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MXNet can integrate with many different kinds of accelerators, including TVM, MKLDNN, TensorRT, Intel nGraph and more. These accelerators in general support a limited number of operators, and thus running computation in a model usually involves in interaction between accelerator operators and MXNet operators.

These accelerators share some common requirements:

  • TVM , MKLDNN and nGraph uses customized data formats. Interaction between these accelerators with MXNet requires data format conversion.
  • TVM, MKLDNN, TensorRT and nGraph fuses operators.

Integration with these accelerators should happen in the granularity of subgraphs instead of in the granularity of operators. To fuse operators, it's obvious that we need to divide a graph into subgraphs so that the operators in a subgraph can be fused into a single operator. To handle customized data formats, we should partition a computation graph into subgraphs as well. Each subgraph contains only TVM, MKLDNN or ngraph operators. In this way, MXNet converts data formats only when entering such a subgraph and the operators inside a subgraph handle format conversion themselves if necessary. This makes interaction of TVM and MKLDNN with MXNet much easier. Neither the MXNet executor nor the MXNet operators need to deal with customized data formats.

Integration with these accelerators may result in two levels of graph partitioning. In the first level, a subgraph only contains the operators supported by the accelerator. In the second level, a subgraph only contains the operators that can be fused.

  • TVM requires two levels of partitioning because TVM searches for global scheduling among fused operators in order to achieve the best performance.
  • MKLDNN requires two levels of partitioning. We want to isolate MKLDNN operators from MXNet operators so that we know where to insert MKLDNN format conversion operators. MKLDNN also wants to fuse operators to achieve the optimal performance.
  • TensorRT also only supports a small set of operators and performs a graph transformation internally to fuse operators both vertically and horizontally for better performance.
  • nGraph probably has the same requirement as MKLDNN.

The partitioning and execution of these accelerators can be different. As such, we define the following interface for accelerators to customize graph partitioning and subgraph execution inside an operator.

class SubgraphProperty {
 public:
  // the criteria of selecting the subgraph nodes.
  virtual SubgraphSelectorPtr CreateSubgraphSelector() const = 0;
  // create an nnvm node for a given subgraph. Here users can customize how to
  // execute the operators in the subgraph.
  virtual nnvm::NodePtr CreateSubgraphNode(const nnvm::Graph &g) const = 0;
};

Step 1: graph partition
Graph partitioning is to traverse a computation graph and group operators into subgraphs based on certain rules. There already exists an TVM fuse pass in NNVM, which groups operators into subgraphs based on certain general rules (e.g., convolution followed by element-wise operations). This graph partitioner is TVM-specific. It doesn't work for other accelerators. We need more graph partitioners. For example, TensorRT and MKLDNN requires a partitioner that finds subgraphs with specific patterns (e.g., convolution followed by batchnorm, followed by activation, etc).

Regardless of the diverse partitioning requirements, we assume all graph partitioning shares the following requirements:

  • all nodes in a subgraph should be connected via either incoming links or outgoing links or both.
  • a node can't belong to two or more subgraphs.

Given these assumptions, we traverse from every node in a graph and explore their neighbor nodes with rules provided by users. The interface below allows users to define the selection rules. Given this interface, users can determine which edges to follow to generate a subgraph. Starting from every node, the graph partitioning algorithm creates a new subgraph selector and tries to grow a subgraph. Two criteria need to meet before a node is selected as a starting node:

  • the node hasn't been selected as part of a subgraph;
  • Select is called on the node and returns true.

