Caffe源代码(caffe version commit: 09868ac , date: 2015.08.15)中有一些重要的头文件，这里介绍下include/caffe/solver.hpp文件的内容：
1. include文件：
<caffe/solver.hpp>：此文件的介绍能够參考： http://blog.csdn.net/fengbingchun/article/details/62423060
2. 模板类Solver：虚基类
3. 模板类WorkerSolver：继承父类Solver，用于多GPU训练时仅计算梯度
4. 模板类SGDSolver：继承父类Solver
5. 模板类NesterovSolver：继承SGDSolver
6. 模板类AdaGradSolver：继承SGDSolver
7. 模板类RMSPropSolver：继承SGDSolver
8. 模板类AdaDeltaSolver：继承SGDSolver
9. 模板类AdamSolver：继承SGDSolver
10. 函数GetSolver：new solver对象
Solver通过协调Net的前向判断计算和反向梯度计算(forward inference and backward gradients)，来对參数进行更新。从而达到降低loss的目的。Caffe模型的学习被分为两个部分：由Solver进行优化、更新參数。由Net计算出loss和gradient。
solver.prototxt是一个配置文件用来告知Caffe如何对网络进行训练。
有了Net就能够进行神经网络的前后向传播计算了。可是还缺少神经网络的训练和预測功能，Solver类进一步封装了训练和预測相关的一些功能。Solver定义了针对Net网络模型的求解方法，记录神经网络的训练过程，保存神经网络模型參数，中断并恢复网络的训练过程。自己定义Solver能够实现不同的神经网络求解方式。
Caffe支持的solvers包含：
(1)、Stochastic Gradient Descent(type: “SGD”)即随机梯度下降：利用负梯度和上一次权重的更新值的线性组合来更新权重。学习率(learning rate)是负梯度的权重。
动量是上一次更新值的权重。一般将学习速率初始化为0.01。然后在训练(training)中当loss达到稳定时，将学习速率除以一个常数(比如10)，将这个过程重复多次。
对于动量一般设置为0.9，动量使weight得更新更为平缓，使学习过程更为稳定、高速。
(2)、AdaDelta(type:“AdaDelta”)：是一种”鲁棒的学习率方法”，同SGD一样是一种基于梯度的优化方法。
(3)、Adaptive Gradient(type: “AdaGrad”)即自适应梯度下降，与随机梯度下降一样是基于梯度的优化方法。
(4)、Adam(type:“Adam”)：也是一种基于梯度的优化方法。
它包含一对自适应时刻预计变量，能够看做是AdaGrad的一种泛化形式。
(5)、Nesterov’s Accelerated Gradient(type: “Nesterov”)：Nesterov提出的加速梯度下降(Nesterov’s accelerated gradient)是凸优化的一种最优算法，其收敛速度能够达到O(1/t^2)，而不是O(1/t)。
虽然在使用Caffe训练深度神经网络时非常难满足O(1/t^2)收敛条件。但实际中NAG对于某些特定结构的深度学习模型仍是一个非常有效的方法。
(6)、RMSprop(type:“RMSProp”)：是一种基于梯度的优化方法(同SGD相似)。
Solver：
(1)、用于优化过程的记录、创建训练网络(用于学习)和測试网络(用于评估)；
(2)、通过forward和backward过程来迭代地优化和更新參数；
(3)、周期性地用測试网络评估模型性能；
(4)、在优化过程中记录模型和solver状态的快照(snapshot)。
每一次迭代过程中：
(1)、调用Net的前向过程计算出输出和loss。
(2)、调用Net的反向过程计算出梯度(loss对每层的权重w和偏置b求导)。
(3)、依据以下所讲的Solver方法。利用梯度更新參数；
(4)、依据学习率(learning rate)。历史数据和求解方法更新solver的状态。使权重从初始化状态逐步更新到终于的学习到的状态。
Solvers的运行模式有CPU/GPU两种模式。
Solver方法：用于最小化损失(loss)值。
给定一个数据集D，优化的目标是D中全部数据损失的均值，即平均损失。取得最小值。
注：以上关于Solver内容的介绍主要摘自由CaffeCN社区翻译的《Caffe官方教程中译本》。
<caffe/solver.hpp>文件的具体介绍例如以下：
#ifndef CAFFE_OPTIMIZATION_SOLVER_HPP_
#define CAFFE_OPTIMIZATION_SOLVER_HPP_
#include <string>
#include <vector>
#include "caffe/net.hpp"
namespace caffe {
/**
* @brief An interface for classes that perform optimization on Net%s.
