Randomness

Randomness#

Flax NNX uses the stateful nnx.Rngs class to simplify Jax’s handling of random states. For example, the code below uses a nnx.Rngs object to define a simple linear model with dropout:

from flax import nnx

class Model(nnx.Module):
  def __init__(self, *, rngs: nnx.Rngs):
    self.linear = nnx.Linear(20, 10, rngs=rngs)
    self.drop = nnx.Dropout(0.1)

  def __call__(self, x, *, rngs):
    return nnx.relu(self.drop(self.linear(x), rngs=rngs))

rngs = nnx.Rngs(0)
model = Model(rngs=rngs)  # pass rngs to initialize parameters
x = rngs.normal((32, 20))  # convenient jax.random methods
y = model(x, rngs=rngs)  # pass rngs for dropout masks

We always pass nnx.Rngs objects to models at initialization (to initialize parameters). For models with nondeterministic outputs like the one above, we also pass nnx.Rngs objects to the model’s __call__ method.

The Flax NNX pseudorandom number generator (PRNG) system has the following main characteristics:

  • It is explicit.

  • It is order-based.

  • It uses dynamic counters.

Note: To learn more about random number generation in JAX, the jax.random API, and PRNG-generated sequences, check out this JAX PRNG tutorial.

Rngs, RngStream, and RngState#

In Flax NNX, the nnx.Rngs type is the primary convenience API for managing the random state(s). Following Flax Linen’s footsteps, nnx.Rngs have the ability to create multiple named PRNG key streams, each with its own state, for the purpose of having tight control over randomness in the context of JAX transformations (transforms).

Here are the main PRNG-related types in Flax NNX:

  • nnx.Rngs: The main user interface. It defines a set of named nnx.RngStream objects.

  • nnx.RngStream: An object that can generate a stream of PRNG keys. It holds a root key and a count inside an nnx.RngKey and nnx.RngCount nnx.Variables, respectively. When a new key is generated, the count is incremented.

  • nnx.RngState: The base type for all RNG-related states.

    • nnx.RngKey: NNX Variable type for holding PRNG keys. It includes a tag attribute containing the name of the PRNG key stream.

    • nnx.RngCount: NNX Variable type for holding PRNG counts. It includes a tag attribute containing the PRNG key stream name.

To create an nnx.Rngs object you can simply pass an integer seed or jax.random.key instance to any keyword argument of your choice in the constructor.

Here’s an example:

rngs = nnx.Rngs(params=0, dropout=random.key(1))
nnx.display(rngs)

Notice that the key and count nnx.Variables contain the PRNG key stream name in a tag attribute. This is primarily used for filtering as we’ll see later.

To generate new keys, you can access one of the streams and use its __call__ method with no arguments. This will return a new key by using random.fold_in with the current key and count. The count is then incremented so that subsequent calls will return new keys.

params_key = rngs.params()
dropout_key = rngs.dropout()

nnx.display(rngs)

Note that the key attribute does not change when new PRNG keys are generated.

Using random state with flax Modules.#

Almost all flax Modules require a random state for initialization. In a Linear layer, for example, we need to sample the weights and biases from the appropriate Normal distribution. Random state is provided using the rngs keyword argument at initialization.

linear = nnx.Linear(20, 10, rngs=rngs)

Specifically, this will use the RngSteam rngs.params for weight initialization. The params stream is also used for initialization of nnx.Conv, nnx.ConvTranspose, and nnx.Embed.

The nnx.Dropout module also requires a random state, but it requires this state at call time rather than initialization. Once again, we can pass it random state using the rngs keyword argument.

dropout = nnx.Dropout(0.5)

import jax.numpy as jnp
dropout(jnp.ones(4), rngs=rngs)

Array([2., 0., 2., 2.], dtype=float32)

The nnx.Dropout layer will use the rng’s dropout stream. This also applies to Modules that use Dropout as a sub-Module, like nnx.MultiHeadAttention.

To summarize, there are only two standard PRNG key stream names used by Flax NNX’s built-in layers, shown in the table below:

PRNG key stream name

Description

params

Used for parameter initialization

dropout

Used by nnx.Dropout to create dropout masks

Default PRNG key stream#

One of the downsides of having named streams is that the user needs to know all the possible names that a model will use when creating the nnx.Rngs object. While this could be solved with some documentation, Flax NNX provides a default stream that can be be used as a fallback when a stream is not found. To use the default PRNG key stream, you can simply pass an integer seed or jax.random.key as the first positional argument.

rngs = nnx.Rngs(0, params=1)

key1 = rngs.params() # Call params.
key2 = rngs.dropout() # Fallback to the default stream.
key3 = rngs() # Call the default stream directly.

nnx.display(rngs)

As shown above, a PRNG key from the default stream can also be generated by calling the nnx.Rngs object itself.

