【深度学习】之卷积（Convolution2D）、最大池化（Max Pooling）和 Dropout 的NumPy实现

1. 2D 卷积操作

import numpy as npdef conv2d(image, kernel, stride=1, padding=0):"""应用2D卷积操作到输入图像上。参数：- image: 输入图像，2D数组。- kernel: 卷积核，2D数组。- stride: 卷积步幅。- padding: 图像周围的零填充数量。返回值：- output: 卷积操作的结果。"""# 对输入图像添加零填充if padding > 0:image = np.pad(image, ((padding, padding), (padding, padding)), mode='constant')kernel_height, kernel_width = kernel.shapeimage_height, image_width = image.shape# 计算输出的尺寸output_height = (image_height - kernel_height) // stride + 1output_width = (image_width - kernel_width) // stride + 1output = np.zeros((output_height, output_width))for i in range(0, output_height):for j in range(0, output_width):start_i = i * stridestart_j = j * strideend_i = start_i + kernel_heightend_j = start_j + kernel_widthoutput[i, j] = np.sum(image[start_i:end_i, start_j:end_j] * kernel)return output# 示例用法
image = np.array([[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12],[13, 14, 15, 16]])kernel = np.array([[1, 0],[0, -1]])conv_result = conv2d(image, kernel, stride=1, padding=1)
print("卷积结果:\n", conv_result)

2. 2D 最大池化操作

def max_pool2d(image, pool_size=2, stride=2, padding=0):"""应用2D最大池化操作到输入图像上。参数：- image: 输入图像，2D数组。- pool_size: 池化窗口的大小。- stride: 池化步幅。- padding: 图像周围的零填充数量。返回值：- output: 最大池化操作的结果。"""# 对输入图像添加零填充if padding > 0:image = np.pad(image, ((padding, padding), (padding, padding)), mode='constant')image_height, image_width = image.shape# 计算输出的尺寸output_height = (image_height - pool_size) // stride + 1output_width = (image_width - pool_size) // stride + 1output = np.zeros((output_height, output_width))for i in range(0, output_height):for j in range(0, output_width):start_i = i * stridestart_j = j * strideend_i = start_i + pool_sizeend_j = start_j + pool_sizeoutput[i, j] = np.max(image[start_i:end_i, start_j:end_j])return output# 示例用法
pool_result = max_pool2d(conv_result, pool_size=2, stride=2, padding=0)
print("最大池化结果:\n", pool_result)

3. Dropout 操作

def dropout(X, drop_prob):"""对输入应用dropout。参数：- X: 输入数组。- drop_prob: 丢弃神经元的概率 (0 <= drop_prob < 1)。返回值：- output: 应用dropout后的结果。"""if drop_prob < 0.0 or drop_prob >= 1.0:raise ValueError("drop_prob必须在范围[0.0, 1.0)内。")keep_prob = 1 - drop_probmask = np.random.rand(*X.shape) < keep_probreturn X * mask / keep_prob# 示例用法
np.random.seed(0)  # 为了结果的可重复性
X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
dropout_result = dropout(X, drop_prob=0.5)
print("Dropout结果:\n", dropout_result)