Transforms#
JAX transformations in general operate on Pytrees of arrays and abide by value semantics, this presents a challenge for Flax NNX which represents Modules as regular Python objects that follow reference semantics. To address this, Flax NNX introduces its own set of transformations that extend JAX transformations to allow Modules and other Flax NNX objects to be passed in and out of transformations while preserving reference semantics.
Flax NNX transformations should feel quite familar to those who have used JAX transformations before as they use the same APIs and behave like the JAX transformations when only working with Pytrees of arrays. However, when working with Flax NNX objects, they allow Python’s reference semantics to be preserved for these objects, this includes:
Preserving shared references across multiple objects in the inputs and outputs of the transformation.
Propagating any state changes made to the objects inside the transformation to the objects outside the transformation.
Enforcing consistency of how objects are transformed when aliases are present across multiple inputs and outputs.
import jax
from jax import numpy as jnp, random
from flax import nnx
Throughout this guide we will use nnx.vmap
as a case study to demonstrate how Flax NNX transformations work but the principles
outlined here extend to all transformations.
Basic Example#
To begin, let’s look at a simple example of using nnx.vmap
to extend an elementwise vector_dot
function to work on
batched inputs. We will define a Weights
Module with no methods to hold some parameters, these weights will be passed
as an input to the vector_dot
function along with some data. Both the weights and data will be batched on axis 0
and we will use
nnx.vmap
to apply vector_dot
to each batch element, and the result will be a batched on axis 1
:
class Weights(nnx.Module):
def __init__(self, kernel: jax.Array, bias: jax.Array):
self.kernel, self.bias = nnx.Param(kernel), nnx.Param(bias)
weights = Weights(
kernel=random.uniform(random.key(0), (10, 2, 3)),
bias=jnp.zeros((10, 3)),
)
x = jax.random.normal(random.key(1), (10, 2))
def vector_dot(weights: Weights, x: jax.Array):
assert weights.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
return x @ weights.kernel + weights.bias
y = nnx.vmap(vector_dot, in_axes=0, out_axes=1)(weights, x)
print(f'{y.shape = }')
nnx.display(weights)
y.shape = (3, 10)
Notice that in_axes
interacts naturally with the Weights
Module, treating it as if it where a Pytree of arrays. Prefix patterns are also allowed, in_axes=(0, 0)
would’ve also worked in this case.
Objects are also allowed as outputs of Flax NNX transformations, this can be useful to transform initializers. For example,
we can define a create_weights
function to create an single Weights
Module and use nnx.vmap
to create a stack of
Weights
with the same shapes as before:
def create_weights(seed: jax.Array):
return Weights(
kernel=random.uniform(random.key(seed), (2, 3)),
bias=jnp.zeros((3,)),
)
seeds = jnp.arange(10)
weights = nnx.vmap(create_weights)(seeds)
nnx.display(weights)
Transforming Methods#
Methods in Python are just functions that take the instance as the first argument, this means that you can decorate methods from Module
and other Flax NNX subtypes. For example, we can refactor Weights
from the previous example and decorate __init__
with vmap
to do the work of create_weights
, and add a __call__
method and decorate it with vmap
to do the work of vector_dot
:
class WeightStack(nnx.Module):
@nnx.vmap
def __init__(self, seed: jax.Array):
self.kernel = nnx.Param(random.uniform(random.key(seed), (2, 3)))
self.bias = nnx.Param(jnp.zeros((3,)))
@nnx.vmap(in_axes=0, out_axes=1)
def __call__(self, x: jax.Array):
assert self.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
return x @ self.kernel + self.bias
weights = WeightStack(jnp.arange(10))
x = jax.random.normal(random.key(1), (10, 2))
y = weights(x)
print(f'{y.shape = }')
nnx.display(weights)
y.shape = (3, 10)
Throughout the rest of the guide we will focus on transforming individual functions, however, note all examples can easily be written in this method style.