Note
For large projects it is recommended to use named streams to avoid potential conflicts. For small projects or quick prototyping just using the default stream is a good choice.

jax.random shorthand methods#

Since a very common pattern is to sample a key and immediately pass it to a function from jax.random, both Rngs and RngStream expose the same functions as methods with the same signature except they don’t require a key:

import jax
rngs = nnx.Rngs(0, params=1)

# using jax.random
z1 = jax.random.normal(rngs(), (2, 3))
z2 = jax.random.bernoulli(rngs.params(), 0.5, (10,))

# shorthand methods
z1 = rngs.normal((2, 3))                 # generates key from rngs.default
z2 = rngs.params.bernoulli(0.5, (10,)) # generates key from rngs.params

Forking random state#

Say you want to train a model that uses dropout on a batch of data. You don’t want to use the same random state for every dropout mask in your batch. Instead, you want to fork the random state into separate pieces for each layer. This can be accomplished with the fork method, as shown below.

class Model(nnx.Module):
  def __init__(self, rngs: nnx.Rngs):
    self.linear = nnx.Linear(20, 10, rngs=rngs)
    self.drop = nnx.Dropout(0.1)

  def __call__(self, x, rngs):
    return nnx.relu(self.drop(self.linear(x), rngs=rngs))

model =  Model(rngs=nnx.Rngs(0))

@nnx.vmap(in_axes=(None, 0, 0), out_axes=0)
def model_forward(model, x, rngs):
  return model(x, rngs=rngs)

dropout_rngs = nnx.Rngs(1)
forked_rngs = dropout_rngs.fork(split=5)
(dropout_rngs, forked_rngs)

(Rngs( # RngState: 2 (12 B)
   default=RngStream( # RngState: 2 (12 B)
     tag='default',
     key=RngKey( # 1 (8 B)
       value=Array((), dtype=key<fry>) overlaying:
       [0 1],
       tag='default'
     ),
     count=RngCount( # 1 (4 B)
       value=Array(1, dtype=uint32),
       tag='default'
     )
   )
 ),
 Rngs( # RngState: 10 (60 B)
   default=RngStream( # RngState: 10 (60 B)
     tag='default',
     key=RngKey( # 5 (40 B)
       value=Array(shape=(5,), dtype=key<fry>),
       tag='default'
     ),
     count=RngCount( # 5 (20 B)
       value=Array(shape=(5,), dtype=dtype('uint32')),
       tag='default'
     )
   )
 ))

model_forward(model, jnp.ones((5, 20)), forked_rngs).shape

(5, 10)

The output of rng.fork is another Rng with keys and counts that have an expanded shape. In the example above, the RngKey and RngCount of dropout_rngs have shape (), but in forked_rngs they have shape (5,).

Implicit Random State#

So far, we have looked at passing random state directly to each Module when it gets called. But there’s another way to handle call-time randomness in flax: we can bundle the random state into the Module itself. This makes the random state is just another type of Module state. Using implicit random state requires passing the rngs keyward argument when initializing the module rather than when calling it. For example, here is how we might construct the simple Module we defined earlier using an implicit style.

class Model(nnx.Module):
  def __init__(self, rngs: nnx.Rngs):
    self.linear = nnx.Linear(20, 10, rngs=rngs)
    self.drop = nnx.Dropout(0.1, rngs=rngs)

  def __call__(self, x):
    return nnx.relu(self.drop(self.linear(x)))

model = Model(nnx.Rngs(params=0, dropout=1))

y = model(x=jnp.ones((1, 20)))
print(f'{y.shape = }')

y.shape = (1, 10)

This implicit state handling style is less verbose than passing RNGs explicitly, and more closely resembles code in other deep learning frameworks like PyTorch. However, as we’ll see in the following sections, using implicit state makes it less obvious how to apply jax transformations to your Modules. With explicit state, you can usually use tranforms like jax.vmap directly. With implicit state, you’ll need to some extra tricks with nnx.vmap to make everything work. Because of this additional complexity, we recommend that new flax projects stick to the explicit style.

Filtering random state#

Implicit random state can be manipulated using Filters just like any other type of state. It can be filtered using types (nnx.RngState, nnx.RngKey, nnx.RngCount) or using strings corresponding to the stream names (refer to the Flax NNX Filter DSL). Here’s an example using nnx.state with various filters to select different substates of the Rngs inside a Model:

model = Model(nnx.Rngs(params=0, dropout=1))

rng_state = nnx.state(model, nnx.RngState) # All random states.
key_state = nnx.state(model, nnx.RngKey) # Only PRNG keys.
count_state = nnx.state(model, nnx.RngCount) # Only counts.
rng_dropout_state = nnx.state(model, 'dropout') # Only `dropout`.

nnx.display(rng_dropout_state)

Reseeding#

In Haiku and Flax Linen, random states are explicitly passed to Module.apply each time before you call the model. This makes it easy to control the randomness of the model when needed (for example, for reproducibility).

