[源码解析]PyTorch如何实现前向传播(2) --- 基础类(下)
0x00 摘要
本系列将通过大概十篇左右文章来分析 PyTorch 的自动微分功能如何实现。本文是前向传播的第二篇，介绍自动微分（梯度计算）所涉及的部分 PyTorch 基础类。因为字数太多（1万两千字），所以拆分成上下两篇。
系列前几篇连接如下：
[源码解析]PyTorch如何实现前向传播(1) --- 基础类(上)
0x01 前文回顾
前文介绍了部分基础类，比如 Variable, Function, Tensor，本文我们继续分析其他基础类。为了行文完整，我们从前文摘取了总体逻辑关系如下，SubBackward0，PowBackward0 和 都是Node 的派生类，在本文我们会细化这个图。
+---------------------+ +----------------------+
| SubBackward0 | | PowBackward0 |
| | Edge | | Edge
| next_functions +-----+--------> | next_functions +----------> ...
| | | | |
+---------------------+ | +----------------------+
|
|
| +----------------------+
| Edge | MulBackward0 |
+--------> | | Edge
| next_functions +----------> ...
| |
+----------------------+
0x02 TensorImpl
2.1 转嫁
PyTorch 之中大量使用了bridge设计模式，at::Tensor就是利用bridge模式把具体实现转交给TensorImpl完成。
class TORCH_API Tensor {
private:
struct unsafe_borrow_t { explicit unsafe_borrow_t() = default; };
explicit Tensor(unsafe_borrow_t, const Tensor& rhs)
: impl_(c10::intrusive_ptr<at::TensorImpl, UndefinedTensorImpl>::reclaim(rhs.impl_.get())) {}
friend MaybeOwnedTraits<Tensor>;
protected:
friend class ::caffe2::Tensor;
void enforce_invariants();
c10::intrusive_ptr<TensorImpl, UndefinedTensorImpl> impl_; // 转嫁出去
};
具体如下：
+------------------------------------------------+ +---------------------------+
|Tensor | |TensorImpl |
| | | |
| | bridge | |
| <TensorImpl, UndefinedTensorImpl> impl_+-----------> | autograd_meta_ |
| | | |
| | | named_tensor_meta_ |
+------------------------------------------------+ | |
| pyobj_ |
| |
| sizes_and_strides_ |
| |
| storage_offset_ |
| |
| data_type_ |
| |
| device_opt_ |
| |
| |
+---------------------------+
2.2 定义
TensorImpl 定义如下，因为本文是自动微分和前向传播相关，因此我们专注这部分功能的相关变量，就是autograd_meta_ 。除了 autograd_meta_ 之外，主要是一些描述Tensor大小的元数据，包含元素的类型（dtype），Tensor所依赖的设备，Strides（步幅）等等。
struct C10_API TensorImpl : public c10::intrusive_ptr_target {
Storage storage_;
private:
// This pointer points to an AutogradMeta struct that stores autograd-specific
// fields (such as grad_ / grad_fn_ / grad_accumulator_). This pointer always
// has unique ownership (meaning only one TensorImpl can own it at a time).
//
// autograd_meta_ can be nullptr, as an optimization. When this occurs, it is
// equivalent to having an autograd_meta_ pointing to a default constructed
// AutogradMeta; intuitively, tensors which don't require grad will have this
// field set to null.
//
// This means accessors on autograd_meta_ have to be careful to test if they
// got a nullptr, and handle default behavior appropriately in that case.
