python深度学习tensorflow1.0参数初始化initializer

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CNN中最重要的就是参数了,包括W,b。 我们训练CNN的最终目的就是得到最好的参数,使得目标函数取得最小值。参数的初始化也同样重要,因此微调受到很多人的重视,那么tf提供了哪些初始化参数的方法呢,我们能不能自己进行初始化呢?

所有初始化方法定义

# Copyright 2015 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # #     http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Operations often used for initializing tensors. All variable initializers returned by functions in this file should have the following signature: def _initializer(shape, dtype=dtypes.float32, partition_info=None): Args: shape: List of `int` representing the shape of the output `Tensor`. Some initializers may also be able to accept a `Tensor`. dtype: (Optional) Type of the output `Tensor`. partition_info: (Optional) variable_scope._PartitionInfo object holding additional information about how the variable is partitioned. May be `None` if the variable is not partitioned. Returns: A `Tensor` of type `dtype` and `shape`. """ from __future__ import absolute_import from __future__ import division from __future__ import print_function import math from tensorflow.python.framework import constant_op from tensorflow.python.framework import dtypes from tensorflow.python.ops import array_ops from tensorflow.python.ops import linalg_ops from tensorflow.python.ops import random_ops class Initializer(object): """Initializer base class: all initializers inherit from this class. """ def __call__(self, shape, dtype=None, partition_info=None): raise NotImplementedError class Zeros(Initializer): """Initializer that generates tensors initialized to 0.""" def __init__(self, dtype=dtypes.float32): self.dtype = dtype def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype return constant_op.constant(False if dtype is dtypes.bool else 0, dtype=dtype, shape=shape) class Ones(Initializer): """Initializer that generates tensors initialized to 1.""" def __init__(self, dtype=dtypes.float32): self.dtype = dtype def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype return constant_op.constant(1, dtype=dtype, shape=shape) class Constant(Initializer): """Initializer that generates tensors with constant values. The resulting tensor is populated with values of type `dtype`, as specified by arguments `value` following the desired `shape` of the new tensor (see examples below). The argument `value` can be a constant value, or a list of values of type `dtype`. If `value` is a list, then the length of the list must be less than or equal to the number of elements implied by the desired shape of the tensor. In the case where the total number of elements in `value` is less than the number of elements required by the tensor shape, the last element in `value` will be used to fill the remaining entries. If the total number of elements in `value` is greater than the number of elements required by the tensor shape, the initializer will raise a `ValueError`. Args: value: A Python scalar, list of values, or a N-dimensional numpy array. All elements of the initialized variable will be set to the corresponding value in the `value` argument. dtype: The data type. verify_shape: Boolean that enables verification of the shape of `value`. If `True`, the initializer will throw an error if the shape of `value` is not compatible with the shape of the initialized tensor. Examples: The following example can be rewritten using a numpy.ndarray instead of the `value` list, even reshaped, as shown in the two commented lines below the `value` list initialization. ```python >>> import numpy as np >>> import tensorflow as tf >>> value = [0, 1, 2, 3, 4, 5, 6, 7] >>> # value = np.array(value) >>> # value = value.reshape([2, 4]) >>> init = tf.constant_initializer(value) >>> print('fitting shape:') >>> with tf.Session(): >>>   x = tf.get_variable('x', shape=[2, 4], initializer=init) >>>   x.initializer.run() >>>   print(x.eval()) fitting shape: [[ 0.  1.  2.  3.] [ 4.  5.  6.  7.]] >>> print('larger shape:') >>> with tf.Session(): >>>   x = tf.get_variable('x', shape=[3, 4], initializer=init) >>>   x.initializer.run() >>>   print(x.eval()) larger shape: [[ 0.  1.  2.  3.] [ 4.  5.  6.  7.] [ 7.  7.  7.  7.]] >>> print('smaller shape:') >>> with tf.Session(): >>>   x = tf.get_variable('x', shape=[2, 3], initializer=init) ValueError: Too many elements provided. Needed at most 6, but received 8 >>> print('shape verification:') >>> init_verify = tf.constant_initializer(value, verify_shape=True) >>> with tf.Session(): >>>   x = tf.get_variable('x', shape=[3, 4], initializer=init_verify) TypeError: Expected Tensor's shape: (3, 4), got (8,). ``` """ def __init__(self, value=0, dtype=dtypes.float32, verify_shape=False): self.value = value self.dtype = dtype self.verify_shape = verify_shape def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype return constant_op.constant(self.value, dtype=dtype, shape=shape, verify_shape=self.verify_shape) class RandomUniform(Initializer): """Initializer that generates tensors with a uniform distribution. Args: minval: A python scalar or a scalar tensor. Lower bound of the range of random values to generate. maxval: A python scalar or a scalar tensor. Upper bound of the range of random values to generate.  