Exercise 4: Neural Networks Learning

需要用到的库

import numpy as np
import scipy.io
import matplotlib.pyplot as plt
import torch
import torch.nn as nn

1. Neural Networks模型

输入的数据为5000x400，共有10个类别，神经网络共有3层，输入层大小为400，输出层大小为10，隐藏层大小为25。第一个隐藏层的激活函数可以是sigmoid或者relu，第二个隐藏层的激活函数为softmax。后面会对不同的激活函数进行比较，也会对不同隐藏层大小进行比较。

input_layer_size  = 400  # 20x20 Input Images of Digits
hidden_layer_size = 25   # 25 hidden units
num_labels = 10          # 10 labels, from 1 to 10


class NeuralNetworks(nn.Module):
    def __init__(self):
        super(NeuralNetworks, self).__init__() 
        self.linear1 = nn.Linear(input_layer_size, hidden_layer_size)
        self.linear2 = nn.Linear(hidden_layer_size, num_labels)
        self.relu = nn.ReLU()
        self.softmax = nn.Softmax(dim=1)
        nn.init.xavier_normal_(self.linear1.weight, gain=0.01)
        nn.init.xavier_normal_(self.linear2.weight, gain=0.01)
        nn.init.constant_(self.linear1.bias, 0)
        nn.init.constant_(self.linear2.bias, 0)
        
 
    def forward(self,x):
        out = self.linear1(x)
        out = self.relu(out)
        out = self.linear2(out)
        out = self.softmax(out)
        return out

2. 加载数据

加载并展示数据，如下图所示。

3. 网络训练

选择的模型为定义好的模型，损失函数为交叉熵函数，优化器选择Adam优化，如果有GPU的话，将训练数据、标签和模型都放在GPU上，可以加快训练速度。

device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
model = NeuralNetworks()
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=1e-2, weight_decay=0)
X_t = torch.from_numpy(X).type(torch.FloatTensor).to(device)
y_t = torch.from_numpy(y).type(torch.LongTensor).to(device)
model = model.to(device)

网络迭代500次，损失函数和准确率变化如图所示。

best_precision = 0
train_loss_curve =[]
train_precision_curve =[]
for epoch in range(500):
    model.train()
    y_pred = model(X_t)
    loss = criterion(y_pred, y_t)
    print(epoch, loss.item())
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    train_loss_curve.append(loss.item())
    model.eval()
    y_pred = model(X_t).cpu().detach().numpy()
    y_pred = np.argmax(y_pred, axis=1)
    precision = np.mean(y_pred == y) * 100
    train_precision_curve.append(precision)
    if precision > best_precision:
        best_precision = precision

损失函数变化曲线