed using backpropagation through time. By providing a
different value then -1, you choose to use truncated BPTT instead
of classical BPTT, where you go for only ``truncate_gradient``
number of steps back in time.
:param go_backwards:
``go_backwards`` is a flag indicating if ``scan`` should go
backwards through the sequences. If you think of each sequence
as indexed by time, making this flag True would mean that
``scan`` goes back in time, namely that for any sequence it
starts from the end and goes towards 0.
:param name:
When profiling ``scan``, it is crucial to provide a name for any
instance of ``scan``. The profiler will produce an overall
profile of your code as well as profiles for the computation of
one step of each instance of ``scan``. The ``name`` of the instance
appears in those profiles and can greatly help to disambiguate
information.
:param mode:
It is recommended to leave this argument to None, especially
when profiling ``scan`` (otherwise the results are not going to
be accurate). If you prefer the computations of one step of
``scan`` to be done differently then the entire function, you
can use this parameter to describe how the computations in this
loop are done (see ``theano.function`` for details about
possible values and their meaning).
:param profile:
Flag or string. If true, or different from the empty string, a
profile object will be created and attached to the inner graph of
scan. In case ``profile`` is True, the profile object will have the
name of the scan instance, otherwise it will have the passed string.
Profile object collect (and print) information only when running the
inner graph with the new cvm linker ( with default modes,
other linkers this argument is useless)
:param allow_gc:
Set the value of allow gc for the internal graph of scan. If
set to None, this will use the value of config.scan.allow_gc.
:param strict:
If true, all the shared variables used in ``fn`` must be provided as a
part of ``non_sequences`` or ``sequences``.
:rtype: tuple
:return: tuple of the form (outputs, updates); ``outputs`` is either a
Theano variable or a list of Theano variables representing the
outputs of ``scan`` (in the same order as in
``outputs_info``). ``updates`` is a subclass of dictionary
specifying the
update rules for all shared variables used in scan
This dictionary should be passed to ``theano.function`` when
you compile your function. The change compared to a normal
dictionary is that we validate that keys are SharedVariable
and addition of those dictionary are validated to be consistent.
"""
# General observation : this code is executed only once, at creation
# of the computational graph, so we don't yet need to be smart about
# anything (to speed things up)
##
# Step 1. Wrap all inputs in dictionaries and add default values
##
# check if inputs are just single variables instead of lists
def wrap_into_list(x):
'''
Wrap the input into a list if it is not already a list
'''
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(outputs_info)
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(non_sequences):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if (hasattr(n_steps, 'dtype') and
str(n_steps.dtype)[:3] not in ('uin', 'int')):
raise ValueError(' n_steps must be an int. dtype provided '
'is %s' % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap sequences in a dictionary if they are not already dictionaries
for i in xrange(n_seqs):
if not isinstance(seqs[i], dict):
seqs[i] = OrderedDict([('input', seqs[i]), ('taps', [0])])
elif seqs[i].get('taps', None) is not None:
seqs[i]['taps'] = wrap_into_list(seqs[i]['taps'])
elif seqs[i].get('taps', None) is None:
# seqs dictionary does not have the ``taps`` key
seqs[i]['taps'] = [0]
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if isinstance(outs_info[i], dict):
# DEPRECATED :
if outs_info[i].get('return_steps', None) is not None:
raise ValueError(
"Using `return_steps` has been deprecated. "
"Simply select the entries you need using a "
"subtensor. Scan will optimize memory "
"consumption, so do not worry about that.")
# END
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = OrderedDict([('initial', outs_info[i]), ('taps', [-1])])
elif (outs_info[i].get('initial', None) is None and
outs_info[i].get('taps', None) is not None):
# ^ no initial state but taps provided
raise ValueError(('If you are using slices of an output '
'you need to provide a initial state '
'for it'), outs_info[i])
elif (outs_info[i].get('initial', None) is not None and
outs_info[i].get('taps', None) is None):
# ^ initial state but taps not provided
if 'taps' in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning('Output %s ( index %d) has a initial '
'state but taps is explicitly set to None ',
getattr(outs_info[i]['initial'], 'name', 'None'),
i)
outs_info[i]['taps'] = [-1]
else:
# if a None is provided as the output info we replace it
# with an empty OrdereDict() to simplify handling
outs_info[i] = OrderedDict()
##
# Step 2. Generate inputs and outputs of the inner functions
# for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
# Note that you can have something like no taps for
# a sequence, though is highly unlikely in practice
if 'taps' in seq:
# go through the indicated slice
mintap = numpy.min(seq['taps'])
maxtap = numpy.max(seq['taps'])
for k in seq['taps']:
# create one slice of the input
# Later on, if we decide not to use scan because we are
# going for just one step, it makes things easier if we
# compute the correct outputs here. This way we can use
# the output of the lambda expression directly to replace
# the output of scan.
# If not we need to use copies, that will be replaced at
# each frame by the corresponding slice
actual_slice = seq['input'][k - mintap]
_seq_val = tensor.as_tensor_variable(seq['input'])
_seq_val_slice = _seq_val[k - mintap]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != 'off':
try:
nw_slice.tag.test_value = gof.Op._get_test_value(
_seq_val_slice)
except AttributeError, e:
if config.compute_test_value != 'ignore':
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(('Cannot compute test value for '
'the inner function of scan, input value '
'missing %s'), e)