Defaults to 1 for float types. seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. """ def __init__(self, minval=0, maxval=None, seed=None, dtype=dtypes.float32): self.minval = minval self.maxval = maxval self.seed = seed self.dtype = dtype def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype return random_ops.random_uniform(shape, self.minval, self.maxval, dtype, seed=self.seed) class RandomNormal(Initializer): """Initializer that generates tensors with a normal distribution. Args: mean: a python scalar or a scalar tensor. Mean of the random values to generate. stddev: a python scalar or a scalar tensor. Standard deviation of the random values to generate. seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. Only floating point types are supported. """ def __init__(self, mean=0.0, stddev=1.0, seed=None, dtype=dtypes.float32): self.mean = mean self.stddev = stddev self.seed = seed self.dtype = _assert_float_dtype(dtype) def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype return random_ops.random_normal(shape, self.mean, self.stddev, dtype, seed=self.seed) class TruncatedNormal(Initializer): """Initializer that generates a truncated normal distribution. These values are similar to values from a `random_normal_initializer` except that values more than two standard deviations from the mean are discarded and re-drawn. This is the recommended initializer for neural network weights and filters. Args: mean: a python scalar or a scalar tensor. Mean of the random values to generate. stddev: a python scalar or a scalar tensor. Standard deviation of the random values to generate. seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. Only floating point types are supported. """ def __init__(self, mean=0.0, stddev=1.0, seed=None, dtype=dtypes.float32): self.mean = mean self.stddev = stddev self.seed = seed self.dtype = _assert_float_dtype(dtype) def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype return random_ops.truncated_normal(shape, self.mean, self.stddev, dtype, seed=self.seed) class UniformUnitScaling(Initializer): """Initializer that generates tensors without scaling variance. When initializing a deep network, it is in principle advantageous to keep the scale of the input variance constant, so it does not explode or diminish by reaching the final layer. If the input is `x` and the operation `x * W`, and we want to initialize `W` uniformly at random, we need to pick `W` from [-sqrt(3) / sqrt(dim), sqrt(3) / sqrt(dim)] to keep the scale intact, where `dim = W.shape[0]` (the size of the input). A similar calculation for convolutional networks gives an analogous result with `dim` equal to the product of the first 3 dimensions.  When nonlinearities are present, we need to multiply this by a constant `factor`. See [Sussillo et al., 2014](https://arxiv.org/abs/1412.6558) ([pdf](http://arxiv.org/pdf/1412.6558.pdf)) for deeper motivation, experiments and the calculation of constants. In section 2.3 there, the constants were numerically computed: for a linear layer it's 1.0, relu: ~1.43, tanh: ~1.15. Args: factor: Float.  A multiplicative factor by which the values will be scaled. seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. Only floating point types are supported. """ def __init__(self, factor=1.0, seed=None, dtype=dtypes.float32): self.factor = factor self.seed = seed self.dtype = _assert_float_dtype(dtype) def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype scale_shape = shape if partition_info is not None: scale_shape = partition_info.full_shape input_size = 1.0 # Estimating input size is not possible to do perfectly, but we try. # The estimate, obtained by multiplying all dimensions but the last one, # is the right thing for matrix multiply and convolutions (see above). for dim in scale_shape[:-1]: input_size *= float(dim) # Avoid errors when initializing zero-size tensors. input_size = max(input_size, 1.0) max_val = math.sqrt(3 / input_size) * self.factor return random_ops.random_uniform(shape, -max_val, max_val, dtype, seed=self.seed) class VarianceScaling(Initializer): """Initializer capable of adapting its scale to the shape of weights tensors. With `distribution="normal"`, samples are drawn from a truncated normal distribution centered on zero, with `stddev = sqrt(scale / n)` where n is: - number of input units in the weight tensor, if mode = "fan_in" - number of output units, if mode = "fan_out" - average of the numbers of input and output units, if mode = "fan_avg" With `distribution="uniform"`, samples are drawn from a uniform distribution within [-limit, limit], with `limit = sqrt(3 * scale / n)`. Arguments: scale: Scaling factor (positive float). mode: One of "fan_in", "fan_out", "fan_avg". distribution: Random distribution to use. One of "normal", "uniform". seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. Only floating point types are supported. Raises: