NNDL 作业8：RNN - 简单循环网络
简单循环网络 （ Simple Recurrent Network，SRN） 只有一个隐藏层的神经网络 。
目录
1. 使用Numpy实现SRN
2. 在1的基础上，增加激活函数tanh
3. 分别使用nn.RNNCell、nn.RNN实现SRN
4. 分析“二进制加法” 源代码（选做）
5. 实现“Character-Level Language Models”源代码
6. 分析“序列到序列”源代码（选做）
7. “编码器-解码器”的简单实现（必做）
心得体会
ref
1. 使用Numpy实现SRN
import numpy as np
inputs = np.array([[1., 1.],
[1., 1.],
[2., 2.]]) # 初始化输入序列
print('inputs is ', inputs)
state_t = np.zeros(2, ) # 初始化存储器
print('state_t is ', state_t)
w1, w2, w3, w4, w5, w6, w7, w8 = 1., 1., 1., 1., 1., 1., 1., 1.
U1, U2, U3, U4 = 1., 1., 1., 1.
print('--------------------------------------')
for input_t in inputs:
print('inputs is ', input_t)
print('state_t is ', state_t)
in_h1 = np.dot([w1, w3], input_t) + np.dot([U2, U4], state_t)
in_h2 = np.dot([w2, w4], input_t) + np.dot([U1, U3], state_t)
state_t = in_h1, in_h2
output_y1 = np.dot([w5, w7], [in_h1, in_h2])
output_y2 = np.dot([w6, w8], [in_h1, in_h2])
print('output_y is ', output_y1, output_y2)
print('---------------')结果：
2. 在1的基础上，增加激活函数tanh
import numpy as np
inputs = np.array([[1., 1.],
[1., 1.],
[2., 2.]]) # 初始化输入序列
print('inputs is ', inputs)
state_t = np.zeros(2, ) # 初始化存储器
print('state_t is ', state_t)
w1, w2, w3, w4, w5, w6, w7, w8 = 1., 1., 1., 1., 1., 1., 1., 1.
U1, U2, U3, U4 = 1., 1., 1., 1.
print('--------------------------------------')
for input_t in inputs:
print('inputs is ', input_t)
print('state_t is ', state_t)
in_h1 = np.tanh(np.dot([w1, w3], input_t) + np.dot([U2, U4], state_t))
in_h2 = np.tanh(np.dot([w2, w4], input_t) + np.dot([U1, U3], state_t))
state_t = in_h1, in_h2
output_y1 = np.dot([w5, w7], [in_h1, in_h2])
output_y2 = np.dot([w6, w8], [in_h1, in_h2])
print('output_y is ', output_y1, output_y2)
print('---------------')结果：
3. 分别使用nn.RNNCell、nn.RNN实现SRN
nn.RNNCell代码:
import torch
batch_size = 1
seq_len = 3 # 序列长度
input_size = 2 # 输入序列维度
hidden_size = 2 # 隐藏层维度
output_size = 2 # 输出层维度
# RNNCell
cell = torch.nn.RNNCell(input_size=input_size, hidden_size=hidden_size)
# 初始化参数 https://zhuanlan.zhihu.com/p/342012463
for name, param in cell.named_parameters():
if name.startswith("weight"):
torch.nn.init.ones_(param)
else:
torch.nn.init.zeros_(param)
# 线性层
liner = torch.nn.Linear(hidden_size, output_size)
liner.weight.data = torch.Tensor([[1, 1], [1, 1]])
liner.bias.data = torch.Tensor([0.0])
seq = torch.Tensor([[[1, 1]],
[[1, 1]],
[[2, 2]]])
hidden = torch.zeros(batch_size, hidden_size)
output = torch.zeros(batch_size, output_size)
for idx, input in enumerate(seq):
print('=' * 20, idx, '=' * 20)
print('Input :', input)
print('hidden :', hidden)
hidden = cell(input, hidden)
output = liner(hidden)
print('output :', output)结果：
nn.RNN代码：
import torch
batch_size = 1
seq_len = 3
input_size = 2
hidden_size = 2
num_layers = 1
output_size = 2
cell = torch.nn.RNN(input_size=input_size, hidden_size=hidden_size, num_layers=num_layers)
