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"""Weight initializer."""
from __future__ import absolute_import, print_function
import re
import logging
import warnings
import json
from math import sqrt
import numpy as np
from .base import string_types
from .ndarray import NDArray, load
from . import random
from . import registry
from . import ndarray
# inherit str for backward compatibility
[docs]class InitDesc(str):
"""
Descriptor for the initialization pattern.
Parameters
----------
name : str
Name of variable.
attrs : dict of str to str
Attributes of this variable taken from ``Symbol.attr_dict``.
global_init : Initializer
Global initializer to fallback to.
"""
def __new__(cls, name, attrs=None, global_init=None):
ret = super(InitDesc, cls).__new__(cls, name)
ret.attrs = attrs or {}
ret.global_init = global_init
return ret
[docs]class Initializer(object):
"""The base class of an initializer."""
def __init__(self, **kwargs):
self._kwargs = kwargs
self._verbose = False
self._print_func = None
[docs] def set_verbosity(self, verbose=False, print_func=None):
"""Switch on/off verbose mode
Parameters
----------
verbose : bool
switch on/off verbose mode
print_func : function
A function that computes statistics of initialized arrays.
Takes an `NDArray` and returns an `str`. Defaults to mean
absolute value str((abs(x)/size(x)).asscalar()).
"""
self._verbose = verbose
if print_func is None:
def asum_stat(x):
"""returns |x|/size(x), async execution."""
return str((ndarray.norm(x)/sqrt(x.size)).asscalar())
print_func = asum_stat
self._print_func = print_func
return self
def _verbose_print(self, desc, init, arr):
"""Internal verbose print function
Parameters
----------
desc : InitDesc or str
name of the array
init : str
initializer pattern
arr : NDArray
initialized array
"""
if self._verbose and self._print_func:
logging.info('Initialized %s as %s: %s', desc, init, self._print_func(arr))
[docs] def dumps(self):
"""Saves the initializer to string
Returns
-------
str
JSON formatted string that describes the initializer.
Examples
--------
>>> # Create initializer and retrieve its parameters
...
>>> init = mx.init.Normal(0.5)
>>> init.dumps()
'["normal", {"sigma": 0.5}]'
>>> init = mx.init.Xavier(factor_type="in", magnitude=2.34)
>>> init.dumps()
'["xavier", {"rnd_type": "uniform", "magnitude": 2.34, "factor_type": "in"}]'
"""
return json.dumps([self.__class__.__name__.lower(), self._kwargs])
def __call__(self, desc, arr):
"""Initialize an array
Parameters
----------
desc : InitDesc
Initialization pattern descriptor.
arr : NDArray
The array to be initialized.
"""
if not isinstance(desc, InitDesc):
self._legacy_init(desc, arr)
return
if desc.global_init is None:
desc.global_init = self
init = desc.attrs.get('__init__', "")
if init:
# when calling Variable initializer
create(init)._init_weight(desc, arr)
self._verbose_print(desc, init, arr)
else:
# register nnvm::FSetInputVariableAttrs in the backend for new patterns
# don't add new cases here.
if desc.endswith('weight'):
self._init_weight(desc, arr)
self._verbose_print(desc, 'weight', arr)
elif desc.endswith('bias'):
self._init_bias(desc, arr)
self._verbose_print(desc, 'bias', arr)
elif desc.endswith('gamma'):
self._init_gamma(desc, arr)
self._verbose_print(desc, 'gamma', arr)
elif desc.endswith('beta'):
self._init_beta(desc, arr)
self._verbose_print(desc, 'beta', arr)
elif desc.endswith('min'):
self._init_zero(desc, arr)
self._verbose_print(desc, 'min', arr)
elif desc.endswith('max'):
self._init_one(desc, arr)
self._verbose_print(desc, 'max', arr)
else:
self._init_default(desc, arr)
def _legacy_init(self, name, arr):
"""Legacy initialization method.
Parameters
----------
name : str
Name of corresponding NDArray.
arr : NDArray
NDArray to be initialized.
