CNN结构：MXNet设计和实现简介

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参考链接：MXNet设计和实现简介

文章翻译于：https://mxnet.incubator.apache.org/architecture/index.html

一、MXNet System Architecture系统概览

This figure shows the major modules and components of the MXNet system and their interaction. The modules are:

• Runtime Dependency Engine: Schedules and executes theoperations according to their read/write dependency.
• Storage Allocator: Efficiently allocates and recycles memory blocks on host (CPU) and devices (GPUs).
• Resource Manager: Manages global resources, such as the random number generatorand temporal space.
• NDArray: Dynamic, asynchronous n-dimensional arrays,which provide flexible imperative programs for MXNet.
• Symbolic Execution: Static symbolic graph executor,which provides efficient symbolic graph execution and optimization.
• Operator: Operators that define static forward and gradientcalculation (backprop).
• SimpleOp: Operators that extend NDArray operators and symbolic operators in a unified fashion.
• Symbol Construction: Symbolic construction, which provides a way to constructa computation graph (net configuration).
• KVStore: Key-value store interface for efficient parameter synchronization.
• Data Loading(IO): Efficient distributed data loading and augmentation.

这个表格显示了MxNet的主要模块和系统内部交互组元。模块拆分为：

• 实时的计算引擎，根据硬件定制的计划性的操作运算。
• 存储分配操作：高效的CPU和GPU内存分配和回收机制。
• Resource Manager: 全局资源管理器，例如随机生成的数据和临时空间。
• NDArray: 同步动态的N维数组，可提供弹性规划的MxNet程序。.
• Symbolic Execution: 静态的符号图，提供高效的符号图的执行和优化。
• Operator: 一个前向计算和回溯优化的操作符。
• SimpleOp: 一个标准样式的扩展了NDArray的操作符系列。
• Symbol Construction: 网络配置-符号表的构建。用以构建计算图的一种通路。
• KVStore: 键-值存储接口，给出了参数同步的有效方式。
• Data Loading(IO): 分布式的IO系统.

MXNet System Components

Execution Engine

You can use MXNet’s engine not only for deep learning,but for any domain-specific problem.It’s designed to solve a general problem:execute a bunch of functions following their dependencies.Execution of any two functions with dependencies should be serialized.

To boost performance, functions with no dependencies can be executed in parallel.For a general discussion of this topic,see our
notes on the dependency engine.

专注于问题解决而不是构架设计。为了提升速度，可以使用并行方法计算。详情请看...............

Interface

The following API is the core interface for the execution engine:

    virtual void PushSync( Fn exec_fun, Context exec_ctx,
                          std::vector<VarHandle> const& const_vars,
                          std::vector<VarHandle> const& mutate_vars) = 0;

This API allows you to push a function (exec_fun),along with its context information and dependencies, to the engine.exec_ctx is
the context information in which the exec_fun should be executed, const_vars denotes the variables that the function reads from,and
mutate_vars are the variables to be modified.The engine provides the following guarantee:

The execution of any two functionsthat modify a common variableis serialized in their push order.

这个API作用是 绑定一个函数到设备，.exec_ctx 是设备信息。mutate_vars必须是一个变量

Function

The function type of the engine is:

    using Fn = std::function<void(RunContext)>;

RunContext contains runtime information, which is determined by the engine:

    struct RunContext {
        // stream pointer which could be safely cast to
        // cudaStream_t* type
        void *stream;
    };

Alternatively, you could use mxnet::engine::DAGEngine::Fn, which has the same type definition.

All of the functions are executed by the engine’s internal threads.In such a model, it’s usually not a good idea to push
blocking functionsto the engine (usually for dealing with I/O tasks like disk, web service, UI, etc.)because it will occupy the execution thread and reduce total throughput.In that case, we provide another
asynchronous function type:

    using Callback = std::function<void()>;
    using AsyncFn = std::function<void(RunContext, Callback)>;

In the AsyncFn function, you can pass the heavy part to your own threadsand safely exit the body of the function.The engine doesn’t consider the function finisheduntil the
Callback function is called.

Context

You can specify the Context of the function to be executed within.This usually includes whether the function should be run on a CPU or a GPU,and if you specify a GPU, which GPU to use.Context
is different from RunContext. Context contains device type (GPU/CPU) and device id,while
RunContext contains information that can be decided only during runtime,for example, on which stream the function should be executed.

配置上下文，确定 函数是运行在哪个地方，CPU还是GPU。上下文包含设备类型和设备ID，RunContext 包含运行时设备信息，例如指定哪个/哪些流处理器执行函数。

VarHandle

VarHandle is used to specify the dependencies of functions.The MXNet engine is designed to be decoupled from other MXNet modules.So
VarHandle is like an engine-provided token you use to represent the external resources the functions can use or modify. It’s designed to be lightweight, so creating,deleting, or copying a variable
incurs little overhead. Upon pushing the functions, you need to specify the variables that will be used (immutable) in the
const_vars vector, and the variables that will be modified (mutable) in the
mutate_vars vector.The engine uses one rule for resolving the dependencies among functions:

The execution of any two functions when one of them modifies at least one common variable is serialized in their push order.

