optree 0.13.1

Optimized PyTree Utilities.

OpTree

Optimized PyTree Utilities.

---

Table of Contents

• Installation
• PyTrees
  • Tree Nodes and Leaves
    • Built-in PyTree Node Types
    • Registering a Container-like Custom Type as Non-leaf Nodes
    • Notes about the PyTree Type Registry
  • None is Non-leaf Node vs. None is Leaf
  • Key Ordering for Dictionaries
• Benchmark
  • Tree Flatten
  • Tree UnFlatten
  • Tree Flatten with Path
  • Tree Copy
  • Tree Map
  • Tree Map (nargs)
  • Tree Map with Path
  • Tree Map with Path (nargs)
• Changelog
• License

---

Installation

Install from PyPI ( / ):

pip3 install --upgrade optree

Install from conda-forge ():

conda install -c conda-forge optree

Install the latest version from GitHub:

pip3 install git+https://github.com/metaopt/optree.git#egg=optree

Or, clone this repo and install manually:

git clone --depth=1 https://github.com/metaopt/optree.git
cd optree
pip3 install .

Compiling from the source requires Python 3.7+, a compiler (gcc / clang / icc / cl.exe) that supports C++20 and a cmake installation.

---

PyTrees

A PyTree is a recursive structure that can be an arbitrarily nested Python container (e.g., tuple, list, dict, OrderedDict, NamedTuple, etc.) or an opaque Python object. The key concepts of tree operations are tree flattening and its inverse (tree unflattening). Additional tree operations can be performed based on these two basic functions (e.g., tree_map = tree_unflatten ∘ map ∘ tree_flatten).

Tree flattening is traversing the entire tree in a left-to-right depth-first manner and returning the leaves of the tree in a deterministic order.

>>> tree = {'b': (2, [3, 4]), 'a': 1, 'c': 5, 'd': 6}
>>> optree.tree_flatten(tree)
([1, 2, 3, 4, 5, 6], PyTreeSpec({'a': *, 'b': (*, [*, *]), 'c': *, 'd': *}))
>>> optree.tree_flatten(1)
([1], PyTreeSpec(*))
>>> optree.tree_flatten(None)
([], PyTreeSpec(None))

This usually implies that the equal pytrees return equal lists of leaves and the same tree structure. See also section Key Ordering for Dictionaries.

>>> {'a': [1, 2], 'b': [3]} == {'b': [3], 'a': [1, 2]}
True
>>> optree.tree_leaves({'a': [1, 2], 'b': [3]}) == optree.tree_leaves({'b': [3], 'a': [1, 2]})
True
>>> optree.tree_structure({'a': [1, 2], 'b': [3]}) == optree.tree_structure({'b': [3], 'a': [1, 2]})
True

Tree Nodes and Leaves

A tree is a collection of non-leaf nodes and leaf nodes, where the leaf nodes have no children to flatten. optree.tree_flatten(...) will flatten the tree and return a list of leaf nodes while the non-leaf nodes will store in the tree specification.

Built-in PyTree Node Types

OpTree out-of-box supports the following Python container types in the registry:

• tuple
• list
• dict
• collections.namedtuple and its subclasses
• collections.OrderedDict
• collections.defaultdict
• collections.deque
• PyStructSequence types created by C API PyStructSequence_NewType

which are considered non-leaf nodes in the tree. Python objects that the type is not registered will be treated as leaf nodes. The registry lookup uses the is operator to determine whether the type is matched. So subclasses will need to explicitly register in the registry, otherwise, an object of that type will be considered a leaf. The NoneType is a special case discussed in section None is non-leaf Node vs. None is Leaf.

Registering a Container-like Custom Type as Non-leaf Nodes

A container-like Python type can be registered in the type registry with a pair of functions that specify:

• flatten_func(container) -> (children, metadata, entries): convert an instance of the container type to a (children, metadata, entries) triple, where children is an iterable of subtrees and entries is an iterable of path entries of the container (e.g., indices or keys).
• unflatten_func(metadata, children) -> container: convert such a pair back to an instance of the container type.

The metadata is some necessary data apart from the children to reconstruct the container, e.g., the keys of the dictionary (the children are values).

The entries can be omitted (only returns a pair) or is optional to implement (returns None). If so, use range(len(children)) (i.e., flat indices) as path entries of the current node. The function signature can be flatten_func(container) -> (children, metadata) or flatten_func(container) -> (children, metadata, None).

