【deep_thoughts】30_PyTorch LSTM和LSTMP的原理及其手写复现

文章目录

LSTM API
手写 lstm_forward 函数
LSTMP
修改 lstm_forward 函数

视频链接： 30、PyTorch LSTM和LSTMP的原理及其手写复现_哔哩哔哩_bilibili

PyTorch LSTM API：https://pytorch.org/docs/stable/generated/torch.nn.LSTM.html?highlight=lstm#torch.nn.LSTM

LSTM API

首先实例化一些参数：

import torch
import torch.nn as nn

# 定义一些常量
batch_size, seq_len, input_size, h_size = 2, 3, 4, 5
input = torch.randn(batch_size, seq_len, input_size)  # 随机初始化一个输入序列
c_0 = torch.randn(batch_size, h_size)  # 初始值，不会参与训练
h_0 = torch.randn(batch_size, h_size)

调用PyTorch中的 LSTM API：

# 调用官方 LSTM API
lstm_layer = nn.LSTM(input_size, h_size, batch_first=True)  # num_layers默认为1
output, (h_n, c_n) = lstm_layer(input, (h_0.unsqueeze(0), c_0.unsqueeze(0)))  # (D*num_layers=1, b, hidden_size)

看一下返回的结果的形状：

print(output.shape)  # [2,3,5] [b, seq_len, hidden_size]
print(h_n.shape)  # [1,2,5] [num_layers, b, hidden_size]
print(c_n.shape)  # [1,2,5] [num_layers, b, hidden_size]

这里输出一下lstm_layer中的参数名称及其形状：

for name, para in lstm_layer.named_parameters():
    print(name, para.shape)

输出结果如下：

weight_ih_l0 torch.Size([20, 4])  # [4*hidden_size, input_size]
weight_hh_l0 torch.Size([20, 5])  # [4*hidden_size, hidden_size]
bias_ih_l0 torch.Size([20])  # [4*hidden_size]
bias_hh_l0 torch.Size([20])  # [4*hidden_size]

手写 lstm_forward 函数

手写一个lstm_forward函数，实现LSTM的计算原理。官网上的计算公式，如下：
$\begin{align} &i_t = \sigma(W_{ii}x_t + b_{ii} + W_{hi}h_{t-1} + b_{hi}) \\ &f_t = \sigma(W_{if}x_t + b_{if} + W_{hf}h_{t-1} + b_{hf}) \\ &g_t = \textup{tanh}(W_{ig}x_t + b_{ig} + W_{hg}h_{t-1} + b_{hg}) \\ &o_t = \sigma(W_{io}x_t + b_{io} + W_{ho}h_{t-1} + b_{ho}) \\ &c_t = f_t \odot c_t + i_t \odot g_t \\ &h_t = o_t \odot \textup{tanh}(c_t) \end{align}$
这里先将lstm_forward函数中的每个参数的维度写出来：

def lstm_forward(input, initial_states, w_ih, w_hh, b_ih, b_hh):
    h_0, c_0 = initial_states  # 初始状态  [b_size, hidden_size]
    b_size, seq_len, input_size = input.shape
    h_size = h_0.shape[-1]

    h_prev, c_prev = h_0, c_0
    # 需要将权重w在batch_size维进行扩维并复制，才能和x与h进行相乘
    w_ih_batch = w_ih.unsqueeze(0).tile(b_size, 1, 1)  # [4*hidden_size, in_size]->[b_size, ,]
    w_hh_batch = w_hh.unsqueeze(0).tile(b_size, 1, 1)  # [4*hidden_size, hidden_size]->[b_size, ,]

    output_size = h_size
    output = torch.zeros(b_size, seq_len, output_size)  # 初始化一个输出序列
    for t in range(seq_len):
        x = input[:, t, :]  # 当前时刻的输入向量 [b,in_size]->[b,in_size,1]
        w_times_x = torch.bmm(w_ih_batch, x.unsqueeze(-1)).squeeze(-1)   # bmm:含有批量大小的矩阵相乘
        # [b, 4*hidden_size, 1]->[b, 4*hidden_size]
        # 这一步就是计算了 Wii*xt|Wif*xt|Wig*xt|Wio*xt
        w_times_h_prev = torch.bmm(w_hh_batch, h_prev.unsqueeze(-1)).squeeze(-1)
        # [b, 4*hidden_size, hidden_size]*[b, hidden_size, 1]->[b,4*hidden_size, 1]->[b, 4*hidden_size]
        # 这一步就是计算了 Whi*ht-1|Whf*ht-1|Whg*ht-1|Who*ht-1