For example, if Fn1 and
Fn2 both mutate
V2 then Fn2
is guaranteed to be executed after Fn1 if
Fn2 is pushed after
Fn1.On the other hand, if
Fn1 and
Fn2 both use V2,their actual execution order could be random.

This design allows the engine to schedule state-mutating operations in a manner that minimizes calls to allocate new memory. For example, the weight update function in DNN can now use the
+= operatorto update the weights in place,rather than generating a new weight array each time.

To create a variable, use the NewVar() API.To delete a variable, use the
PushDelete API.

变量标识符：MxNet设计为引擎和模块解耦的策略，VarHandle用于标识函数依赖。........................................... 
mutate_vars向量.........................

两个函数对变量的改变取决于它们的计算顺序

例如：若Fn1和Fn2 同时锁住了V2，Fn2确定是在Fn1执行之后执行。而实际上，这种有序性是不能保证的。这种设计可以使变量使用+=这种运算更新权值，而不是重新声明一个变量。

在此，变量的创建和销毁使用专门的API，如NewVar() 和
PushDelete API.

Push and Wait

All Push APIs are asynchronous. The API call returns immediately regardless of whether the pushed
Fn is finished or not. This allows the engine to start computing at the same timeas the user thread is pushing functions.
Push APIs are not thread-safe.To be specific, only one thread should make engine API calls at a time.

If you want to wait for a specific Fn to finish,include a callback function in the closure,and call the function at the end of your
Fn.

If you want to wait for all Fns that involve (use or mutate) a certain variable to finish,use the
WaitForVar(var) API.

If you want to wait for all pushed Fns to finish,use the
WaitForAll() API.

顺序和等待：所有的push操作是异步的。API回调忽略变量是否被函数Fn操作完成。因此push API不是线程安全的。因此，引擎API的calls操作必须是单线程的。

若是期待特定Fn完成，使用Fn的闭环，等待Fn完成。

若是期待所有Fns完成对变量var操作，使用WaitForVar(var) API。

若是期待所有Fns完成操作，使用WaitForAll() API。

Save Object Creation Cost

In some cases, you need to push several functions to the engine for a long period of time. If the computation of these functions is light,the overhead of copying lambdas and creating use/mutate variable lists becomes relatively high.We provide an API to
create an OprHandle beforehand:

    virtual OprHandle NewOperator(AsyncFn fn,
                                  std::vector<VarHandle> const& const_vars,
                                  std::vector<VarHandle> const& mutate_vars) = 0;

You can keep pushing the OprHandle without repeatedly creating them:

    virtual void Push(OprHandle op, Context exec_ctx) = 0;

To delete it, call the DeleteOperator(OprHandle
op) API.Ensure that the operator has finished computing before calling this API.

对象创建的代价：有时，需要一段长的时间排列几个函数到引擎。若这些函数其实是轻量计算，那么复制正则表达式和变量维持表变得代价相对巨大。为此提供了专用的API
OprHandle。

...........................

对应的删除操作是：DeleteOperator(OprHandle
op) API。但是使用之前一定要确定所有函数执行完成。

API手册-API Reference

class
mxnet::Engine

Dependency engine that schedules operations.

Public Types

typedef
engine::CallbackOnComplete CallbackOnComplete

callback on complete

typedef
std::function(RunContext)>
SyncFn

Synchronous operation to pass to engine.

typedef
std::function(RunContext, CallbackOnComplete)> AsyncFn

Asynchronous operation to pass to engine.

typedef
engine::VarHandle VarHandle

Variable pointer.

typedef
engine::OprHandle OprHandle

Operator pointer.

Public Functions

virtual void
NotifyShutdown() = 0

Notify the engine about a shutdown, This can help engine to print less messages into display.

User do not have to call this function.

Return

0 when success, -1 when failure happens.

virtual
VarHandle NewVariable() = 0

Allocate a new variable, the variable can then be used to schedule the operation concurrently via dependency patterns.

Return

The new variable allocated.

virtual
OprHandle NewOperator(AsyncFn
fn, std::vector<VarHandle>
const &const_vars, std::vector<VarHandle>
const &mutable_vars, FnProperty prop = FnProperty::kNormal,
const char *opr_name = nullptr) = 0

Create a new operator. The returned operator could be saved externally so that it could be resued for scheduling.

Return

The new operator allocated.

Parameters

• fn: The execution function.
• const_vars: The variables that current operation will use but not mutate.
• mutable_vars: The variables that current operation will mutate.
• prop: Property of the function.
• opr_name: The operator name.

virtual
void DeleteOperator(OprHandle
op) = 0

Delete the given operator.

