下面是一个加入了数据增强、正则化以及学习率调度等改进措施后的完整 Python 代码示例，用于基于 LeNet-5 的手写数字识别任务（MNIST 数据集）。此代码使用 Keras 构建并训练模型。 ```python import numpy as np from tensorflow.keras.datasets import mnist from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Conv2D, MaxPooling2D, Flatten, Dense, Dropout, BatchNormalization from tensorflow.keras.utils import to_categorical from tensorflow.keras.preprocessing.image import ImageDataGenerator from tensorflow.keras.callbacks import LearningRateScheduler import math # 加载 MNIST 数据集 (x_train, y_train), (x_test, y_test) = mnist.load_data() # 归一化处理和reshape输入形状 img_rows, img_cols = 28, 28 x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1).astype('float32') / 255 x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1).astype('float32') / 255 # 将标签转换为 one-hot 编码形式 y_train = to_categorical(y_train, 10) y_test = to_categorical(y_test, 10) # 定义LeNet-5模型，并添加一些改进措施如Dropout 和Batch Normalization model = Sequential() model.add(Conv2D(filters=6, kernel_size=(5, 5), strides=(1, 1), activation='relu', input_shape=(28, 28, 1))) model.add(MaxPooling2D(pool_size=(2, 2))) model.add(BatchNormalization()) model.add(Conv2D(filters=16, kernel_size=(5, 5), strides=(1, 1), activation='relu')) model.add(MaxPooling2D(pool_size=(2, 2))) model.add(Flatten()) model.add(Dense(units=120, activation='relu')) model.add(Dropout(0.5)) # 添加 Dropout 层 model.add(Dense(units=84, activation='relu')) model.add(Dense(units=10, activation='softmax')) # 动态调整学习率的回调函数 def lr_schedule(epoch): initial_lr = 0.01 drop_rate = 0.5 epochs_drop = 10.0 return initial_lr * math.pow(drop_rate, math.floor((epoch)/epochs_drop)) lr_scheduler = LearningRateScheduler(lr_schedule) # 设置图像生成器进行数据扩充 datagen = ImageDataGenerator(rotation_range=10, width_shift_range=0.1, height_shift_range=0.1) datagen.fit(x_train) # 编译模型 model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy']) # 训练模型 batch_size = 64 epochs = 20 history = model.fit(datagen.flow(x_train, y_train, batch_size=batch_size), steps_per_epoch=x_train.shape[0] // batch_size, validation_data=(x_test, y_test), epochs=epochs, callbacks=[lr_scheduler]) # 测试模型 test_loss, test_acc = model.evaluate(x_test, y_test) print("Test accuracy:", test_acc) ```