LeNet-5：包含7个层(layer)，如下图所示：输入层没有计算在内，输入图像大小为32*32*1，是针对灰度图进行训练和预测的。论文名字为” Gradient-Based Learning Applied to Document Recognition”，可以直接从/exdb/publis/pdf/lecun-01a.pdf 下载原始论文。
第一层是卷积层，使用6个5*5的filter，stride为1，padding为0，输出结果为28*28*6，6个feature maps，训练参数(5*5*1)*6+6=156(weights + bias)；
第二层进行平均池化操作，filter为2*2，stride为2，padding为0，输出结果为14*14*6，6个feature maps，训练参数1*6+6=12(coefficient + bias)；
第三层是卷积层，使用16个5*5的filter，stride为1，padding为0，输出结果为10*10*16，16个feature maps， 训练参数(按照论文给的连接方式) (5*5*3+1)*6 + (5*5*4+1)*6+(5*5*4+1)*3+(5*5*6+1)*1 = 1516(weights + bias)；
第四层又是平均池化层，filter为2*2，stride为2，padding为0，输出结果为5*5*16，16个feature maps，训练参数1*16+16=32(coefficient + bias)；
第五层是卷积层，使用120个5*5的fiter,stride为1，输出结果为1*1*120，120个feature maps，训练参数(5*5*6)*120+120=48120(weights + bias)；
第六层是一个全连接层，有84个神经元，训练参数120*84+84=10164(weights + bias)；此layer使用的激活函数为tanh。
第七层得到最后的输出预测y’的值，y’有10个可能的值，对应识别0--9这10个数字，在现在的版本中，使用softmax函数输出10种分类结果，即第七层为softmax。
输入图像size为32*32比训练数据集图像size为28*28大的原因：期望诸如笔划终点(stroke end-points)或角点(corner)这些潜在的特征(potential distinctive feature)能够出现在最高层特征检测器(highest-level feature detectors)的感受野的中心。
没有把layer2中的每个feature map连接到layer3中的每个feature map原因：(1). 不完全的连接机制将连接的数量保持在合理的范围内；(2). 更重要的，它强制破坏了网络的对称性。因为不同的feature maps来自不同的输入，所以不同的feature maps被强制提取不同的features.(The main reason is to break the symmetry in the network and keeps the number of connections within reasonable bounds.)
LeNet-5中的5是指5个隐藏层即卷积层、池化层、卷积层、池化层、卷积层。
不同的filter可以提取不同的特征，如边沿、线性、角等特征。
关于卷积神经网络的基础介绍可参考之前的blog：
/fengbingchun/article/details/50529500
/fengbingchun/article/details/80262495
/fengbingchun/article/details/68065338
/fengbingchun/article/details/69001433
以下是参考Caffe中的测试代码对LeNet-5网络进行测试的代码，与论文中的不同处包括：
(1). 论文中要求输入层图像大小为32*32，这里为28*28；
(2). 论文中第一层卷积层输出是6个feature maps，这里是20个feature maps；
(3). 论文中池化层取均值，而这里取最大值；
(4). 论文中第三层卷积层输出是16个feature maps，这里是50个feature maps，而且这里第二层的feature map是连接到第三层的每个feature map的；
(5). 论文中第五层是卷积层，这里是全连接层并输出500个神经元，激活函数采用ReLU；
(6). 论文中第七层是RBF(Euclidean Radial Basic Function)，这里采用Softmax。
以下是测试代码(lenet-5.cpp)：
#include "funset.hpp"#include "common.hpp"int lenet_5_mnist_train(){#ifdef CPU_ONLYcaffe::Caffe::set_mode(caffe::Caffe::CPU);#elsecaffe::Caffe::set_mode(caffe::Caffe::GPU);#endif#ifdef _MSC_VERconst std::string filename{ "E:/GitCode/Caffe_Test/test_data/Net/lenet-5_mnist_windows_solver.prototxt" };#elseconst std::string filename{ "test_data/Net/lenet-5_mnist_linux_solver.prototxt" };#endifcaffe::SolverParameter solver_param;if (!caffe::ReadProtoFromTextFile(filename.c_str(), &solver_param)) {fprintf(stderr, "parse solver.prototxt fail\n");return -1;}mnist_convert(); // convert MNIST to LMDBcaffe::SGDSolver<float> solver(solver_param);solver.Solve();fprintf(stdout, "train finish\n");return 0;}int lenet_5_mnist_test(){#ifdef CPU_ONLYcaffe::Caffe::set_mode(caffe::Caffe::CPU);#elsecaffe::Caffe::set_mode(caffe::Caffe::GPU);#endif#ifdef _MSC_VERconst std::string param_file{ "E:/GitCode/Caffe_Test/test_data/Net/lenet-5_mnist_windows_test.prototxt" };const std::string trained_filename{ "E:/GitCode/Caffe_Test/test_data/Net/lenet-5_mnist_iter_10000.caffemodel" };const