The delete will not happen immediately, but will wait until all the operations using this operator are completed.

Parameters

• op: The operator to delete.

virtual
void Push(OprHandle
op, Context exec_ctx, int priority = 0, bool profiling = false) = 0

Push an operator to the engine.

Parameters

• op: The operator to push.
• exec_ctx: Execution context.
• priority: Priority of the action, as hint to the engine.
• profiling: The variable indicate whether to profile this operator.

virtual void
PushAsync(AsyncFn
exec_fun, Context exec_ctx, std::vector<VarHandle>
const &const_vars, std::vector<VarHandle>
const &mutable_vars, FnProperty prop = FnProperty::kNormal, int
priority = 0, const char *opr_name = nullptr) = 0

Push an asynchronous operation to the engine.

Parameters

• exec_fun: Execution function, this function takes a parameter on_complete that must be called when the execution completes.
• exec_ctx: Execution context.
• const_vars: The variables that current operation will use but not mutate.
• mutable_vars: The variables that current operation will mutate.
• prop: Property of the function.
• priority: Priority of the action, as hint to the engine.
• opr_name: The operator name.

virtual void
DeleteVariable(SyncFn
delete_fn, Context exec_ctx, VarHandle var) = 0

Schedule the deletion of a variable.

The delete will not happen immediately, but will wait until all the operations depending on var are completed.

Parameters

• delete_fn: A function that will be called after the variable is deleted.
• exec_ctx: Execution context.
• var: The variable to be deleted.

virtual void
WaitForVar(VarHandle
var) = 0

Wait for a variable.

Parameters

• var: The variable we should wait for. This function returns when the variable is ready.

virtual void
WaitForAll() = 0

Wait until all the activity of engine finishes.

virtual
~Engine()

virtual destructor

void
PushSync(SyncFn
exec_fn, Context exec_ctx, std::vector<VarHandle>
const &const_vars, std::vector<VarHandle>
const &mutable_vars, FnProperty prop = FnProperty::kNormal, int
priority = 0, const char *opr_name = nullptr)

Push an synchronous operation to the engine.

Parameters

• exec_fn: Execution function that executes the operation.
• exec_ctx: Execution context.
• const_vars: The variables that current operation will use but not mutate.
• mutable_vars: The variables that current operation will mutate.
• prop: Property of the function.
• priority: Priority of the action, as hint to the engine.
• opr_name: The operator name.

Template Parameters

• SyncFn: the synchronous function to be pushed.

CallbackOnComplete
CreateCallback(void (*callback)(Engine
*, void *), void *param,
)

factory function to create OnComplete callback.

Parameters

• callback: th static callback function.
• param: the paramter passed to callback.

virtual int
num_omp_threads_per_worker()
const = 0

Return the number of OMP threads that should be used per worker.

Return

Number of OMP threads that should be used per worker

virtual void
set_num_omp_threads_per_worker(int
num_omp_threads_per_worker) = 0

Set the number of OMP threads that should be used per worker.

Parameters

• num_threads_per_worker: Number of OMP threads to be used per worker

Public Static Functions

static
Engine *Get()

Return

Engine singleton.

static std::shared_ptr<Engine>
_GetSharedRef()

Get shared pointer reference to engine singleton. Most user should not call this function. This function is called by another singleton X who requires engine to be destructed after X.

Return

A shared pointer to Engine singleton.

算子-Operators in MXNet

In MXNet, an operator is a class that contains both actual computation logicand auxiliary information that can aid the system in performing optimizations,like in-place updates and auto-derivatives.To understand the remainder of the document,we recommend
that you familiarize yourself with the mshadow library,because all operators compute on the tensor-like structure
mshadow::TBlobprovided by the system during runtime.

MXNet’s operator interface allows you to:

• Reduce memory allocation cost by specifying in-place updates.
• Hide some internal arguments from Python to make it cleaner.
• Define the relationships among input tensors and output tensors,which allows the system to perform shape checking for you.
• Acquire additional temporary spaces from the systemto perform computation (e.g., calling
  cudnn routines).

Operator Interface

Forward is the core operator interface:

    virtual void Forward(const OpContext &ctx,
                         const std::vector<TBlob> &in_data,
                         const std::vector<OpReqType> &req,
                         const std::vector<TBlob> &out_data,
                         const std::vector<TBlob> &aux_states) = 0;

The OpContext structure is:

           struct OpContext {
             int is_train;
             RunContext run_ctx;
             std::vector<Resource> requested;
           }

It describes whether the operator is in the train or test phase,which device the operator should be run on (in
run_ctx),and requested resources (covered in the following sections).

