深度学习基础--多层感知机(MLP)

深度学习基础–多层感知机(MLP)

最近在阅读一本书籍–Dive-into-DL-Pytorch(动手学深度学习),链接:https://github.com/newmonkey/Dive-into-DL-PyTorch,自身觉得受益匪浅,在此记录下自己的学习历程。

本篇主要记录关于多层感知机(multilayer perceptron, MLP)的知识。多层感知机是在单层神经网络的基础上引入一个或多个隐藏层。

以单层神经网路SOFTMAX回归为例子。给定一个小批量样本X,假设输出层的softmax回归的权重和偏差参数分别为Wo和bo,输出层的输出记为O,则softmax回归的计算表达式为:
在这里插入图片描述
在上述的SOFTMAX回归中,我们在输入层与输出层间引入一个隐藏层,形成多层感知机。假设隐藏层的输出记为H,隐藏层的权重参数和偏差参数分别为Wh和bh,∅表示激活函数。则这个多层感知机的计算表达式为:
深度学习基础--多层感知机(MLP)_第1张图片
上述式子联立可得:
在这里插入图片描述

利用pytorch实现上述的多层感知机:

0 引入相关的包

import torch
from torch import nn
from torch.nn import init
import numpy as np
import torchvision
import torchvision.transforms as transforms

1 获取数据集

采用的是Fashion-MNIST数据集。
def load_data_fashion_mnist(batch_size, root='~/Datasets/FashionMNIST'):
    transform = transforms.ToTensor()
    mnist_train = torchvision.datasets.FashionMNIST(root=root, train=True, download=True, transform=transform)
    mnist_test = torchvision.datasets.FashionMNIST(root=root, train=False, download=True, transform=transform)
    if sys.platform.startswith('win'):
        num_workers = 0  # 0表示不用额外的进程来加速读取数据
    else:
        num_workers = 4
    train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
    test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)

    return train_iter, test_iter

batch_size = 256
train_iter, test_iter = load_data_fashion_mnist(batch_size)

2 定义和初始化模型

采用ReLU函数作为激活函数。
num_inputs, num_outputs, num_hiddens = 784, 10, 256

class FlattenLayer(torch.nn.Module):
    def __init__(self):
        super(FlattenLayer, self).__init__()
    def forward(self, x): # x shape: (batch, *, *, ...)
        return x.view(x.shape[0], -1)

net = nn.Sequential(
    FlattenLayer(),
    nn.Linear(num_inputs, num_hiddens),
    nn.ReLU(),
    nn.Linear(num_hiddens, num_outputs),
)
for params in net.parameters():
    init.normal_(params, mean=0, std=0.01)

3 定义损失函数

仍是采用SOFTMAX回归使用的交叉熵损失函数
loss = torch.nn.CrossEntropyLoss()

4 定义优化算法

采用⼩批量随机梯度下降(SGD)为优化算法。
optimizer = torch.optim.SGD(net.parameters(), lr=0.5)

5 训练模型

迭代周期设置为5,训练模型。
def evaluate_accuracy(data_iter, net):
    acc_sum, n = 0.0, 0
    for X, y in data_iter:
        acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
        n += y.shape[0]
    return acc_sum / n

def sgd(params, lr, batch_size):
    for param in params:
        param.data -= lr * param.grad / batch_size # 注意这里更改param时用的param.data

def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,params=None, lr=None, optimizer=None):
    for epoch in range(num_epochs):
        train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
        for X, y in train_iter:
            y_hat = net(X)
            l = loss(y_hat, y).sum()
            
            # 梯度清零
            if optimizer is not None:
                optimizer.zero_grad()
            elif params is not None and params[0].grad is not None:
                for param in params:
                    param.grad.data.zero_()
            
            l.backward()
            if optimizer is None:
                sgd(params, lr, batch_size)
            else:
                optimizer.step()
            
            train_l_sum += l.item()
            train_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()
            n += y.shape[0]
        test_acc = evaluate_accuracy(test_iter, net)
        print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'% (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))

num_epochs = 5
train_ch3(net, train_iter, test_iter, loss, num_epochs,batch_size, None, None, optimizer)
#结果
#epoch 1, loss 0.0031, train acc 0.709, test acc 0.798
#epoch 2, loss 0.0019, train acc 0.819, test acc 0.819
#epoch 3, loss 0.0017, train acc 0.844, test acc 0.840
#epoch 4, loss 0.0015, train acc 0.856, test acc 0.820
#epoch 5, loss 0.0014, train acc 0.864, test acc 0.832

END!

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