ValueError: In case of an invalid value for the "scale", mode" or "distribution" arguments. """ def __init__(self, scale=1.0, mode="fan_in", distribution="normal", seed=None, dtype=dtypes.float32): if scale <= 0.: raise ValueError("`scale` must be positive float.") if mode not in {"fan_in", "fan_out", "fan_avg"}: raise ValueError("Invalid `mode` argument:", mode) distribution = distribution.lower() if distribution not in {"normal", "uniform"}: raise ValueError("Invalid `distribution` argument:", distribution) self.scale = scale self.mode = mode self.distribution = distribution self.seed = seed self.dtype = _assert_float_dtype(dtype) def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype scale = self.scale scale_shape = shape if partition_info is not None: scale_shape = partition_info.full_shape fan_in, fan_out = _compute_fans(scale_shape) if self.mode == "fan_in": scale /= max(1., fan_in) elif self.mode == "fan_out": scale /= max(1., fan_out) else: scale /= max(1., (fan_in + fan_out) / 2.) if self.distribution == "normal": stddev = math.sqrt(scale) return random_ops.truncated_normal(shape, 0.0, stddev, dtype, seed=self.seed) else: limit = math.sqrt(3.0 * scale) return random_ops.random_uniform(shape, -limit, limit, dtype, seed=self.seed) class Orthogonal(Initializer): """Initializer that generates an orthogonal matrix. If the shape of the tensor to initialize is two-dimensional, i is initialized with an orthogonal matrix obtained from the singular value decomposition of a matrix of uniform random numbers. If the shape of the tensor to initialize is more than two-dimensional, a matrix of shape `(shape[0] * ... * shape[n - 2], shape[n - 1])` is initialized, where `n` is the length of the shape vector. The matrix is subsequently reshaped to give a tensor of the desired shape. Args: gain: multiplicative factor to apply to the orthogonal matrix dtype: The type of the output. seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. """ def __init__(self, gain=1.0, dtype=dtypes.float32, seed=None): self.gain = gain self.dtype = _assert_float_dtype(dtype) self.seed = seed def __call__(self, shape, dtype=None, partition_info=None): if dtype is None: dtype = self.dtype # Check the shape if len(shape) <2: raise valueerror("the tensor to initialize must be " "at least two-dimensional") # flatten the input shape with last dimension remaining its original so it works for conv2d num_rows dim in shape[:-1]: *=dim num_cols=shape[-1] flat_shape=(num_rows, num_cols) generate a random matrix random_ops.random_uniform(flat_shape, dtype=dtype, seed=self.seed) compute svd _, u, v=linalg_ops.svd(a, full_matrices=False) pick appropriate singular value decomposition if> num_cols: q = u else: # Tensorflow departs from numpy conventions # such that we need to transpose axes here q = array_ops.transpose(v) return self.gain * array_ops.reshape(q, shape) # Aliases. # pylint: disable=invalid-name zeros_initializer = Zeros ones_initializer = Ones constant_initializer = Constant random_uniform_initializer = RandomUniform random_normal_initializer = RandomNormal truncated_normal_initializer = TruncatedNormal uniform_unit_scaling_initializer = UniformUnitScaling variance_scaling_initializer = VarianceScaling orthogonal_initializer = Orthogonal # pylint: enable=invalid-name def glorot_uniform_initializer(seed=None, dtype=dtypes.float32): """The Glorot uniform initializer, also called Xavier uniform initializer. It draws samples from a uniform distribution within [-limit, limit] where `limit` is `sqrt(6 / (fan_in + fan_out))` where `fan_in` is the number of input units in the weight tensor and `fan_out` is the number of output units in the weight tensor. Reference: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf Arguments: seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. Only floating point types are supported. Returns: An initializer. """ return variance_scaling_initializer(scale=1.0, mode="fan_avg", distribution="uniform", seed=seed, dtype=dtype) def glorot_normal_initializer(seed=None, dtype=dtypes.float32): """The Glorot normal initializer, also called Xavier normal initializer. It draws samples from a truncated normal distribution centered on 0 with `stddev = sqrt(2 / (fan_in + fan_out))` where `fan_in` is the number of input units in the weight tensor and `fan_out` is the number of output units in the weight tensor. Reference: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf Arguments: seed: A Python integer. Used to create random seeds. See @{tf.set_random_seed} for behavior. dtype: The data type. Only floating point types are supported. Returns: An initializer. """ return variance_scaling_initializer(scale=1.0, mode="fan_avg", distribution="normal", seed=seed, dtype=dtype) # Utility functions. def _compute_fans(shape): """Computes the number of input and output units for a weight shape. Arguments: shape: Integer shape tuple or TF tensor shape. Returns: A tuple of scalars (fan_in, fan_out). """ if len(shape) <1: # just to avoid errors for constants. fan_in=fan_out>