• in_data and
out_data represent the input and output tensors, respectively.All of the tensor spaces have been allocated by the system.
• req denotes how the computation results are written into the
  out_data.In other words,
  req.size()
== out_data.size() and
req[i]correspond to the write type of
out_data[i].
• The OpReqType is defined as:

           enum OpReqType {
             kNullOp,
             kWriteTo,
             kWriteInplace,
             kAddTo
           };

Normally, the types of all out_data should be
kWriteTo,meaning that the provided
out_data tensor is a
raw memory block,so the operator should write results directly into it.In some cases, for example when calculating the
gradient tensor,it would be great if we could accumulate the result,rather than directly overwrite the tensor contentsso that no extra space needs to be created each time.In such a case, the corresponding
req type is set as
kAddTo,indicating that a
+= should be called.

• aux_states is intentionally designed for auxiliary tensors used to help computation. Currently, it is useless.

Aside from the Forward operator, you could optionally implement the
Backward interface:

    virtual void Backward(const OpContext &ctx,
                          const std::vector<TBlob> &out_grad,
                          const std::vector<TBlob> &in_data,
                          const std::vector<TBlob> &out_data,
                          const std::vector<OpReqType> &req,
                          const std::vector<TBlob> &in_grad,
                          const std::vector<TBlob> &aux_states);

This interface follows the same design principle as the
Forward interface,except that
out_grad, in_data, and
out_data are given,and the operator computes
in_grad as the results.The naming strategy is similar to Torch’s convention,and can be summarized in following figure:

[input/output semantics figure]

Some operators might not require all of the following:out_grad,
in_data and
out_data.You can specify these dependencies with the
DeclareBackwardDependency interface in
OperatorProperty.

Operator Property

One convolution might have several implementations,and you might want to switch among them to achieve the best performance.Therefore, we separate the operator
semantic interfacesfrom the implementation interface (Operator class)into the
OperatorProperty class.The
OperatorProperty interface consists of:

• InferShape:

           virtual bool InferShape(std::vector<TShape> *in_shape,
                                   std::vector<TShape> *out_shape,
                                   std::vector<TShape> *aux_shape) const = 0;

This interface has two purposes:

• Tell the system the size of each input and output tensor,so it can allocate space for them before the
  Forward and
Backward call.
• Perform a size check to make sure that there isn’t an obvious error before running.The shape in
  in_shape is set by the system(from the
  out_shape of the previous operators).It returns
  false when there is not enough informationto infer shapes or throws an error when the shape is inconsistent.
• Request Resources: Operations like
cudnnConvolutionForward need a work space for computation.If the system can manage that, it could then perform optimizations,like reuse the space, and so on.MXNet defines two interfaces to achieve this:

           virtual std::vector<ResourceRequest> ForwardResource(
               const std::vector<TShape> &in_shape) const;
           virtual std::vector<ResourceRequest> BackwardResource(
               const std::vector<TShape> &in_shape) const;

The ResourceRequest structure (in
resource.h) currently contains only a type flag:

           struct ResourceRequest {
             enum Type {
               kRandom,  // get a mshadow::Random object
               kTempSpace,  // request temporary space
             };
             Type type;
           };

If ForwardResource and
BackwardResource return non-empty arrays,the system offers the corresponding resources through the
ctx parameterin the
Forward and
Backward interface of
Operator.Basically, to access those resources, simply write:

           auto tmp_space_res = ctx.requested[kTempSpace].get_space(some_shape, some_stream);
           auto rand_res = ctx.requested[kRandom].get_random(some_stream);

For an example, see src/operator/cudnn_convolution-inl.h.

• Backward dependency: Let’s look at two different operator signatures(we name all of the arguments for demonstration purposes):

           void FullyConnectedForward(TBlob weight, TBlob in_data, TBlob out_data);
           void FullyConnectedBackward(TBlob weight, TBlob in_data, TBlob out_grad, TBlob in_grad);

           void PoolingForward(TBlob in_data, TBlob out_data);
           void PoolingBackward(TBlob in_data, TBlob out_data, TBlob out_grad, TBlob in_grad);

Note that out_data in
FullyConnectedForwardis not used by
FullyConnectedBackward,while
PoolingBackward requires all of the arguments of
PoolingForward.Therefore, for
FullyConnectedForward,the
out_data tensor once consumed could be safely freedbecause the backward function will not need it.This provides a chance for the system to collect some tensorsas garbage as soon as possible.To specify
this situation, we provide an interface:

          virtual std::vector<int> DeclareBackwardDependency(
               const std::vector<int> &out_grad,
               const std::vector<int> &in_data,
               const std::vector<int> &out_data) const;

