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TorchScript

TorchScript is a way to create serializable and optimizable models from PyTorch code. Any TorchScript program can be saved from a Python process and loaded in a process where there is no Python dependency.

We provide tools to incrementally transition a model from a pure Python program to a TorchScript program that can be run independently from Python, such as in a standalone C++ program. This makes it possible to train models in PyTorch using familiar tools in Python and then export the model via TorchScript to a production environment where Python programs may be disadvantageous for performance and multi-threading reasons.

For a gentle introduction to TorchScript, see the Introduction to TorchScript tutorial.

For an end-to-end example of converting a PyTorch model to TorchScript and running it in C++, see the Loading a PyTorch Model in C++ tutorial.

Creating TorchScript Code

script(obj[, optimize, _frames_up, _rcb])

Scripting a function or nn.Module will inspect the source code, compile it as TorchScript code using the TorchScript compiler, and return a ScriptModule or ScriptFunction.

trace(func, example_inputs[, optimize, …])

Trace a function and return an executable or ScriptFunction that will be optimized using just-in-time compilation.

script_if_tracing(fn)

Compiles fn when it is first called during tracing.

trace_module(mod, inputs[, optimize, …])

Trace a module and return an executable ScriptModule that will be optimized using just-in-time compilation.

fork(func, *args, **kwargs)

Creates an asynchronous task executing func and a reference to the value of the result of this execution.

wait(future)

Forces completion of a torch.jit.Future[T] asynchronous task, returning the result of the task.

ScriptModule()

ScriptModule``s wrap a C++ ``torch::jit::Module.

ScriptFunction

Functionally equivalent to a ScriptModule, but represents a single function and does not have any attributes or Parameters.

freeze(mod[, preserved_attrs])

Freezing a ScriptModule will clone it and attempt to inline the cloned module’s submodules, parameters, and attributes as constants in the TorchScript IR Graph.

save(m, f[, _extra_files])

Save an offline version of this module for use in a separate process.

load(f[, map_location, _extra_files])

Load a ScriptModule or ScriptFunction previously saved with torch.jit.save

ignore([drop])

This decorator indicates to the compiler that a function or method should be ignored and left as a Python function.

unused(fn)

This decorator indicates to the compiler that a function or method should be ignored and replaced with the raising of an exception.

isinstance(obj, target_type)

This function provides for conatiner type refinement in TorchScript.

Mixing Tracing and Scripting

In many cases either tracing or scripting is an easier approach for converting a model to TorchScript. Tracing and scripting can be composed to suit the particular requirements of a part of a model.

Scripted functions can call traced functions. This is particularly useful when you need to use control-flow around a simple feed-forward model. For instance the beam search of a sequence to sequence model will typically be written in script but can call an encoder module generated using tracing.

Example (calling a traced function in script):

import torch

def foo(x, y):
    return 2 * x + y

traced_foo = torch.jit.trace(foo, (torch.rand(3), torch.rand(3)))

@torch.jit.script
def bar(x):
    return traced_foo(x, x)

Traced functions can call script functions. This is useful when a small part of a model requires some control-flow even though most of the model is just a feed-forward network. Control-flow inside of a script function called by a traced function is preserved correctly.

Example (calling a script function in a traced function):

import torch

@torch.jit.script
def foo(x, y):
    if x.max() > y.max():
        r = x
    else:
        r = y
    return r


def bar(x, y, z):
    return foo(x, y) + z

traced_bar = torch.jit.trace(bar, (torch.rand(3), torch.rand(3), torch.rand(3)))

This composition also works for nn.Modules as well, where it can be used to generate a submodule using tracing that can be called from the methods of a script module.

Example (using a traced module):

import torch
import torchvision

class MyScriptModule(torch.nn.Module):
    def __init__(self):
        super(MyScriptModule, self).__init__()
        self.means = torch.nn.Parameter(torch.tensor([103.939, 116.779, 123.68])
                                        .resize_(1, 3, 1, 1))
        self.resnet = torch.jit.trace(torchvision.models.resnet18(),
                                      torch.rand(1, 3, 224, 224))

    def forward(self, input):
        return self.resnet(input - self.means)

my_script_module = torch.jit.script(MyScriptModule())

TorchScript Language

TorchScript is a statically typed subset of Python, so many Python features apply directly to TorchScript. See the full TorchScript Language Reference for details.