# Add names to slices for debugging and pretty printing ..
# that is if the input already has a name
if getattr(seq['input'], 'name', None) is not None:
if k > 0:
nw_name = seq['input'].name + '[t+%d]' % k
elif k == 0:
nw_name = seq['input'].name + '[t]'
else:
nw_name = seq['input'].name + '[t%d]' % k
nw_slice.name = nw_name
# We cut the sequence such that seq[i] to correspond to
# seq[i-k]
if maxtap < 0:
offset = abs(maxtap)
else:
offset = 0
if maxtap == mintap and maxtap != 0:
if maxtap < 0:
nw_seq = seq['input'][:maxtap]
else:
nw_seq = seq['input'][maxtap:]
elif maxtap - k != 0:
nw_seq = seq['input'][offset + k - mintap: -(maxtap - k)]
else:
nw_seq = seq['input'][offset + k - mintap:]
if go_backwards:
nw_seq = nw_seq[::-1]
scan_seqs.append(nw_seq)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
def scan(fn,
sequences=None,
outputs_info=None,
non_sequences=None,
n_steps=None,
truncate_gradient=-1,
go_backwards=False,
mode=None,
name=None,
options=None,
profile=False):
"""
This function constructs and applies a Scan op to the provided
arguments.
:param fn:
``fn`` is a function that describes the operations involved in one
step of ``scan``. ``fn`` should construct variables describing the
output of one iteration step. It should expect as input theano
variables representing all the slices of the input sequences
and previous values of the outputs, as well as all other arguments
given to scan as ``non_sequences``. The order in which scan passes
these variables to ``fn`` is the following :
* all time slices of the first sequence
* all time slices of the second sequence
* ...
* all time slices of the last sequence
* all past slices of the first output
* all past slices of the second otuput
* ...
* all past slices of the last output
* all other arguments (the list given as `non_sequences` to
scan)
The order of the sequences is the same as the one in the list
`sequences` given to scan. The order of the outputs is the same
as the order of ``outputs_info``. For any sequence or output the
order of the time slices is the same as the one in which they have
been given as taps. For example if one writes the following :
.. code-block:: python
scan(fn, sequences = [ dict(input= Sequence1, taps = [-3,2,-1])
, Sequence2
, dict(input = Sequence3, taps = 3) ]
, outputs_info = [ dict(initial = Output1, taps = [-3,-5])
, dict(initial = Output2, taps = None)
, Output3 ]
, non_sequences = [ Argument1, Argument 2])
``fn`` should expect the following arguments in this given order:
#. ``Sequence1[t-3]``
#. ``Sequence1[t+2]``
#. ``Sequence1[t-1]``
#. ``Sequence2[t]``
#. ``Sequence3[t+3]``
#. ``Output1[t-3]``
#. ``Output1[t-5]``
#. ``Output3[t-1]``
#. ``Argument1``
#. ``Argument2``
The list of ``non_sequences`` can also contain shared variables
used in the function, though ``scan`` is able to figure those
out on its own so they can be skipped. For the clarity of the
code we recommend though to provide them to scan. To some extend
``scan`` can also figure out other ``non sequences`` (not shared)
even if not passed to scan (but used by `fn`). A simple example of
this would be :
.. code-block:: python
import theano.tensor as TT
W = TT.matrix()
W_2 = W**2
def f(x):
return TT.dot(x,W_2)
The function is expected to return two things. One is a list of
outputs ordered in the same order as ``outputs_info``, with the
difference that there should be only one output variable per
output initial state (even if no tap value is used). Secondly
`fn` should return an update dictionary (that tells how to
update any shared variable after each iteration step). The
dictionary can optionally be given as a list of tuples. There is
no constraint on the order of these two list, ``fn`` can return
either ``(outputs_list, update_dictionary)`` or
``(update_dictionary, outputs_list)`` or just one of the two (in
case the other is empty).
To use ``scan`` as a while loop, the user needs to change the
function ``fn`` such that also a stopping condition is returned.
To do so, he/she needs to wrap the condition in an ``until`` class.
The condition should be returned as a third element, for example:
.. code-block:: python
...
return [y1_t, y2_t], {x:x+1}, theano.scan_module.until(x < 50)
Note that a number of steps (considered in here as the maximum
number of steps ) is still required even though a condition is
passed (and it is used to allocate memory if needed). = {}):
:param sequences:
``sequences`` is the list of Theano variables or dictionaries
describing the sequences ``scan`` has to iterate over. If a
sequence is given as wrapped in a dictionary, then a set of optional
information can be provided about the sequence. The dictionary
should have the following keys:
* ``input`` (*mandatory*) -- Theano variable representing the
sequence.
* ``taps`` -- Temporal taps of the sequence required by ``fn``.