//
// Note that we don't enforce the invariant that if the AutogradMeta is
// default constructed, it is nullptr (to do this, we'd have to continuously
// check if an AutogradMeta became, by mutation, equal to the default
// constructed form. (This might be useful, but it seems rare enough that
// a requires_grad=True variable will turn back into the requires_grad=False
// version.) So there are three representable states:
//
// 1. autograd_meta_ == nullptr
// 2. autograd_meta_ is default constructed (semantically, same as (1))
// 3. autograd_meta_ has nontrivial information content
//
std::unique_ptr<c10::AutogradMetaInterface> autograd_meta_ = nullptr; // 主要关注这里
protected:
std::unique_ptr<c10::NamedTensorMetaInterface> named_tensor_meta_ = nullptr;
c10::VariableVersion version_counter_;
PyObject* pyobj_ = nullptr;
c10::impl::SizesAndStrides sizes_and_strides_;
int64_t storage_offset_ = 0;
int64_t numel_ = 1;
caffe2::TypeMeta data_type_;
c10::optional<c10::Device> device_opt_;
bool is_contiguous_ : 1;
/* HasContiguityPolicy */ uint8_t has_contiguity_ : 2;
bool storage_access_should_throw_ = false;
bool is_channels_last_ : 1;
bool is_channels_last_contiguous_ : 1;
bool is_channels_last_3d_ : 1;
bool is_channels_last_3d_contiguous_ : 1;
bool is_non_overlapping_and_dense_ : 1;
bool is_wrapped_number_ : 1;
bool allow_tensor_metadata_change_ : 1;
bool reserved_ : 1;
DispatchKeySet key_set_;
};
对于自动微分，std::unique_ptr<c10::AutogradMetaInterface> autograd_meta_ = nullptr; 是关键。
此成员变量用来存储自动微分相关的特殊变量，比如grad_ / grad_fn_ / grad_accumulator_，每一个TensorImpl在同一时刻只有唯一一个AutogradMeta。
autograd_meta_ 是区分一个 Variable 是普通张量还是带 autograd 功能张量的唯一标识：
- 对于不需要梯度的张量，autograd_meta_ 这个变量为null。
- 但是出于优化的目的，即使需要梯度，autograd_meta_ 也可以是null，这种情况等同于被赋值成一个缺省的AutogradMeta。所以在使用时候需要仔细校验是否为null。
- 在需要梯度情况下，一般来说，autograd_meta_会被初始化为 AutogradMeta 或者DifferentiableViewMeta。
AutogradMetaInterface 定义如下，这是一个抽象接口，需要派生类来实现具体功能。
struct C10_API AutogradMetaInterface {
virtual void set_requires_grad(
bool requires_grad,
at::TensorImpl* self_impl) = 0;
virtual bool requires_grad() const = 0;
virtual at::Tensor& mutable_grad() = 0;
virtual const at::Tensor& grad() const = 0;
virtual const at::Tensor& fw_grad(uint64_t level, const at::Tensor& self)
const = 0;
virtual void set_fw_grad(
const at::Tensor& new_grad,
const at::Tensor& self,
uint64_t level,
bool is_inplace_op) = 0;
virtual ~AutogradMetaInterface();
};
0x03 自动求导相关类
以下类是与自动求导相关。
3.1 AutogradMeta
AutogradMeta 继承了 AutogradMetaInterface，存储于自动微分相关的东西，比如节点的梯度值和梯度计算函数，其具体定义如下：
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// AutogradMeta
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/// Each `Variable` has one unique `AutogradMeta` struct, which stores autograd
/// metadata fields that are necessary for tracking the Variable's autograd history.
/// As an optimization, a Variable may store a nullptr, in lieu of a default
/// constructed AutogradMeta.
/// 1. A `grad_fn`, if the variable is in the interior of the graph. This is the
/// gradient of the function that produced the variable.
/// 2. A `grad_accumulator`, if the variable is a leaf, which accumulates a
/// scalar gradient value into its `grad` variable.
struct TORCH_API AutogradMeta : public c10::AutogradMetaInterface {
std::string name_;
Variable grad_; // 保存当前Variable的梯度，本身也是一个Variable
std::shared_ptr<Node> grad_fn_; // 非叶子节点才有意义，中间节点负责梯度计算。Pytorch就是判断grad_fn_是否为空来判断一个Variable是否是叶子节点，可以通过grad_fn()方法来访问。
std::weak_ptr<Node> grad_accumulator_; // Node实例，只有叶子节点才有，叶子节点负责对梯度进行累加，grad_accumulator_就是梯度累加处理函数，梯度就被保存在grad_变量之中
// This field is used to store all the forward AD gradients
// associated with this AutogradMeta (and the Tensor it corresponds to)
// There is a semantic 1:1 correspondence between AutogradMeta and
// ForwardGrad but:
// - This field is lazily populated.