The following examples show how to register custom types and utilize them for tree_flatten and tree_map. Please refer to section Notes about the PyTree Type Registry for more information.

# Registry a Python type with lambda functions
optree.register_pytree_node(
    set,
    # (set) -> (children, metadata, None)
    lambda s: (sorted(s), None, None),
    # (metadata, children) -> (set)
    lambda _, children: set(children),
    namespace='set',
)

# Register a Python type into a namespace
import torch

class Torch2NumpyEntry(optree.PyTreeEntry):
    def __call__(self, obj):
        assert self.entry == 0
        return obj.cpu().detach().numpy()

    def codify(self, node=''):
        assert self.entry == 0
        return f'{node}.cpu().detach().numpy()'

optree.register_pytree_node(
    torch.Tensor,
    # (tensor) -> (children, metadata)
    flatten_func=lambda tensor: (
        (tensor.cpu().detach().numpy(),),
        {'dtype': tensor.dtype, 'device': tensor.device, 'requires_grad': tensor.requires_grad},
    ),
    # (metadata, children) -> tensor
    unflatten_func=lambda metadata, children: torch.tensor(children[0], **metadata),
    path_entry_type=Torch2NumpyEntry,
    namespace='torch2numpy',
)

>>> tree = {'weight': torch.ones(size=(1, 2)).cuda(), 'bias': torch.zeros(size=(2,))}
>>> tree
{'weight': tensor([[1., 1.]], device='cuda:0'), 'bias': tensor([0., 0.])}

# Flatten without specifying the namespace
>>> optree.tree_flatten(tree)  # `torch.Tensor`s are leaf nodes
([tensor([0., 0.]), tensor([[1., 1.]], device='cuda:0')], PyTreeSpec({'bias': *, 'weight': *}))

# Flatten with the namespace
>>> leaves, treespec = optree.tree_flatten(tree, namespace='torch2numpy')
>>> leaves, treespec
(
    [array([0., 0.], dtype=float32), array([[1., 1.]], dtype=float32)],
    PyTreeSpec(
        {
            'bias': CustomTreeNode(Tensor[{'dtype': torch.float32, 'device': device(type='cpu'), 'requires_grad': False}], [*]),
            'weight': CustomTreeNode(Tensor[{'dtype': torch.float32, 'device': device(type='cuda', index=0), 'requires_grad': False}], [*])
        },
        namespace='torch2numpy'
    )
)

# `entries` are not defined and use `range(len(children))`
>>> optree.tree_paths(tree, namespace='torch2numpy')
[('bias', 0), ('weight', 0)]

# Custom path entry type defines the pytree access behavior
>>> optree.tree_accessors(tree, namespace='torch2numpy')
[
    PyTreeAccessor(*['bias'].cpu().detach().numpy(), (MappingEntry(key='bias', type=<class 'dict'>), Torch2NumpyEntry(entry=0, type=<class 'torch.Tensor'>))),
    PyTreeAccessor(*['weight'].cpu().detach().numpy(), (MappingEntry(key='weight', type=<class 'dict'>), Torch2NumpyEntry(entry=0, type=<class 'torch.Tensor'>)))
]

# Unflatten back to a copy of the original object
>>> optree.tree_unflatten(treespec, leaves)
{'weight': tensor([[1., 1.]], device='cuda:0'), 'bias': tensor([0., 0.])}

Users can also extend the pytree registry by decorating the custom class and defining an instance method tree_flatten and a class method tree_unflatten.

from collections import UserDict

@optree.register_pytree_node_class(namespace='mydict')
class MyDict(UserDict):
    TREE_PATH_ENTRY_TYPE = optree.MappingEntry  # used by accessor APIs

    def tree_flatten(self):  # -> (children, metadata, entries)
        reversed_keys = sorted(self.keys(), reverse=True)
        return (
            [self[key] for key in reversed_keys],  # children
            reversed_keys,  # metadata
            reversed_keys,  # entries
        )

    @classmethod
    def tree_unflatten(cls, metadata, children):
        return cls(zip(metadata, children))

>>> tree = MyDict(b=4, a=(2, 3), c=MyDict({'d': 5, 'f': 6}))

# Flatten without specifying the namespace
>>> optree.tree_flatten_with_path(tree)  # `MyDict`s are leaf nodes
(
    [()],
    [MyDict(b=4, a=(2, 3), c=MyDict({'d': 5, 'f': 6}))],
    PyTreeSpec(*)
)