Built-in Functions and Modules

TorchScript supports the use of most PyTorch functions and many Python built-ins. See TorchScript Builtins for a full reference of supported functions.

PyTorch Functions and Modules

TorchScript supports a subset of the tensor and neural network functions that PyTorch provides. Most methods on Tensor as well as functions in the torch namespace, all functions in torch.nn.functional and most modules from torch.nn are supported in TorchScript.

See TorchScript Unsupported Pytorch Constructs for a list of unsupported PyTorch functions and modules.

Python Functions and Modules

Many of Python’s built-in functions are supported in TorchScript. The math module is also supported (see math Module for details), but no other Python modules (built-in or third party) are supported.

Python Language Reference Comparison

For a full listing of supported Python features, see Python Language Reference Coverage.

Debugging

Disable JIT for Debugging

PYTORCH_JIT

Setting the environment variable PYTORCH_JIT=0 will disable all script and tracing annotations. If there is hard-to-debug error in one of your TorchScript models, you can use this flag to force everything to run using native Python. Since TorchScript (scripting and tracing) is disabled with this flag, you can use tools like pdb to debug the model code. For example:

@torch.jit.script
def scripted_fn(x : torch.Tensor):
    for i in range(12):
        x = x + x
    return x

def fn(x):
    x = torch.neg(x)
    import pdb; pdb.set_trace()
    return scripted_fn(x)

traced_fn = torch.jit.trace(fn, (torch.rand(4, 5),))
traced_fn(torch.rand(3, 4))

Debugging this script with pdb works except for when we invoke the @torch.jit.script function. We can globally disable JIT, so that we can call the @torch.jit.script function as a normal Python function and not compile it. If the above script is called disable_jit_example.py, we can invoke it like so:

$ PYTORCH_JIT=0 python disable_jit_example.py

and we will be able to step into the @torch.jit.script function as a normal Python function. To disable the TorchScript compiler for a specific function, see @torch.jit.ignore.

Inspecting Code

TorchScript provides a code pretty-printer for all ScriptModule instances. This pretty-printer gives an interpretation of the script method’s code as valid Python syntax. For example:

@torch.jit.script
def foo(len):
    # type: (int) -> torch.Tensor
    rv = torch.zeros(3, 4)
    for i in range(len):
        if i < 10:
            rv = rv - 1.0
        else:
            rv = rv + 1.0
    return rv

print(foo.code)

A ScriptModule with a single forward method will have an attribute code, which you can use to inspect the ScriptModule’s code. If the ScriptModule has more than one method, you will need to access .code on the method itself and not the module. We can inspect the code of a method named foo on a ScriptModule by accessing .foo.code. The example above produces this output:

def foo(len: int) -> Tensor:
    rv = torch.zeros([3, 4], dtype=None, layout=None, device=None, pin_memory=None)
    rv0 = rv
    for i in range(len):
        if torch.lt(i, 10):
            rv1 = torch.sub(rv0, 1., 1)
        else:
            rv1 = torch.add(rv0, 1., 1)
        rv0 = rv1
    return rv0

This is TorchScript’s compilation of the code for the forward method. You can use this to ensure TorchScript (tracing or scripting) has captured your model code correctly.

Interpreting Graphs

TorchScript also has a representation at a lower level than the code pretty- printer, in the form of IR graphs.

TorchScript uses a static single assignment (SSA) intermediate representation (IR) to represent computation. The instructions in this format consist of ATen (the C++ backend of PyTorch) operators and other primitive operators, including control flow operators for loops and conditionals. As an example:

@torch.jit.script
def foo(len):
    # type: (int) -> torch.Tensor
    rv = torch.zeros(3, 4)
    for i in range(len):
        if i < 10:
            rv = rv - 1.0
        else:
            rv = rv + 1.0
    return rv

print(foo.graph)

graph follows the same rules described in the Inspecting Code section with regard to forward method lookup.