// - This field is a shared_ptr but it must never be
// shared by multiple Tensors. See Note [ Using ForwardGrad ]
// Any transition from not_initialized to initialized
// must be protected by mutex_
std::shared_ptr<ForwardGrad> fw_grad_; // forward AD gradients
std::vector<std::shared_ptr<FunctionPreHook>> hooks_;
std::shared_ptr<hooks_list> cpp_hooks_list_;
// Only meaningful on leaf variables (must be false otherwise)
bool requires_grad_; // 此Variable是否需要grad
// Only meaningful on non-leaf variables (must be false otherwise)
bool retains_grad_; // 只有非叶子节点才有意义，是否需要保持图
bool is_view_; // 此Variable是否是一个View（没有实际存储，这是基于base的Variable）
// The "output number" of this variable; e.g., if this variable
// was the second output of a function, then output_nr == 1.
// We use this to make sure we can setup the backwards trace
// correctly when this variable is passed to another function.
uint32_t output_nr_; // Variable是某一个函数的输出数据，output_nr_ 就记录了它是第几个输出，比如 = 0，就表示是函数的第1个输出
// Mutex to ensure that concurrent read operations that modify internal
// state are still thread-safe. Used by grad_fn(), grad_accumulator(),
// fw_grad() and set_fw_grad()
// This is mutable because we need to be able to acquire this from const
// version of this class for the functions above
mutable std::mutex mutex_;
};
AutogradMeta 的主要成员变量如下：
- grad_ ：存储当前Variable实例的梯度，本身也是一个Variable。
- grad_fn ：是个Node实例，非叶子节点才有。通过 grad_fn() 方法来访问，实际上，PyTorch中就是通过 grad_fn是否为空 来判断一个Variable是否是leaf variable。
- grad_accumulator_ ：也是Node的实例，只有叶子节点才有。
- 通过Variable的grad_accumulator()来访问。
- 叶子节点负责对梯度进行累加，grad_accumulator_ 就是梯度累加处理函数。
- 其对应梯度就被保存在 grad_ 变量之中。
- 我们总结一下，对于非叶子节点，grad_fn是计算梯度操作。对于叶子节点，PyTorch 虚拟出了一个特殊计算操作，输出这个叶子节点，同时此虚拟计算操作也作为叶子节点的
grad_accumulator_来累加其梯度，因此叶子节点的output_nr_必定为 0。
- requires_grad_ ：表明此Variable实例是否需要grad。
- retains_grad_ ： 只有非叶子节点才有意义，意义为是否需要保持图。
- is_view_ ：是个flag，表明此Variable实例是否是个view（没有实际存储，基于base的variable）。
- version_counter_ ：version number。
- output_nr_：是个数字。output_nr_表明是 Node 的第几个输出，比如为 0 就 表明这个Variable是Node 的第 1 个输出。
- base_ ：是view的base variable。
具体如下，这里把 grad_fn 配置为 SubBackward0 作为例子：
+----------------------------------------------+ +-------------------------+
|Tensor | |TensorImpl |
| | | |
| | bridge | |
| <TensorImpl, UndefinedTensorImpl> impl_ +-----------> | autograd_meta_ +---------+
| | | | |
| | | named_tensor_meta_ | |
+----------------------------------------------+ | | |
| pyobj_ | |
| | |
| sizes_and_strides_ | |
| | |
| storage_offset_ | |
| | |
| data_type_ | |
| | |
| device_opt_ | |
| | |
| | |
+-------------------------+ |
|
+-------------------------+ |
| AutogradMeta | |
| +<-----------------------------------------+
| |
| grad_accumulator_ |
| | +-------------------------+
| grad_fn_ +--------------------> | SubBackward0 |
| | | |
| hooks_ | | |
| | | |
| retains_grad_ | | next_edges_ |
| | | |
| output_nr_ | | |
| | | |
| fw_grad_ | | |
| | | |
+-------------------------+ +-------------------------+
AutogradMeta 构造函数之中，gradient_edge 参数需要特别注意，其类型为 Edge。
gradient_edge.function就被赋值给AutogradMeta 的grad_fn。gradient_edge.input_nr被赋值给AutoGradMeta的output_nr。
AutogradMeta(at::TensorImpl* self_impl = nullptr, bool requires_grad = false, Edge gradient_edge = Edge() ) {
grad_fn_ = std::move(gradient_edge.function);
requires_grad_ = false;
retains_grad_ = false;
is_view_ = false;
output_nr_ = gradient_edge.input_nr;
// set_requires_grad also checks error conditions.