State propagation#
So far our functions have been stateless. However, the real power of Flax NNX transformations comes when we have stateful functions since one of their main features is to propagate state changes to preserve reference semantics. Let’s update our example by adding
a count
attribute to Weights
and incrementing it in the new stateful_vector_dot
function.
class Count(nnx.Variable): pass
class Weights(nnx.Module):
def __init__(self, kernel: jax.Array, bias: jax.Array, count: jax.Array):
self.kernel, self.bias = nnx.Param(kernel), nnx.Param(bias)
self.count = Count(count)
weights = Weights(
kernel=random.uniform(random.key(0), (10, 2, 3)),
bias=jnp.zeros((10, 3)),
count=jnp.arange(10),
)
x = jax.random.normal(random.key(1), (10, 2))
def stateful_vector_dot(weights: Weights, x: jax.Array):
assert weights.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
weights.count += 1
return x @ weights.kernel + weights.bias
y = nnx.vmap(stateful_vector_dot, in_axes=0, out_axes=1)(weights, x)
weights.count
Count(
value=Array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype=int32)
)
After running stateful_vector_dot
once we verify that the count
attribute was correctly updated. Because Weights is vectorized, count
was initialized as an arange(10)
, and all of its elements were incremented by 1 inside the transformation. The most important part is that updates were propagated to the original Weights
object outside the transformation. Nice!
Graph updates propagation#
JAX transformations see inputs as pytrees of arrays, and Flax NNX see inputs pytrees of arrays and Python references, where references form a graph. Flax NNX’s state propagation machinery can track arbitrary updates to the objects as long as they’re local to the inputs (updates to globals inside transforms are not supported). This means that you can modify graph structure as needed, including updating existing attributes, adding/deleting attributes, swapping attributes, sharing (new) references between objects, sharing Variables between objects, etc. The sky is the limit!
The following example demonstrates performing some arbitrary updates to the Weights
object inside nnx.vmap
and verifying that the updates are correctly propagated to the original Weights
object outside the transformation.
class Count(nnx.Variable): pass
class Weights(nnx.Module):
def __init__(self, kernel: jax.Array, bias: jax.Array, count: jax.Array):
self.kernel, self.bias = nnx.Param(kernel), nnx.Param(bias)
self.count = Count(count)
weights = Weights(
kernel=random.uniform(random.key(0), (10, 2, 3)),
bias=jnp.zeros((10, 3)),
count=jnp.arange(10),
)
x = jax.random.normal(random.key(1), (10, 2))
def crazy_vector_dot(weights: Weights, x: jax.Array):
assert weights.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
weights.count += 1
y = x @ weights.kernel + weights.bias
weights.some_property = ['a', 2, False] # add attribute
del weights.bias # delete attribute
weights.new_param = weights.kernel # share reference
return y
y = nnx.vmap(crazy_vector_dot, in_axes=0, out_axes=1)(weights, x)
nnx.display(weights)
With great power comes great responsibility.
 Uncle Ben
While this feature is very powerful, it must be used with care as it can clash with JAX’s underlying assumptions for certain transformations. For example, jit
expects the structure of the inputs to be stable in order to cache the compiled function, so changing the graph structure inside a nnx.jit
ed function cause continuous recompilations and performance degradation. On the other hand, scan
only allows a fixed carry
structure, so adding/removing substates declared as carry will cause an error.
Transforming Substates (Lift Types)#
Certain JAX transformation allow the use of pytree prefixes to specify how different parts of the inputs/outputs should be transformed. Flax NNX supports pytree prefixes for pytree structures but currently it doesn’t have the notion of a prefix for graph objects. Instead, Flax NNX introduces the concept of Lift Types
which allow specifying how different substates of an object should be transformed. Different transformations support different Lift Types, here is the list of currently supported Lift Types for each transformation:
Lift Type 
Transforms 







NOTE:
shard_map
is not yet implemented.
If we want to specify how to vectorize different substates of an object in nnx.vmap
, we create a StateAxes
which maps a set of substates via Filters to their corresponding axes, and pass the StateAxes
to in_axes
and out_axes
as if it were a pytree prefix. Let’s use the previous stateful_vector_dot
example and
vectorize only the Param
variables and broadcast the count
variable so we only keep a single count for all the batch elements.