# Flatten with the namespace
>>> optree.tree_flatten_with_path(tree, namespace='mydict')
(
    [('c', 'f'), ('c', 'd'), ('b',), ('a', 0), ('a', 1)],
    [6, 5, 4, 2, 3],
    PyTreeSpec(
        CustomTreeNode(MyDict[['c', 'b', 'a']], [CustomTreeNode(MyDict[['f', 'd']], [*, *]), *, (*, *)]),
        namespace='mydict'
    )
)
>>> optree.tree_flatten_with_accessor(tree, namespace='mydict')
(
    [
        PyTreeAccessor(*['c']['f'], (MappingEntry(key='c', type=<class 'MyDict'>), MappingEntry(key='f', type=<class 'MyDict'>))),
        PyTreeAccessor(*['c']['d'], (MappingEntry(key='c', type=<class 'MyDict'>), MappingEntry(key='d', type=<class 'MyDict'>))),
        PyTreeAccessor(*['b'], (MappingEntry(key='b', type=<class 'MyDict'>),)),
        PyTreeAccessor(*['a'][0], (MappingEntry(key='a', type=<class 'MyDict'>), SequenceEntry(index=0, type=<class 'tuple'>))),
        PyTreeAccessor(*['a'][1], (MappingEntry(key='a', type=<class 'MyDict'>), SequenceEntry(index=1, type=<class 'tuple'>)))
    ],
    [6, 5, 4, 2, 3],
    PyTreeSpec(
        CustomTreeNode(MyDict[['c', 'b', 'a']], [CustomTreeNode(MyDict[['f', 'd']], [*, *]), *, (*, *)]),
        namespace='mydict'
    )
)

Notes about the PyTree Type Registry

There are several key attributes of the pytree type registry:

1. The type registry is per-interpreter-dependent. This means registering a custom type in the registry affects all modules that use OpTree.

[!WARNING] For safety reasons, a namespace must be specified while registering a custom type. It is used to isolate the behavior of flattening and unflattening a pytree node type. This is to prevent accidental collisions between different libraries that may register the same type.

2. The elements in the type registry are immutable. Users can neither register the same type twice in the same namespace (i.e., update the type registry), nor remove a type from the type registry. To update the behavior of an already registered type, simply register it again with another namespace.

3. Users cannot modify the behavior of already registered built-in types listed in Built-in PyTree Node Types, such as key order sorting for dict and collections.defaultdict.

4. Inherited subclasses are not implicitly registered. The registry lookup uses type(obj) is registered_type rather than isinstance(obj, registered_type). Users need to register the subclasses explicitly. To register all subclasses, it is easy to implement with metaclass or __init_subclass__, for example:

   from collections import UserDict
   
   @optree.register_pytree_node_class(namespace='mydict')
   class MyDict(UserDict):
       TREE_PATH_ENTRY_TYPE = optree.MappingEntry  # used by accessor APIs
   
       def __init_subclass__(cls):  # define this in the base class
           super().__init_subclass__()
           # Register a subclass to namespace 'mydict'
           optree.register_pytree_node_class(cls, namespace='mydict')
   
       def tree_flatten(self):  # -> (children, metadata, entries)
           reversed_keys = sorted(self.keys(), reverse=True)
           return (
               [self[key] for key in reversed_keys],  # children
               reversed_keys,  # metadata
               reversed_keys,  # entries
           )
   
       @classmethod
       def tree_unflatten(cls, metadata, children):
           return cls(zip(metadata, children))
   