if (requires_grad) {
TORCH_INTERNAL_ASSERT(self_impl);
// NOLINTNEXTLINE(clang-analyzer-optin.cplusplus.VirtualCall)
set_requires_grad(requires_grad, self_impl);
}
TORCH_CHECK(
!grad_fn_ || !requires_grad_,
"requires_grad should be false if grad_fn is set");
}
3.2 DifferentiableViewMeta
对于输入变量，许多操作返回与输入变量共享存储的新变量，返回的变量被称为在基变量之上的视图（view）变量。在PyTorch中，我们有两种类型的视图：可微视图和不可微的视图。为了支持合适的版本校验，无论是哪种类型，基变量和视图变量必须分享同样的版本计数器（version_counter）。
DifferentiableViewMeta 就是用来处理可微视图。
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// DifferentiableViewMeta
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/// DifferentiableViewMeta is created to support gradient tracking of
/// such **in-place** operations. In particular,
/// + if an in-place op is done on base, the grad_fn field of the view may
/// become stale. So accesses should always go through grad_fn(), which
/// reconstructs an updated grad_fn if the version_counter has incremented.
/// All other fields are always valid.
/// + if an in-place op is done on view, in rebase_history() of view, which is
/// called after every in-place op in VariableType.cpp, the grad_fn of base
/// is updated.
/// + if a single autograd Node returns multiple differentiable views, if any
/// output is modified by an inplace operation, the autograd engine will make
/// an equivalent graph (corresponding to the view operations) without using
/// equivalent graph, where each output is treated as if it were produced by a
/// distinct view operation. This discards the original (e.g., user provided)
/// grad_fn. If the provided grad_fn does more than the backward of the view,
/// then the DifferentiableViewMeta must be created with creation_meta=
/// CreationMeta::MULTI_OUTPUT_NODE to prevent the engine from ignoring the
/// provided grad_fn.
enum class CreationMeta: uint8_t { DEFAULT, IN_CUSTOM_FUNCTION, MULTI_OUTPUT_NODE,
NO_GRAD_MODE, MULTI_OUTPUT_SAFE, INFERENCE_MODE};
struct TORCH_API DifferentiableViewMeta : public AutogradMeta {
private:
/// Informations about the views
c10::optional<ViewInfo> backward_info_;
c10::optional<ViewInfo> forward_info_;
// Optimization to reduce the number of ViewInfo we create.
// In the (very common) case where backward_info_ == forward_info_, we only
// populate backward_info_ (that should be used as both the forward and backward
// view information) and set shared_view_info_ = true.
// Invariants:
// - If shared_view_info_ is false, there is no special constraints on
// backward_info_ and forward_info_
// - If shared_view_info_ is true, we must have:
// - backward_info_.has_value() == true
// - forward_info_.has_value() == false
bool shared_view_info_;
/// The two following fields are extra information that we track to ensure that
/// any operation on this backward view is valid.
/// The value of the version_counter at the time grad_fn was created. The
/// grad_fn field is stale if attr_version_ != version_counter.current_version().
uint32_t attr_version_;
CreationMeta creation_meta_;
};
3.3 AutogradContext
AutogradContext 是操作 autograd 的上下文，用来存储在前向过程中产生的信息，这样在后向传播中就可以访问。
/// Context to save information during `forward` that can be accessed in `backward`
/// in custom autograd operations (see `torch::autograd::Function` for details).
struct TORCH_API AutogradContext {
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
AutogradContext() : materialize_grads_(true) {}
AutogradContext(const AutogradContext &other) = delete;
AutogradContext& operator=(const AutogradContext& other) = delete;
/// Can be used to save non-variable data for `backward`.
// NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
ska::flat_hash_map<std::string, at::IValue> saved_data;
/// Saves the list of variables for a future call to `backward`. This
/// should be called at most once from inside of `forward`.
void save_for_backward(variable_list to_save);
/// Marks variables in the list as modified in an in-place operation. This
/// should be called at most once from inside of `forward` and all arguments
/// should be inputs.
void mark_dirty(const variable_list &inputs);
/// Marks outputs in the list as not requiring gradients. This should be called
/// at most once from inside of `forward` and all arguments should be outputs.
void mark_non_differentiable(const variable_list &outputs);
// Sets whether undefined output grad tensors should be expanded to tensors
// full of zeros before calling backward function. Default value is true.
void set_materialize_grads(bool value);
/// Get the list of variables that were saved in `forward` using
/// `save_for_backward()`. Before returning them to the user, a check is made to
/// ensure that they were not modified by any in-place operations.