for name, param in cell.named_parameters(): # 初始化参数
if name.startswith("weight"):
torch.nn.init.ones_(param)
else:
torch.nn.init.zeros_(param)
# 线性层
liner = torch.nn.Linear(hidden_size, output_size)
liner.weight.data = torch.Tensor([[1, 1], [1, 1]])
liner.bias.data = torch.Tensor([0.0])
inputs = torch.Tensor([[[1, 1]],
[[1, 1]],
[[2, 2]]])
hidden = torch.zeros(num_layers, batch_size, hidden_size)
out, hidden = cell(inputs, hidden)
print('Input :', inputs[0])
print('hidden:', 0, 0)
print('Output:', liner(out[0]))
print('--------------------------------------')
print('Input :', inputs[1])
print('hidden:', out[0])
print('Output:', liner(out[1]))
print('--------------------------------------')
print('Input :', inputs[2])
print('hidden:', out[1])
print('Output:', liner(out[2]))结果：
4. 分析“二进制加法” 源代码（选做）
RNN主要学两件事，一个是前一位的进位，一个是当前位的加法操作。只告诉当前阶段和前一阶段的计算结果，让网络自己学习加法和进位操作。
import copy, numpy as np
np.random.seed(0)
# compute sigmoid nonlinearity
def sigmoid(x):
output = 1 / (1 + np.exp(-x))
return output
# convert output of sigmoid function to its derivative
def sigmoid_output_to_derivative(output):
return output * (1 - output)
# training dataset generation
int2binary = {}
binary_dim = 8
largest_number = pow(2, binary_dim)
binary = np.unpackbits(
np.array([range(largest_number)], dtype=np.uint8).T, axis=1)
for i in range(largest_number):
int2binary[i] = binary[i]
# input variables
alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1
# initialize neural network weights
synapse_0 = 2 * np.random.random((input_dim, hidden_dim)) - 1
synapse_1 = 2 * np.random.random((hidden_dim, output_dim)) - 1
synapse_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1
synapse_0_update = np.zeros_like(synapse_0)
synapse_1_update = np.zeros_like(synapse_1)
synapse_h_update = np.zeros_like(synapse_h)
# training logic
for j in range(10000):
# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number / 2) # int version
a = int2binary[a_int] # binary encoding
b_int = np.random.randint(largest_number / 2) # int version
b = int2binary[b_int] # binary encoding
# true answer
c_int = a_int + b_int
c = int2binary[c_int]
# where we'll store our best guess (binary encoded)
d = np.zeros_like(c)
overallError = 0
layer_2_deltas = list()
layer_1_values = list()
layer_1_values.append(np.zeros(hidden_dim))
# moving along the positions in the binary encoding
for position in range(binary_dim):
# generate input and output
X = np.array([[a[binary_dim - position - 1], b[binary_dim - position - 1]]])
y = np.array([[c[binary_dim - position - 1]]]).T
# hidden layer (input ~+ prev_hidden)
layer_1 = sigmoid(np.dot(X, synapse_0) + np.dot(layer_1_values[-1], synapse_h))
# output layer (new binary representation)
layer_2 = sigmoid(np.dot(layer_1, synapse_1))
