Building the model layers 生成模型层

What is a neural network 什么是神经网络

神经网络是按层连接的神经元的集合。每个神经元都是一个小的计算单元，执行简单的计算来共同解决问题。神经元分为 3 种类型的层：输入层、隐藏层和输出层。隐藏层和输出层包含许多神经元。神经网络模仿人脑处理信息的方式。

Components of a neural network 神经网络的组成部分

• activation function 激活函数 决定神经元是否应该被激活。神经网络中发生的计算包括应用激活函数。如果神经元激活，则意味着输入很重要。有不同种类的激活函数。选择使用哪个激活函数取决于您想要的输出。激活函数的另一个重要作用是为模型添加非线性。

  • Binary 如果函数结果为正，则用于将输出节点设置为 1；如果函数结果为零或负，则将输出节点设置为 0。$f(x)=\{\begin{array}{ll}0,& \text{if }x<0\\ 1,& \text{if }x\ge 0\end{array}$
  • Sigmoid 用于预测输出节点介于 0 和 1 之间的概率。$f(x) = {\large \frac{1}{1+e^{-x}}} $
  • Tanh 用于预测输出节点是否在 1 到 -1 之间，用于分类用例。$f(x) = {\large \frac{e^{x} - e^{-x}}{e{x} + e^{-x}}} $
  • ReLU (rectified linear activation function) 如果函数结果为负，则用于将输出节点设置为 0；如果结果为正，则保持结果值。$f(x)=\{\begin{array}{ll}0,& \text{if }x<0\\ x,& \text{if }x\ge 0\end{array}$

• Weights 权重 影响我们网络的输出与预期输出值的接近程度。当输入进入神经元时，它会乘以权重值，所得输出要么被观察，要么被传递到神经网络中的下一层。一层中所有神经元的权重被组织成一个张量。

• Bias 偏差 弥补了激活函数的输出与其预期输出之间的差异。低偏差值表明网络对输出形式做出更多假设，而高偏差值对输出形式做出更少假设。

我们可以说，具有weights $W$ 和bias $b$ 的神经网络层的输出 $y$ 的计算为，输入乘以 weights加上bias的总和。 $x = \sum{(weights * inputs) + bias} $，其中 $f(x)$ 是激活函数。

Build a neural network 构建神经网络

神经网络由对数据执行操作的层/模块组成。torch.nn命名空间提供了构建您自己的神经网络所需的所有构建块。在PyTorch 中，每个模块都是nn.Module 的子类。神经网络本身就是一个模块，由其他模块（层）组成。这种嵌套结构允许轻松构建和管理复杂的架构。

在以下部分中，我们将构建一个神经网络，来对 FashionMNIST 数据集中的图像进行分类。

%matplotlib inline
import os
import torch
from torch import nn
from torch.utils.data import DataLoader
from torchvision import datasets, transforms

Get a hardware device for training 获取用于训练的硬件设备

我们希望能够在 GPU 等硬件加速器（如果可用）上训练我们的模型。让我们检查一下torch.cuda ，否则我们使用 CPU。

device = 'cuda' if torch.cuda.is_available() else 'cpu'
print('Using {} device'.format(device))

Out:

Using cuda device

Define the Class 定义类

我们通过子类化nn.Module来定义我们的神经网络。在__init__中，初始化神经网络层。每个nn.Module子类都在forward方法中实现对输入数据的操作。

我们的神经网络由以下部分组成：

• 输入层具有 28x28 或 784 个特征/像素。
• 第一个线性模块采用输入 784 个特征，并将其转换为具有 512 个特征的隐藏层。
• ReLU 激活函数将应用于转换中。
• 第二个线性模块将第一个隐藏层的 512 个特征作为输入，并将其转换到具有 512 个特征的下一个隐藏层。
• ReLU 激活函数将应用于转换中。
• 第三个线性模块将 512 个特征作为来自第二个隐藏层的输入，并将这些特征转换到输出层，其中 10 是类的数量。
• ReLU 激活函数将应用于转换中。

class NeuralNetwork(nn.Module):def __init__(self):super(NeuralNetwork, self).__init__()self.flatten = nn.Flatten()self.linear_relu_stack = nn.Sequential(nn.Linear(28*28, 512),nn.ReLU(),nn.Linear(512, 512),nn.ReLU(),nn.Linear(512, 10),nn.ReLU())def forward(self, x):x = self.flatten(x)logits = self.linear_relu_stack(x)return logits

我们创建NeuralNetwork 的一个实例，并将其移动到device，并打印其结构。

model = NeuralNetwork().to(device)
print(model)