variable_list get_saved_variables() const;
const std::unordered_set<at::TensorImpl*>& get_and_bump_dirty() const;
const std::unordered_set<at::TensorImpl*>& get_non_differentiable() const;
private:
std::unordered_set<at::TensorImpl*> non_differentiable_;
std::unordered_set<at::TensorImpl*> dirty_inputs_;
std::vector<torch::autograd::SavedVariable> saved_variables_;
variable_list to_save_;
bool materialize_grads_;
// The CppNode in the autograd graph that owns this AutogradContext. We need a
// weak_ptr to avoid a refcycle. Since grad_fn_ owns this AutogradContext, it
// will always be alive when we want to use it.
std::weak_ptr<Node> grad_fn_;
bool has_freed_buffers_;
void save_variables();
template <class T> friend struct CppNode;
};
对用户来说，AutogradContext 主要是在 自定义 Auto Function 方面。以下是注释之中的例子。
/// ```
/// class MyFunction : public Function<MyFunction> {
/// public:
/// static variable_list forward(AutogradContext *ctx, int n, Variable var) {
/// // Save data for backward in context
/// ctx->saved_data["n"] = n;
/// var.mul_(2);
/// // Mark var as modified by inplace operation
/// ctx->mark_dirty({var});
/// return {var};
/// }
///
/// static variable_list backward(AutogradContext *ctx, variable_list
/// grad_output) {
/// // Use data saved in forward
/// auto n = ctx->saved_data["n"].toInt();
/// return {grad_output[0]*n};
/// }
/// };
/// ```
///
/// To use `MyFunction`:
/// ```
/// Variable x;
/// auto y = MyFunction::apply(6, x);
/// // Example backward call
/// y[0].sum().backward();
我们籍此进入到 Auto Function。
3.4 Auto Function
Autograd使用Function来计算结果和梯度，并对操作历史进行编码。在Tensor 上执行的每个操作都会创建一个新的 Function 对象，该对象执行计算并记录发生了什么。操作历史以函数 DAG 的形式保留，边表示数据依赖关系 ( input <- output )。
通常，用户与 Function 交互的唯一方式是创建子类和定义新操作（扩展新的功能），这是扩展 torch.autograd 的推荐方式。有关如何使用此类的更多详细信息，请参阅有关扩展 autograd 引擎的说明： https://pytorch.org/docs/stable/notes/extending.html#extending-torch-autograd
用户如果要使用自定义autograd操作，请使用静态正向和反向函数实现一个Function子类。
forward可以接受任意多个参数，并应返回变量列表或变量。- 任何Variable参数的使用都将在计算图中注册，但是vectors/sets 或者其他数据结构不会遍历注册。
- 您可以使用c10::optional
作为参数之一，如果参数有值，它将在图形中注册为变量。 - forward应该将指向“torch::autograd::AutogradContext”的指针作为第一个参数。变量可以使用“ctx->save_for_backward”，保存在“ctx->saved_data” map中，其他数据将以
<std::string, at::IValue>”对的形式保存在“ctx->saved_data” map中。
backward应该使用指向torch::autograd::AutogradContext的指针 以及一个变量列表作为参数。- 该变量列表包含的变量数量与
forward输出的变量数量相同。 - backward应该返回与输入一样多的变量，其中每个变量都包含与输入相应的梯度。
- “forward”中保存的变量可以通过“ctx->get_saved_Variables”访问，其他保存的数据可以通过“ctx->saved_data”访问。
- 当 backward被调用时，通过调用每个Function对象的方法，并将返回的梯度传递给下一个Function ，我们就可以按照拓扑顺序来处理这个计算图 。
- 该变量列表包含的变量数量与
Function 具体派生子类例子如下：
class Exp(Function):
@staticmethod
def forward(ctx, i):
result = i.exp()
ctx.save_for_backward(result)
return result
@staticmethod
def backward(ctx, grad_output):
result, = ctx.saved_tensors
return grad_output * result
#Use it by calling the apply method:
output = Exp.apply(input)
如前所示，Function 已经被 Node 替换，所以我们再来到了 Node。
0x04 Node
早期版本中，Node的名字是Function，后来修改为Node，应该是想与节点概念更好的对应。
Node 是一个代表操作的抽象类，其输入是0个或者多个Variable，输出是0个或多个Variable。前向图中该Node节点的输入节点，就是后向传播图中该Node节点的输出节点。PyTorch的autograd机制中，所有函数都派生自此类，并重写其“apply”方法。这样子类的实例就可以通过call操作符调用。