The int element of the argument vector is an IDto distinguish different arrays.Let’s see how this interface specifies different dependenciesfor
FullyConnected and
Pooling:

          std::vector<int> FullyConnectedProperty::DeclareBackwardDependency(
              const std::vector<int> &out_grad,
              const std::vector<int> &in_data,
              const std::vector<int> &out_data) const {
            return {out_grad[0], in_data[0]};  // NOTE: out_data[0] is NOT included
          }
          std::vector<int> PoolingProperty::DeclareBackwardDependency(
              const std::vector<int> &out_grad,
              const std::vector<int> &in_data,
              const std::vector<int> &out_data) const {
            return {out_grad[0], in_data[0], out_data[0]};
          }

• In place Option: To further save the cost of memory allocation,you can use in-place updates.They are appropriate for element-wise operationswhen the input tensor and output tensor have the same shape.You specify and in-place update with
  the following interface:

           virtual std::vector<std::pair<int, void*>>    ElewiseOpProperty::ForwardInplaceOption(
               const std::vector<int> &in_data,
               const std::vector<void*> &out_data) const {
             return { {in_data[0], out_data[0]} };
           }
           virtual std::vector<std::pair<int, void*>> ElewiseOpProperty::BackwardInplaceOption(
               const std::vector<int> &out_grad,
               const std::vector<int> &in_data,
               const std::vector<int> &out_data,
               const std::vector<void*> &in_grad) const {
             return { {out_grad[0], in_grad[0]} }
           }

This tells the system that the in_data[0] and
out_data[0] tensors could share the same memory spaces during
Forward, and so do
out_grad[0] and
in_grad[0] during
Backward.

Important: Even if you use the preceding specification, it’s
not guaranteed that the input and output tensors will share the same space. In fact, this is only a suggestion for the system, which makes the final decision. However, in either case, the decision is completely transparent to you, so the actual
Forward and
Backward implementation does not need to consider that.

• Expose Operator to Python: Because of the restrictions of C++, you need user to implement following interfaces:

           // initial the property class from a list of key-value string pairs
           virtual void Init(const vector<pair<string, string>> &kwargs) = 0;
           // return the parameters in a key-value string map
           virtual map<string, string> GetParams() const = 0;
           // return the name of arguments (for generating signature in python)
           virtual vector<string> ListArguments() const;
           // return the name of output values
           virtual vector<string> ListOutputs() const;
           // return the name of auxiliary states
           virtual vector<string> ListAuxiliaryStates() const;
           // return the number of output values
           virtual int NumOutputs() const;
           // return the number of visible outputs
           virtual int NumVisibleOutputs() const;

Create an Operator from the Operator Property

OperatorProperty includes all
semantic attributes of an operation. It’s also responsible for creating the
Operator pointer for actual computation.

Create Operator

Implement the following interface in OperatorProperty:

    virtual Operator* CreateOperator(Context ctx) const = 0;

For example:

    class ConvolutionOp {
     public:
      void Forward( ... ) { ... }
      void Backward( ... ) { ... }
    };
    class ConvolutionOpProperty : public OperatorProperty {
     public:
      Operator* CreateOperator(Context ctx) const {
        return new ConvolutionOp;
      }
    };

Parametrize Operator

When implementing a convolution operator, you need to know the kernel size,the stride size, padding size, and so on.These parameters should be passed to the operatorbefore any
Forward or
Backward interface is called.To do so, you could define a
ConvolutionParam structure, as follows:

    #include
    struct ConvolutionParam : public dmlc::Parameter<ConvolutionParam> {
      TShape kernel, stride, pad;
      uint32_t num_filter, num_group, workspace;
      bool no_bias;
    };

Put it in ConvolutionOpProperty, and pass it to the operator class during construction:

    class ConvolutionOp {
     public:
      ConvolutionOp(ConvolutionParam p): param_(p) {}
      void Forward( ... ) { ... }
      void Backward( ... ) { ... }
     private:
      ConvolutionParam param_;
    };
    class ConvolutionOpProperty : public OperatorProperty {
     public:
      void Init(const vector<pair<string, string>& kwargs) {
        // initialize param_ using kwargs
      }
      Operator* CreateOperator(Context ctx) const {
        return new ConvolutionOp(param_);
      }
     private:
      ConvolutionParam param_;
    };

Register the Operator Property Class and the Parameter Class to MXNet

Use the following macros to register the parameter structure and the operator property class to MXNet:

    DMLC_REGISTER_PARAMETER(ConvolutionParam);
    MXNET_REGISTER_OP_PROPERTY(Convolution, ConvolutionOpProperty);

The first argument is the name string, the second is the property class name.

Interface Summary

We’ve almost covered the entire interface required to define a new operator. Let’s do a recap:

• Use the Operator interface to write your computation logic (Forward and
  Backward).
• Use the OperatorProperty interface to:
  • Pass the parameter to the operator class (you can use the
Init interface).
  • Create an operator using the CreateOperator interface.
  • Correctly implement the operator description interface, such as the names of arguments, etc.
  • Correctly implement the InferShape interface to set the output tensor shape.
  • [Optional] If additional resources are needed, check
ForwardResource and
BackwardResource.
  • [Optional] If Backward doesn’t need all of the input and output of
    Forward, check
DeclareBackwardDependency.
  • [Optional] If in-place update is supported, check
ForwardInplaceOption and
BackwardInplaceOption.
• Register the OperatorProperty class and the parameter class.

