1. 什么是 RNN
循环神经网络（Recurrent Neural Network，RNN）是一种以序列数据为输入来进行建模的深度学习模型，它是 NLP 中最常用的模型。其结构如下图：
x是输入，h是隐层单元，o为输出，L为损失函数，y为训练集的标签.
这些元素右上角带的t代表t时刻的状态，其中需要注意的是，因策单元h在t时刻的表现不仅由此刻的输入决定，还受t时刻之前时刻的影响。V、W、U是权值，同一类型的权连接权值相同。
有了上面的理解，前向传播算法其实非常简单，对于t时刻：
其中为激活函数，一般来说会选择tanh函数，b为偏置。
t时刻的输出就更为简单：
最终模型的预测输出为：
其中为激活函数，通常RNN用于分类，故这里一般用softmax函数。
2. 实验代码
2.1. 搭建一个只有一层RNN和Dense网络的模型。
def simple_rnn_layer():
# Create a dense layer with 10 output neurons and input shape of (None, 20)
model = Sequential()
model.add(SimpleRNN(units=3, input_shape=(3, 2),)) # 3 units in the RNN layer, input_shape=(timesteps, features)
model.add(Dense(1)) # Output layer with one neuron
# Print the summary of the dense layer
print(model.summary())
if __name__ == '__main__':
simple_rnn_layer()输出
Model: "sequential"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
simple_rnn (SimpleRNN) (None, 3) 18
dense (Dense) (None, 1) 4
=================================================================
Total params: 22
Trainable params: 22
Non-trainable params: 0
_________________________________________________________________
None2.2. 验证RNN里的逻辑
写代码验证这个过程，看看结果是不是一样的。
import keras.optimizers.optimizer
import numpy as np
from keras.models import Sequential
from keras.layers import SimpleRNN, Dense
def change_weight():
# Create a simple Dense layer
rnn_layer = SimpleRNN(units=3, input_shape=(3, 2), activation=None, return_sequences=True)
# Simulate input data (batch size of 1 for demonstration)
input_data = np.array([
[[1.0, 2], [2, 3], [3, 4]],
[[5, 6], [6, 7], [7, 8]],
[[9, 10], [10, 11], [11, 12]]
])
# Pass the input data through the layer to initialize the weights and biases
_ = rnn_layer(input_data)
# Access the weights and biases of the dense layer
kernel, recurrent_kernel, biases = rnn_layer.get_weights()
# Print the initial weights and biases
print("recurrent_kernel:", recurrent_kernel) # (3,3)
print('kernal:',kernel) #(2,3)
print('biase: ',biases) # (3)
kernel = np.array([[1, 0, 2], [2, 1, 3]])
recurrent_kernel = np.array([[1, 2, 1.0], [1, 0, 1], [0, 1, 0]])
biases = np.array([0, 0, 1.0])
rnn_layer.set_weights([kernel, recurrent_kernel, biases])
print(rnn_layer.get_weights())
test_data = np.array([
[[1.0, 3], [1, 1], [2, 3]]
])
output = rnn_layer(test_data)
print(output)
if __name__ == '__main__':
change_weight()
输出结果如下：可以看到结果是我手算的是一致的。
recurrent_kernel: [[ 0.06973135 0.40464386 0.9118119 ]
[ 0.6186313 -0.7345941 0.27868783]
[ 0.7825809 0.5446422 -0.3015495 ]]
kernal: [[-0.48868906 0.52718353 -0.08321357]
[-1.0569452 -0.9872779 0.72809434]]
biase: [0. 0. 0.]
[array([[1., 0., 2.],
[2., 1., 3.]], dtype=float32), array([[1., 2., 1.],
[1., 0., 1.],
[0., 1., 0.]], dtype=float32), array([0., 0., 1.], dtype=float32)]
tf.Tensor(
[[[ 7. 3. 12.]
[13. 27. 16.]
[48. 45. 54.]]], shape=(1, 3, 3), dtype=float32)2.3 代码实现一个简单的例子
import keras.optimizers.optimizer
import numpy as np
import tensorflow as tf
from keras.models import Sequential
from keras.layers import SimpleRNN, Dense
# Sample sequential data
# Each sequence has three timesteps, and each timestep has two features
data = np.array([
[[1, 2], [2, 3], [3, 4]],
[[5, 6], [6, 7], [7, 8]],
[[9, 10], [10, 11], [11, 12]]
])
print('data.shape= ',data.shape)
# Define the RNN model
model = Sequential()
model.add(SimpleRNN(units=4, input_shape=(3, 2), name="simpleRNN")) # 4 units in the RNN layer, input_shape=(timesteps, features)
model.add(Dense(1, name= "output")) # Output layer with one neuron
# Compile the model
model.compile(loss='mse', optimizer=keras.optimizers.Adam(learning_rate=0.01))
# Print the model summary
model.summary()
before_RNN_weight = model.get_layer("simpleRNN").get_weights()
print('before train ', before_RNN_weight)
# Train the model
model.fit(data, np.array([[10], [20], [30]]), epochs=2000, verbose=1)
RNN_weight = model.get_layer("simpleRNN").get_weights()
print('after train ', len(RNN_weight),)
for i in range(len(RNN_weight)):
print('====',RNN_weight[i].shape, RNN_weight[i])
# Make predictions
predictions = model.predict(data)
print("Predictions:", predictions.flatten())
代码输出
data.shape= (3, 3, 2)
Model: "sequential"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
simpleRNN (SimpleRNN) (None, 4) 28
output (Dense) (None, 1) 5
=================================================================
Total params: 33
Trainable params: 33
Non-trainable params: 0
_________________________________________________________________
before train [array([[-0.00466371, 0.53100157, 0.5298798 , 0.05514288],
[-0.08896947, 0.43185067, 0.7861788 , -0.80616236]],
dtype=float32), array([[-0.10712242, -0.03620092, -0.02182053, -0.9933471 ],
[-0.6549012 , -0.02620655, 0.7532524 , 0.05503315],
[-0.01986913, 0.9989996 , 0.02001702, -0.03470401],
[-0.74781984, 0.00159313, -0.657065 , 0.09502006]],
dtype=float32), array([0., 0., 0., 0.], dtype=float32)]
2023-08-05 16:02:44.111298: W tensorflow/tsl/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz
Epoch 1/2000
....
Epoch 1999/2000
1/1 [==============================] - 0s 11ms/step - loss: 0.0071
Epoch 2000/2000
1/1 [==============================] - 0s 13ms/step - loss: 0.0070
after train 3
==== (2, 4) [[ 0.27645147 0.6025058 1.6083356 -0.38382724]
[ 0.11586202 0.32901326 1.4760928 -1.2268958 ]]
==== (4, 4) [[-0.99628973 -2.444563 1.7412992 -1.5265529 ]
[ 0.80340594 0.9488743 2.44552 -0.7439341 ]
[-0.1827681 -1.3091801 1.547736 -0.6644555 ]
[-0.5724374 2.3090494 -2.1779017 0.35992467]]
==== (4,) [-0.40184066 -1.2391611 0.33460653 -0.29144585]
1/1 [==============================] - 0s 78ms/step
Predictions: [10.000422 19.999924 29.85534 ]