将autograd系统视为计算图时，Node是通过（有向）Edge相互连接的顶点或节点，其本身通过（Node，input_nr）对来表示。Variable 是Node 的输入和输出，并在图形执行期间在这些边之间移动。当两个或多个“边”（来自不同来源）指向一个“节点”的同一输入时，沿所有这些边生成的值在转发到目标“节点”之前将被隐式求和。
其子类通常用来表示可微函数及其梯度算子。然而，请注意，由于“节点”的定义非常笼统，“节点”接受零或更多的输入并产生零或更多的输出。“节点”的使用非常灵活，超出了纯数学运算的范围。例如，AccumageGrad函数是一个sink，它接受一个输入，但不产生输出，而是将输入作为副作用进行累积。在另一端，“GraphRoot”函数不接收来自其他函数的输入，而是产生多个输出。具体可以参见 torch/csrc/autograd/function.h 的注释。
4.1 定义
我们看看 Node 类的定义，为了更好的说明，这里只保留成员变量，删除成员函数。
using edge_list = std::vector<Edge>;
struct TORCH_API Node : std::enable_shared_from_this<Node> {
protected:
/// Performs the `Node`'s actual operation.
virtual variable_list apply(variable_list&& inputs) = 0;
/// Calls `apply()`, but instruments it with tracing machinery.
variable_list traced_apply(variable_list inputs);
/// NOTE [ Sequence Number]
///
/// The sequence_nr has two main usages in autograd:
///
/// 1) Helps determine the node's execution priority in the engine.
/// All else being equal, nodes with higher priority numbers are executed first.
/// Thus, nodes corresponding to ops executed later are the first to be executed in
/// the backward pass. One caveat is that we prioritize AccumulateGrad nodes by
/// explicitly setting its sequence_nr to be UINT64_MAX.
/// 2) The sequence number of this `Node` is paired with with thread_id it was created in
/// as a unique identifier by the profiler to annotate recorded events.
/// The purpose of this is to help users (and possibly programs) interpreting the profiler's
/// output to correlate backward nodes with its forward ops.
/// We need both sequence_nr and thread_id to identify a node because sequence_nr is
/// thread_local, i.e., starts counting up from zero in a new thread
// Sequence number used to correlate backward nodes with forward ops in the
// profiler and provide determinisim in the engine.
const uint64_t sequence_nr_;
// NOTE [ Topological Number ]
//
// topological_nr is used to prune branches in the DAG during autograd discovery as
// maintaining topological_nr helps us check in O(1) if there does NOT exist
// a directed path between two nodes.
//
// The topological order number of this `Node` representing the length of the
// longest possible path from this Node to any leaf node. If you are leaf node,
// aka AccumulateGrad, this will be zero. This value has the property that
// For every pair of nodes X, Y in G, existence of a directed path from X to Y
// implies topo_nr(X) > topo_nr(Y). The converse is not true, however, so we
// cannot prove existence of a path from X to Y, only non-existence.
//
// One assumption we make when using topo_nr is that once a node
// has been used, i.e., has a parent node, its own topo_nr does not change
// we have added some checks with the `has_parent_` field to enforce this.
//
// What NOT to do:
//
// 1) 2 -> 1 -> 0 In this diagram we label nodes with their topo_nr.
// 2 -> 1 -> 0 We have two simple graphs that can each arise from
// `t.exp().exp()`, for example.
// 2) 2 -> 1 -> 0
// /
// 2 -> 1 -> 0 We add 2 as a next edge to 1 even though 1 already
// has a parent.
// 3) 2 -> 1 -> 0
// /
// 2 -> 3 -> 0 2 < 3, yet there exists a path from 2 to 3!