Out:

NeuralNetwork((flatten): Flatten(start_dim=1, end_dim=-1)(linear_relu_stack): Sequential((0): Linear(in_features=784, out_features=512, bias=True)(1): ReLU()(2): Linear(in_features=512, out_features=512, bias=True)(3): ReLU()(4): Linear(in_features=512, out_features=10, bias=True)(5): ReLU())
)

为了使用该model，我们将输入数据传递给它。这将执行model的forward以及一些background operations。不要直接调用model.forward()！在输入上调用model会返回一个二维张量，其中 dim=0 对应于每个类的 10 个原始predicted values的每个输出，dim=1 对应于每个输出的各个值。

我们通过，将它传递给nn.Softmax模块的实例，来获得prediction probabilities。

X = torch.rand(1, 28, 28, device=device)
logits = model(X)
pred_probab = nn.Softmax(dim=1)(logits)
y_pred = pred_probab.argmax(1)
print(f"Predicted class: {y_pred}")

Out:

Predicted class: tensor([7], device='cuda:0')

Weight and Bias 权重和偏差

nn.Linear 模块随机初始化每层的权重和偏差，并在内部将值存储在张量中。

print(f"First Linear weights: {model.linear_relu_stack[0].weight} \n")print(f"First Linear biases: {model.linear_relu_stack[0].bias} \n")

Out:

First Linear weights: Parameter containing:
tensor([[ 8.9385e-03, -2.4055e-02,  1.9085e-03,  ..., -1.8426e-05,-9.0800e-04,  1.9594e-02],[-7.0768e-03,  2.6314e-02,  2.8988e-02,  ...,  2.2543e-02,9.9050e-03, -4.3447e-03],[-2.5320e-02, -3.2440e-02, -3.0216e-02,  ..., -3.1892e-02,-2.0309e-03, -2.5925e-02],...,[-6.6404e-03, -1.9659e-03, -3.3045e-02,  ..., -5.3951e-03,-1.1355e-02,  1.0398e-04],[ 1.3734e-02,  3.3571e-02,  3.4846e-02,  ...,  3.1258e-02,-9.9484e-03, -1.1788e-02],[-1.3908e-02,  1.1488e-02, -6.8923e-03,  ..., -9.5730e-03,-6.6496e-03, -4.7810e-03]], requires_grad=True) First Linear biases: Parameter containing:
tensor([ 5.9986e-03,  1.9926e-02, -9.0487e-03,  9.3418e-03,  3.1350e-02,-3.1133e-02, -1.9971e-02,  9.2257e-03,  2.4641e-02, -3.9794e-03,-1.9599e-02,  1.5554e-02, -1.1251e-02,  2.0161e-02,  1.9584e-02,-2.3056e-02,  6.4135e-03, -1.2719e-02,  2.8192e-02, -1.1354e-02,-2.5184e-02,  1.4313e-02,  1.9746e-02, -2.6794e-02,  4.5221e-03,-1.9318e-02,  2.5716e-02,  2.3134e-03, -3.2787e-02,  2.5133e-02,1.3309e-02, -2.2916e-02, -2.9163e-02,  2.0085e-02, -1.9987e-02,-1.6186e-02,  2.7146e-02,  3.8904e-03,  3.3362e-02,  1.6783e-02,-3.2172e-02, -2.0039e-02,  1.5975e-02, -1.7357e-02, -6.5472e-03,-1.0733e-03, -6.6345e-03,  2.6318e-02, -1.3912e-02,  2.8931e-02,-8.0001e-03,  2.2949e-02,  3.3579e-02, -1.4285e-02, -3.5026e-02,-4.6408e-03, -3.2110e-02,  7.9603e-03,  1.6381e-02, -3.5188e-02,2.5518e-02,  2.2947e-02,  2.8763e-02,  2.4568e-02,  3.1417e-02,-4.2958e-03,  5.4503e-03, -2.6941e-02, -3.1337e-02,  6.5361e-03,1.5351e-02,  2.4380e-02,  3.4527e-02,  1.9956e-02, -1.6002e-02,-2.1571e-02, -3.1452e-02, 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-1.5272e-02,-3.6956e-03, -8.6415e-03, -2.1750e-02, -3.3776e-02,  3.4642e-02,1.6748e-04, -9.6430e-03,  3.1374e-02,  2.2172e-02, -2.1042e-02,2.7340e-02,  6.1807e-03,  1.2675e-03, -1.6533e-02, -1.1356e-03,2.8314e-02,  7.1925e-03, -2.1810e-02, -4.2207e-03,  5.8930e-03,-3.1270e-02, -2.1335e-02, -1.2622e-02, -2.5292e-02, -2.4345e-03,3.3701e-02, -5.3965e-03,  1.0012e-02, -8.9052e-04, -2.1508e-02,3.4990e-02, -3.1931e-02,  2.1711e-02,  1.7907e-02,  1.1928e-02,-2.4449e-02,  1.3951e-02, -1.2408e-02, -9.4584e-03,  1.6864e-02,-2.8035e-02,  2.9146e-02, -3.4494e-02, -3.4326e-02,  6.5326e-03,3.3425e-02, -2.1809e-02, -2.9216e-02, -6.3335e-03,  1.5225e-03,-2.3894e-02, -1.1101e-02,  9.0631e-03,  2.9225e-02,  5.1517e-03,-1.8896e-02,  2.1768e-02, -3.5104e-02, -2.2003e-02,  8.9227e-03,2.4530e-02,  4.0939e-03,  4.1382e-03,  5.8822e-03, -1.1990e-02,1.1077e-02, -9.5397e-03, -3.5084e-02, -2.9436e-02, -1.1752e-02,-1.3748e-02,  3.5164e-02, -1.6435e-02, -3.4502e-02,  3.3773e-03,-2.9251e-02, -2.1990e-02,  4.2471e-03, -2.3697e-02,  9.6990e-05,-3.2504e-02, -7.1421e-03,  1.7027e-02,  3.3400e-02,  6.4107e-03,1.1713e-03,  2.4070e-02, -1.2695e-02, -8.9952e-04,  2.4428e-02,-2.7448e-02, -3.6027e-03,  1.6652e-02, -1.2338e-03,  1.0408e-02,4.3328e-03,  1.8153e-02,  3.1082e-02,  2.7676e-02,  5.3654e-03,6.1815e-03, -2.0798e-02, -2.4612e-02, -3.3156e-02,  2.5055e-02,2.5179e-02, -1.5044e-02, -2.1547e-02, -2.2172e-02,  2.7281e-02,2.0324e-02,  2.7768e-02, -3.5495e-02, -1.7735e-02, -1.8990e-02,-7.6506e-03,  2.4374e-02, -2.6513e-02, -2.2248e-02,  4.7401e-03,1.5162e-02,  1.1040e-02, -2.7058e-02, -9.3053e-03, -1.1417e-03,1.9759e-02,  8.8142e-03, -1.1458e-02, -3.0437e-02,  2.6083e-03,2.3219e-02, -1.3296e-02,  2.3401e-02,  2.9435e-02, -2.4347e-02,-2.8407e-02,  3.2922e-03, -9.7309e-03, -3.1861e-03,  1.5294e-02,-3.1260e-02,  1.6128e-02, -2.6976e-02, -2.3860e-02, -2.8258e-02,3.3300e-02,  2.1957e-02,  1.8276e-02,  3.3821e-02,  3.2459e-02,-1.4380e-02,  2.8679e-02, -1.8167e-02,  1.4250e-02, -2.6868e-02,4.6922e-03,  3.0262e-02,  3.3328e-02,  1.7418e-03, -1.3915e-03,2.1020e-02, -3.2912e-04,  2.7675e-02,  2.8924e-02,  2.6323e-02,1.4407e-03,  1.7175e-02, -1.7259e-02, -2.4208e-02,  2.5289e-02,3.4845e-02,  8.8181e-03,  1.3848e-02,  2.3637e-02,  2.6063e-02,1.7485e-02, -5.0237e-03,  1.5242e-02, -5.2527e-03,  2.8615e-02,-6.4647e-03,  2.7292e-02,  1.2469e-02,  1.4604e-02,  2.3259e-02,-1.3001e-02, -1.4321e-02, -7.7171e-03,  9.9475e-03,  1.7257e-03,-1.4338e-02,  2.7782e-03, -1.9520e-02, -1.1003e-03, -3.5199e-02,5.0515e-03,  6.2458e-03,  3.1785e-02,  2.2085e-02, -1.8765e-02,-1.9637e-02,  5.6673e-03,  3.9483e-03,  6.8746e-03, -9.1332e-03,3.7987e-03, -1.3767e-02, -1.0537e-02,  2.8263e-02,  3.3773e-02,3.3666e-02, -9.3893e-03, -1.2266e-03,  3.4049e-02,  2.3165e-03,-3.1737e-02, -3.4418e-02, -5.2358e-03, -1.8076e-02, -1.0501e-02,7.2267e-03, -2.5573e-02,  1.2106e-02,  2.1317e-02,  1.4924e-02,7.0579e-03, -1.9364e-02, -6.4564e-03, -2.1039e-02, -1.1712e-02,-1.3358e-02,  2.7151e-02, -1.2927e-03, -5.1539e-03, -2.5093e-02,-1.7757e-02, -2.6099e-02,  1.2471e-02,  1.8767e-02, -1.4756e-02,-2.7813e-02, -1.0629e-02,  2.9636e-02,  7.8347e-03, -4.1875e-03,-5.7266e-03, -2.7923e-02, -2.1416e-02,  3.4688e-02, -1.2472e-02,1.8679e-02,  2.6543e-02,  1.3168e-02,  2.9893e-02,  1.3526e-02,-1.8278e-02, -8.5952e-03, -1.6681e-02, -2.1498e-03,  3.2721e-02,-1.2839e-02, -3.3540e-02, -1.6349e-02, -3.5600e-02, -1.3388e-02,-1.4139e-02, -1.4343e-02, -1.3964e-02, -2.3136e-02,  3.4252e-02,1.4078e-02,  2.8221e-02,  8.8933e-03, -2.3626e-02,  1.8151e-03,2.0952e-02,  2.1661e-02], requires_grad=True) 