*
* Requires implementation of ApplyUpdate to compute a parameter update
* given the current state of the Net parameters.
*/
template <typename Dtype>
class Solver { // Solver模板类，虚基类
public:
// 显示构造函数, 内部会调用Init函数
explicit Solver(const SolverParameter& param, const Solver* root_solver = NULL);
explicit Solver(const string& param_file, const Solver* root_solver = NULL);
// 成员变量赋值，包含param_、iter_、current_step_,并调用InitTrainNet和InitTestNets函数
void Init(const SolverParameter& param);
// 为成员变量net_赋值
void InitTrainNet();
// 为成员变量test_nets_赋值
void InitTestNets();
// The main entry of the solver function. In default, iter will be zero. Pass
// in a non-zero iter number to resume training for a pre-trained net.
// 依次调用函数Restore、Step、Snapshot，然后运行net_的前向传播函数ForwardPrefilled，最后调用TestAll函数
virtual void Solve(const char* resume_file = NULL);
inline void Solve(const string resume_file) { Solve(resume_file.c_str()); }
// 重复运行net前向传播反向传播计算,期间会调用函数TestAll、ApplyUpdate、Snapshot及类Callback两个成员函数
void Step(int iters);
// The Restore method simply dispatches to one of the
// RestoreSolverStateFrom___ protected methods. You should implement these
// methods to restore the state from the appropriate snapshot type.
// 载入已有的模型
void Restore(const char* resume_file);
// 虚析构函数
virtual ~Solver() {}
// 获得slover parameter
inline const SolverParameter& param() const { return param_; }
// 获得train Net
inline shared_ptr<Net<Dtype> > net() { return net_; }
// 获得test Net
inline const vector<shared_ptr<Net<Dtype> > >& test_nets() {
return test_nets_;
}
// 获得当前的迭代数
int iter() { return iter_; }
// Invoked at specific points during an iteration
// 内部Callback类，仅在多卡GPU模式下使用
class Callback {
protected:
virtual void on_start() = 0;
virtual void on_gradients_ready() = 0;
template <typename T>
friend class Solver;
};
// 获得Callback
const vector<Callback*>& callbacks() const { return callbacks_; }
// 加入一个Callback
void add_callback(Callback* value) { callbacks_.push_back(value); }
protected:
// Make and apply the update value for the current iteration.
// 更新net的权值和偏置
virtual void ApplyUpdate() = 0;
// The Solver::Snapshot function implements the basic snapshotting utility
// that stores the learned net. You should implement the SnapshotSolverState()
// function that produces a SolverState protocol buffer that needs to be
// written to disk together with the learned net.
// 快照，内部会调用SnapshotToBinaryProto或SnapshotToHDF5、SnapshotSolverState函数
void Snapshot();
// 获取快照文件名称
string SnapshotFilename(const string extension);
// 写proto到.caffemodel
string SnapshotToBinaryProto();
// 写proto到HDF5文件
string SnapshotToHDF5();
// The test routine
// 内部会循环调用Test函数
void TestAll();
// 运行測试网络。net前向传播
void Test(const int test_net_id = 0);
// 存储snapshot solver state
virtual void SnapshotSolverState(const string& model_filename) = 0;
// 读HDF5文件到solver state
virtual void RestoreSolverStateFromHDF5(const string& state_file) = 0;
// 读二进制文件.solverstate到solver state
virtual void RestoreSolverStateFromBinaryProto(const string& state_file) = 0;
// dummy function，仅仅有声明没有实现
void DisplayOutputBlobs(const int net_id);
// Caffe中类的成员变量名都带有后缀"_"。这样就easy区分暂时变量和类成员变量
SolverParameter param_; // solver parameter
int iter_; // 当前的迭代数
int current_step_; //
shared_ptr<Net<Dtype> > net_; // train net
vector<shared_ptr<Net<Dtype> > > test_nets_; // test net
vector<Callback*> callbacks_; // Callback
// The root solver that holds root nets (actually containing shared layers)
// in data parallelism
const Solver* const root_solver_;
// 禁止使用Solver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(Solver);
};
/**
* @brief Solver that only computes gradients, used as worker
* for multi-GPU training.