They are provided as a list of integers, where a value ``k``
impiles that at iteration step ``t`` scan will pass to ``fn``
the slice ``t+k``. Default value is ``[0]``
Any Theano variable in the list ``sequences`` is automatically
wrapped into a dictionary where ``taps`` is set to ``[0]``
:param outputs_info:
``outputs_info`` is the list of Theano variables or dictionaries
describing the initial state of the outputs computed
recurrently. When this initial states are given as dictionary
optional information can be provided about the output corresponding
to these initial states. The dictionary should have the following
keys:
* ``initial`` -- Theano variable that represents the initial
state of a given output. In case the output is not computed
recursively (think of a map) and does not require a initial
state this field can be skiped. Given that only the previous
time step of the output is used by ``fn`` the initial state
should have the same shape as the output. If multiple time
taps are used, the initial state should have one extra
dimension that should cover all the possible taps. For example
if we use ``-5``, ``-2`` and ``-1`` as past taps, at step 0,
``fn`` will require (by an abuse of notation) ``output[-5]``,
``output[-2]`` and ``output[-1]``. This will be given by
the initial state, which in this case should have the shape
(5,)+output.shape. If this variable containing the initial
state is called ``init_y`` then ``init_y[0]`` *corresponds to*
``output[-5]``. ``init_y[1]`` *correponds to* ``output[-4]``,
``init_y[2]`` corresponds to ``output[-3]``, ``init_y[3]``
coresponds to ``output[-2]``, ``init_y[4]`` corresponds to
``output[-1]``. While this order might seem strange, it comes
natural from splitting an array at a given point. Assume that
we have a array ``x``, and we choose ``k`` to be time step
``0``. Then our initial state would be ``x[:k]``, while the
output will be ``x[k:]``. Looking at this split, elements in
``x[:k]`` are ordered exactly like those in ``init_y``.
* ``taps`` -- Temporal taps of the output that will be pass to
``fn``. They are provided as a list of *negative* integers,
where a value ``k`` implies that at iteration step ``t`` scan
will pass to ``fn`` the slice ``t+k``.
``scan`` will follow this logic if partial information is given:
* If an output is not wrapped in a dictionary, ``scan`` will wrap
it in one assuming that you use only the last step of the output
(i.e. it makes your tap value list equal to [-1]).
* If you wrap an output in a dictionary and you do not provide any
taps but you provide an initial state it will assume that you are
using only a tap value of -1.
* If you wrap an output in a dictionary but you do not provide any
initial state, it assumes that you are not using any form of
taps.
* If you provide a ``None`` instead of a variable or a empty
dictionary ``scan`` assumes that you will not use any taps for
this output (like for example in case of a map)
If ``outputs_info`` is an empty list or None, ``scan`` assumes
that no tap is used for any of the outputs. If information is
provided just for a subset of the outputs an exception is
raised (because there is no convention on how scan should map
the provided information to the outputs of ``fn``)
:param non_sequences:
``non_sequences`` is the list of arguments that are passed to
``fn`` at each steps. One can opt to exclude variable
used in ``fn`` from this list as long as they are part of the
computational graph, though for clarity we encourage not to do so.
:param n_steps:
``n_steps`` is the number of steps to iterate given as an int
or Theano scalar. If any of the input sequences do not have
enough elements, scan will raise an error. If the *value is 0* the
outputs will have *0 rows*. If the value is negative, ``scan``
will run backwards in time. If the ``go_backwards`` flag is already
set and also ``n_steps`` is negative, ``scan`` will run forward
in time. If n stpes is not provided, ``scan`` will figure
out the amount of steps it should run given its input sequences.
:param truncate_gradient:
``truncate_gradient`` is the number of steps to use in truncated
BPTT. If you compute gradients through a scan op, they are
computed using backpropagation through time. By providing a
different value then -1, you choose to use truncated BPTT instead
of classical BPTT, where you go for only ``truncate_gradient``
number of steps back in time.
:param go_backwards:
``go_backwards`` is a flag indicating if ``scan`` should go
backwards through the sequences. If you think of each sequence
as indexed by time, making this flag True would mean that
``scan`` goes back in time, namely that for any sequence it
starts from the end and goes towards 0.
:param name:
When profiling ``scan``, it is crucial to provide a name for any
instance of ``scan``. The profiler will produce an overall
profile of your code as well as profiles for the computation of
one step of each instance of ``scan``. The ``name`` of the instance
appears in those profiles and can greatly help to disambiguate
information.
:param mode:
It is recommended to leave this argument to None, especially
when profiling ``scan`` (otherwise the results are not going to
be accurate). If you prefer the computations of one step of
``scan`` to be done differently then the entire function, you
can use this parameter to describe how the computations in this
loop are done (see ``theano.function`` for details about
possible values and their meaning).
:param profile:
Flag or string. If true, or different from the empty string, a
profile object will be created and attached to the inner graph of
scan. In case ``profile`` is True, the profile object will have the
name of the scan instance, otherwise it will have the passed string.
Profile object collect (and print) information only when running the
inner graph with the new cvm linker ( with default modes,
other linkers this argument is useless)
:rtype: tuple
:return: tuple of the form (outputs, updates); ``outputs`` is either a
Theano variable or a list of Theano variables representing the
outputs of ``scan`` (in the same order as in
``outputs_info``). ``updates`` is a subclass of dictionary
specifying the
update rules for all shared variables used in scan
This dictionary should be passed to ``theano.function`` when
you compile your function. The change compared to a normal
dictionary is that we validate that keys are SharedVariable
and addition of those dictionary are validated to be consistent.