   # Subclasses will be automatically registered in namespace 'mydict'
   class MyAnotherDict(MyDict):
       pass
   

   >>> tree = MyDict(b=4, a=(2, 3), c=MyAnotherDict({'d': 5, 'f': 6}))
   >>> optree.tree_flatten_with_path(tree, namespace='mydict')
   (
       [('c', 'f'), ('c', 'd'), ('b',), ('a', 0), ('a', 1)],
       [6, 5, 4, 2, 3],
       PyTreeSpec(
           CustomTreeNode(MyDict[['c', 'b', 'a']], [CustomTreeNode(MyAnotherDict[['f', 'd']], [*, *]), *, (*, *)]),
           namespace='mydict'
       )
   )
   >>> optree.tree_accessors(tree, namespace='mydict')
   [
       PyTreeAccessor(*['c']['f'], (MappingEntry(key='c', type=<class 'MyDict'>), MappingEntry(key='f', type=<class 'MyAnotherDict'>))),
       PyTreeAccessor(*['c']['d'], (MappingEntry(key='c', type=<class 'MyDict'>), MappingEntry(key='d', type=<class 'MyAnotherDict'>))),
       PyTreeAccessor(*['b'], (MappingEntry(key='b', type=<class 'MyDict'>),)),
       PyTreeAccessor(*['a'][0], (MappingEntry(key='a', type=<class 'MyDict'>), SequenceEntry(index=0, type=<class 'tuple'>))),
       PyTreeAccessor(*['a'][1], (MappingEntry(key='a', type=<class 'MyDict'>), SequenceEntry(index=1, type=<class 'tuple'>)))
   ]
   

5. Be careful about the potential infinite recursion of the custom flatten function. The returned children from the custom flatten function are considered subtrees. They will be further flattened recursively. The children can have the same type as the current node. Users must design their termination condition carefully.

   import numpy as np
   import torch
   
   optree.register_pytree_node(
       np.ndarray,
       # Children are nest lists of Python objects
       lambda array: (np.atleast_1d(array).tolist(), array.ndim == 0),
       lambda scalar, rows: np.asarray(rows) if not scalar else np.asarray(rows[0]),
       namespace='numpy1',
   )
   
   optree.register_pytree_node(
       np.ndarray,
       # Children are Python objects
       lambda array: (
           list(array.ravel()),  # list(1DArray[T]) -> List[T]
           dict(shape=array.shape, dtype=array.dtype)
       ),
       lambda metadata, children: np.asarray(children, dtype=metadata['dtype']).reshape(metadata['shape']),
       namespace='numpy2',
   )
   
   optree.register_pytree_node(
       np.ndarray,
       # Returns a list of `np.ndarray`s without termination condition
       lambda array: ([array.ravel()], array.dtype),
       lambda shape, children: children[0].reshape(shape),
       namespace='numpy3',
   )
   
   optree.register_pytree_node(
       torch.Tensor,
       # Children are nest lists of Python objects
       lambda tensor: (torch.atleast_1d(tensor).tolist(), tensor.ndim == 0),
       lambda scalar, rows: torch.tensor(rows) if not scalar else torch.tensor(rows[0])),
       namespace='torch1',
   )
   
   optree.register_pytree_node(
       torch.Tensor,
       # Returns a list of `torch.Tensor`s without termination condition
       lambda tensor: (
           list(tensor.view(-1)),  # list(1DTensor[T]) -> List[0DTensor[T]] (STILL TENSORS!)
           tensor.shape
       ),
       lambda shape, children: torch.stack(children).reshape(shape),
       namespace='torch2',
   )
   

   >>> optree.tree_flatten(np.arange(9).reshape(3, 3), namespace='numpy1')
   (
       [0, 1, 2, 3, 4, 5, 6, 7, 8],
       PyTreeSpec(
           CustomTreeNode(ndarray[False], [[*, *, *], [*, *, *], [*, *, *]]),
           namespace='numpy1'
       )
   )
   # Implicitly casts `float`s to `np.float64`
   >>> optree.tree_map(lambda x: x + 1.5, np.arange(9).reshape(3, 3), namespace='numpy1')
   array([[1.5, 2.5, 3.5],
          [4.5, 5.5, 6.5],
          [7.5, 8.5, 9.5]])
   
   >>> optree.tree_flatten(np.arange(9).reshape(3, 3), namespace='numpy2')
   (
       [0, 1, 2, 3, 4, 5, 6, 7, 8],
       PyTreeSpec(
           CustomTreeNode(ndarray[{'shape': (3, 3), 'dtype': dtype('int64')}], [*, *, *, *, *, *, *, *, *]),
           namespace='numpy2'
       )
   )
   # Explicitly casts `float`s to `np.int64`
   >>> optree.tree_map(lambda x: x + 1.5, np.arange(9).reshape(3, 3), namespace='numpy2')
   array([[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9]])
   
   # Children are also `np.ndarray`s, recurse without termination condition.
   >>> optree.tree_flatten(np.arange(9).reshape(3, 3), namespace='numpy3')
   Traceback (most recent call last):
       ...
   RecursionError: Maximum recursion depth exceeded during flattening the tree.
   
