要求动手从0实现 softmax 回归（只借助Tensor和Numpy相关的库）在Fashion-MNIST数据 集上进行训练和测试，并从loss、训练集以及测试集上的准确率等多个角度对结果进行分析 （要求从零实现交叉熵损失函数）

好的，以下是使用Tensor和Numpy库从零实现softmax回归并在Fashion-MNIST数据集上进行训练和测试的步骤：

首先，导入所需的库：

import torch
import numpy as np
from torchvision import datasets, transforms

然后，加载Fashion-MNIST数据集并进行预处理：

# 定义数据转换
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])

# 加载训练集和测试集
train_dataset = datasets.FashionMNIST(root='./data', train=True, transform=transform, download=True)
test_dataset = datasets.FashionMNIST(root='./data', train=False, transform=transform, download=True)

# 创建数据加载器
train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=64, shuffle=True)
test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=64, shuffle=False)

接下来，定义softmax函数：

def softmax(x):
    e_x = np.exp(x - np.max(x))
    return e_x / np.sum(e_x, axis=1, keepdims=True)

然后，定义模型参数和优化器：

# 初始化模型参数
num_features = 28 * 28
num_classes = 10
W = np.random.randn(num_features, num_classes) / np.sqrt(num_features)
b = np.zeros(num_classes)

# 定义学习率和迭代次数
learning_rate = 0.1
num_epochs = 10

接着，进行模型的训练：

for epoch in range(num_epochs):
    total_loss = 0
    for images, labels in train_loader:
        # 将图片转换为二维数组
        images = images.view(-1, num_features)

        # 前向传播
        scores = np.dot(images.numpy(), W) + b
        probs = softmax(scores)
        
        # 计算损失函数
        batch_size = images.shape[0]
        y = np.zeros_like(probs)
        y[np.arange(batch_size), labels.numpy()] = 1
        loss = -np.sum(y * np.log(probs)) / batch_size
        total_loss += loss
        
        # 反向传播
        grad_scores = (probs - y) / batch_size
        grad_W = np.dot(images.numpy().T, grad_scores)
        grad_b = np.sum(grad_scores, axis=0)
        
        # 参数更新
        W -= learning_rate * grad_W
        b -= learning_rate * grad_b
    
    # 打印每个epoch的损失函数值
    print('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, total_loss))

最后，对模型进行测试并分析结果：

# 在训练集上进行预测
correct_train = 0
total_train = 0

for images, labels in train_loader:
    images = images.view(-1, num_features)
    scores = np.dot(images.numpy(), W) + b
    probs = softmax(scores)
    predicted_labels = np.argmax(probs, axis=1)
    
    total_train += labels.size(0)
    correct_train += (predicted_labels == labels.numpy()).sum().item()

train_accuracy = correct_train / total_train

# 在测试集上进行预测
correct_test = 0
total_test = 0

for images, labels in test_loader:
    images = images.view(-1, num_features)
    scores = np.dot(images.numpy(), W) + b
    probs = softmax(scores)
    predicted_labels = np.argmax(probs, axis=1)
    
    total_test += labels.size(0)
    correct_test += (predicted_labels == labels.numpy()).sum().item()

test_accuracy = correct_test / total_test

print('Train Accuracy: {:.2f}%'.format(train_accuracy * 100))
print('Test Accuracy: {:.2f}%'.format(test_accuracy * 100))

通过以上步骤，我们可以从零实现softmax回归并在Fashion-MNIST数据集上进行训练和测试，并从loss、训练集以及测试集上的准确率等多个角度对结果进行分析。可以观察每个epoch的损失函数逐渐减小，同时计算训练集和测试集上的准确率来评估模型的性能。