        # 分别计算输入门(i)、遗忘门(f)、cell门(g)、输出门(o)  维度均为 [b, h_size]
        i_t = torch.sigmoid(w_times_x[:, :h_size] + w_times_h_prev[:, :h_size] + b_ih[:h_size] + b_hh[:h_size])  # 取前四分之一
        f_t = torch.sigmoid(w_times_x[:, h_size:2*h_size] + w_times_h_prev[:, h_size:2*h_size]
                            + b_ih[h_size:2*h_size] + b_hh[h_size:2*h_size])
        g_t = torch.tanh(w_times_x[:, 2*h_size:3*h_size] + w_times_h_prev[:, 2*h_size:3*h_size]
                         + b_ih[2*h_size:3*h_size] + b_hh[2*h_size:3*h_size])
        o_t = torch.sigmoid(w_times_x[:, 3*h_size:] + w_times_h_prev[:, 3*h_size:]
                            + b_ih[3*h_size:] + b_hh[3*h_size:])
        c_prev = f_t * c_prev + i_t * g_t
        h_prev = o_t * torch.tanh(c_prev)

        output[:, t, :] = h_prev

    return output, (h_prev.unsqueeze(0), c_prev.unsqueeze(0))  # 官方是三维，在第0维扩一维

验证一下 lstm_forward 的准确性：

# 这里使用 lstm_layer 中的参数
# 加了me表示自己手写的
output_me, (h_n_me, c_n_me) = lstm_forward(input, (h_0, c_0), lstm_layer.weight_ih_l0,
                                           lstm_layer.weight_hh_l0, lstm_layer.bias_ih_l0, lstm_layer.bias_hh_l0)

打印一下，看两个的计算结果是否相同：

print("PyTorch API output:")
print(output)  # [2,3,5] [b, seq_len, hidden_size]
print(h_n)  # [1,2,5] [num_layers, b, hidden_size]
print(c_n)  # [1,2,5] [num_layers, b, hidden_size]
print("\nlstm_forward function output:")
print(output_me)  # [2,3,5] [b, seq_len, hidden_size]
print(h_n_me)  # [1,2,5] [num_layers, b, hidden_size]
print(c_n_me)

结果如下，完全一致，说明手写的是对的：

PyTorch API output:
tensor([[[ 0.1671,  0.2493,  0.2603, -0.1448, -0.1951],
         [-0.0680,  0.0478,  0.0218,  0.0735, -0.0604],
         [ 0.0144,  0.0507, -0.0556, -0.2600,  0.1234]],

        [[ 0.4561, -0.0015, -0.0776, -0.0644, -0.5319],
         [ 0.1667,  0.0111,  0.0114, -0.1227, -0.2369],
         [-0.0220,  0.0637, -0.2353,  0.0404, -0.1309]]],
       grad_fn=<TransposeBackward0>)
tensor([[[ 0.0144,  0.0507, -0.0556, -0.2600,  0.1234],
         [-0.0220,  0.0637, -0.2353,  0.0404, -0.1309]]],
       grad_fn=<StackBackward0>)
tensor([[[ 0.0223,  0.1574, -0.1572, -0.4663,  0.2110],
         [-0.0382,  0.6440, -0.4334,  0.0779, -0.3198]]],
       grad_fn=<StackBackward0>)

lstm_forward function output:
tensor([[[ 0.1671,  0.2493,  0.2603, -0.1448, -0.1951],
         [-0.0680,  0.0478,  0.0218,  0.0735, -0.0604],
         [ 0.0144,  0.0507, -0.0556, -0.2600,  0.1234]],