"""
warnings.warn(
"\033[91mCalling initializer with init(str, NDArray) has been deprecated." \
"please use init(mx.init.InitDesc(...), NDArray) instead.\033[0m",
DeprecationWarning, stacklevel=3)
if not isinstance(name, string_types):
raise TypeError('name must be string')
if not isinstance(arr, NDArray):
raise TypeError('arr must be NDArray')
if name.startswith('upsampling'):
self._init_bilinear(name, arr)
elif name.startswith('stn_loc') and name.endswith('weight'):
self._init_zero(name, arr)
elif name.startswith('stn_loc') and name.endswith('bias'):
self._init_loc_bias(name, arr)
elif name.endswith('bias'):
self._init_bias(name, arr)
elif name.endswith('gamma'):
self._init_gamma(name, arr)
elif name.endswith('beta'):
self._init_beta(name, arr)
elif name.endswith('weight'):
self._init_weight(name, arr)
elif name.endswith("moving_mean"):
self._init_zero(name, arr)
elif name.endswith("moving_var"):
self._init_one(name, arr)
elif name.endswith("moving_inv_var"):
self._init_zero(name, arr)
elif name.endswith("moving_avg"):
self._init_zero(name, arr)
elif name.endswith('min'):
self._init_zero(name, arr)
elif name.endswith('max'):
self._init_one(name, arr)
else:
self._init_default(name, arr)
def _init_bilinear(self, _, arr):
weight = np.zeros(np.prod(arr.shape), dtype='float32')
shape = arr.shape
f = np.ceil(shape[3] / 2.)
c = (2 * f - 1 - f % 2) / (2. * f)
for i in range(np.prod(shape)):
x = i % shape[3]
y = (i / shape[3]) % shape[2]
weight[i] = (1 - abs(x / f - c)) * (1 - abs(y / f - c))
arr[:] = weight.reshape(shape)
def _init_loc_bias(self, _, arr):
shape = arr.shape
assert(shape[0] == 6)
arr[:] = np.array([1.0, 0, 0, 0, 1.0, 0])
def _init_zero(self, _, arr):
arr[:] = 0.0
def _init_one(self, _, arr):
arr[:] = 1.0
def _init_bias(self, _, arr):
arr[:] = 0.0
def _init_gamma(self, _, arr):
arr[:] = 1.0
def _init_beta(self, _, arr):
arr[:] = 0.0
def _init_weight(self, name, arr):
"""Abstract method to Initialize weight."""
raise NotImplementedError("Must override it")
def _init_default(self, name, _):
raise ValueError(
'Unknown initialization pattern for %s. ' \
'Default initialization is now limited to '\
'"weight", "bias", "gamma" (1.0), and "beta" (0.0).' \
'Please use mx.sym.Variable(init=mx.init.*) to set initialization pattern' % name)
# pylint: disable=invalid-name
_register = registry.get_register_func(Initializer, 'initializer')
alias = registry.get_alias_func(Initializer, 'initializer')
create = registry.get_create_func(Initializer, 'initializer')
# pylint: enable=invalid-name
[docs]def register(klass):
"""Registers a custom initializer.
Custom initializers can be created by extending `mx.init.Initializer` and implementing the
required functions like `_init_weight` and `_init_bias`. The created initializer must be
registered using `mx.init.register` before it can be called by name.
Parameters
----------
klass : class
A subclass of `mx.init.Initializer` that needs to be registered as a custom initializer.
Example
-------
>>> # Create and register a custom initializer that
... # initializes weights to 0.1 and biases to 1.
...
>>> @mx.init.register
... @alias('myinit')
... class CustomInit(mx.init.Initializer):
... def __init__(self):
... super(CustomInit, self).__init__()
... def _init_weight(self, _, arr):
... arr[:] = 0.1
... def _init_bias(self, _, arr):
... arr[:] = 1
...
>>> # Module is an instance of 'mxnet.module.Module'
...
>>> module.init_params("custominit")
>>> # module.init_params("myinit")
>>> # module.init_params(CustomInit())
"""
return _register(klass)
[docs]class Load(object):
"""Initializes variables by loading data from file or dict.
**Note** Load will drop ``arg:`` or ``aux:`` from name and
initialize the variables that match with the prefix dropped.
Parameters
----------
param: str or dict of str->`NDArray`
Parameter file or dict mapping name to NDArray.
default_init: Initializer
Default initializer when name is not found in `param`.
verbose: bool
Flag for enabling logging of source when initializing.
