Tensorflow中BasicRNNCell的相关参数shape说明

按道理看完RNN的原理之后，我们就应该来用某种框架来实现了。可偏偏在RNN的实现上，对于一个初学者来说Tensorflow的表达总是显得那么生涩难懂，比起CNN那确实是差了一点。比如里面的参数就显示不是那么的友好。num_units到底指啥？原谅我最开始以为指的是RNN单元的个数。zero_state()中的参数为啥要指定batch_size?

1.结论

先回忆一下RNN的计算公式：
$output = new\_state = \tanh(input*W + state*U + B)$

output_size = 10
batch_size = 32
cell = tf.nn.rnn_cell.BasicRNNCell(num_units=output_size)
input = tf.placeholder(dtype=tf.float32,shape=[batch_size,150])
h0 = cell.zero_state(batch_size=batch_size,dtype=tf.float32)
output,h1 = cell.call(input,h0)

上面是一个RNN单元最简单的定义形式，可是每个参数又到底是什么含义呢？我们知道一个最基本的RNN单元中有三个可训练的参数 $W,U,B$ ，以及两个输入变量。所以我们在构造RNN的时候就需要指定各个参数的维度了。可上面6行代码中，各个参数又是谁跟谁呢？下图就是直接结果。
Tensorflow中BasicRNNCell的相关参数shape说明

结合着上图和代码，可以发现：
第一：第3行代码的num_units=output_size就告诉我们，最终输出的类别数是output_size(例如：10个数字的可能性；)，以及参数 $W$ 的第二个维度为output_size;
第二：第4行代码的shape=[batch_size,150]就告诉了我们余下所有参数的形状；

2.怎么来的

class BasicRNNCell(RNNCell):
  """The most basic RNN cell.

  Args:
    num_units: int, The number of units in the RNN cell.
    activation: Nonlinearity to use.  Default: `tanh`.
    reuse: (optional) Python boolean describing whether to reuse variables
     in an existing scope.  If not `True`, and the existing scope already has
     the given variables, an error is raised.
  """

  def __init__(self, num_units, activation=None, reuse=None):
    super(BasicRNNCell, self).__init__(_reuse=reuse)
    self._num_units = num_units
    self._activation = activation or math_ops.tanh

  @property
  def state_size(self):
    return self._num_units

  @property
  def output_size(self):
    return self._num_units

  def call(self, inputs, state):
    """Most basic RNN: output = new_state = act(W * input + U * state + B)."""
    output = self._activation(_linear([inputs, state], self._num_units, True))
    return output, output
    
def _linear(args,
            output_size,
            bias,
            bias_initializer=None,
            kernel_initializer=None):
            
    -------此处删除了很多行--------------------------
    
    with vs.variable_scope(outer_scope) as inner_scope:
      inner_scope.set_partitioner(None)
      if bias_initializer is None:
        bias_initializer = init_ops.constant_initializer(0.0, dtype=dtype)
      biases = vs.get_variable(
          _BIAS_VARIABLE_NAME, [output_size],
          dtype=dtype,
          initializer=bias_initializer)
    return nn_ops.bias_add(res, biases)

从Class BasicRNNCell的源码第22行可以看出num_units和output_size是一回事；从第43行可以看出，output_size指的是偏置B的维度，只要弄清楚了这两点，其他的就一目了然了

2.验证

2.1 从计算维度来验证

import tensorflow as tf

output_size = 10
batch_size = 32
cell = tf.nn.rnn_cell.BasicRNNCell(num_units=output_size)
print(cell.output_size)
input = tf.placeholder(dtype=tf.float32,shape=[batch_size,150])
h0 = cell.zero_state(batch_size=batch_size,dtype=tf.float32)
output,h1 = cell.call(input,h0)
print(output)
print(h1)

按照上面的推断各个参数的维度为：input: [32,150]; W: [150,10]; h0: [32,10]; U: [10,10] B: [10]；所以最终输出的维度就应该为[32,10]

10
Tensor("Tanh:0", shape=(32, 10), dtype=float32)
Tensor("Tanh:0", shape=(32, 10), dtype=float32)

2.1 从计算结果来验证

import tensorflow as tf
import numpy as np
from tensorflow.python.ops import variable_scope as vs
output_size = 4
batch_size = 3
dim = 5
cell = tf.nn.rnn_cell.BasicRNNCell(num_units=output_size)
input = tf.placeholder(dtype=tf.float32, shape=[batch_size, dim])
h0 = cell.zero_state(batch_size=batch_size, dtype=tf.float32)
output, h1 = cell.call(input, h0)

x = np.array([[1, 2, 1, 1, 1], [2, 0, 0, 1, 1], [2, 1, 0, 1, 0]])


scope = vs.get_variable_scope()
with vs.variable_scope(scope,reuse=True) as outer_scope:
    weights = vs.get_variable(
        "kernel", [9, output_size],
        dtype=tf.float32,
        initializer= None)

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    a,b,w= sess.run([output,h1,weights],feed_dict={input:x})
    print('output:')
    print(a)
    print('h1:')
    print(b)
    print("weights:")
    print(w)# shape = (9,4)

state = np.zeros(shape=(3,4))# shape = (3,4)
all_input = np.concatenate((x,state),axis=1)# shape = (3,9)
result = np.tanh(np.matmul(all_input,w))
print('result:')
print(result)

由以上代码可知：input: [3,5]; W: [5,4]; h0: [3,4]; U: [4,4] B: [4]；所以最终输出的维度就应该为[3,4]

注：
1.Tensorflow在实现的时候把W,U合并成了一个矩阵，把input和h0也合并成了一个矩阵，所以weight的形状才为(9,4);
2.此处偏置为0;

结果：

>>
weights:
[[ 0.590749    0.31745368 -0.27975678  0.33500886]
 [-0.02256793 -0.34533614 -0.09014118 -0.5189797 ]
 [-0.24466929  0.17519772  0.20553339 -0.25595042]
 [-0.48579523  0.67465043  0.62406075 -0.32061592]
 [-0.0713594   0.3825792   0.6132684   0.00536895]
 [ 0.43795645  0.55633724  0.31295568 -0.37173718]
 [ 0.6170727   0.14996111 -0.321027   -0.624057  ]
 [ 0.42747557  0.4424585  -0.59979784  0.23592204]
 [-0.0294565   0.3372593  -0.14695019  0.07108325]]
output:
[[-0.2507479   0.69584984  0.7542856  -0.8549179 ]
 [ 0.5541449   0.9344188   0.5900975   0.3405997 ]
 [ 0.5870382   0.74615407 -0.0255884  -0.16797088]]
h1:
[[-0.2507479   0.69584984  0.7542856  -0.8549179 ]
 [ 0.5541449   0.9344188   0.5900975   0.3405997 ]
 [ 0.5870382   0.74615407 -0.0255884  -0.16797088]]
result:
[[-0.25074791  0.69584978  0.75428552 -0.85491791]
 [ 0.55414493  0.93441886  0.59009744  0.34059968]
 [ 0.58703823  0.74615404 -0.02558841 -0.16797091]]

result是通过numpy计算得到的输出值！

Tensorflow中BasicRNNCell的相关参数shape说明

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