# did we miss?... if so, by how much?
layer_2_error = y - layer_2
layer_2_deltas.append((layer_2_error) * sigmoid_output_to_derivative(layer_2))
overallError += np.abs(layer_2_error[0])
# decode estimate so we can print it out
d[binary_dim - position - 1] = np.round(layer_2[0][0])
# store hidden layer so we can use it in the next timestep
layer_1_values.append(copy.deepcopy(layer_1))
future_layer_1_delta = np.zeros(hidden_dim)
for position in range(binary_dim):
X = np.array([[a[position], b[position]]])
layer_1 = layer_1_values[-position - 1]
prev_layer_1 = layer_1_values[-position - 2]
# error at output layer
layer_2_delta = layer_2_deltas[-position - 1]
# error at hidden layer
layer_1_delta = (future_layer_1_delta.dot(synapse_h.T) + layer_2_delta.dot(
synapse_1.T)) * sigmoid_output_to_derivative(layer_1)
# let's update all our weights so we can try again
synapse_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)
synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta)
synapse_0_update += X.T.dot(layer_1_delta)
future_layer_1_delta = layer_1_delta
synapse_0 += synapse_0_update * alpha
synapse_1 += synapse_1_update * alpha
synapse_h += synapse_h_update * alpha
synapse_0_update *= 0
synapse_1_update *= 0
synapse_h_update *= 0
# print out progress
if (j % 1000 == 0):
print
"Error:" + str(overallError)
print("Pred:" + str(d))
print("True:" + str(c))
out = 0
for index, x in enumerate(reversed(d)):
out += x * pow(2, index)
print(str(a_int) + " + " + str(b_int) + " = " + str(out))
print("------------")结果：
Pred:[0 0 0 0 0 0 0 1]
True:[0 1 0 0 0 1 0 1]
9 + 60 = 1
------------
Pred:[1 1 1 1 1 1 1 1]
True:[0 0 1 1 1 1 1 1]
28 + 35 = 255
------------
Pred:[0 1 0 0 1 0 0 0]
True:[1 0 1 0 0 0 0 0]
116 + 44 = 72
------------
Pred:[1 1 0 1 1 1 1 1]
True:[0 1 0 0 1 1 0 1]
4 + 73 = 223
------------
Pred:[0 0 0 0 1 0 0 0]
True:[0 1 0 1 0 0 1 0]
71 + 11 = 8
------------
Pred:[1 0 1 0 0 0 1 0]
True:[1 1 0 0 0 0 1 0]
81 + 113 = 162
------------
Pred:[0 1 0 1 0 0 0 1]
True:[0 1 0 1 0 0 0 1]
81 + 0 = 81
------------
Pred:[1 0 0 0 0 0 0 1]
True:[1 0 0 0 0 0 0 1]
4 + 125 = 129
------------
Pred:[0 0 1 1 1 0 0 0]
True:[0 0 1 1 1 0 0 0]
39 + 17 = 56
------------
Pred:[0 0 0 0 1 1 1 0]
True:[0 0 0 0 1 1 1 0]
11 + 3 = 14
------------
- 1.先定义sigmoid和sigmoid导数函数，方便后序运算。
- 2.初始化8位二进制序列的编码，0-256分别对应00000000-11111111的编码序列。
- 3.随机产生网络权重，设置随机种子保证每次产生的权重相同，d是存储器，即具有记忆功能的代码。
- 4.每次训练我们在0-128中随机产生两个数（不是0-256防止溢出），找到对应的8位二进制序列，进行数据输入。
- 5.开始训练，每1000次查看一次中间结果，产生的结果和正确的结果进行误差计算，从而更新随机网络权重的参数，再次训练再更新，直至我们训练10000次为止（或者可以设置误差小于多少停止）。
5. 实现“Character-Level Language Models”源代码
假设我们只有四个可能的字母“helo”的词汇表，并且想在训练序列“hello”上训练一个RNN。这个训练序列实际上是 4 个独立训练示例的来源：1. 给定 “h” 上下文时，“e”的概率应该可能，2. “l”应该在“he”的上下文中出现，3. “l”也应该在给定“hel”的上下文中，最后是 4。“o”应该可能被赋予“地狱”的上下文。