*/
template <typename Dtype>
class WorkerSolver : public Solver<Dtype> { // 模板类WorkerSolver。继承父类Solver
public:
// 显示构造函数
explicit WorkerSolver(const SolverParameter& param, const Solver<Dtype>* root_solver = NULL)
: Solver<Dtype>(param, root_solver) {}
protected:
void ApplyUpdate() {}
void SnapshotSolverState(const string& model_filename) {
LOG(FATAL) << "Should not be called on worker solver.";
}
void RestoreSolverStateFromBinaryProto(const string& state_file) {
LOG(FATAL) << "Should not be called on worker solver.";
}
void RestoreSolverStateFromHDF5(const string& state_file) {
LOG(FATAL) << "Should not be called on worker solver.";
}
};
/**
* @brief Optimizes the parameters of a Net using
* stochastic gradient descent (SGD) with momentum.
*/
template <typename Dtype>
class SGDSolver : public Solver<Dtype> { // 模板类SGDSolver,继承父类Solver
public:
// 显示构造函数，调用PreSolve函数
explicit SGDSolver(const SolverParameter& param) : Solver<Dtype>(param) { PreSolve(); }
explicit SGDSolver(const string& param_file) : Solver<Dtype>(param_file) { PreSolve(); }
// 获取history数据
const vector<shared_ptr<Blob<Dtype> > >& history() { return history_; }
protected:
// 成员变量history_, update_, temp_初始化
void PreSolve();
// 获取学习率
Dtype GetLearningRate();
// 内部会调用ClipGradients、Normalize、Regularize、ComputeUpdateValue，更新net权值和偏置
virtual void ApplyUpdate();
// 调用caffe_scal函数
virtual void Normalize(int param_id);
// 调用caffe_axpy函数
virtual void Regularize(int param_id);
// 计算并更新对应Blob值，调用caffe_cpu_axpby和caffe_copy函数
virtual void ComputeUpdateValue(int param_id, Dtype rate);
// clip parameter gradients to that L2 norm，假设梯度值过大，就会对梯度做一个修剪。
// 对全部的參数乘以一个缩放因子，使得全部參数的平方和不超过參数中设定的梯度总值
virtual void ClipGradients();
// 存储snapshot solver state，内部会掉用SnapshotSolverStateToBinaryProto或SnapshotSolverStateToHDF5函数
virtual void SnapshotSolverState(const string& model_filename);
// 写solver state到二进制文件.solverstate
virtual void SnapshotSolverStateToBinaryProto(const string& model_filename);
// 写solver state到HDF5
virtual void SnapshotSolverStateToHDF5(const string& model_filename);
// 读HDF5文件到solver state
virtual void RestoreSolverStateFromHDF5(const string& state_file);
// 读二进制文件.solverstate到solver state
virtual void RestoreSolverStateFromBinaryProto(const string& state_file);
// history maintains the historical momentum data.
// update maintains update related data and is not needed in snapshots.
