What is a pytree?#

In JAX, we use the term pytree to refer to a tree-like structure built out of container-like Python objects. Classes are considered container-like if they are in the pytree registry, which by default includes lists, tuples, and dicts. That is:

  1. any object whose type is not in the pytree container registry is considered a leaf pytree;

  2. any object whose type is in the pytree container registry, and which contains pytrees, is considered a pytree.

For each entry in the pytree container registry, a container-like type is registered with a pair of functions that specify how to convert an instance of the container type to a (children, metadata) pair and how to convert such a pair back to an instance of the container type. Using these functions, JAX can canonicalize any tree of registered container objects into tuples.

Example pytrees:

[1, "a", object()]  # 3 leaves

(1, (2, 3), ())  # 3 leaves

[1, {"k1": 2, "k2": (3, 4)}, 5]  # 5 leaves

JAX can be extended to consider other container types as pytrees; see Extending pytrees below.

Pytrees and JAX functions#

Many JAX functions, like jax.lax.scan(), operate over pytrees of arrays. JAX function transformations can be applied to functions that accept as input and produce as output pytrees of arrays.

Applying optional parameters to pytrees#

Some JAX function transformations take optional parameters that specify how certain input or output values should be treated (e.g. the in_axes and out_axes arguments to vmap()). These parameters can also be pytrees, and their structure must correspond to the pytree structure of the corresponding arguments. In particular, to be able to “match up” leaves in these parameter pytrees with values in the argument pytrees, the parameter pytrees are often constrained to be tree prefixes of the argument pytrees.

For example, if we pass the following input to vmap() (note that the input arguments to a function are considered a tuple):

(a1, {"k1": a2, "k2": a3})

We can use the following in_axes pytree to specify that only the k2 argument is mapped (axis=0) and the rest aren’t mapped over (axis=None):

(None, {"k1": None, "k2": 0})

The optional parameter pytree structure must match that of the main input pytree. However, the optional parameters can optionally be specified as a “prefix” pytree, meaning that a single leaf value can be applied to an entire sub-pytree. For example, if we have the same vmap() input as above, but wish to only map over the dictionary argument, we can use:

(None, 0)  # equivalent to (None, {"k1": 0, "k2": 0})

Or, if we want every argument to be mapped, we can simply write a single leaf value that is applied over the entire argument tuple pytree:


This happens to be the default in_axes value for vmap()!

The same logic applies to other optional parameters that refer to specific input or output values of a transformed function, e.g. vmap’s out_axes.

Viewing the pytree definition of an object#

To view the pytree definition of an arbitrary object for debugging purposes, you can use:

from jax.tree_util import tree_structure

Developer information#

This is primarily JAX internal documentation, end-users are not supposed to need to understand this to use JAX, except when registering new user-defined container types with JAX. Some of these details may change.

Internal pytree handling#

JAX flattens pytrees into lists of leaves at the boundary (and also in control flow primitives). This keeps downstream JAX internals simpler: transformations like grad(), jit(), and vmap() can handle user functions that accept and return the myriad different Python containers, while all the other parts of the system can operate on functions that only take (multiple) array arguments and always return a flat list of arrays.

When JAX flattens a pytree it will produce a list of leaves and a treedef object that encodes the structure of the original value. The treedef can then be used to construct a matching structured value after transforming the leaves. Pytrees are tree-like, rather than DAG-like or graph-like, in that we handle them assuming referential transparency and that they can’t contain reference cycles.

Here is a simple example:

from jax.tree_util import tree_flatten, tree_unflatten
import jax.numpy as jnp

# The structured value to be transformed
value_structured = [1., (2., 3.)]

# The leaves in value_flat correspond to the `*` markers in value_tree
value_flat, value_tree = tree_flatten(value_structured)

# Transform the flat value list using an element-wise numeric transformer
transformed_flat = list(map(lambda v: v * 2., value_flat))

# Reconstruct the structured output, using the original
transformed_structured = tree_unflatten(value_tree, transformed_flat)
value_flat=[1.0, 2.0, 3.0]
value_tree=PyTreeDef([*, (*, *)])
transformed_flat=[2.0, 4.0, 6.0]
transformed_structured=[2.0, (4.0, 6.0)]

By default, pytree containers can be lists, tuples, dicts, namedtuple, None, OrderedDict. Other types of values, including numeric and ndarray values, are treated as leaves:

from collections import namedtuple
Point = namedtuple('Point', ['x', 'y'])

example_containers = [
    (1., [2., 3.]),
    (1., {'b': 2., 'a': 3.}),
    Point(1., 2.)
def show_example(structured):
  flat, tree = tree_flatten(structured)
  unflattened = tree_unflatten(tree, flat)
  print(f"{structured=}\n  {flat=}\n  {tree=}\n  {unflattened=}")

for structured in example_containers:
structured=(1.0, [2.0, 3.0])
  flat=[1.0, 2.0, 3.0]
  tree=PyTreeDef((*, [*, *]))
  unflattened=(1.0, [2.0, 3.0])
structured=(1.0, {'b': 2.0, 'a': 3.0})
  flat=[1.0, 3.0, 2.0]
  tree=PyTreeDef((*, {'a': *, 'b': *}))
  unflattened=(1.0, {'a': 3.0, 'b': 2.0})
structured=Array([0., 0.], dtype=float32)
  flat=[Array([0., 0.], dtype=float32)]
  unflattened=Array([0., 0.], dtype=float32)
structured=Point(x=1.0, y=2.0)
  flat=[1.0, 2.0]
  tree=PyTreeDef(CustomNode(namedtuple[Point], [*, *]))
  unflattened=Point(x=1.0, y=2.0)