Unifying the NDArray Operator and Symbolic Operator

NDArray operations are similar to symbolic operations,except that sometimes you can’t write in place to the operandswithout a complete dependency graph.However, the logic underlying NDArray and symbolic operations are almost identical.SimpleOp,
a new unified operator API,unifies different invoking processesand returns to the fundamental elements of operators.Because most mathematical operators attend to one or two operands,and more operands make dependency-related optimization useful,the unified
operator is specifically designed for unary and binary operations.

Consider the elements of an operation.Ideally, you need only functions and derivativesto describe an operation.Let’s restrict that to the space of unary and binary operations.How do we classify all operations to maximize the possibilityof in-place write
optimization?Note that you can separate functions by the number of operands.Derivatives are a bit more complex.To construct a dependency graph, you need to know whether output value,input data, or neither are needed alongside head gradient.Gradient functions
in the unified API are differentiatedby the types of operands it takes for calculation.

Before you learn more about the SimpleOp interface,we recommend that you review themshadow library guidebecause calculations will be done in the
mshadow::TBlob structure.

In the following example, we’ll create an operatorfunctioning as a smooth l1 loss,which is a mixture of l1 loss and l2 loss. The loss itself can be written as:

    loss = outside_weight .* f(inside_weight .* (data - label))
    grad = outside_weight .* inside_weight .* f'(inside_weight .* (data - label))

.* stands for element-wise multiplication, and
f,
f' is the smooth l1 loss function,which we are assuming is in
mshadow for now.At first glance, it’s impossible to implementthis particular loss as a unary or binary operator.But we have automatic differentiation in symbolic execution.That simplifies the loss
to f and
f' directly.This loss is no more complex than a
sin or an abs function,and can certainly be implemented as a unary operator.

SimpleOp: The Unified Operator API

Define Shapes

The mshadow library requires explicit memory allocation.As a consequence, all data shapesmust be provided before any calculation occurs.Before we proceed with defining functions and gradient,let’s
check input data shape consistency and provide output shape.

    typedef TShape (*UnaryShapeFunction)(const TShape& src,
                                         const EnvArguments& env);
    typedef TShape (*BinaryShapeFunction)(const TShape&                                         const TShape& rhs,lhs,

                                          const EnvArguments& env);

You can use mshadow::TShape to check input data shape and designate output data shape.If you don’t define this function, the default output shape is the same as the input shape.In the case of
a binary operator, the shape of lhs and
rhs is checked as the same by default.

You can also use shape functions to check if any additional arguments and resources are present.Refer to the additional usages of
EnvArguments to accomplish this.

Before we start on our smooth l1 loss example, we define a
XPU to cpu or
gpu in the headersmooth_l1_unary-inl.h implementation so that we reuse the same code in
smooth_l1_unary.cc andsmooth_l1_unary.cu.

    #include
    #if defined(__CUDACC__)
    #define XPU gpu
    #else
    #define XPU cpu
    #endif

In our smooth l1 loss example, it’s okay to use the default behavior whereby the output has the same shape as the source.Written explicitly, it is:

    inline TShape SmoothL1Shape_(const TShape& src,
                                 const EnvArguments& env) {
      return TShape(src);

Define Functions

Create a unary or binary function with one output:
mshadow::TBlob.

    typedef void (*UnaryFunction)(const TBlob& src,
                                  const EnvArguments& env,
                                  TBlob* ret,
                                  OpReqType req,
                                  RunContext ctx);
    typedef void (*BinaryFunction)(const TBlob& lhs,
                                   const TBlob& rhs,
                                   const EnvArguments& env,
                                   TBlob* ret,
                                   OpReqType req,
                                   RunContext ctx);

• Functions are differentiated by the types of input arguments.
• RunContext
ctx contains information needed during runtime for execution.

        struct RunContext {
          void *stream;  // the stream of the device, can be NULL or Stream* in GPU mode
          template<typename xpu> inline mshadow::Stream<xpu>* get_stream() // get mshadow stream from Context
        }  // namespace mxnet

mshadow::stream
*s = ctx.get_stream(); is an example of obtaining a stream from
ctx.

• OpReqType
req denotes how computation results are written into
ret.

        enum OpReqType {
          kNullOp,  // no operation, do not write anything
          kWriteTo,  // write gradient to provided space
          kWriteInplace,  // perform an in-place write
          kAddTo  // add to the provided space
        };

A macro is defined in operator_util.h for a simplified use of
OpReqType.ASSIGN_DISPATCH(out,
req, exp) checks
req and performs an assignment.