To do this we will define a StateAxes
with a filter that matches the Param
variables and maps them to axis 0
, and all the Count
variables to None
, and pass this StateAxes
to in_axes
for the Weights
object.
class Weights(nnx.Module):
def __init__(self, kernel: jax.Array, bias: jax.Array, count: jax.Array):
self.kernel, self.bias = nnx.Param(kernel), nnx.Param(bias)
self.count = Count(count)
weights = Weights(
kernel=random.uniform(random.key(0), (10, 2, 3)),
bias=jnp.zeros((10, 3)),
count=jnp.array(0),
)
x = jax.random.normal(random.key(1), (10, 2))
def stateful_vector_dot(weights: Weights, x: jax.Array):
assert weights.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
weights.count += 1
return x @ weights.kernel + weights.bias
state_axes = nnx.StateAxes({nnx.Param: 0, Count: None}) # broadcast Count
y = nnx.vmap(stateful_vector_dot, in_axes=(state_axes, 0), out_axes=1)(weights, x)
weights.count
Count(
value=Array(1, dtype=int32, weak_type=True)
)
Here count is now a scalar since its not being vectorized. Also, note that StateAxes
can only be used directly on Flax NNX objects, it cannot be used as a prefix for a pytree of objects.
Random State#
In Flax NNX random state is just regular state. This means that its stored inside Modules that need it and its treated as any other type of state. This is a simplification over Flax Linen where random state was handled by a separate mechanism. In practice Modules simply need to keep a reference to a Rngs
object that is passed to them during initialization, and use it to generate a unique key for each random operation. For the purposes of this guide, this means that random state can be transformed like any other type of state but we also need be aware of how the state is laid out so we can transform it correctly.
Let’s suppose we want change things up a bit and apply the same weights to all elements in the batch but we want to add different random noise to each element. To do this we will add a Rngs
attribute to Weights
, created from a seed
key argument passed during construction, this seed key must be split
before hand so we can vectorize it succesfully. For pedagogical reasons, we will assign the seed key to a noise
Stream and sample from it. To vectorize the RNG state we must configure StateAxes
to map all RngState
(base class for all variables in Rngs
) to axis 0
, and Param
and Count
to None
.
class Weights(nnx.Module):
def __init__(self, kernel, bias, count, seed):
self.kernel, self.bias = nnx.Param(kernel), nnx.Param(bias)
self.count = Count(count)
self.rngs = nnx.Rngs(noise=seed)
weights = Weights(
kernel=random.uniform(random.key(0), (2, 3)),
bias=jnp.zeros((3,)),
count=jnp.array(0),
seed=random.split(random.key(0), num=10),
)
x = random.normal(random.key(1), (10, 2))
def noisy_vector_dot(weights: Weights, x: jax.Array):
assert weights.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
weights.count += 1
y = x @ weights.kernel + weights.bias
return y + random.normal(weights.rngs.noise(), y.shape)
state_axes = nnx.StateAxes({nnx.RngState: 0, (nnx.Param, Count): None})
y1 = nnx.vmap(noisy_vector_dot, in_axes=(state_axes, 0))(weights, x)
y2 = nnx.vmap(noisy_vector_dot, in_axes=(state_axes, 0))(weights, x)
print(jnp.allclose(y1, y2))
nnx.display(weights)
False
Because Rngs
’s state is updated in place and automatically propagated by nnx.vmap
, we will get a different result every time that noisy_vector_dot
is called.
In the example above we manually split the random state during construction, this is fine as it makes the intention clear but it also doesn’t let us use Rngs
outside of vmap
since its state is always split. To solve this we pass an unplit seed and use the nnx.split_rngs
decorator before vmap
to split the RngState
right before each call to the function and then “lower” it back so its usable.
weights = Weights(
kernel=random.uniform(random.key(0), (2, 3)),
bias=jnp.zeros((3,)),
count=jnp.array(0),
seed=0,
)
x = random.normal(random.key(1), (10, 2))
state_axes = nnx.StateAxes({nnx.RngState: 0, (nnx.Param, Count): None})
@nnx.split_rngs(splits=10)
@nnx.vmap(in_axes=(state_axes, 0))
def noisy_vector_dot(weights: Weights, x: jax.Array):
assert weights.kernel.ndim == 2, 'Batch dimensions not allowed'
assert x.ndim == 1, 'Batch dimensions not allowed'
weights.count += 1
y = x @ weights.kernel + weights.bias
return y + random.normal(weights.rngs.noise(), y.shape)
y1 = noisy_vector_dot(weights, x)
y2 = noisy_vector_dot(weights, x)
print(jnp.allclose(y1, y2))
nnx.display(weights)
False
Consistent aliasing#
The main issue with allowing for reference semantics in transforms that references can be shared across inputs and outputs, this can be problematic if not taken care of because it would lead to illdefined or inconsistent behavior. In the example below we have a single Weights
Module m
whose reference appears in multiple places in arg1
and arg2
. The problem is that we also specified we wanted to vectorize arg1
in axis 0
and arg2
in axis 1
, this is fine in JAX due to referential transparency of pytrees but its problematic in Flax NNX since we are trying to vectorize m
in two different ways. NNX will enforce consistency by raising an error.