具体来说，我们将使用 1-of-k 编码将每个字符编码到一个向量中（即除了词汇表中字符索引处的单个字符之外的所有字符均为零），并使用函数一次将它们馈送到 RNN 中。然后，我们将观察一个 4 维输出向量序列（每个字符一个维度），我们将其解释为 RNN 当前分配给序列中下一个字符的置信度。下图如下：
例如，我们看到，在第一个时间步中，当 RNN 看到字符 “h” 时，它为下一个字母 “h” 分配了 1.0 的置信度，为字母 “e” 分配了 2.2，为 “l” 分配了 -3.0，为 “o” 分配了 4.1 的置信度。由于在我们的训练数据（字符串“hello”）中，下一个正确的字符是“e”，我们希望增加它的置信度（绿色）并降低所有其他字母（红色）的置信度。同样，我们在 4 个时间步中的每一个都有一个期望的目标字符，我们希望网络为其分配更大的置信度。由于 RNN 完全由可微运算组成，我们可以运行反向传播算法（这只是微积分中链式规则的递归应用）来弄清楚我们应该在哪个方向调整其每个权重以增加正确目标的分数（绿色粗体数字）。然后，我们可以执行参数更新，在这个梯度方向上稍微推动每个权重。如果我们在参数更新后将相同的输入提供给 RNN，我们会发现正确字符的分数（例如第一个时间步中的“e”）会略高（例如 2.3 而不是 2.2），而不正确字符的分数会略低。然后，我们一遍又一遍地重复这个过程，直到网络收敛，并且它的预测最终与训练数据一致，因为接下来总是预测正确的字符。
一个更技术性的解释是，我们同时在每个输出向量上使用标准的 Softmax 分类器（通常也称为交叉熵损失）。RNN 使用小批量随机梯度下降进行训练，我喜欢使用RMSProp或 Adam（每参数自适应学习率方法）来稳定更新。
另请注意，第一次输入字符“l”时，目标是“l”，但第二次输入目标是“o”。因此，RNN 不能单独依赖输入，必须使用其循环连接来跟踪上下文以实现此任务。
The Unreasonable Effectiveness of Recurrent Neural Networks
import torch
# 使用RNN 有嵌入层和线性层
num_class = 4 # 4个类别
input_size = 4 # 输入维度是4
hidden_size = 8 # 隐层是8个维度
embedding_size = 10 # 嵌入到10维空间
batch_size = 1
num_layers = 2 # 两层的RNN
seq_len = 5 # 序列长度是5
# 准备数据
idx2char = ['e', 'h', 'l', 'o'] # 字典
x_data = [[1, 0, 2, 2, 3]] # hello 维度（batch,seqlen）
y_data = [3, 1, 2, 3, 2] # ohlol 维度 (batch*seqlen)
inputs = torch.LongTensor(x_data)
labels = torch.LongTensor(y_data)
# 构造模型
class Model(torch.nn.Module):
def __init__(self):
super(Model, self).__init__()
self.emb = torch.nn.Embedding(input_size, embedding_size)
self.rnn = torch.nn.RNN(input_size=embedding_size, hidden_size=hidden_size, num_layers=num_layers,
batch_first=True)
self.fc = torch.nn.Linear(hidden_size, num_class)
def forward(self, x):
hidden = torch.zeros(num_layers, x.size(0), hidden_size)
x = self.emb(x) # (batch,seqlen,embeddingsize)
x, _ = self.rnn(x, hidden)
x = self.fc(x)
return x.view(-1, num_class) # 转变维2维矩阵，seq*batchsize*numclass -》((seq*batchsize),numclass)
model = Model()
# 损失函数和优化器
criterion = torch.nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.05) # lr = 0.01学习的太慢
# 训练
for epoch in range(15):
optimizer.zero_grad()
outputs = model(inputs) # inputs是（seq,Batchsize,Inputsize） outputs是(seq,Batchsize,Hiddensize)
loss = criterion(outputs, labels) # labels是（seq，batchsize，1）
loss.backward()
optimizer.step()
_, idx = outputs.max(dim=1)
idx = idx.data.numpy()
print("Predicted:", ''.join([idx2char[x] for x in idx]), end='')
print(",Epoch {}/15 loss={:.3f}".format(epoch + 1, loss.item()))结果：
6. 分析“序列到序列”源代码（选做）
# Model
class Seq2Seq(nn.Module):
def __init__(self):
super(Seq2Seq, self).__init__()
self.encoder = nn.RNN(input_size=n_class, hidden_size=n_hidden, dropout=0.5) # encoder
self.decoder = nn.RNN(input_size=n_class, hidden_size=n_hidden, dropout=0.5) # decoder
self.fc = nn.Linear(n_hidden, n_class)
def forward(self, enc_input, enc_hidden, dec_input):
