PyTrees Are Not One Thing: JAX, PyTorch, and TensorFlow Compared

PyTrees look deceptively simple. You flatten a nested Python object into leaves, keep a structure descriptor, and later rebuild or map over the same shape. That abstraction is powerful enough to carry optimizer states, model parameters, batched inputs, gradients, and sharding annotations. It is also just ambiguous enough that three major frameworks implement three subtly different languages under the same idea.

This note compares JAX jax.tree_util, PyTorch torch.utils._pytree, and TensorFlow tf.nest. I tested the behavior in two environments: an older stack with JAX 0.4.35, PyTorch 2.2.2, TensorFlow 2.20.0, and a newer stack with JAX 0.10.0, PyTorch 2.12.0, TensorFlow 2.21.0. Most flatten/unflatten semantics were stable across these versions. The main version-sensitive result is PyTorch: _pytree.tree_map in 2.2.2 accepts only one pytree, while 2.12.0 supports multiple pytrees and behaves much closer to JAX prefix-style mapping.

The short version: JAX treats pytrees as a transformation language, PyTorch is converging toward that model in torch.func, and TensorFlow exposes a broader nested-structure utility through tf.nest. Those differences show up exactly where backend-agnostic libraries usually hurt: None, dictionary order, custom containers, tree_map, autodiff, and vectorization.

The Shape Of The APIs

The three APIs have the same surface story but not the same contract.

from jax import tree_util as jtu
from torch.utils import _pytree as tpu
import tensorflow as tf

leaves, treedef = jtu.tree_flatten(tree)
tree = jtu.tree_unflatten(treedef, leaves)
tree = jtu.tree_map(f, *trees)

leaves, spec = tpu.tree_flatten(tree)
tree = tpu.tree_unflatten(leaves, spec)
tree = tpu.tree_map(f, tree)          # PyTorch 2.2.2
tree = tpu.tree_map(f, *trees)        # PyTorch 2.12.0

leaves = tf.nest.flatten(tree)
tree = tf.nest.pack_sequence_as(structure, leaves)
tree = tf.nest.map_structure(f, *structures)

Flattening means "which objects are leaves?" Unflattening means "what metadata is needed to reconstruct the original container?" Mapping means "what does it mean for several structures to match?" Those three questions are where the frameworks diverge.

JAX calls its structure descriptor a PyTreeDef, so treedef is the conventional variable name. PyTorch calls the analogous descriptor a TreeSpec, so examples and internals often name it spec. Conceptually they play the same role: they describe the container skeleton and the metadata needed to rebuild it from a flat leaf list. TensorFlow's tf.nest does not return a separate treedef object from flatten; instead, pack_sequence_as takes an existing nested structure as the template.

There is also a small argument-order trap. JAX unflattens as tree_unflatten(treedef, leaves), while PyTorch unflattens as tree_unflatten(leaves, spec). TensorFlow's equivalent is pack_sequence_as(structure, leaves).

A Compact Map Of The Differences

Case	JAX	PyTorch _pytree	TensorFlow tf.nest
Scalar	Leaf	Leaf	Leaf
None	Empty pytree, 0 leaves	Leaf	Leaf
list, tuple	Containers	Containers	Containers
namedtuple	Container, type-strict	Container, type-strict	Container, type-strict
plain dict order	Sorted keys	Insertion order	Sorted-key leaf order
OrderedDict order	Insertion order	Insertion order	Sorted-key leaf order
defaultdict order	Sorted keys	Insertion order	Sorted-key leaf order
defaultdict.default_factory	Preserved	Preserved	Preserved
custom dict subclass	Leaf unless registered	Leaf unless registered	Container
custom list/tuple subclass	Leaf unless registered	Leaf unless registered	Container
dataclass instance	Leaf unless registered	Leaf unless registered	Leaf by default
multi-arg tree_map	Supported, prefix semantics	PyTorch 2.2.2: not supported; PyTorch 2.12.0: supported with prefix semantics	Supported, strict same structure
unflatten arity mismatch	Raises ValueError	Raises ValueError	Raises ValueError

The rest of the note explains why these rows matter.

None: A Ghost Node In JAX, A Leaf Elsewhere

The cleanest way to feel the philosophical split is None. In JAX, None is not a value to map over. It is a zero-leaf structural marker.

jtu.tree_flatten(None)
# leaves: []
# treedef: PyTreeDef(None)

jtu.tree_map(lambda x: ("mapped", x), None)
# None

In PyTorch and TensorFlow, None is a leaf.

tpu.tree_flatten(None)
# [None]

tf.nest.flatten(None)
# [None]

tpu.tree_map(lambda x: ("mapped", x), None)
# ("mapped", None)

tf.nest.map_structure(lambda x: ("mapped", x), None)
# ("mapped", None)

The nested case makes the difference visible:

tree = [1, None, 3]

jtu.tree_flatten(tree)[0]
# [1, 3]

tpu.tree_flatten(tree)[0]
# [1, None, 3]

tf.nest.flatten(tree)
# [1, None, 3]

If None means "optional value absent", JAX treats it structurally. If None means "a value in my tree", PyTorch and TensorFlow are closer to that intuition.