"""
def __init__(self, param, default_init=None, verbose=False):
if isinstance(param, str):
param = load(param)
assert isinstance(param, dict)
self.param = {}
for name, arr in param.items():
if name.startswith('arg:') or name.startswith('aux:'):
self.param[name[4:]] = arr
else:
self.param[name] = arr
self.default_init = default_init
self.verbose = verbose
def __call__(self, name, arr):
if name in self.param:
assert arr.shape == self.param[name].shape, \
'Parameter %s cannot be initialized from loading. '%name + \
'Shape mismatch, target %s vs loaded %s'%(str(arr.shape),
self.param[name].shape)
arr[:] = self.param[name]
if self.verbose:
logging.info('Initialized %s by loading', name)
else:
assert self.default_init is not None, \
"Cannot Initialize %s. Not found in loaded param "%name + \
"and no default Initializer is provided."
self.default_init(name, arr)
if self.verbose:
logging.info('Initialized %s by default', name)
[docs]class Mixed(object):
"""Initialize parameters using multiple initializers.
Parameters
----------
patterns: list of str
List of regular expressions matching parameter names.
initializers: list of Initializer
List of initializers corresponding to `patterns`.
Example
-------
>>> # Given 'module', an instance of 'mxnet.module.Module', initialize biases to zero
... # and every other parameter to random values with uniform distribution.
...
>>> init = mx.initializer.Mixed(['bias', '.*'], [mx.init.Zero(), mx.init.Uniform(0.1)])
>>> module.init_params(init)
>>>
>>> for dictionary in module.get_params():
... for key in dictionary:
... print(key)
... print(dictionary[key].asnumpy())
...
fullyconnected1_weight
[[ 0.0097627 0.01856892 0.04303787]]
fullyconnected1_bias
[ 0.]
"""
def __init__(self, patterns, initializers):
assert len(patterns) == len(initializers)
self.map = list(zip([re.compile(p) for p in patterns], initializers))
def __call__(self, name, arr):
for prog, init in self.map:
if prog.match(name):
init(name, arr)
return
raise ValueError('Parameter name %s did not match any pattern. Consider' +
'add a ".*" pattern at the and with default Initializer.')
@register
@alias("zeros")
[docs]class Zero(Initializer):
"""Initializes weights to zero.
Example
-------
>>> # Given 'module', an instance of 'mxnet.module.Module', initialize weights to zero.
...
>>> init = mx.initializer.Zero()
>>> module.init_params(init)
>>> for dictionary in module.get_params():
... for key in dictionary:
... print(key)
... print(dictionary[key].asnumpy())
...
fullyconnected0_weight
[[ 0. 0. 0.]]
"""
def __init__(self):
super(Zero, self).__init__()
def _init_weight(self, _, arr):
arr[:] = 0
@register
@alias("ones")
[docs]class One(Initializer):
"""Initializes weights to one.
Example
-------
>>> # Given 'module', an instance of 'mxnet.module.Module', initialize weights to one.
...
>>> init = mx.initializer.One()
>>> module.init_params(init)
>>> for dictionary in module.get_params():
... for key in dictionary:
... print(key)
... print(dictionary[key].asnumpy())
...
fullyconnected0_weight
[[ 1. 1. 1.]]
"""
def __init__(self):
super(One, self).__init__()
def _init_weight(self, _, arr):
arr[:] = 1
@register
[docs]class Constant(Initializer):
"""Initializes the weights to a given value.
The value passed in can be a scalar or a NDarray that matches the shape
of the parameter to be set.
Parameters
----------
value : float, NDArray
Value to set.
"""
def __init__(self, value):
super(Constant, self).__init__(value=value)
self.value = value
def _init_weight(self, _, arr):
arr[:] = self.value
@register
@register
[docs]class Normal(Initializer):
"""Initializes weights with random values sampled from a normal distribution
with a mean of zero and standard deviation of `sigma`.
Parameters
----------
sigma : float, optional
Standard deviation of the normal distribution.
Default standard deviation is 0.01.
Example
-------
>>> # Given 'module', an instance of 'mxnet.module.Module', initialize weights
>>> # to random values sampled from a normal distribution.
...
