Writing Graph Transformations on ATen IR


Since the ATen IR sits at the FX Graph/GraphModule level, any transformations written for FX Graphs can be easily applied onto the ATen IR. If you’re familiar with writing FX graph transformations, then this will be the same.

The most direct way of writing transformations is by looping through the given graph and directly manipulating the nodes within the graph.

For example, let’s say we want to replace torch.ops.aten.add.Tensor() calls with torch.ops.aten.mul.Tensor() calls:

import torch

def replace_add_with_mul(gm: torch.fx.GraphModule) -> torch.fx.GraphModule:
    for node in gm.graph.nodes:
        if node.op == "call_function" and == torch.ops.aten.add.Tensor:
   = torch.ops.aten.mul.Tensor

We can also delete and append new nodes through FX utility functions that can be found in the Graph documentation. For example, if we want to insert a torch.ops.aten.relu.default() after the add call:

import torch

def insert_relu_after_add(gm: torch.fx.GraphModule) -> torch.fx.GraphModule:
    for node in gm.graph.nodes:
        if node.op == "call_function" and == torch.ops.aten.add.Tensor:

            # Specifies the insertion point. Any nodes added to the graph within
            # this scope will be inserted after `node`
            with gm.graph.inserting_after(node):
                # Insert a new `call_function` node with op `torch.ops.aten.relu.default`
                new_relu_node = gm.graph.call_function(torch.ops.aten.relu.default, args=(node,))
                # Replace all the places that use `node` to now use the `new_relu_node`

In general, transformations can be roughly categorized into a couple of axis:

Axis A: 1. Creating one-to-X mapping (eg. decomposition) 2. Creating many-to-one mapping (eg. fusion)

Axis B: 1. Doing forwards iteration (eg. shape propagation) 2. Doing backwards iteration (eg. dead code elimination)

Axis C: 1. Dependent on local node information (eg. out-variant conversion) 2. Dependent on global graph information (eg. memory planning)

Our projection on the frequency of these use cases are: 1. A.1, B.1, C.1 2. A.2 3. B.2, C.2

Although we can make all graph transformations through directly manipulating the graph, we also provide some helper utilities for some ease of use for the level 1 and 2 use-cases.


For level 1 uses cases (creating one-to-X mappings, doing forwards iterations, and looking at local node information), we can utilize the Transformer class to execute each node and recreate a graph, except with the transformations specified.

One-to-One Pass

An example for one-to-one mappings, if we wanted to replace an op A with another op B, we can run the GraphModule, and very time we see op A, return op B.

An example is:

class ReplaceAddWithMul(torch.fx.Transformer):
    def call_function(self, target, args, kwargs):
        if target != torch.ops.aten.add.Tensor:
            return super().call_function(target, args, kwargs)
        return super().call_function(torch.ops.aten.mul.Tensor, args, kwargs)

transformed_graph_module = ReplaceAddWithMul(graph_module).transform()

The super().call_function(target, args, kwargs, meta) call creates a call_function FX node, and returns the result of running the operator with the given arguments.

One-to-X Pass

If we wanted to do one-to-X mappings, like replacing op A with 2 other ops B and C, we would then make 2 calls to super().call_function to create 2 FX nodes, one with op B and another with op C, and return the result of running op C.

For example:

class ReplaceAddWithMulSub(torch.fx.Transformer):
        def f(x, y):
            return x + y

    After pass:
        def f(x, y):
            z = x * y
            return z - y
    def call_function(self, target, args, kwargs):
        if target != torch.ops.aten.add.Tensor:
            return super().call_function(target, args, kwargs)

        x, y = args

        mul_res = super().call_function(torch.ops.aten.mul.Tensor, args, {})
        return super().call_function(torch.ops.aten.sub.Tensor, (mul_res, y), {})

transformed_graph_module = ReplaceAddWithMulSub(graph_module).transform()

One-to-None Pass

If we wanted to remove an op, we can just return the value passed into the function:

class RemoveDetachPass(torch.fx.Transformer):
    def call_function(self, target, args, kwargs):
        if target not in (
            return super().call_function(target, args, kwargs, meta)

        assert len(args) == 1
        return args[0]

transformed_graph_module = RemoveDetachPass(graph_module).transform()