In Flax NNX, there are two ways to approach this:

  1. By passing an nnx.Rngs object through the __call__ stack manually, as shown previously.

  2. By using nnx.reseed to set the random state of the model to a specific configuration. This option is less intrusive and can be used even if the model is not designed to enable manual control over the random state.

nnx.reseed is a function that accepts an arbitrary graph node (this includes pytrees of nnx.Modules) and some keyword arguments containing the new seed or key value for the nnx.RngStreams specified by the argument names. nnx.reseed will then traverse the graph and update the random state of the matching nnx.RngStreams, this includes both setting the key to a possibly new value and resetting the count to zero.

Here’s an example of how to use nnx.reseed to reset the random state of the nnx.Dropout layer and verify that the computation is identical to the first time the model was called:

model = Model(nnx.Rngs(params=0, dropout=1))
x = jnp.ones((1, 20))

y1 = model(x)
y2 = model(x)

nnx.reseed(model, dropout=1) # reset dropout RngState
y3 = model(x)

assert not jnp.allclose(y1, y2) # different
assert jnp.allclose(y1, y3)     # same

Forking implicit random state#

We saw above how to use rng.fork when passing explicit random state through Flax NNX transforms like nnx.vmap or nnx.pmap. The decorator nnx.fork_rngs allows this for implicit random state. Consider the example below, which generates a batch of samples from the nondeterministic model we defined above.

rng_axes = nnx.StateAxes({'dropout': 0, ...: None})

@nnx.fork_rngs(split={'dropout': 5})
@nnx.vmap(in_axes=(rng_axes, None), out_axes=0)
def sample_from_model(model, x):
    return model(x)

print(sample_from_model(model, x).shape)

(5, 1, 10)

Here sample_from_model is modified by two decorators:

  • The function we get from the nnx.vmap decorator expects that the random state of the model argument has already been split into 5 pieces. It runs the model once for each random key.

  • The function we get from the nnx.fork_rngs decorator splits the random state of its model argument into five pieces before passing it on to the inner function.

Transforming implicit state#

In the previous section, we showed how to use nnx.vmap with a module that contained implicit random state. But we can use other nnx transformations too! Remember: implicit random state isn’t different from any other type of Model state, and this applies to Flax NNX transforms too. This means you can use the Flax NNX state handling APIs of each transform to get the results you want. For a more involved example, let’s explore how to implement recurrent dropout on an RNNCell using nnx.scan.

We’ll start by constructing the RNNCell class:

  • First, create an nnx.Dropout layer that will sample PRNG keys from a custom recurrent_dropout stream.

  • Apply dropout (drop) to the hidden state h of the RNNCell.

  • Then, define an initial_state function to create the initial state of the RNNCell.

  • Finally, instantiate RNNCell.

class Count(nnx.Variable): pass

class RNNCell(nnx.Module):
  def __init__(self, din, dout, rngs):
    self.linear = nnx.Linear(dout + din, dout, rngs=rngs)
    self.drop = nnx.Dropout(0.1, rngs=rngs, rng_collection='recurrent_dropout')
    self.dout = dout
    self.count = Count(jnp.array(0, jnp.uint32))

  def __call__(self, h, x) -> tuple[jax.Array, jax.Array]:
    h = self.drop(h) # Recurrent dropout.
    y = nnx.relu(self.linear(jnp.concatenate([h, x], axis=-1)))
    self.count.value += 1
    return y, y

  def initial_state(self, batch_size: int):
    return jnp.zeros((batch_size, self.dout))

cell = RNNCell(8, 16, nnx.Rngs(params=0, recurrent_dropout=1))

Next, use nnx.scan over an unroll function to implement the rnn_forward operation:

  • The key ingredient of recurrent dropout is to apply the same dropout mask across all time steps. Therefore, to achieve this you will pass nnx.StateAxes to nnx.scan’s in_axes, specifying that the cell’s recurrent_dropout PRNG stream will be broadcast, and the rest of the RNNCell’s state will be carried over.

  • Also, the hidden state h will be the nnx.scan’s Carry variable, and the sequence x will be scanned over its axis 1.

@nnx.jit
def rnn_forward(cell: RNNCell, x: jax.Array):
  h = cell.initial_state(batch_size=x.shape[0])

  # Broadcast the 'recurrent_dropout' PRNG state to have the same mask on every step.
  state_axes = nnx.StateAxes({'recurrent_dropout': None, ...: nnx.Carry})
  @nnx.scan(in_axes=(state_axes, nnx.Carry, 1), out_axes=(nnx.Carry, 1))
  def unroll(cell: RNNCell, h, x) -> tuple[jax.Array, jax.Array]:
    h, y = cell(h, x)
    return h, y

  h, y = unroll(cell, h, x)
  return y

x = jnp.ones((4, 20, 8))
y = rnn_forward(cell, x)

print(f'{y.shape = }')
print(f'{cell.count.value = }')

y.shape = (4, 20, 16)
cell.count.value = Array(20, dtype=uint32)
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