// temp maintains other information that might be needed in computation
// of gradients/updates and is not needed in snapshots
// Caffe中类的成员变量名都带有后缀"_"，这样就easy区分暂时变量和类成员变量
vector<shared_ptr<Blob<Dtype> > > history_, update_, temp_;
// 禁止使用SGDSolver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(SGDSolver);
};
template <typename Dtype>
class NesterovSolver : public SGDSolver<Dtype> { // 模板类NesterovSolver，继承SGDSolver
public:
// 显示构造函数
explicit NesterovSolver(const SolverParameter& param) : SGDSolver<Dtype>(param) {}
explicit NesterovSolver(const string& param_file) : SGDSolver<Dtype>(param_file) {}
protected:
// 计算并更新对应Blob值,调用caffe_cpu_axpby和caffe_copy函数
virtual void ComputeUpdateValue(int param_id, Dtype rate);
// 禁止使用NesterovSolver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(NesterovSolver);
};
template <typename Dtype>
class AdaGradSolver : public SGDSolver<Dtype> { // 模板类AdaGradSolver,继承SGDSolver
public:
// 显示构造函数，调用constuctor_sanity_check函数
explicit AdaGradSolver(const SolverParameter& param) : SGDSolver<Dtype>(param) { constructor_sanity_check(); }
explicit AdaGradSolver(const string& param_file) : SGDSolver<Dtype>(param_file) { constructor_sanity_check(); }
protected:
// 计算并更新对应Blob值
virtual void ComputeUpdateValue(int param_id, Dtype rate);
void constructor_sanity_check() {
CHECK_EQ(0, this->param_.momentum())
<< "Momentum cannot be used with AdaGrad.";
}
// 禁止使用AdaGradSolver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(AdaGradSolver);
};
template <typename Dtype>
class RMSPropSolver : public SGDSolver<Dtype> { // 模板类RMSPropSolver,继承SGDSolver
public:
// 显示构造函数。调用constructor_sanity_check函数
explicit RMSPropSolver(const SolverParameter& param) : SGDSolver<Dtype>(param) { constructor_sanity_check(); }
explicit RMSPropSolver(const string& param_file) : SGDSolver<Dtype>(param_file) { constructor_sanity_check(); }
protected:
// 计算并更新对应Blob值
virtual void ComputeUpdateValue(int param_id, Dtype rate);
void constructor_sanity_check() {
CHECK_EQ(0, this->param_.momentum())
<< "Momentum cannot be used with RMSProp.";
CHECK_GE(this->param_.rms_decay(), 0)
<< "rms_decay should lie between 0 and 1.";
CHECK_LT(this->param_.rms_decay(), 1)
<< "rms_decay should lie between 0 and 1.";
}
// 禁止使用RMSPropSolver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(RMSPropSolver);
};
template <typename Dtype>
class AdaDeltaSolver : public SGDSolver<Dtype> { // 模板类AdaDeltaSolver。继承SGDSolver
public:
// 显示构造函数，调用AdaDeltaPreSolve函数
explicit AdaDeltaSolver(const SolverParameter& param) : SGDSolver<Dtype>(param) { AdaDeltaPreSolve(); }
explicit AdaDeltaSolver(const string& param_file) : SGDSolver<Dtype>(param_file) { AdaDeltaPreSolve(); }
protected:
void AdaDeltaPreSolve();
// 计算并更新对应Blob值
virtual void ComputeUpdateValue(int param_id, Dtype rate);
// 禁止使用AdaDeltaSolver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(AdaDeltaSolver);
};
/**
* @brief AdamSolver, an algorithm for first-order gradient-based optimization
* of stochastic objective functions, based on adaptive estimates of
* lower-order moments. Described in [1].
*
* [1] D. P. Kingma and J. L. Ba, "ADAM: A Method for Stochastic Optimization."
* arXiv preprint arXiv:1412.6980v8 (2014).
*/
template <typename Dtype>
class AdamSolver : public SGDSolver<Dtype> { // 模板类AdamSolver。继承SGDSolver
public:
// 显示构造函数，调用AdamPreSolve函数
explicit AdamSolver(const SolverParameter& param) : SGDSolver<Dtype>(param) { AdamPreSolve();}
explicit AdamSolver(const string& param_file) : SGDSolver<Dtype>(param_file) { AdamPreSolve(); }
protected:
void AdamPreSolve();
// 计算并更新对应Blob值
virtual void ComputeUpdateValue(int param_id, Dtype rate);
// 禁止使用AdamSolver类的拷贝和赋值操作
DISABLE_COPY_AND_ASSIGN(AdamSolver);
};
// new一个指定的solver方法对象
template <typename Dtype>
Solver<Dtype>* GetSolver(const SolverParameter& param) {
SolverParameter_SolverType type = param.solver_type();
switch (type) {
case SolverParameter_SolverType_SGD:
return new SGDSolver<Dtype>(param);
case SolverParameter_SolverType_NESTEROV:
return new NesterovSolver<Dtype>(param);
case SolverParameter_SolverType_ADAGRAD:
return new AdaGradSolver<Dtype>(param);
case SolverParameter_SolverType_RMSPROP:
return new RMSPropSolver<Dtype>(param);
case SolverParameter_SolverType_ADADELTA:
return new AdaDeltaSolver<Dtype>(param);
case SolverParameter_SolverType_ADAM:
return new AdamSolver<Dtype>(param);
default:
LOG(FATAL) << "Unknown SolverType: " << type;
}
return (Solver<Dtype>*) NULL;
}
} // namespace caffe
#endif // CAFFE_OPTIMIZATION_SOLVER_HPP_
在caffe.proto文件里。主要有一个message是与solver相关的，例如以下：
// NOTE
// Update the next available ID when you add a new SolverParameter field.