"""
# Note : see the internal documentation of the scan op for naming
# conventions and all other details
if options is None:
options = {}
rvals = scan_utils.canonical_arguments(sequences,
outputs_info,
non_sequences,
go_backwards,
n_steps)
inputs, states_and_outputs_info, parameters, T = rvals
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
T_value = None
if isinstance(n_steps, (float, int)):
T_value = int(n_steps)
else:
try:
T_value = opt.get_scalar_constant_value(n_steps)
except (TypeError, AttributeError):
T_value = None
if T_value in (1, -1):
return one_step_scan(fn,
inputs,
states_and_outputs_info,
parameters,
truncate_gradient)
# 1. Variable representing the current time step
t = scalar_shared(numpy.int64(0), name='t')
# 2. Allocate memory for the states of scan.
mintaps = []
lengths = []
for pos, arg_info in enumerate(states_and_outputs_info):
if arg_info.get('taps', None) == [-1]:
mintaps.append(1)
lengths.append(scalar_shared(numpy.int64(0),
name='l%d' % pos))
arg_info['initial'] = scan_utils.expand(tensor.unbroadcast(
tensor.shape_padleft(arg_info['initial']), 0), T)
elif arg_info.get('taps', None):
if numpy.any(numpy.array(arg_info.get('taps', [])) > 0):
# Make sure we do not have requests for future values of a
# sequence we can not provide such values
raise ValueError('Can not use future taps of outputs',
arg_info)
mintap = abs(numpy.min(arg_info['taps']))
lengths.append(scalar_shared(numpy.int64(0),
name='l%d' % pos))
mintaps.append(mintap)
arg_info['initial'] = scan_utils.expand(
arg_info['initial'][:mintap], T)
else:
mintaps.append(0)
lengths.append(scalar_shared(numpy.int64(0),
name='l%d' % pos))
# 3. Generate arguments for the function passed to scan. This will
# function will return the outputs that need to be computed at every
# timesteps
inputs_slices = [input[t] for input in inputs]
states_slices = []
for n, state in enumerate(states_and_outputs_info):
# Check if it is actually a state and not an output
if mintaps[n] != 0:
for k in state['taps']:
states_slices.append(
state['initial'][(t + mintaps[n] + k) % lengths[n]])
# 4. Construct outputs that are to be computed by the inner
# function of scan
args = inputs_slices + states_slices + parameters
cond, states_and_outputs, updates = \
scan_utils.get_updates_and_outputs(fn(*args))
# User is allowed to provide no information if it only behaves like a
# map
if (len(states_and_outputs) != len(states_and_outputs_info) and
len(states_and_outputs_info) == 0):
mintaps = [0] * len(states_and_outputs)
# 5. Construct the scan op
# 5.1 Construct list of shared variables with updates (those that
# can be treated as states (i.e. of TensorType) and those that can not
# (like Random States)
if cond is not None:
_cond = [cond]
else:
_cond = []
rvals = rebuild_collect_shared(
states_and_outputs + _cond,
updates=updates,
rebuild_strict=True,
copy_inputs_over=True,
no_default_updates=False)
# extracting the arguments
input_variables, cloned_outputs, other_rval = rvals
clone_d, update_d, update_expr, shared_inputs = other_rval
additional_input_states = []
additional_output_states = []
additional_lengths = []
additional_mintaps = []
original_numeric_shared_variables = []
non_numeric_input_states = []
non_numeric_output_states = []
original_non_numeric_shared_variables = []
pos = len(lengths)
for sv in shared_inputs:
if sv in update_d:
if isinstance(sv, (TensorVariable, TensorSharedVariable)):
# We can treat it as a sit sot
nw_state = scan_utils.expand(
tensor.unbroadcast(tensor.shape_padleft(sv), 0), T)
additional_lengths.append(scalar_shared(numpy.int64(0),
name='l%d' % pos))
pos = pos + 1
additional_mintaps.append(1)
additional_input_states.append(nw_state)
additional_output_states.append(
scan_utils.clone(tensor.set_subtensor(
nw_state[(t + 1) % additional_lengths[-1]],
update_d[sv])))
original_numeric_shared_variables.append(sv)
else:
non_numeric_input_states.append(sv)
non_numeric_output_states.append(update_d[sv])
original_non_numeric_shared_variables.append(sv)
# Replace shared variables in the update
_additional_output_states = []
replace = {}
for sv, buf in zip(original_numeric_shared_variables,
additional_input_states):
replace[sv] = buf[t]
for out in additional_output_states:
_additional_output_states.append(
scan_utils.clone(out, replace=replace))
additional_output_states = _additional_output_states
# 5.2 Collect inputs/outputs of the inner function
inputs = []
outputs = []
for n, mintap in enumerate(mintaps):
if mintap != 0:
input_state = states_and_outputs_info[n]['initial']
inputs.append(input_state)
outputs.append(
tensor.set_subtensor(
input_state[(t + mintap) % lengths[n]],
states_and_outputs[n]))
else:
mem_buffer = scan_utils.allocate_memory(
T, states_and_outputs_info[n], states_and_outputs[n])
inputs.append(output)
outputs.append(
tensor.set_subtensor(output[t % lengths[n]],
states_and_outputs[n]))
inputs.extend(additional_input_states)
outputs.extend(additional_output_states)
lengths.extend(additional_lengths)
mintaps.extend(additional_mintaps)
inputs.extend(non_numeric_input_states)
outputs.extend(non_numeric_output_states)
all_other_inputs = gof.graph.inputs(outputs)
parameters = [x for x in all_other_inputs
if (x not in inputs and x not in lengths and x is not t