Utilizing Local Information

An example of utilizing local node information is, if we wanted to convert all the scalars within the graph to tensors, we can run the given fx.GraphModule, and for every argument that contains a scalar, we convert it to a tensor. It might look something like:

def args_map(target, fn, args, kwargs):
    assert isinstance(args, tuple)
    assert isinstance(kwargs, dict)
    args = list(args)
    kwargs = kwargs.copy()

    # Update the argument based on the function passed
    def update(key, args, schema):
        args[key] = fn(args[key], schema)

    # Update each argument in the schema
    for i, schema in enumerate(target._schema.arguments):
        if in kwargs:
            update(, kwargs, schema)
        elif not schema.kwarg_only and i < len(args):
            update(i, args, schema)
    return tuple(args), kwargs

class ScalarToTensorPass(torch.fx.Transformer):
    def call_function(self, target, args, kwargs):
        def try_coerce(value, arg):
            return (
                if isinstance(value, (float, int, bool))
                and type(arg.type) == torch.TensorType
                else value

        args, kwargs = args_map(target, try_coerce, args, kwargs)
        return super().call_function(target, args, kwargs)

transformed_graph_module = ScalarToTensorPass(graph_module).transform()

Subgraph Rewriter

For creating many-to-one mappings, we can utilize FX’s subgraph rewriter. Given a pattern, it creates a subgraph of operators matching to the pattern, and then replaces each matched subgraph with the replacement.


This is an inplace operation.

The pattern and replacement inputs must be callable functions or GraphModules containing the same operators that are used within the graph (ATen ops) so that the subgraph rewriter can find the correct pattern in the graph. Inputs to the pattern/replacement callables will be treated as wildcards when matching.

An example:

from torch.fx import subgraph_rewriter

def replace_patterns(graph_module):
    def pattern(x, y):
        x = torch.ops.aten.add.Tensor(x, y)
        x = torch.ops.aten.mul.Tensor(x, y)
        return x

    def replacement(x, y):
        return torch.ops.aten.sub.Tensor(x, y)

replaced_patterns = subgraph_rewriter.replace_pattern_with_filters(
    traced_module, pattern, replacement

The subgraph rewriter returns a list of ReplacedPatterns:

class ReplacedPatterns:
    # Node from which the match was found
    anchor: Node
    # Maps nodes in the pattern subgraph to nodes in the larger graph
    nodes_map: Dict[Node, Node]
    # List of nodes that were added into the graph
    replacements: List[Node]


The nodes created by the subgraph rewriter will not have the metadata that
is populated in the matched nodes, but you can use
`ReplacedPatterns.nodes_map` to find the nodes in the original graph that
were matched, and `ReplacedPatterns.replacements` to find the nodes that
were replaced in the transformed graph.

Pass Manager

The `PassManager <>`__ is a class used to run multiple passes on a given graph module. When initializing a PassManager instance, we pass in a list of passes that we want to run and set a couple of flags. To run the collection of passes on a graph module, we can pass the graph module directly to the PassManager instance.

An example:

from torch.fx.passes.infra.pass_manager import PassManager

pm = PassManager(
    passes=[replace_add_with_div, replace_div_with_mul],
graph_module_out = pm(graph_module)

To add a common set of checks that are run after each pass, we can call the function set_checks(check: Callable) which takes in a callable function as input. If the run_checks_after_each_pass flag is set, the check will be called after each pass is run on the graph module.

An example:

pm = PassManager(passes=[replace_add_with_div, replace_div_with_mul])

def check_div_target(graph_module):
    for node in graph_module.graph.nodes:
        if node.op == "call_function" and != torch.div:
            raise ValueError("Target should be div!")


pm(graph_module)    # raises ValueError after replace_div_with_mul pass


There are a couple of common FX graph based partitioners we can use to partition the graph.

Subgraph Matcher

For finding subgraphs within a graph that match a specific pattern, we can utilize FX’s `SubgraphMatcher <>`__.