//
// SolverParameter next available ID: 40 (last added: momentum2)
message SolverParameter { // Solver參数
//////////////////////////////////////////////////////////////////////////////
// Specifying the train and test networks
//
// Exactly one train net must be specified using one of the following fields:
// train_net_param, train_net, net_param, net
// One or more test nets may be specified using any of the following fields:
// test_net_param, test_net, net_param, net
// If more than one test net field is specified (e.g., both net and
// test_net are specified), they will be evaluated in the field order given
// above: (1) test_net_param, (2) test_net, (3) net_param/net.
// A test_iter must be specified for each test_net.
// A test_level and/or a test_stage may also be specified for each test_net.
//////////////////////////////////////////////////////////////////////////////
// Proto filename for the train net, possibly combined with one or more test nets.
optional string net = 24; // .prototxt文件名称， train or test net
// Inline train net param, possibly combined with one or more test nets.
optional NetParameter net_param = 25; // net parameter类
optional string train_net = 1; // Proto filename for the train net, .prototxt文件名称，train net
repeated string test_net = 2; // Proto filenames for the test nets, .prototxt文件名称，test net
optional NetParameter train_net_param = 21; // Inline train net params, train net parameter类
repeated NetParameter test_net_param = 22; // Inline test net params, test net parameter类
// The states for the train/test nets. Must be unspecified or
// specified once per net.
//
// By default, all states will have solver = true;
// train_state will have phase = TRAIN,
// and all test_state's will have phase = TEST.
// Other defaults are set according to the NetState defaults.
optional NetState train_state = 26; // train net state
repeated NetState test_state = 27; // test net state
// The number of iterations for each test net.
repeated int32 test_iter = 3; // 对于測试网络(用于评估)运行一次须要迭代的次数, test_iter * batch_size = 測试图像总数量
// The number of iterations between two testing phases.
optional int32 test_interval = 4 [default = 0]; // 指定运行多少次训练网络运行一次測试网络
optional bool test_compute_loss = 19 [default = false]; // 运行測试网络时是否计算loss
// If true, run an initial test pass before the first iteration,
// ensuring memory availability and printing the starting value of the loss.
optional bool test_initialization = 32 [default = true]; // 在总的開始前，是否先运行一次測试网络
optional float base_lr = 5; // The base learning rate,基础学习率
// the number of iterations between displaying info. If display = 0, no info
// will be displayed.
optional int32 display = 6; // 指定迭代多少次显示一次结果信息
// Display the loss averaged over the last average_loss iterations
optional int32 average_loss = 33 [default = 1]; //
optional int32 max_iter = 7; // the maximum number of iterations
// accumulate gradients over `iter_size` x `batch_size` instances
optional int32 iter_size = 36 [default = 1]; //
// The learning rate decay policy. The currently implemented learning rate
// policies are as follows: // 学习率衰减策略
// - fixed: always return base_lr.
// - step: return base_lr * gamma ^ (floor(iter / step))
// - exp: return base_lr * gamma ^ iter
// - inv: return base_lr * (1 + gamma * iter) ^ (- power)
// - multistep: similar to step but it allows non uniform steps defined by
// stepvalue
// - poly: the effective learning rate follows a polynomial decay, to be
// zero by the max_iter. return base_lr (1 - iter/max_iter) ^ (power)
// - sigmoid: the effective learning rate follows a sigmod decay
// return base_lr ( 1/(1 + exp(-gamma * (iter - stepsize))))
//
// where base_lr, max_iter, gamma, step, stepvalue and power are defined
// in the solver parameter protocol buffer, and iter is the current iteration.
optional string lr_policy = 8; // 学习策略,可取的值包含：fixed、step、exp、inv、multistep、poly、sigmoid
optional float gamma = 9; // The parameter to compute the learning rate.
optional float power = 10; // The parameter to compute the learning rate.