std::string image_path{ "E:/GitCode/Caffe_Test/test_data/images/handwritten_digits/" };#elseconst std::string param_file{ "test_data/Net/lenet-5_mnist_linux_test.prototxt" };const std::string trained_filename{ "test_data/Net/lenet-5_mnist_iter_10000.caffemodel" };const std::string image_path{ "test_data/images/handwritten_digits/" };#endifcaffe::Net<float> caffe_net(param_file, caffe::TEST);caffe_net.CopyTrainedLayersFrom(trained_filename);const boost::shared_ptr<caffe::Blob<float> > blob_data_layer = caffe_net.blob_by_name("data");int image_channel_data_layer = blob_data_layer->channels();int image_height_data_layer = blob_data_layer->height();int image_width_data_layer = blob_data_layer->width();const std::vector<caffe::Blob<float>*> output_blobs = caffe_net.output_blobs();int require_blob_index{ -1 };const int digit_category_num{ 10 };for (int i = 0; i < output_blobs.size(); ++i) {if (output_blobs[i]->count() == digit_category_num)require_blob_index = i;}if (require_blob_index == -1) {fprintf(stderr, "ouput blob don't match\n");return -1;}std::vector<int> target{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };std::vector<int> result;for (auto num : target) {std::string str = std::to_string(num);str += ".png";str = image_path + str;cv::Mat mat = cv::imread(str.c_str(), 1);if (!mat.data) {fprintf(stderr, "load image error: %s\n", str.c_str());return -1;}if (image_channel_data_layer == 1)cv::cvtColor(mat, mat, CV_BGR2GRAY);else if (image_channel_data_layer == 4)cv::cvtColor(mat, mat, CV_BGR2BGRA);cv::resize(mat, mat, cv::Size(image_width_data_layer, image_height_data_layer));cv::bitwise_not(mat, mat);boost::shared_ptr<caffe::MemoryDataLayer<float> > memory_data_layer =boost::static_pointer_cast<caffe::MemoryDataLayer<float>>(caffe_net.layer_by_name("data"));mat.convertTo(mat, CV_32FC1, 0.00390625);float dummy_label[1] {0};memory_data_layer->Reset((float*)(mat.data), dummy_label, 1);float loss{ 0.0 };const std::vector<caffe::Blob<float>*>& results = caffe_net.ForwardPrefilled(&loss);const float* output = results[require_blob_index]->cpu_data();float tmp{ -1 };int pos{ -1 };for (int j = 0; j < 10; j++) {//fprintf(stdout, "Probability to be Number %d is: %.3f\n", j, output[j]);if (tmp < output[j]) {pos = j;tmp = output[j];}}result.push_back(pos);}for (auto i = 0; i < 10; i++)fprintf(stdout, "actual digit is: %d, result digit is: %d\n", target[i], result[i]);fprintf(stdout, "predict finish\n");return 0;}
solver.prototxt文件内容如下：
# solver.prototxt是一个配置文件用来告知Caffe怎样对网络进行训练# 其文件内的各字段名需要在caffe.proto的message SolverParameter中存在，否则会解析不成功net: "test_data/Net/lenet-5_mnist_linux_train.prototxt" # 训练网络文件名test_iter: 100 # test_iter * test_batch_size = 测试图像总数量test_interval: 500 # 指定执行多少次训练网络执行一次测试网络base_lr: 0.01 # 学习率lr_policy: "inv" # 学习策略, return base_lr * (1 + gamma * iter) ^ (- power)momentum: 0.9 # 动量weight_decay: 0.0005 # 权值衰减gamma: 0.0001 # 学习率计算参数power: 0.75 # 学习率计算参数display: 100 # 指定训练多少次在屏幕上显示一次结果信息，如loss值等max_iter: 10000 # 最多训练次数snapshot: 5000 # 执行多少次训练保存一次中间结果snapshot_prefix: "test_data/Net/lenet-5_mnist" # 结果保存位置前缀solver_type: SGD # 随机梯度下降
train时的prototxt文件内容如下：