and isinstance(x, gof.Variable) and
not isinstance(x, gof.Constant))]
inputs.extend(parameters)
# 5.3 Construct the the options dictionary
options['name'] = name
options['profile'] = profile
options['mode'] = mode
options['inplace'] = False
options['gpu'] = False
options['truncate_gradient'] = truncate_gradient
options['hash_inner_graph'] = 0
# 5.4 Construct the ScanOp instance
local_op = scan_op.ScanOp(inputs=inputs,
outputs=outputs,
lengths=lengths,
switches=[],
mintaps=mintaps,
index=t,
options=options,
as_repeatUntil=cond)
# Note that we get here all the outputs followed by the update rules to
# the shared variables we had in our scan
# we know that we have (in this given order):
# * len(states_and_outputs) real outputs
# * len(additional_input_states) updates for numeric shared variable
# * len(non_numeric_input_states) updates for non numeric shared
# variables
scan_inputs = [T] + inputs
scan_outputs_update_rules = scan_utils.to_list(local_op(*scan_inputs))
# 5.5 Collect outputs and add permutation object
scan_outputs = []
for pos in xrange(len(states_and_outputs)):
out = scan_utils.ScanPermutation(mintaps[pos])(
scan_outputs_update_rules[pos], t)
scan_outputs.append(out[mintaps[pos]:])
# 5.6 Construct updates dictionary
update_rules = scan_outputs_update_rules[len(states_and_outputs):]
updates = {}
for v, u in izip(original_numeric_shared_variables,
update_rules[:len(additional_input_states)]):
updates[v] = u[-1]
for v, u in izip(original_non_numeric_shared_variables,
update_rules[len(additional_input_states):]):
updates[v] = u
# Step 5.7 We are done and can return everything back to the user
return scan_outputs, updates
def scan(
fn, sequences=None, states=None, params=None, n_steps=None, mode=None, name=None, profile=False, allow_gc=None
):
"""
Similar to Theano's official scan, this function gives the user more
control over the scan op, avoiding certain difficulties that arose from
missing optimizations.
:param fn: lambda function that describes one step of scan (see the
official Theano scan function)
:param sequences: similar to the official Theano's scan. This version
of scan does not support taps for the sequences (it can only be a
list of tensor). Scan assumes that sequences have the right length
and it does not check for this.
:param states: similar to outputs_info of the official scan function.
There is one crucial difference though, namely that the `initial`
key in the dictionary has been replace by 'membuf' key. This
reflects the change of meaning. Instead of passing to scan just
the initial steps misisng, one has now to pass a memory buffer in
which scan will try to store its output. In this memory buffer the
first entries should be set to the initial states of the
corresponding states.
Providing a memory buffer that has less entries then the number of
steps, mneans scan will only use that amount of memory. The user has
to match the memory buffer size with the number of steps, otherwise
scan will produce wrong results. Also if gradients are to be
computed through the scan, the memory buffer should have the same
length as the number of steps.
For states that do not require a initial state, one has to provide a
dictionary with a single key 'steps' that says how many intermediate
results to store. See examples below for more insight.
:param n_steps: This parameter is mandatory and it will represent the
number of steps scan will do (scan will not check sequences or any
other source of information to figure out how many steps it needs
to do).
:param mode: Same as for the official scan
:param name: Same as for the official scan
:param profile: Same as for the official scan
Note:
- there is no truncate / go_backwards anymore !
- the outputs returned by scan contain the initial states as well (i.e.
if I loop over k steps, with my smallest tap for an output -3 and keep
al intermediate results, my output will be of length k+3
Examples:
(a) if you do not want to store any intermediate results (just the
last one)
# The memory buffer can be the initial state, just that we need to
# add one extra dimension in front of it
state = TT.unbroadcast(TT.shape_padleft(x0),0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
# Once we got our result we need to remove the extra dimension
out = out[0]
(b) if you want to keep every intermediate results
state = TT.alloc(TT.constant(0), 6, x0.shape[0])
state = TT.set_subtensor(state[0], x0)
out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
out = out[1:]
"""
def wrap_into_list(x):
"""
Wrap the input into a list if it is not already a list
"""
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(states)
if allow_gc is None:
allow_gc = config.scan.allow_gc
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(params):
if not isinstance(elem, gof.Variable):
non_seqs.append(tensor.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = opt.get_scalar_constant_value(n_steps)
except tensor.basic.NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if hasattr(n_steps, "dtype") and str(n_steps.dtype)[:3] not in ("uin", "int"):
raise ValueError(" n_steps must be an int. dtype provided " "is %s" % n_steps.dtype)
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap outputs info in a dictionary if they are not already in one