optional float momentum = 11; // The momentum value, 动量
optional float weight_decay = 12; // The weight decay. //
// regularization types supported: L1 and L2
// controlled by weight_decay
optional string regularization_type = 29 [default = "L2"]; // L1 or L2
// the stepsize for learning rate policy "step"
optional int32 stepsize = 13; //
// the stepsize for learning rate policy "multistep"
repeated int32 stepvalue = 34; //
// Set clip_gradients to >= 0 to clip parameter gradients to that L2 norm,
// whenever their actual L2 norm is larger.
optional float clip_gradients = 35 [default = -1]; //
optional int32 snapshot = 14 [default = 0]; // The snapshot interval, 迭代多少次保存下结果(如权值、偏置)
optional string snapshot_prefix = 15; // The prefix for the snapshot,指定保存文件名称的前缀
// whether to snapshot diff in the results or not. Snapshotting diff will help
// debugging but the final protocol buffer size will be much larger.
optional bool snapshot_diff = 16 [default = false]; //
enum SnapshotFormat {
HDF5 = 0;
BINARYPROTO = 1;
}
optional SnapshotFormat snapshot_format = 37 [default = BINARYPROTO]; // HDF5 or BINARYPROTO
// the mode solver will use: 0 for CPU and 1 for GPU. Use GPU in default.
enum SolverMode {
CPU = 0;
GPU = 1;
}
optional SolverMode solver_mode = 17 [default = GPU]; // 指定solve mode是CPU还是GPU
// the device_id will that be used in GPU mode. Use device_id = 0 in default.
optional int32 device_id = 18 [default = 0]; // GPU mode下使用
// If non-negative, the seed with which the Solver will initialize the Caffe
// random number generator -- useful for reproducible results. Otherwise,
// (and by default) initialize using a seed derived from the system clock.
optional int64 random_seed = 20 [default = -1]; //
// Solver type
enum SolverType { // solver优化方法
SGD = 0;
NESTEROV = 1;
ADAGRAD = 2;
RMSPROP = 3;
ADADELTA = 4;
ADAM = 5;
}
optional SolverType solver_type = 30 [default = SGD]; // 指定solver优化方法
// numerical stability for RMSProp, AdaGrad and AdaDelta and Adam
optional float delta = 31 [default = 1e-8]; //
// parameters for the Adam solver
optional float momentum2 = 39 [default = 0.999]; //
// RMSProp decay value
// MeanSquare(t) = rms_decay*MeanSquare(t-1) + (1-rms_decay)*SquareGradient(t)
optional float rms_decay = 38; //
// If true, print information about the state of the net that may help with
// debugging learning problems.
optional bool debug_info = 23 [default = false]; //
// If false, don't save a snapshot after training finishes.
optional bool snapshot_after_train = 28 [default = true]; //
}
solver的測试代码例如以下：
"HDF5" : "BINARYPROTO"); caffe::SolverParameter_SolverMode solver_mode = param.solver_mode(); fprintf(stderr, "solver mode: %sn", solver_mode == 0 ? "CPU" : "GPU"); if (param.has_device_id()) fprintf(stderr, "device id: %dn", param.device_id()); fprintf(stderr, "random seed: %dn", param.random_seed()); caffe::SolverParameter_SolverType solver_type = param.solver_type(); std::string solver_method[] {"SGD", "NESTEROV", "ADAGRAD", "RMSPROP", "ADADELTA", "ADAM"}; fprintf(stderr, "solver type: %sn", solver_method[solver_type].c_str()); fprintf(stderr, "delta: %fn", param.delta()); fprintf(stderr, "momentum2: %fn", param.momentum2()); if (param.has_rms_decay()) fprintf(stderr, "rms decy: %fn", param.rms_decay()); fprintf(stderr, "debug info: %dn", param.debug_info()); fprintf(stderr, "snapshot after train: %dn", param.snapshot_after_train()); boost::shared_ptr<caffe::Net<float>> net = solver->net(); std::vector<boost::shared_ptr<caffe::Net<float>>> test_nets = solver->test_nets(); fprintf(stderr, "test nets size: %dn", test_nets.size()); fprintf(stderr, "iter: %dn", solver->iter()); return 0;}
部分输出结果例如以下：
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