   >>> optree.tree_flatten(torch.arange(9).reshape(3, 3), namespace='torch1')
   (
       [0, 1, 2, 3, 4, 5, 6, 7, 8],
       PyTreeSpec(
           CustomTreeNode(Tensor[False], [[*, *, *], [*, *, *], [*, *, *]]),
           namespace='torch1'
       )
   )
   # Implicitly casts `float`s to `torch.float32`
   >>> optree.tree_map(lambda x: x + 1.5, torch.arange(9).reshape(3, 3), namespace='torch1')
   tensor([[1.5000, 2.5000, 3.5000],
           [4.5000, 5.5000, 6.5000],
           [7.5000, 8.5000, 9.5000]])
   
   # Children are also `torch.Tensor`s, recurse without termination condition.
   >>> optree.tree_flatten(torch.arange(9).reshape(3, 3), namespace='torch2')
   Traceback (most recent call last):
       ...
   RecursionError: Maximum recursion depth exceeded during flattening the tree.
   

None is Non-leaf Node vs. None is Leaf

The None object is a special object in the Python language. It serves some of the same purposes as null (a pointer does not point to anything) in other programming languages, which denotes a variable is empty or marks default parameters. However, the None object is a singleton object rather than a pointer. It may also serve as a sentinel value. In addition, if a function has returned without any return value or the return statement is omitted, the function will also implicitly return the None object.

By default, the None object is considered a non-leaf node in the tree with arity 0, i.e., a non-leaf node that has no children. This is like the behavior of an empty tuple. While flattening a tree, it will remain in the tree structure definitions rather than in the leaves list.

>>> tree = {'b': (2, [3, 4]), 'a': 1, 'c': None, 'd': 5}
>>> optree.tree_flatten(tree)
([1, 2, 3, 4, 5], PyTreeSpec({'a': *, 'b': (*, [*, *]), 'c': None, 'd': *}))
>>> optree.tree_flatten(tree, none_is_leaf=True)
([1, 2, 3, 4, None, 5], PyTreeSpec({'a': *, 'b': (*, [*, *]), 'c': *, 'd': *}, NoneIsLeaf))
>>> optree.tree_flatten(1)
([1], PyTreeSpec(*))
>>> optree.tree_flatten(None)
([], PyTreeSpec(None))
>>> optree.tree_flatten(None, none_is_leaf=True)
([None], PyTreeSpec(*, NoneIsLeaf))

OpTree provides a keyword argument none_is_leaf to determine whether to consider the None object as a leaf, like other opaque objects. If none_is_leaf=True, the None object will be placed in the leaves list. Otherwise, the None object will remain in the tree specification (structure).

>>> import torch

>>> linear = torch.nn.Linear(in_features=3, out_features=2, bias=False)
>>> linear._parameters  # a container has None
OrderedDict({
    'weight': Parameter containing:
              tensor([[-0.6677,  0.5209,  0.3295],
                      [-0.4876, -0.3142,  0.1785]], requires_grad=True),
    'bias': None
})

>>> optree.tree_map(torch.zeros_like, linear._parameters)
OrderedDict({
    'weight': tensor([[0., 0., 0.],
                      [0., 0., 0.]]),
    'bias': None
})

>>> optree.tree_map(torch.zeros_like, linear._parameters, none_is_leaf=True)
Traceback (most recent call last):
    ...
TypeError: zeros_like(): argument 'input' (position 1) must be Tensor, not NoneType

>>> optree.tree_map(lambda t: torch.zeros_like(t) if t is not None else 0, linear._parameters, none_is_leaf=True)
OrderedDict({
    'weight': tensor([[0., 0., 0.],
                      [0., 0., 0.]]),
    'bias': 0
})

Key Ordering for Dictionaries

The built-in Python dictionary (i.e., builtins.dict) is an unordered mapping that holds the keys and values. The leaves of a dictionary are the values. Although since Python 3.6, the built-in dictionary is insertion ordered (PEP 468). The dictionary equality operator (==) does not check for key ordering. To ensure referential transparency that "equal dict" implies "equal ordering of leaves", the order of values of the dictionary is sorted by the keys. This behavior is also applied to collections.defaultdict.