Model Layers 模型层

让我们分解 FashionMNIST model中的layers。为了说明这一点，我们将采用 3 张大小为 28x28 的图像的小批量样本，看看当我们将其传递到网络时会发生什么。

input_image = torch.rand(3,28,28)
print(input_image.size())

Out:

torch.Size([3, 28, 28])

nn.Flatten

我们初始化nn.Flatten layer，将每个 2D 28x28 图像转换为 784 个像素值的连续数组，维持小批量维度（在 dim=0 时）。

flatten = nn.Flatten()
flat_image = flatten(input_image)
print(flat_image.size())

Out:

torch.Size([3, 784])

nn.Linear

linear layer是一个使用其存储的权重和偏差对输入应用线性变换的模块。输入层中每个像素的灰度值将连接到隐藏层中的神经元进行计算。用于转换的计算是 ${{weight * input + bias}} $。

layer1 = nn.Linear(in_features=28*28, out_features=20)
hidden1 = layer1(flat_image)
print(hidden1.size())

Out:

torch.Size([3, 20])

nn.ReLU

非线性激活是在模型的输入和输出之间创建复杂映射的原因。它们在线性变换后应用以引入非线性，帮助神经网络学习各种现象。

在此模型中，我们在线性层之间使用nn.ReLU，但还有其他激活可以在模型中引入非线性。

ReLU 激活函数获取线性层计算的输出，并将负值替换为零。
Linear output: ${ x = {weight * input + bias}} $。
ReLU:
$
f(x)=
\begin{cases}
0, & \text{if } x < 0\
x, & \text{if } x\geq 0\
\end{cases}
$

print(f"Before ReLU: {hidden1}\n\n")
hidden1 = nn.ReLU()(hidden1)
print(f"After ReLU: {hidden1}")

Out:

Before ReLU: tensor([[ 0.4158, -0.0130, -0.1144,  0.3960,  0.1476, -0.0690, -0.0269,  0.2690,0.1353,  0.1975,  0.4484,  0.0753,  0.4455,  0.5321, -0.1692,  0.4504,0.2476, -0.1787, -0.2754,  0.2462],[ 0.2326,  0.0623, -0.2984,  0.2878,  0.2767, -0.5434, -0.5051,  0.4339,0.0302,  0.1634,  0.5649, -0.0055,  0.2025,  0.4473, -0.2333,  0.6611,0.1883, -0.1250,  0.0820,  0.2778],[ 0.3325,  0.2654,  0.1091,  0.0651,  0.3425, -0.3880, -0.0152,  0.2298,0.3872,  0.0342,  0.8503,  0.0937,  0.1796,  0.5007, -0.1897,  0.4030,0.1189, -0.3237,  0.2048,  0.4343]], grad_fn=<AddmmBackward0>)After ReLU: tensor([[0.4158, 0.0000, 0.0000, 0.3960, 0.1476, 0.0000, 0.0000, 0.2690, 0.1353,0.1975, 0.4484, 0.0753, 0.4455, 0.5321, 0.0000, 0.4504, 0.2476, 0.0000,0.0000, 0.2462],[0.2326, 0.0623, 0.0000, 0.2878, 0.2767, 0.0000, 0.0000, 0.4339, 0.0302,0.1634, 0.5649, 0.0000, 0.2025, 0.4473, 0.0000, 0.6611, 0.1883, 0.0000,0.0820, 0.2778],[0.3325, 0.2654, 0.1091, 0.0651, 0.3425, 0.0000, 0.0000, 0.2298, 0.3872,0.0342, 0.8503, 0.0937, 0.1796, 0.5007, 0.0000, 0.4030, 0.1189, 0.0000,0.2048, 0.4343]], grad_fn=<ReluBackward0>)