>>> init = mx.init.Normal(0.5)
>>> module.init_params(init)
>>> for dictionary in module.get_params():
... for key in dictionary:
... print(key)
... print(dictionary[key].asnumpy())
...
fullyconnected0_weight
[[-0.3214761 -0.12660924 0.53789419]]
"""
def __init__(self, sigma=0.01):
super(Normal, self).__init__(sigma=sigma)
self.sigma = sigma
def _init_weight(self, _, arr):
random.normal(0, self.sigma, out=arr)
@register
[docs]class Orthogonal(Initializer):
"""Initialize weight as orthogonal matrix.
This initializer implements *Exact solutions to the nonlinear dynamics of
learning in deep linear neural networks*, available at
https://arxiv.org/abs/1312.6120.
Parameters
----------
scale : float optional
Scaling factor of weight.
rand_type: string optional
Use "uniform" or "normal" random number to initialize weight.
"""
def __init__(self, scale=1.414, rand_type="uniform"):
super(Orthogonal, self).__init__(scale=scale, rand_type=rand_type)
self.scale = scale
self.rand_type = rand_type
def _init_weight(self, _, arr):
nout = arr.shape[0]
nin = np.prod(arr.shape[1:])
if self.rand_type == "uniform":
tmp = random.uniform(-1.0, 1.0, shape=(nout, nin)).asnumpy()
elif self.rand_type == "normal":
tmp = random.normal(0.0, 1.0, shape=(nout, nin)).asnumpy()
u, _, v = np.linalg.svd(tmp, full_matrices=False) # pylint: disable=invalid-name
if u.shape == tmp.shape:
res = u
else:
res = v
res = self.scale * res.reshape(arr.shape)
arr[:] = res
@register
[docs]class Xavier(Initializer):
"""Returns an initializer performing "Xavier" initialization for weights.
This initializer is designed to keep the scale of gradients roughly the same
in all layers.
By default, `rnd_type` is ``'uniform'`` and `factor_type` is ``'avg'``,
the initializer fills the weights with random numbers in the range
of :math:`[-c, c]`, where :math:`c = \\sqrt{\\frac{3.}{0.5 * (n_{in} + n_{out})}}`.
:math:`n_{in}` is the number of neurons feeding into weights, and :math:`n_{out}` is
the number of neurons the result is fed to.
If `rnd_type` is ``'uniform'`` and `factor_type` is ``'in'``,
the :math:`c = \\sqrt{\\frac{3.}{n_{in}}}`.
Similarly when `factor_type` is ``'out'``, the :math:`c = \\sqrt{\\frac{3.}{n_{out}}}`.
If `rnd_type` is ``'gaussian'`` and `factor_type` is ``'avg'``,
the initializer fills the weights with numbers from normal distribution with
a standard deviation of :math:`\\sqrt{\\frac{3.}{0.5 * (n_{in} + n_{out})}}`.
Parameters
----------
rnd_type: str, optional
Random generator type, can be ``'gaussian'`` or ``'uniform'``.
factor_type: str, optional
Can be ``'avg'``, ``'in'``, or ``'out'``.
magnitude: float, optional
Scale of random number.
"""
def __init__(self, rnd_type="uniform", factor_type="avg", magnitude=3):
super(Xavier, self).__init__(rnd_type=rnd_type, factor_type=factor_type,
magnitude=magnitude)
self.rnd_type = rnd_type
self.factor_type = factor_type
self.magnitude = float(magnitude)
def _init_weight(self, name, arr):
shape = arr.shape
hw_scale = 1.
if len(shape) < 2:
raise ValueError('Xavier initializer cannot be applied to vector {0}. It requires at'
' least 2D.'.format(name))
if len(shape) > 2:
hw_scale = np.prod(shape[2:])
fan_in, fan_out = shape[1] * hw_scale, shape[0] * hw_scale
factor = 1.
if self.factor_type == "avg":
factor = (fan_in + fan_out) / 2.0
elif self.factor_type == "in":
factor = fan_in
elif self.factor_type == "out":
factor = fan_out
else:
raise ValueError("Incorrect factor type")
scale = np.sqrt(self.magnitude / factor)
if self.rnd_type == "uniform":
random.uniform(-scale, scale, out=arr)
elif self.rnd_type == "gaussian":
random.normal(0, scale, out=arr)
else:
raise ValueError("Unknown random type")
@register
[docs]class MSRAPrelu(Xavier):
"""Initialize the weight according to a MSRA paper.