//
uint64_t topological_nr_ = 0;
// Tracks whether this node has been added as the next_edge of another node
// via set_next_edge(s), which always calls topological_nr() of all its children
// See NOTE [ Topological Number ] for why we need this.
mutable bool has_parent_ = false;
// Id of the thread that created the instance
uint64_t thread_id_ = 0;
std::mutex mutex_;
// 前向过程中的输入variable，在前向过程中与该算子相关联的边
edge_list next_edges_;
PyObject* pyobj_ = nullptr; // weak reference
std::unique_ptr<AnomalyMetadata> anomaly_metadata_ = nullptr;
std::vector<std::unique_ptr<FunctionPreHook>> pre_hooks_;
std::vector<std::unique_ptr<FunctionPostHook>> post_hooks_;
at::SmallVector<InputMetadata, 2> input_metadata_;
// 这里对运算符()进行重载，核心其实就是调用apply()
variable_list operator()(variable_list&& inputs) {
// In the first iteration of named tensors, autograd ignores names and
// operates on unnamed tensors. In the long term, autograd should
// probably operate with names.
at::NoNamesGuard no_names_guard;
bool pre_sampled = false;
if (at::shouldRunRecordFunction(&pre_sampled)) {
// Using RecordFunction to trigger observers in the backward pass
at::RecordFunction guard(at::RecordScope::BACKWARD_FUNCTION, pre_sampled);
if (guard.isActive()) {
// Using sequence number and thread id to correlate with
// the forward pass function
guard.setForwardThreadId(thread_id_);
if (guard.needsInputs()) {
guard.before(
name(),
std::vector<c10::IValue>(inputs.begin(), inputs.end()),
sequence_nr());
} else {
guard.before(name(), sequence_nr());
}
}
// keeping stack guard object alive during the call
return apply(std::move(inputs));
} else {
return apply(std::move(inputs));
}
}
};
其构造函数是：
explicit Node(
uint64_t sequence_nr,
edge_list&& next_edges = edge_list())
: sequence_nr_(sequence_nr),
next_edges_(std::move(next_edges)) {
for (const Edge& edge: next_edges_) {
update_topological_nr(edge);
}
if (AnomalyMode::is_enabled()) {
metadata()->store_stack();
// If anomaly mode is enabled and graph is constructed, then assign the
// currently evaluating node as the parent of this node.
// A parent is a Node where this Node is created.
// We are tracking the parents to track multiple backward operations.
assign_parent();
}
// Store the thread_id of the forward operator.
// See NOTE [ Sequence Numbers ]
thread_id_ = at::RecordFunction::currentThreadId();
}
4.2 重要成员变量
我们具体解释一些重要成员变量。
4.2.1 input_metadata_
input_metadata_ 代表了 input data 的元信息，界定了一个Function的输入参数。
4.2.2 next_edges_
这是在前向过程中与该算子相关联的边。
我们将 PyTorch的autograd系统看作是一个图，每个 Node 实例就是图节点，各个 Node 实例之间则是通过Edge连接的。Edge是个结构体，通过 (Function, input_nr) 的配对来代表graph中的边。Node 的成员 next_edges_ 正是一组这样的Edge实例，其代表此 Node 实例的返回值要输出到的（另外）Node，即 next_edges_是 Node 和Node 之间的纽带。
Node 的输入输出都是Variable实例，因此当一个graph被执行的时候，Variable实例就在这些edges之间来传输流动。当两个或者多个Edge指向同一个Node的时候（这个节点的入度大于1），这些edges的输出将被隐含相加起来再送给指向的目标 Node。
用户可以使用add_next_edge()来向 Node 添加一个edge, 通过next_edge(index)获取对应的edge，通过next_edges()方法获得迭代edge的迭代器。
4.2.3 sequence_nr_
该变量用于将网络中的后向节点与前向操作关联起来，并且在引擎中提供确定信息。sequence_nr_ 随着Function实例的不断构建而单调增长，具体有两个用处：
-
帮助确定节点在引擎中的执行优先级。在所有其他条件相同的情况下，优先级较高的节点将首先执行。因此，前向传播时后执行的操作就是后向传播之中先执行的操作。需要注意的一点是，对于 AccumulateGrad 节点，我们将sequence_nr显式地设置为UINT64_MAX。在PyTorch的反向图计算中，
AccumulateGrad类型代表的就是叶子节点类型，也就是计算图终止节点。AccumulateGrad类中有一个.variable属性指向叶子节点。 -
此“节点”的 sequence_nr_ 与 thread_id 一起搭配，作为一个节点的唯一标示，在 profiler 之中记录事件。这样做的目的是帮助用户（可能还有程序）解释 profiler 的输出，以便将向后的节点与其向前的操作关联起来。因为 sequence_nr 是 thread_local 类型变量，即在新线程中从零开始计数。