# enc_input(=input_batch): [batch_size, n_step+1, n_class]
# dec_inpu(=output_batch): [batch_size, n_step+1, n_class]
enc_input = enc_input.transpose(0, 1) # enc_input: [n_step+1, batch_size, n_class]
dec_input = dec_input.transpose(0, 1) # dec_input: [n_step+1, batch_size, n_class]
# h_t : [num_layers(=1) * num_directions(=1), batch_size, n_hidden]
_, h_t = self.encoder(enc_input, enc_hidden)
# outputs : [n_step+1, batch_size, num_directions(=1) * n_hidden(=128)]
outputs, _ = self.decoder(dec_input, h_t)
model = self.fc(outputs) # model : [n_step+1, batch_size, n_class]
return model
model = Seq2Seq().to(device)
criterion = nn.CrossEntropyLoss().to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=0.001)seq2seq模型由编码与解码两部分构成，编码部分将输入编码为状态向量，解码部分将状态向量作为输入输出序列。
7. “编码器-解码器”的简单实现（必做）
import torch
import numpy as np
import torch.nn as nn
import torch.utils.data as Data
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
letter = [c for c in 'SE?abcdefghijklmnopqrstuvwxyz']
letter2idx = {n: i for i, n in enumerate(letter)}
seq_data = [['man', 'women'], ['black', 'white'], ['king', 'queen'], ['girl', 'boy'], ['up', 'down'], ['high', 'low']]
# Seq2Seq Parameter
n_step = max([max(len(i), len(j)) for i, j in seq_data]) # max_len(=5)
n_hidden = 128
n_class = len(letter2idx) # classfication problem
batch_size = 3
def make_data(seq_data):
enc_input_all, dec_input_all, dec_output_all = [], [], []
for seq in seq_data:
for i in range(2):
seq[i] = seq[i] + '?' * (n_step - len(seq[i])) # 'man??', 'women'
enc_input = [letter2idx[n] for n in (seq[0] + 'E')] # ['m', 'a', 'n', '?', '?', 'E']
dec_input = [letter2idx[n] for n in ('S' + seq[1])] # ['S', 'w', 'o', 'm', 'e', 'n']
dec_output = [letter2idx[n] for n in (seq[1] + 'E')] # ['w', 'o', 'm', 'e', 'n', 'E']
enc_input_all.append(np.eye(n_class)[enc_input])
dec_input_all.append(np.eye(n_class)[dec_input])
dec_output_all.append(dec_output) # not one-hot
# make tensor
return torch.Tensor(enc_input_all), torch.Tensor(dec_input_all), torch.LongTensor(dec_output_all)
enc_input_all, dec_input_all, dec_output_all = make_data(seq_data)
class TranslateDataSet(Data.Dataset):
def __init__(self, enc_input_all, dec_input_all, dec_output_all):
self.enc_input_all = enc_input_all
self.dec_input_all = dec_input_all
self.dec_output_all = dec_output_all
def __len__(self): # return dataset size
return len(self.enc_input_all)
def __getitem__(self, idx):
return self.enc_input_all[idx], self.dec_input_all[idx], self.dec_output_all[idx]
loader = Data.DataLoader(TranslateDataSet(enc_input_all, dec_input_all, dec_output_all), batch_size, True)
# Model
class Seq2Seq(nn.Module):
def __init__(self):
super(Seq2Seq, self).__init__()
self.encoder = nn.RNN(input_size=n_class, hidden_size=n_hidden, dropout=0.5) # encoder
self.decoder = nn.RNN(input_size=n_class, hidden_size=n_hidden, dropout=0.5) # decoder
