PyTorch正态分布随机数生成指南

torch.normal() 函数基础

torch.normal() 是 PyTorch 中用于生成服从正态分布随机张量的函数。其基本语法为：

torch.normal(mean, std, size=None)

其中 mean 是均值，std 是标准差，size 指定输出张量的形状。当 mean 和 std 都是张量时，它们必须具有相同的形状。

生成基础正态分布数据

生成一个形状为 (3, 2) 的随机张量，均值为 0，标准差为 1：

import torch
data = torch.normal(mean=0, std=1, size=(3,2))
print(data)

为数据添加噪声的方法

高斯噪声添加

使用 torch.normal() 直接生成噪声并叠加到原始数据上：

clean_data = torch.rand(3, 2) * 10  # 模拟原始数据
noise = torch.normal(mean=0, std=0.5, size=(3,2))  # 生成噪声
noisy_data = clean_data + noise

控制噪声强度

通过调整标准差参数控制噪声强度：

weak_noise = torch.normal(mean=0, std=0.1, size=clean_data.shape)
strong_noise = torch.normal(mean=0, std=2.0, size=clean_data.shape)

非对称噪声分布

生成非零均值的噪声模拟系统偏差：

bias_noise = torch.normal(mean=1.5, std=0.8, size=clean_data.shape)
biased_data = clean_data + bias_noise

可视化噪声效果

使用 matplotlib 可视化噪声添加前后的对比：

import matplotlib.pyplot as plt

plt.figure(figsize=(12,4))
plt.subplot(1,2,1)
plt.imshow(clean_data, cmap='viridis')
plt.title('Clean Data')

plt.subplot(1,2,2)
plt.imshow(noisy_data, cmap='viridis')
plt.title('Noisy Data')
plt.show()

应用场景示例

数据增强

在训练神经网络时为输入数据添加随机噪声：

def add_noise(batch, std=0.1):
    noise = torch.normal(mean=0, std=std, size=batch.size())
    return batch + noise

鲁棒性测试

测试模型对噪声的鲁棒性：

def test_robustness(model, test_loader, noise_std):
    correct = 0
    for data, target in test_loader:
        noisy_data = data + torch.normal(mean=0, std=noise_std, size=data.size())
        output = model(noisy_data)
        pred = output.argmax(dim=1)
        correct += pred.eq(target).sum().item()
    accuracy = 100. * correct / len(test_loader.dataset)
    return accuracy

注意事项

torch.normal() 在不同设备上的行为一致，既支持 CPU 也支持 CUDA 张量。对于可重复实验，需要设置随机种子：

torch.manual_seed(42)

当需要生成大量随机数据时，考虑使用 torch.randn() 结合缩放操作可能更高效：

# 等效于 torch.normal(mean=0, std=1)
data = torch.randn(3,2)

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