The example script above produces the graph:

graph(%len.1 : int):
  %24 : int = prim::Constant[value=1]()
  %17 : bool = prim::Constant[value=1]() # test.py:10:5
  %12 : bool? = prim::Constant()
  %10 : Device? = prim::Constant()
  %6 : int? = prim::Constant()
  %1 : int = prim::Constant[value=3]() # test.py:9:22
  %2 : int = prim::Constant[value=4]() # test.py:9:25
  %20 : int = prim::Constant[value=10]() # test.py:11:16
  %23 : float = prim::Constant[value=1]() # test.py:12:23
  %4 : int[] = prim::ListConstruct(%1, %2)
  %rv.1 : Tensor = aten::zeros(%4, %6, %6, %10, %12) # test.py:9:10
  %rv : Tensor = prim::Loop(%len.1, %17, %rv.1) # test.py:10:5
    block0(%i.1 : int, %rv.14 : Tensor):
      %21 : bool = aten::lt(%i.1, %20) # test.py:11:12
      %rv.13 : Tensor = prim::If(%21) # test.py:11:9
        block0():
          %rv.3 : Tensor = aten::sub(%rv.14, %23, %24) # test.py:12:18
          -> (%rv.3)
        block1():
          %rv.6 : Tensor = aten::add(%rv.14, %23, %24) # test.py:14:18
          -> (%rv.6)
      -> (%17, %rv.13)
  return (%rv)

Take the instruction %rv.1 : Tensor = aten::zeros(%4, %6, %6, %10, %12) # test.py:9:10 for example.

  • %rv.1 : Tensor means we assign the output to a (unique) value named rv.1, that value is of Tensor type and that we do not know its concrete shape.

  • aten::zeros is the operator (equivalent to torch.zeros) and the input list (%4, %6, %6, %10, %12) specifies which values in scope should be passed as inputs. The schema for built-in functions like aten::zeros can be found at Builtin Functions.

  • # test.py:9:10 is the location in the original source file that generated this instruction. In this case, it is a file named test.py, on line 9, and at character 10.

Notice that operators can also have associated blocks, namely the prim::Loop and prim::If operators. In the graph print-out, these operators are formatted to reflect their equivalent source code forms to facilitate easy debugging.

Graphs can be inspected as shown to confirm that the computation described by a ScriptModule is correct, in both automated and manual fashion, as described below.

Tracer

Tracing Edge Cases

There are some edge cases that exist where the trace of a given Python function/module will not be representative of the underlying code. These cases can include:

  • Tracing of control flow that is dependent on inputs (e.g. tensor shapes)

  • Tracing of in-place operations of tensor views (e.g. indexing on the left-hand side of an assignment)

Note that these cases may in fact be traceable in the future.

Automatic Trace Checking

One way to automatically catch many errors in traces is by using check_inputs on the torch.jit.trace() API. check_inputs takes a list of tuples of inputs that will be used to re-trace the computation and verify the results. For example:

def loop_in_traced_fn(x):
    result = x[0]
    for i in range(x.size(0)):
        result = result * x[i]
    return result

inputs = (torch.rand(3, 4, 5),)
check_inputs = [(torch.rand(4, 5, 6),), (torch.rand(2, 3, 4),)]

traced = torch.jit.trace(loop_in_traced_fn, inputs, check_inputs=check_inputs)

Gives us the following diagnostic information:

ERROR: Graphs differed across invocations!
Graph diff:

            graph(%x : Tensor) {
            %1 : int = prim::Constant[value=0]()
            %2 : int = prim::Constant[value=0]()
            %result.1 : Tensor = aten::select(%x, %1, %2)
            %4 : int = prim::Constant[value=0]()
            %5 : int = prim::Constant[value=0]()
            %6 : Tensor = aten::select(%x, %4, %5)
            %result.2 : Tensor = aten::mul(%result.1, %6)
            %8 : int = prim::Constant[value=0]()
            %9 : int = prim::Constant[value=1]()
            %10 : Tensor = aten::select(%x, %8, %9)
        -   %result : Tensor = aten::mul(%result.2, %10)
        +   %result.3 : Tensor = aten::mul(%result.2, %10)
        ?          ++
            %12 : int = prim::Constant[value=0]()
            %13 : int = prim::Constant[value=2]()
            %14 : Tensor = aten::select(%x, %12, %13)
        +   %result : Tensor = aten::mul(%result.3, %14)
        +   %16 : int = prim::Constant[value=0]()
        +   %17 : int = prim::Constant[value=3]()
        +   %18 : Tensor = aten::select(%x, %16, %17)
        -   %15 : Tensor = aten::mul(%result, %14)
        ?     ^                                 ^
        +   %19 : Tensor = aten::mul(%result, %18)
        ?     ^                                 ^
        -   return (%15);
        ?             ^
        +   return (%19);
        ?             ^
            }

This message indicates to us that the computation differed between when we first traced it and when we traced it with the check_inputs. Indeed, the loop within the body of loop_in_traced_fn depends on the shape of the input x, and thus when we try another x with a different shape, the trace differs.