        [[ 0.4561, -0.0015, -0.0776, -0.0644, -0.5319],
         [ 0.1667,  0.0111,  0.0114, -0.1227, -0.2369],
         [-0.0220,  0.0637, -0.2353,  0.0404, -0.1309]]], grad_fn=<CopySlices>)
tensor([[[ 0.0144,  0.0507, -0.0556, -0.2600,  0.1234],
         [-0.0220,  0.0637, -0.2353,  0.0404, -0.1309]]],
       grad_fn=<UnsqueezeBackward0>)
tensor([[[ 0.0223,  0.1574, -0.1572, -0.4663,  0.2110],
         [-0.0382,  0.6440, -0.4334,  0.0779, -0.3198]]],
       grad_fn=<UnsqueezeBackward0>)

LSTMP

# 定义一些常量
batch_size, seq_len, input_size, h_size = 2, 3, 4, 5
proj_size = 3  # 要比hidden_size小

input = torch.randn(batch_size, seq_len, input_size)
c_0 = torch.randn(batch_size, h_size)
h_0 = torch.randn(batch_size, proj_size)  # 注意这里从原来的 h_size 换成了 proj_size

# 调用官方 LSTM API
lstm_layer = nn.LSTM(input_size, h_size, batch_first=True, proj_size=proj_size)  
output, (h_n, c_n) = lstm_layer(input, (h_0.unsqueeze(0), c_0.unsqueeze(0)))

打印一下返回的结果的形状：

print(output.shape)  # [2,3,3] [b, seq_len, proj_size]
print(h_n.shape)  # [1,2,3] [num_layers, b, proj_size]
print(c_n.shape)  # [1,2,5] [num_layers, b, hidden_size]

这里输出一下lstm_layer中的参数名称及其形状：

for name, para in lstm_layer.named_parameters():
    print(name, para.shape)

输出结果如下输出结果如下：

weight_ih_l0 torch.Size([20, 4])  # [4*hidden_size, input_size]
weight_hh_l0 torch.Size([20, 3])  # [4*hidden_size, proj_size]
bias_ih_l0 torch.Size([20])
bias_hh_l0 torch.Size([20])
weight_hr_l0 torch.Size([3, 5])  # 这个参数就是对 hidden_state 进行压缩的 [hidden_size, proj_size]

修改 lstm_forward 函数

修改lstm_forward函数，从而能够实现LSTMP：

def lstm_forward(input, initial_states, w_ih, w_hh, b_ih, b_hh, w_hr=None):
    h_0, c_0 = initial_states  # 初始状态  [b, proj_size][b, hidden_size]
    b_size, seq_len, input_size = input.shape
    h_size = c_0.shape[-1]

    h_prev, c_prev = h_0, c_0
    # 需要将权重w在batch_size维进行扩维并复制，才能和x与h进行相乘
    w_ih_batch = w_ih.unsqueeze(0).tile(b_size, 1, 1)  # [4*hidden_size, in_size]->[b_size, ,]
    w_hh_batch = w_hh.unsqueeze(0).tile(b_size, 1, 1)  # [4*hidden_size, hidden_size]->[b_size, ,]


    if w_hr is not None:
        proj_size = w_hr.shape[0]
        output_size = proj_size
        w_hr_batch = w_hr.unsqueeze(0).tile(b_size, 1, 1)  # [proj_size, hidden_size]->[b_size, ,]
    else:
        output_size = h_size

    output = torch.zeros(b_size, seq_len, output_size)  # 初始化一个输出序列
    for t in range(seq_len):
        x = input[:, t, :]  # 当前时刻的输入向量 [b,in_size]->[b,in_size,1]
        w_times_x = torch.bmm(w_ih_batch, x.unsqueeze(-1)).squeeze(-1)   # bmm:含有批量大小的矩阵相乘
        # [b, 4*hidden_size, 1]->[b, 4*hidden_size]
        # 这一步就是计算了 Wii*xt|Wif*xt|Wig*xt|Wio*xt
        w_times_h_prev = torch.bmm(w_hh_batch, h_prev.unsqueeze(-1)).squeeze(-1)
        # [b, 4*hidden_size, hidden_size]*[b, hidden_size, 1]->[b,4*hidden_size, 1]->[b, 4*hidden_size]
        # 这一步就是计算了 Whi*ht-1|Whf*ht-1|Whg*ht-1|Who*ht-1