Dictionaries: The Same Keys, Different Time Arrows

Plain dict is a container everywhere, but the traversal order differs. JAX sorts keys, PyTorch follows insertion order, and TensorFlow assigns leaves by sorted keys while preserving the original mapping order when rebuilding.

tree = {"b": 2, "a": 1}

jtu.tree_flatten(tree)[0]
# [1, 2]   # a, then b

tpu.tree_flatten(tree)[0]
# [2, 1]   # b, then a

tf.nest.flatten(tree)
# [1, 2]   # a, then b

Replacing the leaves with [10, 20] shows the reconstruction contract:

# JAX
{"a": 10, "b": 20}

# PyTorch
{"b": 10, "a": 20}

# TensorFlow
{"b": 20, "a": 10}

TensorFlow's result is the surprising one on first read. It maps values according to sorted keys, but prints in the original insertion order. The object order and the leaf assignment order are not the same concept.

Mixed incomparable key types are another consequence of sorting. JAX and TensorFlow fail on {1: "one", "2": "two"} because 1 < "2" is not defined. PyTorch does not sort and therefore flattens this case in insertion order.

jtu.tree_flatten({1: "one", "2": "two"})
# ValueError: Comparator raised exception while sorting pytree dictionary keys.

tf.nest.flatten({1: "one", "2": "two"})
# TypeError: '<' not supported between instances of 'str' and 'int'

tpu.tree_flatten({1: "one", "2": "two"})[0]
# ["one", "two"]

Ordered Containers Are Not Just Dicts With Better Manners

OrderedDict has explicit order metadata, and JAX treats that metadata as part of the tree structure. PyTorch uses insertion order too. TensorFlow again uses sorted-key leaf assignment.

from collections import OrderedDict

tree = OrderedDict([("b", 2), ("a", 1)])

jtu.tree_flatten(tree)[0]
# [2, 1]

tpu.tree_flatten(tree)[0]
# [2, 1]

tf.nest.flatten(tree)
# [1, 2]

All three preserve the OrderedDict type when rebuilding, but TensorFlow assigns replacement leaves by sorted key:

tf.nest.pack_sequence_as(OrderedDict([("b", 2), ("a", 1)]), [10, 20])
# OrderedDict([("b", 20), ("a", 10)])

Multi-argument mapping reveals another difference. JAX rejects two OrderedDicts with the same keys but different order because the custom node metadata differs.

a = OrderedDict([("b", 2), ("a", 1)])
b = OrderedDict([("a", 10), ("b", 20)])

jtu.tree_map(lambda x, y: (x, y), a, b)
# ValueError: Mismatch custom node data: ('b', 'a') != ('a', 'b')

TensorFlow accepts this and pairs by key while preserving the first structure's order. PyTorch 2.12.0 also accepts it and returns the same visible result:

OrderedDict([("b", (2, 20)), ("a", (1, 10))])

defaultdict: Losing The Type Changes Behavior

defaultdict is not a decorative subclass. It carries a default_factory, which changes lookup behavior.

from collections import defaultdict

counter = defaultdict(int)
counter["missing"]
# 0

plain = {}
plain["missing"]
# KeyError

All three frameworks preserve the default_factory, but they disagree about leaf order just as with dictionaries.

tree = defaultdict(int, {"b": 2, "a": 1})

jtu.tree_flatten(tree)[0]
# [1, 2]

tpu.tree_flatten(tree)[0]
# [2, 1]

tf.nest.flatten(tree)
# [1, 2]

Rebuilding with [10, 20] gives:

# JAX
defaultdict(int, {"a": 10, "b": 20})

# PyTorch
defaultdict(int, {"b": 10, "a": 20})

# TensorFlow
defaultdict(int, {"b": 20, "a": 10})

This matters for any pure Python fallback. If it flattens a defaultdict as a mapping but reconstructs a plain dict, it is wrong, not merely imprecise.

Custom Containers: Either Register Them Or Treat Them As Leaves

JAX and PyTorch are conservative about arbitrary subclasses. TensorFlow is more eager to recurse into sequence and mapping subclasses.

class MyDict(dict):
    pass

class MyList(list):
    pass

class MyTuple(tuple):
    pass

JAX and PyTorch treat these as leaves unless explicitly registered:

jtu.tree_flatten(MyDict({"b": 2, "a": 1}))[0]
# [MyDict({"b": 2, "a": 1})]

tpu.tree_flatten(MyList([1, 2]))[0]
# [MyList([1, 2])]

TensorFlow traverses them:

tf.nest.flatten(MyDict({"b": 2, "a": 1}))
# [1, 2]

tf.nest.flatten(MyList([1, 2]))
# [1, 2]

tf.nest.flatten(MyTuple((1, 2)))
# [1, 2]

Namedtuple is the standard exception. All three frameworks recognize it as a structural container and preserve its type. They are also strict about namedtuple type matching: Point(1, 2) is not the same structure as (1, 2) or RGB(1, 2).