>>> optree.tree_flatten({'a': [1, 2], 'b': [3]})
([1, 2, 3], PyTreeSpec({'a': [*, *], 'b': [*]}))
>>> optree.tree_flatten({'b': [3], 'a': [1, 2]})
([1, 2, 3], PyTreeSpec({'a': [*, *], 'b': [*]}))

If users want to keep the values in the insertion order in pytree traversal, they should use collections.OrderedDict, which will take the order of keys under consideration:

>>> OrderedDict([('a', [1, 2]), ('b', [3])]) == OrderedDict([('b', [3]), ('a', [1, 2])])
False
>>> optree.tree_flatten(OrderedDict([('a', [1, 2]), ('b', [3])]))
([1, 2, 3], PyTreeSpec(OrderedDict({'a': [*, *], 'b': [*]})))
>>> optree.tree_flatten(OrderedDict([('b', [3]), ('a', [1, 2])]))
([3, 1, 2], PyTreeSpec(OrderedDict({'b': [*], 'a': [*, *]})))

Since OpTree v0.9.0, the key order of the reconstructed output dictionaries from tree_unflatten is guaranteed to be consistent with the key order of the input dictionaries in tree_flatten.

>>> leaves, treespec = optree.tree_flatten({'b': [3], 'a': [1, 2]})
>>> leaves, treespec
([1, 2, 3], PyTreeSpec({'a': [*, *], 'b': [*]}))
>>> optree.tree_unflatten(treespec, leaves)
{'b': [3], 'a': [1, 2]}
>>> optree.tree_map(lambda x: x, {'b': [3], 'a': [1, 2]})
{'b': [3], 'a': [1, 2]}
>>> optree.tree_map(lambda x: x + 1, {'b': [3], 'a': [1, 2]})
{'b': [4], 'a': [2, 3]}

This property is also preserved during serialization/deserialization.

>>> leaves, treespec = optree.tree_flatten({'b': [3], 'a': [1, 2]})
>>> leaves, treespec
([1, 2, 3], PyTreeSpec({'a': [*, *], 'b': [*]}))
>>> restored_treespec = pickle.loads(pickle.dumps(treespec))
>>> optree.tree_unflatten(treespec, leaves)
{'b': [3], 'a': [1, 2]}
>>> optree.tree_unflatten(restored_treespec, leaves)
{'b': [3], 'a': [1, 2]}

[!NOTE] Note that there are no restrictions on the dict to require the keys to be comparable (sortable). There can be multiple types of keys in the dictionary. The keys are sorted in ascending order by key=lambda k: k first if capable otherwise fallback to key=lambda k: (f'{k.__class__.__module__}.{k.__class__.__qualname__}', k). This handles most cases.

>>> sorted({1: 2, 1.5: 1}.keys())
[1, 1.5]
>>> sorted({'a': 3, 1: 2, 1.5: 1}.keys())
Traceback (most recent call last):
    ...
TypeError: '<' not supported between instances of 'int' and 'str'
>>> sorted({'a': 3, 1: 2, 1.5: 1}.keys(), key=lambda k: (f'{k.__class__.__module__}.{k.__class__.__qualname__}', k))
[1.5, 1, 'a']

---

Benchmark

We benchmark the performance of:

• tree flatten
• tree unflatten
• tree copy (i.e., unflatten(flatten(...)))
• tree map

compared with the following libraries:

• OpTree (@v0.9.0)
• JAX XLA (jax[cpu] == 0.4.6)
• PyTorch (torch == 2.0.0)
• DM-Tree (dm-tree == 0.1.8)

Average Time Cost (↓)	OpTree (v0.9.0)	JAX XLA (v0.4.6)	PyTorch (v2.0.0)	DM-Tree (v0.1.8)
Tree Flatten	x1.00	2.33	22.05	1.12
Tree UnFlatten	x1.00	2.69	4.28	16.23
Tree Flatten with Path	x1.00	16.16	Not Supported	27.59
Tree Copy	x1.00	2.56	9.97	11.02
Tree Map	x1.00	2.56	9.58	10.62
Tree Map (nargs)	x1.00	2.89	Not Supported	31.33
Tree Map with Path	x1.00	7.23	Not Supported	19.66
Tree Map with Path (nargs)	x1.00	6.56	Not Supported	29.61

All results are reported on a workstation with an AMD Ryzen 9 5950X CPU @ 4.45GHz in an isolated virtual environment with Python 3.10.9. Run with the following commands:

conda create --name optree-benchmark anaconda::python=3.10 --yes --no-default-packages
conda activate optree-benchmark
python3 -m pip install --editable '.[benchmark]' --extra-index-url https://download.pytorch.org/whl/cpu
python3 benchmark.py --number=10000 --repeat=5