1、tf.constant_initializer()

也可以简写为tf.Constant()

初始化为常数,这个非常有用,通常偏置项就是用它初始化的。

由它衍生出的两个初始化方法:

a、 tf.zeros_initializer(), 也可以简写为tf.Zeros()

b、tf.ones_initializer(), 也可以简写为tf.Ones()

例:在卷积层中,将偏置项b初始化为0,则有多种写法:

conv1 = tf.layers.conv2d(batch_images, filters=64, kernel_size=7, strides=2, activation=tf.nn.relu, kernel_initializer=tf.TruncatedNormal(stddev=0.01) bias_initializer=tf.Constant(0), )

或者:

bias_initializer=tf.constant_initializer(0)

或者:

bias_initializer=tf.zeros_initializer()

或者:

bias_initializer=tf.Zeros()

例:如何将W初始化成拉普拉斯算子?

value = [1, 1, 1, 1, -8, 1, 1, 1,1] init = tf.constant_initializer(value) W= tf.get_variable('W', shape=[3, 3], initializer=init)

2、tf.truncated_normal_initializer()

或者简写为tf.TruncatedNormal()

生成截断正态分布的随机数,这个初始化方法好像在tf中用得比较多。

它有四个参数(mean=0.0, stddev=1.0, seed=None, dtype=dtypes.float32),分别用于指定均值、标准差、随机数种子和随机数的数据类型,一般只需要设置stddev这一个参数就可以了。

例:

conv1 = tf.layers.conv2d(batch_images, filters=64, kernel_size=7, strides=2, activation=tf.nn.relu, kernel_initializer=tf.TruncatedNormal(stddev=0.01) bias_initializer=tf.Constant(0), )

或者:

conv1 = tf.layers.conv2d(batch_images, filters=64, kernel_size=7, strides=2, activation=tf.nn.relu, kernel_initializer=tf.truncated_normal_initializer(stddev=0.01) bias_initializer=tf.zero_initializer(), )

3、tf.random_normal_initializer()

可简写为 tf.RandomNormal()

生成标准正态分布的随机数,参数和truncated_normal_initializer一样。

4、random_uniform_initializer = RandomUniform()

可简写为tf.RandomUniform()

生成均匀分布的随机数,参数有四个(minval=0, maxval=None, seed=None, dtype=dtypes.float32),分别用于指定最小值,最大值,随机数种子和类型。

5、tf.uniform_unit_scaling_initializer()

可简写为tf.UniformUnitScaling()

和均匀分布差不多,只是这个初始化方法不需要指定最小最大值,是通过计算出来的。参数为(factor=1.0, seed=None, dtype=dtypes.float32)

max_val = math.sqrt(3 / input_size) * factor

这里的input_size是指输入数据的维数,假设输入为x, 运算为x * W,则input_size= W.shape[0]

它的分布区间为[ -max_val, max_val]

6、tf.variance_scaling_initializer()

可简写为tf.VarianceScaling()

参数为(scale=1.0,mode="fan_in",distribution="normal",seed=None,dtype=dtypes.float32)

scale: 缩放尺度(正浮点数)

mode:  "fan_in", "fan_out", "fan_avg"中的一个,用于计算标准差stddev的值。

distribution:分布类型,"normal"或“uniform"中的一个。

当 distribution="normal" 的时候,生成truncated normal   distribution(截断正态分布) 的随机数,其中stddev = sqrt(scale / n) ,n的计算与mode参数有关。

  • 如果mode = "fan_in", n为输入单元的结点数;         
  • 如果mode = "fan_out",n为输出单元的结点数;
  • 如果mode = "fan_avg",n为输入和输出单元结点数的平均值。

当distribution="uniform”的时候 ,生成均匀分布的随机数,假设分布区间为[-limit, limit],则

limit = sqrt(3 * scale / n)

7、tf.orthogonal_initializer()

简写为tf.Orthogonal()

生成正交矩阵的随机数。

当需要生成的参数是2维时,这个正交矩阵是由均匀分布的随机数矩阵经过SVD分解而来。

8、tf.glorot_uniform_initializer()

也称之为Xavier uniform initializer,由一个均匀分布(uniform distribution)来初始化数据。

假设均匀分布的区间是[-limit, limit],则

limit=sqrt(6 / (fan_in + fan_out))

其中的fan_in和fan_out分别表示输入单元的结点数和输出单元的结点数。

9、glorot_normal_initializer()

也称之为 Xavier normal initializer. 由一个 truncated normal distribution来初始化数据.

stddev = sqrt(2 / (fan_in + fan_out))

其中的fan_in和fan_out分别表示输入单元的结点数和输出单元的结点数。

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