Class Attributes:

  • pattern (Graph): The targeted matching pattern. Placeholder nodes in the graph will be treated as wildcards when matching.

  • match_output (bool): If True, output node in the pattern graph will be treated as a part of the targeted pattern. If False, output node is ignored during match.

  • match_placeholder (bool): If True, placeholder node in the pattern graph will be treated as a part of the targeted pattern. If False, placeholder nodes will be used a wildcard.

  • remove_overlapping_matches (bool): If True, in the case of overlapping matches, only the first match will be returned.

  • ignore_literals (bool): If True, will not check if literals are equal and will instead treat them as wildcards.

An example:

from torch.fx.passes.utils.matcher_utils import SubgraphMatcher

class LargeModel(torch.nn.Module):
    def __init__(self):
        self._weight = torch.nn.Parameter(torch.ones(3, 3))
        self._bias = torch.nn.Parameter(torch.ones(3, 3))

    def forward(self, x):
        return torch.ops.aten.addmm.default(self._bias, x, self._weight)

large_model_graph = torch.export(LargeModel(), inputs).graph

class PatternModel(torch.nn.Module):
    def __init__(self):
        self._weight_1 = torch.nn.Parameter(torch.ones(5, 5))
        self._bias_1 = torch.nn.Parameter(torch.ones(5, 5))

    def forward(self, x):
        return torch.ops.aten.addmm.default(self._bias_1, x, self._weight_1)

pattern_graph = torch.export(PatternModel(), inputs).graph

subgraph_matcher = SubgraphMatcher(pattern_graph)
match_result = subgraph_matcher.match(large_model_graph)

The match function returns a list of InternalMatch:

class InternalMatch():
    # Nodes from which the match was found
    anchors: List[Node]
    # Maps nodes in the pattern subgraph to nodes in the larger graph
    nodes_map: Dict[Node, Node] = field(default_factory=dict)
    # Nodes in target graph that are matched placeholder in pattern
    placeholder_nodes: List[Node] = field(default_factory=list)
    # Nodes in matched subgraph returned by output
    returning_nodes: List[Node] = field(default_factory=list)

Capability Based Partitioner

To find the largest subgraphs of nodes that support a specific invariant, we can utilize FX’s `CapabilityBasedPartitioner <>`__.

Class Attributes

  • graph_module (torch.fx.GraphModule): The graph module we are partitioning on.

  • operator_support (OperatorSupportBase): The object used to determine if a node in the graph is supported in the partition.

  • allows_single_node_partition (bool): If True, allows single node partitions to be formed.

  • non_compute_ops (Optional[Sequence[str]]): A set of ops that are considered to be “non-compute” (ex torch.ops.aten.view and _operator.getitem, so that the partitioner will not create graphs that only contain these non-compute ops

  • allowed_single_node_partition_ops (Optional[Sequence[str]]): A set of ops that are allowed to be in a single node partition.

The `OperatorSupportBase <>`__ class is used by the partitioner to determine if a specific node in the graph belongs in the partition. This is done by overriding the is_node_supported function. You can chain multiple OperatorSupportBase by using `chain <>`__(which returns False if any of the OperatorSupportBase return False) and `any_chain <>`__ (which returns True if any of the OperatorSupportBase returns True).

An example:

from torch.fx.passes.infra.partitioner import CapabilityBasedPartitioner
from torch.fx.passes.operator_support import any_chain, OperatorSupportBase

class AddMulOperatorSupport(OperatorSupportBase):
    def is_node_supported(self, submodules, node: torch.fx.Node) -> bool:
        return node.op == "call_function" and in [
            torch.ops.aten.add.Tensor, torch.ops.aten.mul.Tensor,

capability_partitioner = CapabilityBasedPartitioner(

# Returns a list of partitions (list of nodes that belong in each partition)
partition_list = capability_partitioner.propose_partitions()
# Fuses the partitions into graph modules and inserts `call_module` nodes in the graph
fused_graph_module = capability_partitioner.fuse_partitions(partition_list)


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