In this case, data-dependent control flow like this can be captured using torch.jit.script() instead:

def fn(x):
    result = x[0]
    for i in range(x.size(0)):
        result = result * x[i]
    return result

inputs = (torch.rand(3, 4, 5),)
check_inputs = [(torch.rand(4, 5, 6),), (torch.rand(2, 3, 4),)]

scripted_fn = torch.jit.script(fn)
print(scripted_fn.graph)
#print(str(scripted_fn.graph).strip())

for input_tuple in [inputs] + check_inputs:
    torch.testing.assert_allclose(fn(*input_tuple), scripted_fn(*input_tuple))

Which produces:

graph(%x : Tensor) {
    %5 : bool = prim::Constant[value=1]()
    %1 : int = prim::Constant[value=0]()
    %result.1 : Tensor = aten::select(%x, %1, %1)
    %4 : int = aten::size(%x, %1)
    %result : Tensor = prim::Loop(%4, %5, %result.1)
    block0(%i : int, %7 : Tensor) {
        %10 : Tensor = aten::select(%x, %1, %i)
        %result.2 : Tensor = aten::mul(%7, %10)
        -> (%5, %result.2)
    }
    return (%result);
}

Tracer Warnings

The tracer produces warnings for several problematic patterns in traced computation. As an example, take a trace of a function that contains an in-place assignment on a slice (a view) of a Tensor:

def fill_row_zero(x):
    x[0] = torch.rand(*x.shape[1:2])
    return x

traced = torch.jit.trace(fill_row_zero, (torch.rand(3, 4),))
print(traced.graph)

Produces several warnings and a graph which simply returns the input:

fill_row_zero.py:4: TracerWarning: There are 2 live references to the data region being modified when tracing in-place operator copy_ (possibly due to an assignment). This might cause the trace to be incorrect, because all other views that also reference this data will not reflect this change in the trace! On the other hand, if all other views use the same memory chunk, but are disjoint (e.g. are outputs of torch.split), this might still be safe.
    x[0] = torch.rand(*x.shape[1:2])
fill_row_zero.py:6: TracerWarning: Output nr 1. of the traced function does not match the corresponding output of the Python function. Detailed error:
Not within tolerance rtol=1e-05 atol=1e-05 at input[0, 1] (0.09115803241729736 vs. 0.6782537698745728) and 3 other locations (33.00%)
    traced = torch.jit.trace(fill_row_zero, (torch.rand(3, 4),))
graph(%0 : Float(3, 4)) {
    return (%0);
}

We can fix this by modifying the code to not use the in-place update, but rather build up the result tensor out-of-place with torch.cat:

def fill_row_zero(x):
    x = torch.cat((torch.rand(1, *x.shape[1:2]), x[1:2]), dim=0)
    return x

traced = torch.jit.trace(fill_row_zero, (torch.rand(3, 4),))
print(traced.graph)

Frequently Asked Questions

Q: I would like to train a model on GPU and do inference on CPU. What are the best practices?

First convert your model from GPU to CPU and then save it, like so:

cpu_model = gpu_model.cpu()
sample_input_cpu = sample_input_gpu.cpu()
traced_cpu = torch.jit.trace(traced_cpu, sample_input_cpu)
torch.jit.save(traced_cpu, "cpu.pth")

traced_gpu = torch.jit.trace(traced_gpu, sample_input_gpu)
torch.jit.save(traced_gpu, "gpu.pth")

# ... later, when using the model:

if use_gpu:
  model = torch.jit.load("gpu.pth")
else:
  model = torch.jit.load("cpu.pth")

model(input)

This is recommended because the tracer may witness tensor creation on a specific device, so casting an already-loaded model may have unexpected effects. Casting the model before saving it ensures that the tracer has the correct device information.