This initializer implements *Delving Deep into Rectifiers: Surpassing
Human-Level Performance on ImageNet Classification*, available at
https://arxiv.org/abs/1502.01852.
This initializer is proposed for initialization related to ReLu activation,
it maked some changes on top of Xavier method.
Parameters
----------
factor_type: str, optional
Can be ``'avg'``, ``'in'``, or ``'out'``.
slope: float, optional
initial slope of any PReLU (or similar) nonlinearities.
"""
def __init__(self, factor_type="avg", slope=0.25):
magnitude = 2. / (1 + slope ** 2)
super(MSRAPrelu, self).__init__("gaussian", factor_type, magnitude)
self._kwargs = {'factor_type': factor_type, 'slope': slope}
@register
[docs]class Bilinear(Initializer):
"""Initialize weight for upsampling layers."""
def __init__(self):
super(Bilinear, self).__init__()
def _init_weight(self, _, arr):
weight = np.zeros(np.prod(arr.shape), dtype='float32')
shape = arr.shape
f = np.ceil(shape[3] / 2.)
c = (2 * f - 1 - f % 2) / (2. * f)
for i in range(np.prod(shape)):
x = i % shape[3]
y = (i / shape[3]) % shape[2]
weight[i] = (1 - abs(x / f - c)) * (1 - abs(y / f - c))
arr[:] = weight.reshape(shape)
@register
[docs]class LSTMBias(Initializer):
"""Initialize all biases of an LSTMCell to 0.0 except for
the forget gate whose bias is set to custom value.
Parameters
----------
forget_bias: float, default 1.0
bias for the forget gate. Jozefowicz et al. 2015 recommends
setting this to 1.0.
"""
def __init__(self, forget_bias=1.0):
super(LSTMBias, self).__init__(forget_bias=forget_bias)
self.forget_bias = forget_bias
def _init_weight(self, name, arr):
arr[:] = 0.0
# in the case of LSTMCell the forget gate is the second
# gate of the 4 LSTM gates, we modify the according values.
num_hidden = int(arr.shape[0] / 4)
arr[num_hidden:2*num_hidden] = self.forget_bias
@register
[docs]class FusedRNN(Initializer):
"""Initialize parameters for fused rnn layers.
Parameters
----------
init : Initializer
initializer applied to unpacked weights. Fall back to global
initializer if None.
num_hidden : int
should be the same with arguments passed to FusedRNNCell.
num_layers : int
should be the same with arguments passed to FusedRNNCell.
mode : str
should be the same with arguments passed to FusedRNNCell.
bidirectional : bool
should be the same with arguments passed to FusedRNNCell.
forget_bias : float
should be the same with arguments passed to FusedRNNCell.
"""
def __init__(self, init, num_hidden, num_layers, mode, bidirectional=False, forget_bias=1.0):
if isinstance(init, string_types):
klass, kwargs = json.loads(init)
init = registry._REGISTRY[klass.lower()](**kwargs)
super(FusedRNN, self).__init__(init=init.dumps() if init is not None else None,
num_hidden=num_hidden, num_layers=num_layers, mode=mode,
bidirectional=bidirectional, forget_bias=forget_bias)
self._init = init
self._num_hidden = num_hidden
self._num_layers = num_layers
self._mode = mode
self._bidirectional = bidirectional
self._forget_bias = forget_bias
def _init_weight(self, desc, arr): # pylint: disable=arguments-differ
from .rnn import rnn_cell
cell = rnn_cell.FusedRNNCell(self._num_hidden, self._num_layers,
self._mode, self._bidirectional,
forget_bias=self._forget_bias, prefix='')
args = cell.unpack_weights({'parameters': arr})
for name in args:
arg_desc = InitDesc(name, global_init=desc.global_init)
# for lstm bias, we use a custom initializer
# which adds a bias to the forget gate
if self._mode == 'lstm' and name.endswith("_f_bias"):
args[name][:] = self._forget_bias
elif self._init is None:
desc.global_init(arg_desc, args[name])
else:
self._init(arg_desc, args[name])
arr[:] = cell.pack_weights(args)['parameters']