4.2.4 topological_nr_
此变量是 “节点”的拓扑顺序号，表示从该节点到任何叶节点的最长可能路径的长度。如果有一个叶节点，即AccumulateGrad，topological_nr_ 将是零。
topological_nr_ 用于在autograd发现期间对DAG中的分支进行修剪，维护拓扑 topological_nr_有助于我们在两个节点之间不存在有向路径时，在O(1) 时间完成检查。
topological_nr_ 具有以下属性：
- 对于G中的每一对节点X，Y，如果存在从X到Y的有向路径，则意味着 topo_nr(X) > topo_nr(Y)。然而，事实并非如此，因此我们无法证明从X到Y的路径的存在性，只能证明不存在。
- 我们在使用 topological_nr_ 时所做的一个假设是：一旦使用了一个节点，即它有一个父节点，那么它自己的topological_nr_ 就不会改变。我们在“has_parent_”字段中添加了一些检查来强制执行这一点。
4.2.5 operator()
variable_list operator()(variable_list&& inputs)是Node的主要方法。该方法接收vector封装的多个Variable实例，并输出vector封装的多个Variable实例，然后调用apply 具体业务函数。该方法依靠C++的多态，将对operator 的调用转化为对自身（子类）的apply方法调用。
PyTorch中所有用于反向传播计算的函数都继承自Function类，并重写Function类中的apply纯虚函数。
0x05 Edge
从名字可知，Edge 就是计算图的边。主要变量是：
- std::shared_ptr
function ：本边指向的目标Node。 - uint32_t input_nr ： 指定本Edge是 function 的第几个输入 。
using tensor_list = std::vector<at::Tensor>;
using variable_list = std::vector<Variable>;
using edge_list = std::vector<Edge>;
using saved_variable_list = std::vector<SavedVariable>;
using IndexRange = std::pair<size_t, size_t>;
/// Represents a particular input of a function.
struct Edge {
Edge() noexcept : function(nullptr), input_nr(0) {}
Edge(std::shared_ptr<Node> function_, uint32_t input_nr_) noexcept
: function(std::move(function_)), input_nr(input_nr_) {}
/// Convenience method to test if an edge is valid.
bool is_valid() const noexcept {
return function != nullptr;
}
// Required for use in associative containers.
bool operator==(const Edge& other) const noexcept {
return this->function == other.function && this->input_nr == other.input_nr;
}
bool operator!=(const Edge& other) const noexcept {
return !(*this == other);
}
/// The function this `Edge` points to.
std::shared_ptr<Node> function; // 指向的Node
/// The identifier of a particular input to the function.
uint32_t input_nr; //指定本Edge是function的第几个输入
};
}} // namespace torch::autograd
0x06 逻辑图
我们把文初的逻辑图细化如下，上半部分是 Python 世界，下半部分是 C++世界：
+--------------------------------------------+ +------------------------------+
| SubBackward0 | | PowBackward0 |
| | | | Edge
| | | next_functions +----------> ...
| next_functions[0] = (PowBackward0, 0) +----------> | |
| | +------------------------------+
| |
| | +-------------------------------+
| next_functions[1] = (MulBackward0, 0) +----------> | MulBackward0 |
| | | | Edge
| | | next_functions +----------> ...
+--------------------------------------------+ | |
+-------------------------------+
^
|
|
| Python
+--------------------------------------------------------------------------------------------------------+
| C++
|
v
+---------------------------------------------+ +----------------------+ +------------------+
| SubBackward0 | | Edge 1 | | PowBackward0 |
| +-------------------------> | | | |
| | | | function +----------> | |
| + | | | | |
| next_edges_ = [Edge 1, Edge 2] | | input_nr = 0 | | |
| + | +----------------------+ +------------------+
| | |
| | |
+---------------------------------------------+ +----------------------+ +------------------+
| | Edge 2 | | MulBackward0 |
| | | | |
+----------------> | function +----------> | |
| | | |
| input_nr = 0 | | |
| | | |
+----------------------+ +------------------+
手机如下：
至此，传播过程中的基础类已经分析完毕，下一篇我们介绍如何使用这些类来完成前向传播。
0xFF 参考
https://github.com/KeithYin/read-pytorch-source-code/
pytorch学习笔记（十三）：backward过程的底层实现解析
How autograd encodes the history
https://pytorch.org/tutorials/beginner/blitz/autograd_tutorial.html