class Weights(nnx.Module):
def __init__(self, array: jax.Array):
self.param = nnx.Param(array)
m = Weights(jnp.arange(10))
arg1 = {'a': {'b': m}, 'c': m}
arg2 = [(m, m), m]
@nnx.vmap(in_axes=(0, 1))
def f(arg1, arg2):
...
try:
f(arg1, arg2)
except ValueError as e:
print(e)
Inconsistent aliasing detected. The following nodes have different prefixes:
Node: <class 'flax.nnx.variables.Param'>
param: 0
param: 0
param: 1
Node: <class '__main__.Weights'>
<root>: 0
<root>: 0
<root>: 1
Inconsistent aliasing can also happen between inputs and outputs. In the next example we have a trivial function that accepts and immediately return arg1
, however arg1
is vectorized on axis 0
on the input and axis 1
on the output. As expected, this is problematic and Flax NNX will raise an error.
@nnx.vmap(in_axes=0, out_axes=1)
def f(arg1):
return arg1
try:
f(arg1)
except ValueError as e:
print(e)
Inconsistent aliasing detected. The following nodes have different prefixes:
Node: <class 'flax.nnx.variables.Param'>
param: 0
param: 0
param: 1
Node: <class '__main__.Weights'>
<root>: 0
<root>: 0
<root>: 1
Axes Metadata#
Flax NNX Variables can have hold arbitrary metadata which can be added by simply passing them as keyword arguments to their constructor. This is often used to store sharding
information which is used by the nnx.spmd
APIs like nnx.get_partition_spec
and nnx.get_named_sharding
. However, its often important to keep this axesrelated information in sync to what the actual state of the axes is when transforms are involved, for example, if we vectorize a variable on axis 1
we should remove the sharding
information at position 1
when inside a vmap
or scan
to reflect the fact that the axes is temporarily removed. To achieve this Flax NNX transforms provide a nonstandard transform_metadata
dictionary argument, when the nnx.PARTITION_NAME
key is present the sharding
metadata will be updated as specified by in_axes
and out_axes
. Let’s see an example of this in action:
class Weights(nnx.Module):
def __init__(self, array: jax.Array, sharding: tuple[str  None, ...]):
self.param = nnx.Param(array, sharding=sharding)
m = Weights(jnp.ones((3, 4, 5)), sharding=('a', 'b', None))
@nnx.vmap(in_axes=1, transform_metadata={nnx.PARTITION_NAME: 'b'})
def f(m: Weights):
print(f'Inner {m.param.shape = }')
print(f'Inner {m.param.sharding = }')
f(m)
print(f'Outter {m.param.shape = }')
print(f'Outter {m.param.sharding = }')
Inner m.param.shape = (3, 5)
Inner m.param.sharding = ('a', None)
Outter m.param.shape = (3, 4, 5)
Outter m.param.sharding = ('a', 'b', None)
Here we added a sharding
metadata to the Param
variables and used transform_metadata
to update the sharding
metadata to reflect the axes changes, specifically we can see that first axis b
was removed from the sharding
metadata when inside vmap
and then added back when outside vmap
.
We can verify that this also works when Modules are created inside the transformation, the new sharding
axes will be added to the Module’s Variables outside the transformation, matching the axes of the transformed Variables.
@nnx.vmap(out_axes=1, axis_size=4, transform_metadata={nnx.PARTITION_NAME: 'b'})
def init_vmap():
return Weights(jnp.ones((3, 5)), sharding=('a', None))
m = init_vmap()
print(f'Outter {m.param.shape = }')
print(f'Outter {m.param.sharding = }')
Outter m.param.shape = (3, 4, 5)
Outter m.param.sharding = ('a', 'b', None)