In our smooth l1 loss example, we use UnaryFunction to define the function of this operator.

    template<typename xpu>
    void SmoothL1Forward_(const TBlob& src,
                          const EnvArguments& env,
                          TBlob *ret,
                          OpReqType req,
                          RunContext ctx) {
      using namespace mshadow;
      using namespace mshadow::expr;
      mshadow::Stream<xpu> *s = ctx.get_stream<xpu>();
      real_t sigma2 = env.scalar * env.scalar;
      MSHADOW_TYPE_SWITCH(ret->type_flag_, DType, {
        mshadow::Tensor<xpu, 2, DType> out = ret->get<xpu, 2, DType>(s);
        mshadow::Tensor<xpu, 2, DType> in = src.get<xpu, 2, DType>(s);
        ASSIGN_DISPATCH(out, req,
                        F<mshadow_op::smooth_l1_loss>(in, ScalarExp<DType>(sigma2)));
      });
    }

After obtaining mshadow::Stream from
RunContext, we get
mshadow::Tensor from
mshadow::TBlob.mshadow::F is a shortcut to initiate a
mshadow expression. The macro
MSHADOW_TYPE_SWITCH(type,
DType, ...)handles details on different types, and the macro
ASSIGN_DISPATCH(out,
req, exp) checks
OpReqType andperforms actions accordingly.
sigma2 is a special parameter in this loss, which we will cover later.

Define Gradients (Optional)

定义梯度-可选方案.

Create a gradient function with various types of inputs.

    // depending only on out_grad
    typedef void (*UnaryGradFunctionT0)(const OutputGrad& out_grad,
                                        const EnvArguments& env,
                                        TBlob* in_grad,
                                        OpReqType req,
                                        RunContext ctx);
    // depending only on out_value
    typedef void (*UnaryGradFunctionT1)(const OutputGrad& out_grad,
                                        const OutputValue& out_value,
                                        const EnvArguments& env,
                                        TBlob* in_grad,
                                        OpReqType req,
                                         RunContext ctx);
    // depending only on in_data
    typedef void (*UnaryGradFunctionT2)(const OutputGrad& out_grad,
                                        const Input0& in_data0,
                                        const EnvArguments& env,
                                        TBlob* in_grad,
                                        OpReqType req,
                                        RunContext ctx);

Gradient functions of binary operators have similar structures, except that
Input, TBlob, and
OpReqTypeare doubled.

GradFunctionArgument

Input0,
Input, OutputValue, and
OutputGrad all share the structure of
GradFunctionArgument,which is defined as:

      struct GradFunctionArgument {
          TBlob data;
      }

In our smooth l1 loss example, note that it’s an
f'(x),which utilizes input for the gradient calculation,so the
UnaryGradFunctionT2 is suitable.To enable the chain rule of the gradient,we also need to multiply
out_grad from the top to the result of
in_grad.

    template<typename xpu>
    void SmoothL1BackwardUseIn_(const OutputGrad& out_grad,
                                const Input0& in_data0,
                                const EnvArguments& env,
                                TBlob *in_grad,
                                OpReqType req,
                                RunContext ctx) {
      using namespace mshadow;
      using namespace mshadow::expr;
      mshadow::Stream<xpu> *s = ctx.get_stream<xpu>();
      real_t sigma2 = env.scalar * env.scalar;
      MSHADOW_TYPE_SWITCH(in_grad->type_flag_, DType, {
        mshadow::Tensor<xpu, 2, DType> src = in_data0.data.get<xpu, 2, DType>(s);
        mshadow::Tensor<xpu, 2, DType> ograd = out_grad.data.get<xpu, 2, DType>(s);
        mshadow::Tensor<xpu, 2, DType> igrad = in_grad->get<xpu, 2, DType>(s);
         ASSIGN_DISPATCH(igrad, req,
                        ograd * F<mshadow_op::smooth_l1_gradient>(src, ScalarExp<DType>(sigma2)));
      });
    }

Register SimpleOp to MXNet

After creating the shape, function, and gradient, restore them into both an NDArray operator anda symbolic operator. To simplify this process, use the registration macro defined in
operator_util.h.

    MXNET_REGISTER_SIMPLE_OP(Name, DEV)
    .set_shape_function(Shape)
    .set_function(DEV::kDevMask, Function<XPU>, SimpleOpInplaceOption)
    .set_gradient(DEV::kDevMask, Gradient<XPU>, SimpleOpInplaceOption)
    .describe("description");

SimpleOpInplaceOption is defined as:

    enum SimpleOpInplaceOption {
      kNoInplace,  // do not allow inplace in arguments
      kInplaceInOut,  // allow inplace in with out (unary)
      kInplaceOutIn,  // allow inplace out_grad with in_grad (unary)
      kInplaceLhsOut,  // allow inplace left operand with out (binary)
      kInplaceOutLhs  // allow inplace out_grad with lhs_grad (binary)
    };

In our example, we have a gradient function that relies on input data, so the function can’t be written inplace. The output gradient has no purpose after gradient computation, so the gradient can be written in place.