The test inputs are nested containers (i.e., pytrees) extracted from torch.nn.Module objects. They are:

tiny_mlp = nn.Sequential(
    nn.Linear(1, 1, bias=True),
    nn.BatchNorm1d(1, affine=True, track_running_stats=True),
    nn.ReLU(),
    nn.Linear(1, 1, bias=False),
    nn.Sigmoid(),
)

and AlexNet, ResNet18, ResNet34, ResNet50, ResNet101, ResNet152, VisionTransformerH14 (ViT-H/14), and SwinTransformerB (Swin-B) from torchvsion. Please refer to benchmark.py for more details.

Tree Flatten

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	29.70	71.06	583.66	31.32	2.39	19.65	1.05
AlexNet	188	103.92	262.56	2304.36	119.61	2.53	22.17	1.15
ResNet18	698	368.06	852.69	8440.31	420.43	2.32	22.93	1.14
ResNet34	1242	644.96	1461.55	14498.81	712.81	2.27	22.48	1.11
ResNet50	1702	919.95	2080.58	20995.96	1006.42	2.26	22.82	1.09
ResNet101	3317	1806.36	3996.90	40314.12	1955.48	2.21	22.32	1.08
ResNet152	4932	2656.92	5812.38	57775.53	2826.92	2.19	21.75	1.06
ViT-H/14	3420	1863.50	4418.24	41334.64	2128.71	2.37	22.18	1.14
Swin-B	2881	1631.06	3944.13	36131.54	2032.77	2.42	22.15	1.25
					Average	2.33	22.05	1.12

Tree UnFlatten

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	55.13	152.07	231.94	940.11	2.76	4.21	17.05
AlexNet	188	226.29	678.29	972.90	4195.04	3.00	4.30	18.54
ResNet18	698	766.54	1953.26	3137.86	12049.88	2.55	4.09	15.72
ResNet34	1242	1309.22	3526.12	5759.16	20966.75	2.69	4.40	16.01
ResNet50	1702	1914.96	5002.83	8369.43	29597.10	2.61	4.37	15.46
ResNet101	3317	3672.61	9633.29	15683.16	57240.20	2.62	4.27	15.59
ResNet152	4932	5407.58	13970.88	23074.68	82072.54	2.58	4.27	15.18
ViT-H/14	3420	4013.18	11146.31	17633.07	66723.58	2.78	4.39	16.63
Swin-B	2881	3595.34	9505.31	15054.88	57310.03	2.64	4.19	15.94
					Average	2.69	4.28	16.23

Tree Flatten with Path

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	36.49	543.67	N/A	919.13	14.90	N/A	25.19
AlexNet	188	115.44	2185.21	N/A	3752.11	18.93	N/A	32.50
ResNet18	698	431.84	7106.55	N/A	12286.70	16.46	N/A	28.45
ResNet34	1242	845.61	13431.99	N/A	22860.48	15.88	N/A	27.03
ResNet50	1702	1166.27	18426.52	N/A	31225.05	15.80	N/A	26.77
ResNet101	3317	2312.77	34770.49	N/A	59346.86	15.03	N/A	25.66
ResNet152	4932	3304.74	50557.25	N/A	85847.91	15.30	N/A	25.98
ViT-H/14	3420	2235.25	37473.53	N/A	64105.24	16.76	N/A	28.68
Swin-B	2881	1970.25	32205.83	N/A	55177.50	16.35	N/A	28.01
					Average	16.16	N/A	27.59

Tree Copy

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	89.81	232.26	845.20	981.48	2.59	9.41	10.93
AlexNet	188	334.58	959.32	3360.46	4316.05	2.87	10.04	12.90
ResNet18	698	1128.11	2840.71	11471.07	12297.07	2.52	10.17	10.90
ResNet34	1242	2160.57	5333.10	20563.06	21901.91	2.47	9.52	10.14
ResNet50	1702	2746.84	6823.88	29705.99	28927.88	2.48	10.81	10.53
ResNet101	3317	5762.05	13481.45	56968.78	60115.93	2.34	9.89	10.43
ResNet152	4932	8151.21	20805.61	81024.06	84079.57	2.55	9.94	10.31
ViT-H/14	3420	5963.61	15665.91	59813.52	68377.82	2.63	10.03	11.47
Swin-B	2881	5401.59	14255.33	53361.77	62317.07	2.64	9.88	11.54
					Average	2.56	9.97	11.02