for i in xrange(n_outs):
if outs_info[i] is not None:
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
elif not outs_info[i].get("membuf", None) and outs_info[i].get("taps", None):
# ^ no initial state but taps provided
raise ValueError(
("If you are using slices of an output " "you need to provide a memory buffer for " "the state "),
outs_info[i],
)
elif outs_info[i].get("membuf", None) and not outs_info[i].get("taps", None):
# ^ initial state but taps not provided
if "taps" in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning(
"Output %s (index %d) has a memory " "buffer but taps is explicitly set to None ",
getattr(outs_info[i]["membuf"], "name", "None"),
i,
)
outs_info[i]["taps"] = [-1]
else:
# if a None is provided as the output info we replace it
# with an dict(steps=n_steps) to simplify handling
outs_info[i] = dict(steps=n_steps)
##
# Step 2. Generate inputs and outputs of the inner functions
# for compiling a dummy function (Iteration #1)
##
# create theano inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
if isinstance(seq, dict):
seq = seq["input"]
actual_slice = seq[0]
_seq_val = tensor.as_tensor_variable(seq)
_seq_val_slice = _seq_val[0]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != "off":
try:
nw_slice.tag.test_value = gof.Op._get_test_value(_seq_val_slice)
except AttributeError as e:
if config.compute_test_value != "ignore":
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(
("Cannot compute test value for " "the inner function of scan, input value " "missing %s"), e
)
if seq.name:
nw_slice.name = seq.name + "[t]"
scan_seqs.append(_seq_val)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
actual_n_steps = tensor.as_tensor(n_steps)
# Conventions :
# mit_mot = multiple input taps, multiple output taps ( only provided
# by the gradient function )
# mit_sot = multiple input taps, single output tap (t + 0)
# sit_sot = single input tap, single output tap (t + 0)
# nit_sot = no input tap, single output tap (t + 0)
# MIT_MOT -- not provided by the user only by the grad function
n_mit_mot = 0
n_mit_mot_outs = 0
mit_mot_scan_inputs = []
mit_mot_inner_inputs = []
mit_mot_inner_outputs = []
mit_mot_out_slices = []
mit_mot_rightOrder = []
# SIT_SOT -- provided by the user
n_mit_sot = 0
mit_sot_scan_inputs = []
mit_sot_inner_inputs = []
mit_sot_inner_slices = []
mit_sot_inner_outputs = []
mit_sot_return_steps = OrderedDict()
mit_sot_tap_array = []
mit_sot_rightOrder = []
n_sit_sot = 0
sit_sot_scan_inputs = []
sit_sot_inner_inputs = []
sit_sot_inner_slices = []
sit_sot_inner_outputs = []
sit_sot_return_steps = OrderedDict()
sit_sot_rightOrder = []
nit_sot_steps = []
# go through outputs picking up time slices as needed
for i, init_out in enumerate(outs_info):
# Note that our convention dictates that if an output uses
# just the previous time step, as a initial state we will only
# provide a tensor of the same dimension as one time step; This
# makes code much cleaner for those who do not use taps. Otherwise
# they would always had to shape_padleft the initial state ..
# which is ugly
# Note, 'taps' might not be in the dictionary
if "taps" in init_out and init_out["taps"] == [-1]:
actual_arg = init_out["membuf"]
arg = safe_new(init_out["membuf"][0])
if isinstance(arg, tensor.Constant):
# safe new returns a clone of the constants, but that is not
# what we need for initial states
arg = arg.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != "off":
try:
arg.tag.test_value = gof.Op._get_test_value(actual_arg)
except AttributeError as e:
if config.compute_test_value != "ignore":
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(
("Cannot compute test value for the " "inner function of scan, input value missing %s"), e
)
if getattr(init_out["membuf"], "name", None) is not None:
arg.name = init_out["membuf"].name + "[t-1]"
# We need now to allocate space for storing the output and copy
# the initial state over. We do this using the expand function
# defined in scan utils
sit_sot_scan_inputs.append(actual_arg)
sit_sot_inner_slices.append(actual_arg[0])
if i in return_steps:
sit_sot_return_steps[n_sit_sot] = return_steps[i]
sit_sot_inner_inputs.append(arg)
sit_sot_rightOrder.append(i)
n_sit_sot += 1
elif init_out.get("taps", None):
if numpy.any(numpy.array(init_out.get("taps", [])) > 0):
# Make sure we do not have requests for future values of a
# sequence we can not provide such values
raise ValueError("Can not use future taps of outputs", init_out)
# go through the taps
mintap = abs(numpy.min(init_out["taps"]))
mit_sot_tap_array.append(init_out["taps"])
idx_offset = abs(numpy.min(init_out["taps"]))
# Sequence
mit_sot_scan_inputs.append(init_out["membuf"])
if i in return_steps:
mit_sot_return_steps[n_mit_sot] = return_steps[i]
mit_sot_rightOrder.append(i)
n_mit_sot += 1
for k in init_out["taps"]:
# create a new slice
actual_nw_slice = init_out["membuf"][k + mintap]
_init_out_var = tensor.as_tensor_variable(init_out["membuf"])
_init_out_var_slice = _init_out_var[k + mintap]
nw_slice = _init_out_var_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != "off":
try:
nw_slice.tag.test_value = gof.Op._get_test_value(_init_out_var_slice)
except AttributeError as e:
if config.compute_test_value != "ignore":