Q: How do I store attributes on a ScriptModule?

Say we have a model like:

import torch

class Model(torch.nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.x = 2

    def forward(self):
        return self.x

m = torch.jit.script(Model())

If Model is instantiated it will result in a compilation error since the compiler doesn’t know about x. There are 4 ways to inform the compiler of attributes on ScriptModule:

1. nn.Parameter - Values wrapped in nn.Parameter will work as they do on nn.Modules

2. register_buffer - Values wrapped in register_buffer will work as they do on nn.Modules. This is equivalent to an attribute (see 4) of type Tensor.

3. Constants - Annotating a class member as Final (or adding it to a list called __constants__ at the class definition level) will mark the contained names as constants. Constants are saved directly in the code of the model. See builtin-constants for details.

4. Attributes - Values that are a supported type can be added as mutable attributes. Most types can be inferred but some may need to be specified, see module attributes for details.

Q: I would like to trace module’s method but I keep getting this error:

RuntimeError: Cannot insert a Tensor that requires grad as a constant. Consider making it a parameter or input, or detaching the gradient

This error usually means that the method you are tracing uses a module’s parameters and you are passing the module’s method instead of the module instance (e.g. my_module_instance.forward vs my_module_instance).

  • Invoking trace with a module’s method captures module parameters (which may require gradients) as constants.

  • On the other hand, invoking trace with module’s instance (e.g. my_module) creates a new module and correctly copies parameters into the new module, so they can accumulate gradients if required.

To trace a specific method on a module, see torch.jit.trace_module

Appendix

Migrating to PyTorch 1.2 Recursive Scripting API

This section details the changes to TorchScript in PyTorch 1.2. If you are new to TorchScript you can skip this section. There are two main changes to the TorchScript API with PyTorch 1.2.

1. torch.jit.script will now attempt to recursively compile functions, methods, and classes that it encounters. Once you call torch.jit.script, compilation is “opt-out”, rather than “opt-in”.

2. torch.jit.script(nn_module_instance) is now the preferred way to create ScriptModules, instead of inheriting from torch.jit.ScriptModule. These changes combine to provide a simpler, easier-to-use API for converting your nn.Modules into ScriptModules, ready to be optimized and executed in a non-Python environment.

The new usage looks like this:

import torch
import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

my_model = Model()
my_scripted_model = torch.jit.script(my_model)
  • The module’s forward is compiled by default. Methods called from forward are lazily compiled in the order they are used in forward.

  • To compile a method other than forward that is not called from forward, add @torch.jit.export.

  • To stop the compiler from compiling a method, add @torch.jit.ignore or @torch.jit.unused. @ignore leaves the

  • method as a call to python, and @unused replaces it with an exception. @ignored cannot be exported; @unused can.

  • Most attribute types can be inferred, so torch.jit.Attribute is not necessary. For empty container types, annotate their types using PEP 526-style class annotations.

  • Constants can be marked with a Final class annotation instead of adding the name of the member to __constants__.

  • Python 3 type hints can be used in place of torch.jit.annotate

As a result of these changes, the following items are considered deprecated and should not appear in new code:
  • The @torch.jit.script_method decorator

  • Classes that inherit from torch.jit.ScriptModule

  • The torch.jit.Attribute wrapper class

  • The __constants__ array

  • The torch.jit.annotate function

Modules

Warning

The @torch.jit.ignore annotation’s behavior changes in PyTorch 1.2. Before PyTorch 1.2 the @ignore decorator was used to make a function or method callable from code that is exported. To get this functionality back, use @torch.jit.unused(). @torch.jit.ignore is now equivalent to @torch.jit.ignore(drop=False). See @torch.jit.ignore and @torch.jit.unused for details.

When passed to the torch.jit.script function, a torch.nn.Module’s data is copied to a ScriptModule and the TorchScript compiler compiles the module. The module’s forward is compiled by default. Methods called from forward are lazily compiled in the order they are used in forward, as well as any @torch.jit.export methods.

torch.jit.export(fn)[source]

This decorator indicates that a method on an nn.Module is used as an entry point into a ScriptModule and should be compiled.

forward implicitly is assumed to be an entry point, so it does not need this decorator. Functions and methods called from forward are compiled as they are seen by the compiler, so they do not need this decorator either.