The Real Trap: tree_map Does Not Always Mean Same-Structure Map

JAX tree_map uses the first argument as the reference structure. Later arguments are flattened "up to" that structure. If the first tree has a leaf, the corresponding value in a later tree may be an entire subtree.

jtu.tree_map(lambda x, y: (x, y), [1, 2], [[3], {"x": 4}])
# [(1, [3]), (2, {"x": 4})]

The first tree says: "I am a list of two leaves." Therefore the second tree only needs to be a list of two objects. Those objects are passed whole to the function.

The scalar case is even clearer:

jtu.tree_map(lambda x, y: (x, y), 1, [2, 3])
# (1, [2, 3])

jtu.tree_map(lambda x, y: (x, y), [1, 2], 3)
# ValueError: Expected list, got 3.

PyTorch 2.12.0 behaves similarly:

tpu.tree_map(lambda x, y: (x, y), [1, 2], [[3], {"x": 4}])
# [(1, [3]), (2, {"x": 4})]

tpu.tree_map(lambda x, y: (x, y), 1, [2, 3])
# (1, [2, 3])

tpu.tree_map(lambda x, y: (x, y), [1, 2], 3)
# ValueError: Node type mismatch; expected <class 'list'>, but got <class 'int'>.

PyTorch 2.2.2 did not support this multi-pytree call through _pytree.tree_map. TensorFlow supports multiple structures, but it requires strict structural equality:

tf.nest.map_structure(lambda x, y: (x, y), [1, 2], [[3], {"x": 4}])
# ValueError: structures do not have the same nested structure

Transform APIs: PyTree Support Is Not Just Flattening

Tree semantics matter most when they meet transforms. Here the frameworks differ again.

JAX transformations are natively pytree-based. grad accepts nested inputs and returns gradients with the same structure:

import jax
import jax.numpy as jnp

def f(params):
    return params["x"] ** 2 + params["y"][0] ** 3

params = {"x": jnp.array(2.0), "y": [jnp.array(3.0)]}
jax.grad(f)(params)
# {"x": Array(4., dtype=float32), "y": [Array(27., dtype=float32)]}

JAX vmap accepts nested pytree inputs too:

def g(params):
    return params["x"] + params["y"][0]

batched = {"x": jnp.arange(3.0), "y": [jnp.arange(3.0) + 10]}
jax.vmap(g)(batched)
# Array([10., 12., 14.], dtype=float32)

Because None is a zero-leaf node in JAX, it can sit inside a vmapped input without becoming a batched argument:

def h(params):
    return params["x"]

jax.vmap(h)({"x": jnp.arange(3.0), "y": [None]})
# Array([0., 1., 2.], dtype=float32)

Classic PyTorch autograd is different. torch.autograd.grad expects tensors or gradient edges as inputs, not an arbitrary nested pytree:

x = torch.tensor(2.0, requires_grad=True)
y = torch.tensor(3.0, requires_grad=True)
loss = x ** 2 + y ** 3

torch.autograd.grad(loss, (x, y))
# (tensor(4.), tensor(27.))

nested = {"x": x, "y": [y]}
torch.autograd.grad(loss, nested)
# RuntimeError: all inputs have to be Tensors or GradientEdges, but got str

The newer torch.func stack does understand nested pytree-like parameter structures:

from torch.func import grad, vmap

def f(params):
    return params["x"] ** 2 + params["y"][0] ** 3

params = {"x": torch.tensor(2.0), "y": [torch.tensor(3.0)]}
grad(f)(params)
# {"x": tensor(4.), "y": [tensor(27.)]}

def g(params):
    return params["x"] + params["y"][0]

batched = {"x": torch.arange(3.0), "y": [torch.arange(3.0) + 10]}
vmap(g)(batched)
# tensor([10., 12., 14.])

TensorFlow's transform support follows tf.nest. GradientTape.gradient accepts nested sources and returns gradients in the same structure:

x = tf.Variable(2.0)
y = tf.Variable(3.0)
nested = {"x": x, "y": [y]}

with tf.GradientTape() as tape:
    loss = nested["x"] ** 2 + nested["y"][0] ** 3

tape.gradient(loss, nested)
# {"x": tf.Tensor(4.0), "y": [tf.Tensor(27.0)]}

tf.vectorized_map also accepts nested input structures:

def g(params):
    return params["x"] + params["y"][0]

batched = {"x": tf.range(3.0), "y": [tf.range(3.0) + 10]}
tf.vectorized_map(g, batched)
# tf.Tensor([10. 12. 14.], shape=(3,), dtype=float32)

tf.function accepts nested structures as ordinary function arguments:

@tf.function
def f(params):
    return params["x"] ** 2 + params["y"][0] ** 3

f({"x": tf.constant(2.0), "y": [tf.constant(3.0)]})
# tf.Tensor(31.0, shape=(), dtype=float32)

The right summary is more specific: JAX transforms are pytree-native; PyTorch classic autograd is not, while torch.func is; TensorFlow transform APIs accept nested structures.

Closing

PyTrees are a small abstraction with a long tail. Simple examples make every framework look compatible; real optimizer states, optional values, ordered mappings, custom containers, and transform APIs expose the differences quickly.