多层感知机（MLP）是经典的人工神经网络模型，常用于解决分类和回归问题，下面给出不同复杂度的Pytorch实现多层感知机（MLP）示例。 ### 简单三层MLP示例 ```python import torch from torch.nn import functional as F # 输入x的特征有10个 x = torch.randn(1, 10) # 一个隐藏层，节点个数为3 w = torch.randn(3, 10, requires_grad=True) b = torch.randn(1, 3, requires_grad=True) # 预测值 pre = torch.sigmoid(x @ w.t() + b) # 目标值 trage = torch.ones(1, 3) # loss function loss = F.mse_loss(pre, trage) # 反向传播 loss.backward() # 假设学习率 lr = 0.01 # 更新权值 w = w - lr * w.grad b = b - lr * b.grad ``` 该示例实现了一个简单的三层MLP，包含输入层、一个隐藏层和输出层，使用sigmoid作为激活函数，均方误差作为损失函数进行训练 [^2]。 ### 定义MLP类构建模型示例 ```python import torch import torch.nn as nn class MLP(nn.Module): def __init__(self, input_size, hidden_size, num_classes): super(MLP, self).__init__() self.fc1 = nn.Linear(input_size, hidden_size) self.relu = nn.ReLU() self.fc2 = nn.Linear(hidden_size, num_classes) def forward(self, x): out = self.fc1(x) out = self.relu(out) out = self.fc2(out) return out # 示例使用 input_size = 10 hidden_size = 20 num_classes = 2 model = MLP(input_size, hidden_size, num_classes) input_tensor = torch.randn(1, input_size) output = model(input_tensor) ``` 此示例定义了一个MLP类，该MLP由输入层、隐藏层和输出层组成，每个层都由全连接层（Linear）和ReLU激活函数组成 [^3]。 ### 包含两个隐含层示例 ```python import torch import torch.nn as nn class MLPWithTwoHidden(nn.Module): def __init__(self, input_size, hidden_size1, hidden_size2, num_classes): super(MLPWithTwoHidden, self).__init__() self.fc1 = nn.Linear(input_size, hidden_size1) self.relu1 = nn.ReLU() self.fc2 = nn.Linear(hidden_size1, hidden_size2) self.relu2 = nn.ReLU() self.fc3 = nn.Linear(hidden_size2, num_classes) def forward(self, x): out = self.fc1(x) out = self.relu1(out) out = self.fc2(out) out = self.relu2(out) out = self.fc3(out) return out # 示例使用 input_size = 784 hidden_size1 = 128 hidden_size2 = 64 num_classes = 10 model = MLPWithTwoHidden(input_size, hidden_size1, hidden_size2, num_classes) # 假设输入数据维度为[64, 784] input_tensor = torch.randn(64, input_size) output = model(input_tensor) ``` 该示例构建了一个包含两个隐含层的MLP，可用于如MNIST分类等任务 [^4]。