self.fc = nn.Linear(n_hidden, n_class)
def forward(self, enc_input, enc_hidden, dec_input):
# enc_input(=input_batch): [batch_size, n_step+1, n_class]
# dec_inpu(=output_batch): [batch_size, n_step+1, n_class]
enc_input = enc_input.transpose(0, 1) # enc_input: [n_step+1, batch_size, n_class]
dec_input = dec_input.transpose(0, 1) # dec_input: [n_step+1, batch_size, n_class]
# h_t : [num_layers(=1) * num_directions(=1), batch_size, n_hidden]
_, h_t = self.encoder(enc_input, enc_hidden)
# outputs : [n_step+1, batch_size, num_directions(=1) * n_hidden(=128)]
outputs, _ = self.decoder(dec_input, h_t)
model = self.fc(outputs) # model : [n_step+1, batch_size, n_class]
return model
model = Seq2Seq().to(device)
criterion = nn.CrossEntropyLoss().to(device)
optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
for epoch in range(5000):
for enc_input_batch, dec_input_batch, dec_output_batch in loader:
# make hidden shape [num_layers * num_directions, batch_size, n_hidden]
h_0 = torch.zeros(1, batch_size, n_hidden).to(device)
(enc_input_batch, dec_intput_batch, dec_output_batch) = (
enc_input_batch.to(device), dec_input_batch.to(device), dec_output_batch.to(device))
# enc_input_batch : [batch_size, n_step+1, n_class]
# dec_intput_batch : [batch_size, n_step+1, n_class]
# dec_output_batch : [batch_size, n_step+1], not one-hot
pred = model(enc_input_batch, h_0, dec_intput_batch)
# pred : [n_step+1, batch_size, n_class]
pred = pred.transpose(0, 1) # [batch_size, n_step+1(=6), n_class]
loss = 0
for i in range(len(dec_output_batch)):
# pred[i] : [n_step+1, n_class]
# dec_output_batch[i] : [n_step+1]
loss += criterion(pred[i], dec_output_batch[i])
if (epoch + 1) % 1000 == 0:
print('Epoch:', '%04d' % (epoch + 1), 'cost =', '{:.6f}'.format(loss))
optimizer.zero_grad()
loss.backward()
optimizer.step()
# Test
def translate(word):
enc_input, dec_input, _ = make_data([[word, '?' * n_step]])
enc_input, dec_input = enc_input.to(device), dec_input.to(device)
# make hidden shape [num_layers * num_directions, batch_size, n_hidden]
hidden = torch.zeros(1, 1, n_hidden).to(device)
output = model(enc_input, hidden, dec_input)
# output : [n_step+1, batch_size, n_class]
predict = output.data.max(2, keepdim=True)[1] # select n_class dimension
decoded = [letter[i] for i in predict]
translated = ''.join(decoded[:decoded.index('E')])
return translated.replace('?', '')
print('test')
print('man ->', translate('man'))
print('mans ->', translate('mans'))
print('king ->', translate('king'))
print('black ->', translate('black'))
print('up ->', translate('up'))结果:
心得体会
通过本次作业，掌握了SRN的不同实现方法以及二进制加法代码的构成与实现，了解了序列到序列学习（Seq2Seq）是指训练模型从而把一个域的序列（比如英语语句）转化为另一个域的序列比如法语中的对应语句）。RNN同样也可以看成一个编码器-解码器结构，编码器将文本编码成向量，而解码器将向量解码成我们想要的输出。
ref
序列到序列的语言翻译模型代码(tensorflow)解析
使用Python建立RNN实现二进制加法的示例代码
通俗易懂的RNN_长竹Danko的博客-CSDN博客_rnn