Example (using @torch.jit.export on a method):

import torch
import torch.nn as nn

class MyModule(nn.Module):
    def implicitly_compiled_method(self, x):
        return x + 99

    # `forward` is implicitly decorated with `@torch.jit.export`,
    # so adding it here would have no effect
    def forward(self, x):
        return x + 10

    @torch.jit.export
    def another_forward(self, x):
        # When the compiler sees this call, it will compile
        # `implicitly_compiled_method`
        return self.implicitly_compiled_method(x)

    def unused_method(self, x):
        return x - 20

# `m` will contain compiled methods:
#     `forward`
#     `another_forward`
#     `implicitly_compiled_method`
# `unused_method` will not be compiled since it was not called from
# any compiled methods and wasn't decorated with `@torch.jit.export`
m = torch.jit.script(MyModule())

Functions

Functions don’t change much, they can be decorated with @torch.jit.ignore or torch.jit.unused if needed.

# Same behavior as pre-PyTorch 1.2
@torch.jit.script
def some_fn():
    return 2

# Marks a function as ignored, if nothing
# ever calls it then this has no effect
@torch.jit.ignore
def some_fn2():
    return 2

# As with ignore, if nothing calls it then it has no effect.
# If it is called in script it is replaced with an exception.
@torch.jit.unused
def some_fn3():
  import pdb; pdb.set_trace()
  return 4

# Doesn't do anything, this function is already
# the main entry point
@torch.jit.export
def some_fn4():
    return 2

TorchScript Classes

Warning

TorchScript class support is experimental. Currently it is best suited for simple record-like types (think a NamedTuple with methods attached).

Everything in a user defined TorchScript Class is exported by default, functions can be decorated with @torch.jit.ignore if needed.

Attributes

The TorchScript compiler needs to know the types of module attributes. Most types can be inferred from the value of the member. Empty lists and dicts cannot have their types inferred and must have their types annotated with PEP 526-style class annotations. If a type cannot be inferred and is not explicitly annotated, it will not be added as an attribute to the resulting ScriptModule

Old API:

from typing import Dict
import torch

class MyModule(torch.jit.ScriptModule):
    def __init__(self):
        super(MyModule, self).__init__()
        self.my_dict = torch.jit.Attribute({}, Dict[str, int])
        self.my_int = torch.jit.Attribute(20, int)

m = MyModule()

New API:

from typing import Dict

class MyModule(torch.nn.Module):
    my_dict: Dict[str, int]

    def __init__(self):
        super(MyModule, self).__init__()
        # This type cannot be inferred and must be specified
        self.my_dict = {}

        # The attribute type here is inferred to be `int`
        self.my_int = 20

    def forward(self):
        pass

m = torch.jit.script(MyModule())

Constants

The Final type constructor can be used to mark members as constant. If members are not marked constant, they will be copied to the resulting ScriptModule as an attribute. Using Final opens opportunities for optimization if the value is known to be fixed and gives additional type safety.

Old API:

class MyModule(torch.jit.ScriptModule):
    __constants__ = ['my_constant']

    def __init__(self):
        super(MyModule, self).__init__()
        self.my_constant = 2

    def forward(self):
        pass
m = MyModule()

New API:

try:
    from typing_extensions import Final
except:
    # If you don't have `typing_extensions` installed, you can use a
    # polyfill from `torch.jit`.
    from torch.jit import Final

class MyModule(torch.nn.Module):

    my_constant: Final[int]

    def __init__(self):
        super(MyModule, self).__init__()
        self.my_constant = 2

    def forward(self):
        pass

m = torch.jit.script(MyModule())

Variables

Containers are assumed to have type Tensor and be non-optional (see Default Types for more information). Previously, torch.jit.annotate was used to tell the TorchScript compiler what the type should be. Python 3 style type hints are now supported.

import torch
from typing import Dict, Optional

@torch.jit.script
def make_dict(flag: bool):
    x: Dict[str, int] = {}
    x['hi'] = 2
    b: Optional[int] = None
    if flag:
        b = 2
    return x, b

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