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.info(
(
"Cannot compute test value for "
"the inner function of scan, input value "
"missing. %s"
),
e,
)
# give it a name or debugging and pretty printing
if getattr(init_out["membuf"], "name", None) is not None:
if k > 0:
nw_slice.name = init_out["membuf"].name + "[t+%d]" % k
elif k == 0:
nw_slice.name = init_out["membuf"].name + "[t]"
else:
nw_slice.name = init_out["membuf"].name + "[t%d]" % k
mit_sot_inner_inputs.append(nw_slice)
mit_sot_inner_slices.append(actual_nw_slice)
else:
pass
# Re-order args
max_mit_sot = numpy.max([-1] + mit_sot_rightOrder) + 1
max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
n_elems = numpy.max([max_mit_sot, max_sit_sot])
_ordered_args = [[] for x in xrange(n_elems)]
offset = 0
for idx in xrange(n_mit_sot):
n_inputs = len(mit_sot_tap_array[idx])
if n_fixed_steps == 1:
_ordered_args[mit_sot_rightOrder[idx]] = mit_sot_inner_slices[offset : offset + n_inputs]
else:
_ordered_args[mit_sot_rightOrder[idx]] = mit_sot_inner_inputs[offset : offset + n_inputs]
offset += n_inputs
for idx in xrange(n_sit_sot):
if n_fixed_steps == 1:
_ordered_args[sit_sot_rightOrder[idx]] = [sit_sot_inner_slices[idx]]
else:
_ordered_args[sit_sot_rightOrder[idx]] = [sit_sot_inner_inputs[idx]]
ordered_args = []
for ls in _ordered_args:
ordered_args += ls
if n_fixed_steps == 1:
args = inner_slices + ordered_args + non_seqs
else:
args = inner_seqs + ordered_args + non_seqs
# add only the non-shared variables and non-constants to the arguments of
# the dummy function [ a function should not get shared variables or
# constants as input ]
dummy_args = [arg for arg in args if (not isinstance(arg, SharedVariable) and not isinstance(arg, tensor.Constant))]
# when we apply the lambda expression we get a mixture of update rules
# and outputs that needs to be separated
lambda_result = fn(*args)
condition, outputs, updates = scan_utils.get_updates_and_outputs(lambda_result)
if condition is not None:
as_while = True
else:
as_while = False
##
# Step 3. Check if we actually need scan and remove it if we don't
##
if n_fixed_steps == 1:
# We do not need to use the scan op anymore, so we can just return
# the outputs and updates we have
if condition is not None:
_logger.warning(
(
"When the number of steps is fixed and equal " "to 1, the provided stopping condition, ",
str(condition),
" is ignored",
)
)
for pos, inner_out in enumerate(outputs):
# we need to see if we need to pad our sequences with an
# unbroadcastable dimension; case example : we return an
# output for which we want all intermediate. If n_steps is 1
# then, if we return the output as given by the innner function
# this will represent only a slice and it will have one
# dimension less.
if isinstance(inner_out.type, tensor.TensorType) and return_steps.get(pos, 0) != 1:
outputs[pos] = tensor.unbroadcast(tensor.shape_padleft(inner_out), 0)
if len(outputs) == 1:
outputs = outputs[0]
return (outputs, updates)
##
# Step 4. Compile the dummy function
##
# We can now compile a dummy function just to see what shared variable
# we have and what are their update rules (note that the user has
# the option not to pass the shared variable to scan, so we need to
# pick them manually and add them to scan)
# make the compilation as fast as possible by not applying any
# optimization or conversion to C [ note this region is not important
# for performance so we can do stuff as unoptimal as we wish ]
# extract still missing inputs (there still might be so) and add them
# as non sequences at the end of our args
fake_nonseqs = [x.type() for x in non_seqs]
fake_outputs = scan_utils.clone(outputs + updates.values(), replace=dict(zip(non_seqs, fake_nonseqs)))
all_inputs = itertools.ifilter(
lambda x: (
isinstance(x, gof.Variable) and not isinstance(x, SharedVariable) and not isinstance(x, gof.Constant)
),
gof.graph.inputs(fake_outputs),
)
extra_inputs = filter(lambda x: x not in args + fake_nonseqs, all_inputs)
non_seqs += extra_inputs
# Note we do not use all_inputs directly since the order of variables
# in args is quite important
dummy_args += extra_inputs
dummy_outs = outputs
if condition is not None:
dummy_outs.append(condition)
# If we use a regular dict here, the results are non-deterministic
if not isinstance(updates, (list, tuple)):
if isinstance(updates, dict) and not isinstance(updates, OrderedDict):
warnings.warn("Using non-deterministic dictionary.")
dummy_f = function(
dummy_args,
dummy_outs,
updates=updates,
mode=compile.mode.Mode(linker="py", optimizer=None),
on_unused_input="ignore",
)
##
# Step 5. Re-arange inputs of scan into a more strict order
##
# Step 5.0 Check the outputs of the dummy function to see if they
# match with user provided data
# if the number of outputs to the function does not match the number of
# assumed outputs until now (provided by the user) there can be
# only one explanation: No information is provided for any of the
# outputs (i.e. we are dealing with a map)
tmp_dummy_f_outs = len(dummy_f.maker.outputs)
if as_while:
tmp_dummy_f_outs -= 1
if not (tmp_dummy_f_outs == n_outs or outs_info == []):
raise ValueError(
"Please provide None as output_info for "
"any output that does not feed back into "
"scan (i.e. it behaves like a map) "
)
if outs_info == []:
n_outs = len(dummy_f.maker.outputs)
if as_while:
n_outs = n_outs - 1
outs_info = [dict(steps=n_steps) for x in xrange(n_outs)]
# Step 5.1 Outputs with taps different then -1
for i, out in enumerate(outs_info):
if "taps" in out and out["taps"] != [-1]:
mit_sot_inner_outputs.append(outputs[i])
# Step 5.2 Outputs with tap equal to -1
for i, out in enumerate(outs_info):
if "taps" in out and out["taps"] == [-1]:
sit_sot_inner_outputs.append(outputs[i])
# Step 5.3 Outputs that correspond to update rules of shared variables
givens = OrderedDict()
n_shared_outs = 0
shared_scan_inputs = []
shared_inner_inputs = []
shared_inner_outputs = []
for input in dummy_f.maker.expanded_inputs:
if isinstance(input.variable, SharedVariable) and input.update:
new_var = safe_new(input.variable)
if getattr(input.variable, "name", None) is not None:
new_var.name = input.variable.name + "_copy"
shared_inner_inputs.append(new_var)
shared_scan_inputs.append(input.variable)
shared_inner_outputs.append(input.update)
givens[input.variable] = new_var
n_shared_outs += 1
# Step 5.4 Outputs with no taps used in the input
n_nit_sot = 0
nit_sot_inner_outputs = []
nit_sot_return_steps = OrderedDict()
nit_sot_rightOrder = []
for i, out in enumerate(outs_info):
if not "taps" in out:
nit_sot_inner_outputs.append(outputs[i])
if i in return_steps:
nit_sot_return_steps[n_nit_sot] = return_steps[i]
nit_sot_rightOrder.append(i)
nit_sot_steps.append(out["steps"])
n_nit_sot += 1
# Step 5.5 all other arguments including extra inputs
other_scan_args = []
other_inner_args = []
other_scan_args += [
arg for arg in non_seqs if (not isinstance(arg, SharedVariable) and not isinstance(arg, tensor.Constant))
]
# Step 5.6 all shared variables with no update rules
other_inner_args += [
safe_new(arg, "_copy")
for arg in non_seqs
if (not isinstance(arg, SharedVariable) and not isinstance(arg, tensor.Constant))
]
givens.update(dict(zip(other_scan_args, other_inner_args)))
other_shared_scan_args = [
arg.variable
for arg in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and not arg.update)
]
other_shared_inner_args = [
safe_new(arg.variable, "_copy")
for arg in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and not arg.update)
]
givens.update(dict(zip(other_shared_scan_args, other_shared_inner_args)))
##
# Step 6. Re-order the outputs and clone them replacing things
# using the givens
##
inner_inputs = (
inner_seqs
+ mit_mot_inner_inputs
+ mit_sot_inner_inputs
+ sit_sot_inner_inputs
+ shared_inner_inputs
+ other_shared_inner_args
+ other_inner_args
)
inner_outs = (
mit_mot_inner_outputs
+ mit_sot_inner_outputs
+ sit_sot_inner_outputs
+ nit_sot_inner_outputs
+ shared_inner_outputs
)
if condition is not None:
inner_outs.append(condition)
new_givens = OrderedDict()
for w, w_copy in givens.iteritems():
new_givens[w] = w.type.filter_variable(w_copy)
new_outs = scan_utils.clone(inner_outs, replace=new_givens)
##
# Step 7. Create the Scan Op
##
tap_array = mit_sot_tap_array + [[-1] for x in xrange(n_sit_sot)]
info = OrderedDict()
info["tap_array"] = tap_array
info["n_seqs"] = n_seqs
info["n_mit_mot"] = n_mit_mot
info["n_mit_mot_outs"] = n_mit_mot_outs
info["mit_mot_out_slices"] = mit_mot_out_slices
info["n_mit_sot"] = n_mit_sot
info["n_sit_sot"] = n_sit_sot
info["n_shared_outs"] = n_shared_outs
info["n_nit_sot"] = n_nit_sot
info["truncate_gradient"] = -1
info["name"] = name
info["mode"] = mode
info["destroy_map"] = OrderedDict()
info["inplace"] = False
info["gpu"] = False
info["as_while"] = as_while
info["profile"] = profile
info["_scan_savemem_visited"] = True
info["allow_gc"] = allow_gc
local_op = scan_op.Scan(inner_inputs, new_outs, info)
##
# Step 8. Compute the outputs using the scan op
##
_scan_inputs = (
scan_seqs
+ mit_mot_scan_inputs
+ mit_sot_scan_inputs
+ sit_sot_scan_inputs
+ shared_scan_inputs
+ nit_sot_steps
+ other_shared_scan_args
+ other_scan_args
)
scan_inputs = []
for arg in [actual_n_steps] + _scan_inputs:
if not isinstance(arg, gof.Variable):
arg = tensor.as_tensor_variable(arg)
scan_inputs += [arg]
scan_outs = local_op(*scan_inputs)
if type(scan_outs) not in (list, tuple):
scan_outs = [scan_outs]
##
# Step 9. Figure out which outs are update rules for shared variables
# and so on ...
##
update_map = OrderedUpdates()
offset = n_mit_mot
offsets = [abs(numpy.min(x)) for x in mit_sot_tap_array]
mit_sot_outs = scan_outs[offset : offset + n_mit_sot]
offset += n_mit_sot
offsets = [1 for x in xrange(n_sit_sot)]
sit_sot_outs = scan_outs[offset : offset + n_sit_sot]
offset += n_sit_sot
nit_sot_outs = scan_outs[offset : offset + n_nit_sot]
offset += n_nit_sot
for idx, update_rule in enumerate(scan_outs[offset : offset + n_shared_outs]):
update_map[shared_scan_inputs[idx]] = update_rule
_scan_out_list = mit_sot_outs + sit_sot_outs + nit_sot_outs
# Step 10. I need to reorder the outputs to be in the order expected by
# the user
rightOrder = mit_sot_rightOrder + sit_sot_rightOrder + nit_sot_rightOrder
scan_out_list = [None] * len(rightOrder)
for idx, pos in enumerate(rightOrder):
scan_out_list[pos] = _scan_out_list[idx]
if len(scan_out_list) == 1:
scan_out_list = scan_out_list[0]
elif len(scan_out_list) == 0:
scan_out_list = None
assert isinstance(update_map, OrderedDict)
return (scan_out_list, update_map)