name: "LeNet-5"layer {name: "mnist"type: "Data"top: "data"top: "label"include {phase: TRAIN}transform_param {scale: 0.00390625}data_param {source: "test_data/MNIST/train"batch_size: 64backend: LMDB}}layer {name: "mnist"type: "Data"top: "data"top: "label"include {phase: TEST}transform_param {scale: 0.00390625}data_param {source: "test_data/MNIST/test"batch_size: 100backend: LMDB}}layer {name: "conv1"type: "Convolution"bottom: "data"top: "conv1"param {lr_mult: 1}param {lr_mult: 2}convolution_param {num_output: 20kernel_size: 5stride: 1weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "pool1"type: "Pooling"bottom: "conv1"top: "pool1"pooling_param {pool: MAXkernel_size: 2stride: 2}}layer {name: "conv2"type: "Convolution"bottom: "pool1"top: "conv2"param {lr_mult: 1}param {lr_mult: 2}convolution_param {num_output: 50kernel_size: 5stride: 1weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "pool2"type: "Pooling"bottom: "conv2"top: "pool2"pooling_param {pool: MAXkernel_size: 2stride: 2}}layer {name: "ip1"type: "InnerProduct"bottom: "pool2"top: "ip1"param {lr_mult: 1}param {lr_mult: 2}inner_product_param {num_output: 500weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "relu1"type: "ReLU"bottom: "ip1"top: "ip1"}layer {name: "ip2"type: "InnerProduct"bottom: "ip1"top: "ip2"param {lr_mult: 1}param {lr_mult: 2}inner_product_param {num_output: 10weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "accuracy"type: "Accuracy"bottom: "ip2"bottom: "label"top: "accuracy"include {phase: TEST}}layer {name: "loss"type: "SoftmaxWithLoss"bottom: "ip2"bottom: "label"top: "loss"}
train.prototxt可视化结果如下：
test时的test.prototxt文件内容如下：
name: "LeNet-5"layer {name: "data"type: "MemoryData"top: "data" #top: "label"memory_data_param {batch_size: 1channels: 1height: 28width: 28}transform_param {scale: 0.00390625}}layer {name: "conv1"type: "Convolution"bottom: "data"top: "conv1"param {lr_mult: 1}param {lr_mult: 2}convolution_param {num_output: 20kernel_size: 5stride: 1weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "pool1"type: "Pooling"bottom: "conv1"top: "pool1"pooling_param {pool: MAXkernel_size: 2stride: 2}}layer {name: "conv2"type: "Convolution"bottom: "pool1"top: "conv2"param {lr_mult: 1}param {lr_mult: 2}convolution_param {num_output: 50kernel_size: 5stride: 1weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "pool2"type: "Pooling"bottom: "conv2"top: "pool2"pooling_param {pool: MAXkernel_size: 2stride: 2}}layer {name: "ip1"type: "InnerProduct"bottom: "pool2"top: "ip1"param {lr_mult: 1}param {lr_mult: 2}inner_product_param {num_output: 500weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "relu1"type: "ReLU"bottom: "ip1"top: "ip1"}layer {name: "ip2"type: "InnerProduct"bottom: "ip1"top: "ip2"param {lr_mult: 1}param {lr_mult: 2}inner_product_param {num_output: 10weight_filler {type: "xavier"}bias_filler {type: "constant"}}}layer {name: "prob"type: "Softmax"bottom: "ip2"top: "prob"}
test.prototxt可视化结果如下：
train时测试代码执行结果如下：
test是测试代码执行结果如下：
GitHub：/fengbingchun/Caffe_Test