Tree Map

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	95.13	243.86	867.34	1026.99	2.56	9.12	10.80
AlexNet	188	348.44	987.57	3398.32	4354.81	2.83	9.75	12.50
ResNet18	698	1190.62	2982.66	11719.94	12559.01	2.51	9.84	10.55
ResNet34	1242	2205.87	5417.60	20935.72	22308.51	2.46	9.49	10.11
ResNet50	1702	3128.48	7579.55	30372.71	31638.67	2.42	9.71	10.11
ResNet101	3317	6173.05	14846.57	59167.85	60245.42	2.41	9.58	9.76
ResNet152	4932	8641.22	22000.74	84018.65	86182.21	2.55	9.72	9.97
ViT-H/14	3420	6211.79	17077.49	59790.25	69763.86	2.75	9.63	11.23
Swin-B	2881	5673.66	14339.69	53309.17	59764.61	2.53	9.40	10.53
					Average	2.56	9.58	10.62

Tree Map (nargs)

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	137.06	389.96	N/A	3908.77	2.85	N/A	28.52
AlexNet	188	467.24	1496.96	N/A	15395.13	3.20	N/A	32.95
ResNet18	698	1603.79	4534.01	N/A	50323.76	2.83	N/A	31.38
ResNet34	1242	2907.64	8435.33	N/A	90389.23	2.90	N/A	31.09
ResNet50	1702	4183.77	11382.51	N/A	121777.01	2.72	N/A	29.11
ResNet101	3317	7721.13	22247.85	N/A	238755.17	2.88	N/A	30.92
ResNet152	4932	11508.05	31429.39	N/A	360257.74	2.73	N/A	31.30
ViT-H/14	3420	8294.20	24524.86	N/A	270514.87	2.96	N/A	32.61
Swin-B	2881	7074.62	20854.80	N/A	241120.41	2.95	N/A	34.08
					Average	2.89	N/A	31.33

Tree Map with Path

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	109.82	778.30	N/A	2186.40	7.09	N/A	19.91
AlexNet	188	365.16	2939.36	N/A	8355.37	8.05	N/A	22.88
ResNet18	698	1308.26	9529.58	N/A	25758.24	7.28	N/A	19.69
ResNet34	1242	2527.21	18084.89	N/A	45942.32	7.16	N/A	18.18
ResNet50	1702	3226.03	22935.53	N/A	61275.34	7.11	N/A	18.99
ResNet101	3317	6663.52	46878.89	N/A	126642.14	7.04	N/A	19.01
ResNet152	4932	9378.19	66136.44	N/A	176981.01	7.05	N/A	18.87
ViT-H/14	3420	7033.69	50418.37	N/A	142508.11	7.17	N/A	20.26
Swin-B	2881	6078.15	43173.22	N/A	116612.71	7.10	N/A	19.19
					Average	7.23	N/A	19.66

Tree Map with Path (nargs)

Module	Nodes	OpTree (μs)	JAX XLA (μs)	PyTorch (μs)	DM-Tree (μs)	Speedup (J / O)	Speedup (P / O)	Speedup (D / O)
TinyMLP	53	146.05	917.00	N/A	3940.61	6.28	N/A	26.98
AlexNet	188	489.27	3560.76	N/A	15434.71	7.28	N/A	31.55
ResNet18	698	1712.79	11171.44	N/A	50219.86	6.52	N/A	29.32
ResNet34	1242	3112.83	21024.58	N/A	95505.71	6.75	N/A	30.68
ResNet50	1702	4220.70	26600.82	N/A	121897.57	6.30	N/A	28.88
ResNet101	3317	8631.34	54372.37	N/A	236555.54	6.30	N/A	27.41
ResNet152	4932	12710.49	77643.13	N/A	353600.32	6.11	N/A	27.82
ViT-H/14	3420	8753.09	58712.71	N/A	286365.36	6.71	N/A	32.72
Swin-B	2881	7359.29	50112.23	N/A	228866.66	6.81	N/A	31.10
					Average	6.56	N/A	29.61

---

Changelog

See CHANGELOG.md.

---

License

OpTree is released under the Apache License 2.0.

OpTree is heavily based on JAX's implementation of the PyTree utility, with deep refactoring and several improvements. The original licenses can be found at JAX's Apache License 2.0 and Tensorflow's Apache License 2.0.