From this starting node, SelectInput and SelectOutput are called to determine if a neighbor node (that hasn't been selected by another subgraph before) should be selected as a candidate for the subgraph. The search continues when a new node is selected as a candidate, and terminates when no more nodes are found. When the process of searching for candidate nodes ends, all of the candidate nodes will passed to Filter to finalize the subgraph. The filter step gives the user the last opportunity to drop out some of the candidate nodes. The selector is stateful. It can change its own state when seeing a new node.

class SubgraphSelector {
 public:
  // Select a starting node for a subgraph.
  virtual bool Select(const nnvm::Node &n) = 0;
  // The two methods below select neighbors in the incoming or outgoing links as candidate nodes of a subgraph.
  virtual bool SelectInput(const nnvm::Node &curr_node, const nnvm::Node &new_node) = 0;
  virtual bool SelectOutput(const nnvm::Node &curr_node, const nnvm::Node &new_node) = 0;
  // After collecting all candidate nodes for a subgraph, users can use this method to prune some of the nodes
  // to finalize the subgraph.
  virtual std::vector<nnvm::Node*> Filter(nnvm::Graph* g, const std::vector<nnvm::Node*>& candidates) = 0;
};

We provide a default selector called ContainOpSelector, which extracts a subgraph with operators supported by an accelerator. This selector or its variant is commonly needed by most of the accelerators.

When a subgraph is found, the partitioning algorithm invokes SubgraphProperty::CreateSubgraphNode to create a new node for the subgraph and connects the new node back to the original graph to replace the subgraph. The subgraph passed to CreateSubgraphNode contains shape/dtype/storage information of the input nodes. This is important because accelerators, such as TVM and TensorRT, need these information to compile and select the best kernel. CreateSubgraphNode allows any customization on the subgraph and the node, which gives users many opportunities the subgraph. For example, TensorRT can optimize a computation graph based on its input shapes and data types in CreateSubgraphNode; some of the accelerators, such as TVM and MKLDNN, can perform another level of graph partitioning for fused operators.

To perform graph partitioning, we attach a graph property (a class that implement SubgraphProperty) and invoke PartitionGraph.

g.attrs["subgraph_property"] = std::make_shared<nnvm::any>(std::move(property));
g = ApplyPass(std::move(g), "PartitionGraph");

Step 2: subgraph operator (function call)
Although there are two levels of graph partitioning, we only need to handle one level of subgraphs in the executor because the subgraphs in the second level are fused into operators. We can execute these subgraphs inside special operators, which is specific to the accelerator.

  • TVM execution operator: loads a subgraph from a TVM compiled binary, a graph JSON file and weight arrays, and executes the subgraph composed of fused operators. We can first use the TVM executor to execute the subgraph, but in the future we should use the MXNet executor because MXNet executes operators in multiple threads, which is useful for task parallelism. The operator needs to convert all output NDArrays of the subgraph to the default format.
  • MKLDNN execution operator: gets a subgraph from the first step and runs operators in the MXNet executors. Like TVM operator, this operator also needs to convert all output NDArrays of the subgraph to the default format.
  • TensorRT has its engine for executing the optimized subgraph.
  • nGraph execution operators: it's up to the Intel folks, most likely similar to the MKLDNN operator.

To customize the subgraph execution, an accelerator needs to provide their own operator implementation and attach the operator to the subgraph node when SubgraphProperty::CreateSubgraphNode is called. The subgraph operator should be a stateful operator and contain a computation graph. We provide a default subgraph operator implementation (“_subgraph_op”) that executes operators with MXNet Executor.

For fast inference in TVM and MKLDNN, the subgraph operators need to maintain a copy of weight arrays (similar to the closure of a function). In this way, we can convert the data format of the weight arrays and cache the array inside the subgraph operator to avoid any redundant format conversion. The original weight arrays will still be part of the inputs of the subgraph operator. Even though the weight arrays are normally not modified, we still need to handle this case correctly. One solution is to maintain a version number for the var of an NDArray, which is increased by one whenever the NDArray is modified in the execution engine. We can use the version number to determine the weight arrays have been modified whenever the subgraph operator is invoked.

The benefit of invoking a subgraph inside an operator
Introducing a subgraph operator for TVM and MKLDNN may sound like unnecessary complexity. It actually significantly reduces the complexity of the integration. By using the subgraph operator, we can completely isolate TVM operators and MKLDNN operators from MXNet operators as well as the default MXNet memory planning. Inside the subgraph operators, we don't need to deal with data format conversion and can use a completely different memory plan for the subgraph.


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