    MXNET_REGISTER_SIMPLE_OP(smooth_l1, XPU)
    .set_function(XPU::kDevMask, SmoothL1Forward_<XPU>, kNoInplace)
    .set_gradient(XPU::kDevMask, SmoothL1BackwardUseIn_<XPU>, kInplaceOutIn)
    .set_enable_scalar(true)
    .describe("Calculate Smooth L1 Loss(lhs, scalar)");

Remember from the discussion of shape functions that a default behavior without
set_shape_function forces the inputs(if they’re binary) to be the same shape and yield the same shape for output. We’ll discuss
set_enable_scalar later.

NDArray Operator Summary

• Create a shape function for determining the output shape.
• Create a function as the forward routine by choosing a suitable function type.
• Create a gradient as the backward routine by choosing a suitable gradient type.
• Register the operator using the registration process.

Additional Information on SimpleOp

Using SimpleOp on EnvArguments

Some operations might need a scalar as input, such as a gradient scale, a set of keyword argumentscontrolling behavior, or a temporary space to speed up calculations.EnvArguments provides additional
arguments and resources to make calculations more scalableand efficient.

    struct EnvArguments {
      real_t scalar;  // scalar argument, if enabled
      std::vector<std::pair<std::string, std::string> > kwargs;  // keyword arguments
      std::vector<Resource> resource;  // pointer to the resources requested
    };

More registration parameters are required to enable these additional features. To prevent confusion on parameters,
scalar and
kwargscan’t be present at the same time. To enable
scalar, useset_enable_scalar(bool
enable_scalar) in registration. Then, in forward functions and gradients, the
scalar can be accessed from
env.scalar as in the function parameter
EnvArguments
env.

To enable kwargs, use
set_enable_kwargs(bool
enable_kwargs) in registration. Then, in forwardfunctions and gradients, additional arguments are contained in
env.kwarg, which is defined asstd::vector
std::string> >. Use the DMLC parameter structure tosimplify parsing keyword arguments. For more details, see the
guide on parameter structure.

Additional resources like mshadow::Random and temporary memory space can also be requested andaccessed from
EnvArguments.resource. The registration routine is
set_resource_request(ResourceRequest
req)or set_resource_request(const
std::vector), where
mxnet::ResourceRequest is defined as:

    struct ResourceRequest {
      enum Type {  // Resource type, indicating what the pointer type is
        kRandom,  // mshadow::Random object
        kTempSpace  // A dynamic temp space that can be arbitrary size
      };
      Type type;  // type of resources
    };

Registration will request the declared resource requests from
mxnet::ResourceManager, and place resourcesin
std::vector resource in
EnvArguments. To access resources, use the following:

    auto tmp_space_res = env.resources[0].get_space(some_shape, some_stream);
    auto rand_res = env.resources[0].get_random(some_stream);

For an example, see src/operator/loss_binary_op-inl.h.

In our smooth l1 loss example, a scalar input is needed to mark the turning point of a loss function. Therefore,in the registration process, we use
set_enable_scalar(true), and use
env.scalar in function and gradientdeclarations.

Crafting a Tensor Operation

Because computation utilizes the mshadow library and we sometimes don’t have functions readily available, wecan craft tensor operations in operator implementations. If you define such functions
as element-wise, youcan implement them as a mxnet::op::mshadow_op.
src/operator/mshadow_op.h that contains a lot of
mshadow_op,for example.
mshadow_op are expression mappers. They deal with the scalar case of desired functions. For details, seemshadow
expression API guide.

If an operation can’t be done in an element-wise way, like the softmax loss and gradient, then you need to create a new tensor operation. You need to create as
mshadow function and as
mshadow::cudafunction directly. For details, see the
mshadow library. For an example, see
src/operator/roi_pooling.cc.

In our smooth l1 loss example, we create two mappers, namely the scalar cases of smooth l1 loss and gradient.

    namespace mshadow_op {
    struct smooth_l1_loss {
      // a is x, b is sigma2
      MSHADOW_XINLINE static real_t Map(real_t a, real_t b) {
        if (a > 1.0f / b) {
          return a - 0.5f / b;
        } else if (a < -1.0f / b) {
          return -a - 0.5f / b;
        } else {
          return 0.5f * a * a * b;
        }
      }
    };
    }

The gradient, which can be found in src/operator/smooth_l1_unary-inl.h, is similar.

Beyond Two Operands

The new unified API is designed to fulfill the fundamentals of an operation. For operators with more than two inputs,more than one output, or that need more features, see the original
Operator API.