        # 分别计算输入门(i)、遗忘门(f)、cell门(g)、输出门(o)  维度均为 [b, h_size]
        i_t = torch.sigmoid(w_times_x[:, :h_size] + w_times_h_prev[:, :h_size] + b_ih[:h_size] + b_hh[:h_size])  # 取前四分之一
        f_t = torch.sigmoid(w_times_x[:, h_size:2*h_size] + w_times_h_prev[:, h_size:2*h_size]
                            + b_ih[h_size:2*h_size] + b_hh[h_size:2*h_size])
        g_t = torch.tanh(w_times_x[:, 2*h_size:3*h_size] + w_times_h_prev[:, 2*h_size:3*h_size]
                         + b_ih[2*h_size:3*h_size] + b_hh[2*h_size:3*h_size])
        o_t = torch.sigmoid(w_times_x[:, 3*h_size:] + w_times_h_prev[:, 3*h_size:]
                            + b_ih[3*h_size:] + b_hh[3*h_size:])
        c_prev = f_t * c_prev + i_t * g_t
        h_prev = o_t * torch.tanh(c_prev)  # [b_size, h_size]

        if w_hr is not None:  # 对 h_prev 进行压缩，做projection
            h_prev = torch.bmm(w_hr_batch, h_prev.unsqueeze(-1))  # [b,proj_size,hidden_size]*[b,h_size,1]=[b,proj_size,1]
            h_prev = h_prev.squeeze(-1)  # [b, proj_size]

        output[:, t, :] = h_prev

    return output, (h_prev.unsqueeze(0), c_prev.unsqueeze(0))  # 官方是三维，在第0维扩一维

验证一下 lstm_forward 的准确性：

output_me, (h_n_me, c_n_me) = lstm_forward(input, (h_0, c_0), lstm_layer.weight_ih_l0, lstm_layer.weight_hh_l0,
                                           lstm_layer.bias_ih_l0, lstm_layer.bias_hh_l0, lstm_layer.weight_hr_l0)

print("PyTorch API output:")
print(output)  # [2,3,3] [b, seq_len, proj_size]
print(h_n)  # [1,2,3] [num_layers, b, proj_size]
print(c_n)  # [1,2,5] [num_layers, b, hidden_size]
print("\nlstm_forward function output:")
print(output_me)  # [2,3,3] [b, seq_len, proj_size]
print(h_n_me)  # [1,2,3] [num_layers, b, proj_size]
print(c_n_me)  # [1,2,5] [num_layers, b, hidden_size]

输出的结果如下，完全一致，说明手写的是对的：

PyTorch API output:
tensor([[[ 0.0392, -0.3149, -0.1264],
         [ 0.0141, -0.2619, -0.0760],
         [ 0.0306, -0.2166,  0.0915]],

        [[-0.0777, -0.1205, -0.0555],
         [-0.0646, -0.0926,  0.0391],
         [-0.0456, -0.0576,  0.1849]]], grad_fn=<TransposeBackward0>)
tensor([[[ 0.0306, -0.2166,  0.0915],
         [-0.0456, -0.0576,  0.1849]]], grad_fn=<StackBackward0>)
tensor([[[ 1.9913, -0.2683, -0.1221,  0.1751, -0.6072],
         [-0.2383, -0.2253, -0.0385, -0.8820, -0.1794]]],
       grad_fn=<StackBackward0>)

lstm_forward function output:
tensor([[[ 0.0392, -0.3149, -0.1264],
         [ 0.0141, -0.2619, -0.0760],
         [ 0.0306, -0.2166,  0.0915]],

        [[-0.0777, -0.1205, -0.0555],
         [-0.0646, -0.0926,  0.0391],
         [-0.0456, -0.0576,  0.1849]]], grad_fn=<CopySlices>)
tensor([[[ 0.0306, -0.2166,  0.0915],
         [-0.0456, -0.0576,  0.1849]]], grad_fn=<UnsqueezeBackward0>)
tensor([[[ 1.9913, -0.2683, -0.1221,  0.1751, -0.6072],
         [-0.2383, -0.2253, -0.0385, -0.8820, -0.1794]]],
       grad_fn=<UnsqueezeBackward0>)