nn.Sequential

nn.Sequential是模块的有序容器。数据按照定义的相同顺序传递通过所有模块。您可以使用顺序容器来组合一个快速网络，例如seq_modules.

seq_modules = nn.Sequential(flatten,layer1,nn.ReLU(),nn.Linear(20, 10)
)
input_image = torch.rand(3,28,28)
logits = seq_modules(input_image)

nn.Softmax

神经网络的最后一个线性层返回logits （ [-infty, infty] 中的原始值）被传递到 nn.Softmax模块。Softmax激活函数用于计算神经网络输出的概率。它仅用于神经网络的输出层。Logits 缩放为值 [0, 1]，表示模型对每个类别的预测概率。dim参数指示维度，沿该维度值的总和必须为 1。具有最高概率的节点预测所需的输出。

softmax = nn.Softmax(dim=1)
pred_probab = softmax(logits)

Model Parameters 模型参数

神经网络内的许多层都是参数化的。在训练期间，优化的相关权重和偏差。子类化nn.Module会自动跟踪模型对象中定义的所有字段，并使所有参数都可以使用模型parameters()或named_parameters()方法进行访问。

在此示例中，我们迭代每个参数，并打印其大小及其值的预览。

print(f"Model structure: {model}\n\n")for name, param in model.named_parameters():print(f"Layer: {name} | Size: {param.size()} | Values : {param[:2]} \n")

Out:

Model structure: NeuralNetwork((flatten): Flatten(start_dim=1, end_dim=-1)(linear_relu_stack): Sequential((0): Linear(in_features=784, out_features=512, bias=True)(1): ReLU()(2): Linear(in_features=512, out_features=512, bias=True)(3): ReLU()(4): Linear(in_features=512, out_features=10, bias=True))
)Layer: linear_relu_stack.0.weight | Size: torch.Size([512, 784]) | Values : tensor([[ 0.0273,  0.0296, -0.0084,  ..., -0.0142,  0.0093,  0.0135],[-0.0188, -0.0354,  0.0187,  ..., -0.0106, -0.0001,  0.0115]],device='cuda:0', grad_fn=<SliceBackward0>)Layer: linear_relu_stack.0.bias | Size: torch.Size([512]) | Values : tensor([-0.0155, -0.0327], device='cuda:0', grad_fn=<SliceBackward0>)Layer: linear_relu_stack.2.weight | Size: torch.Size([512, 512]) | Values : tensor([[ 0.0116,  0.0293, -0.0280,  ...,  0.0334, -0.0078,  0.0298],[ 0.0095,  0.0038,  0.0009,  ..., -0.0365, -0.0011, -0.0221]],device='cuda:0', grad_fn=<SliceBackward0>)Layer: linear_relu_stack.2.bias | Size: torch.Size([512]) | Values : tensor([ 0.0148, -0.0256], device='cuda:0', grad_fn=<SliceBackward0>)Layer: linear_relu_stack.4.weight | Size: torch.Size([10, 512]) | Values : tensor([[-0.0147, -0.0229,  0.0180,  ..., -0.0013,  0.0177,  0.0070],[-0.0202, -0.0417, -0.0279,  ..., -0.0441,  0.0185, -0.0268]],device='cuda:0', grad_fn=<SliceBackward0>)Layer: linear_relu_stack.4.bias | Size: torch.Size([10]) | Values : tensor([ 0.0070, -0.0411], device='cuda:0', grad_fn=<SliceBackward0>)

知识检查

PyTorch 中所有神经网络模块的基类为 torch.nn.Module

Further Reading 进一步阅读

• torch.nn API

Build the Neural Network — PyTorch Tutorials 2.2.0+cu121 documentation
Build the Neural Network — PyTorch Tutorials 2.2.0+cu121 documentation

References 参考资料

使用 PyTorch 进行机器学习的简介 - Training | Microsoft Learn

使用 PyTorch 进行机器学习的简介 - Training | Microsoft Learn

Github

storm-ice/PyTorch_Fundamentals

storm-ice/PyTorch_Fundamentals