Extending pytrees#

By default, any part of a structured value that is not recognized as an internal pytree node (i.e. container-like) is treated as a leaf:

class Special(object):
  def __init__(self, x, y):
    self.x = x
    self.y = y

  def __repr__(self):
    return "Special(x={}, y={})".format(self.x, self.y)

show_example(Special(1., 2.))
structured=Special(x=1.0, y=2.0)
  flat=[Special(x=1.0, y=2.0)]
  unflattened=Special(x=1.0, y=2.0)

The set of Python types that are considered internal pytree nodes is extensible, through a global registry of types, and values of registered types are traversed recursively. To register a new type, you can use register_pytree_node():

from jax.tree_util import register_pytree_node

class RegisteredSpecial(Special):
  def __repr__(self):
    return "RegisteredSpecial(x={}, y={})".format(self.x, self.y)

def special_flatten(v):
  """Specifies a flattening recipe.

    v: the value of registered type to flatten.
    a pair of an iterable with the children to be flattened recursively,
    and some opaque auxiliary data to pass back to the unflattening recipe.
    The auxiliary data is stored in the treedef for use during unflattening.
    The auxiliary data could be used, e.g., for dictionary keys.
  children = (v.x, v.y)
  aux_data = None
  return (children, aux_data)

def special_unflatten(aux_data, children):
  """Specifies an unflattening recipe.

    aux_data: the opaque data that was specified during flattening of the
      current treedef.
    children: the unflattened children

    a re-constructed object of the registered type, using the specified
    children and auxiliary data.
  return RegisteredSpecial(*children)

# Global registration
    special_flatten,    # tell JAX what are the children nodes
    special_unflatten   # tell JAX how to pack back into a RegisteredSpecial

show_example(RegisteredSpecial(1., 2.))
structured=RegisteredSpecial(x=1.0, y=2.0)
  flat=[1.0, 2.0]
  tree=PyTreeDef(CustomNode(RegisteredSpecial[None], [*, *]))
  unflattened=RegisteredSpecial(x=1.0, y=2.0)

Alternatively, you can define appropriate tree_flatten and tree_unflatten methods on your class and decorate it with register_pytree_node_class():

from jax.tree_util import register_pytree_node_class

class RegisteredSpecial2(Special):
  def __repr__(self):
    return "RegisteredSpecial2(x={}, y={})".format(self.x, self.y)

  def tree_flatten(self):
    children = (self.x, self.y)
    aux_data = None
    return (children, aux_data)

  def tree_unflatten(cls, aux_data, children):
    return cls(*children)

show_example(RegisteredSpecial2(1., 2.))
structured=RegisteredSpecial2(x=1.0, y=2.0)
  flat=[1.0, 2.0]
  tree=PyTreeDef(CustomNode(RegisteredSpecial2[None], [*, *]))
  unflattened=RegisteredSpecial2(x=1.0, y=2.0)

When defining unflattening functions, in general children should contain all the dynamic elements of the data structure (arrays, dynamic scalars, and pytrees), while aux_data should contain all the static elements that will be rolled into the treedef structure. JAX sometimes needs to compare treedef for equality, or compute its hash for use in the JIT cache, and so care must be taken to ensure that the auxiliary data specified in the flattening recipe supports meaningful hashing and equality comparisons.

The whole set of functions for operating on pytrees are in jax.tree_util.

Custom PyTrees and Initialization#

One common gotcha with user-defined PyTree objects is that JAX transformations occasionally initialize them with unexpected values, so that any input validation done at initialization may fail. For example:

class MyTree:
  def __init__(self, a):
    self.a = jnp.asarray(a)

register_pytree_node(MyTree, lambda tree: ((tree.a,), None),
    lambda _, args: MyTree(*args))

tree = MyTree(jnp.arange(5.0))

jax.vmap(lambda x: x)(tree)      # Error because object() is passed to MyTree.
jax.jacobian(lambda x: x)(tree)  # Error because MyTree(...) is passed to MyTree

In the first case, JAX’s internals use arrays of object() values to infer the structure of the tree; in the second case, the jacobian of a function mapping a tree to a tree is defined as a tree of trees.

For this reason, the __init__ and __new__ methods of custom PyTree classes should generally avoid doing any array conversion or other input validation, or else anticipate and handle these special cases. For example:

class MyTree:
  def __init__(self, a):
    if not (type(a) is object or a is None or isinstance(a, MyTree)):
      a = jnp.asarray(a)
    self.a = a

Another possibility is to structure your tree_unflatten function so that it avoids calling __init__; for example:

def tree_unflatten(aux_data, children):
  del aux_data  # unused in this class
  obj = object.__new__(MyTree)
  obj.a = a
  return obj

If you go this route, make sure that your tree_unflatten function stays in-sync with __init__ if and when the code is updated.