Randomness

Randomness#

Random state handling in Flax NNX was radically simplified compared to systems like Haiku and Flax Linen because Flax NNX defines the random state as an object state. In essence, this means that in Flax NNX, the random state is: 1) just another type of state; 2) stored in nnx.Variables; and 3) held by the models themselves.

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

  • It is explicit.

  • It is order-based.

  • It uses dynamic counters.

This is a bit different from Flax Linen’s PRNG system, which is (path + order)-based, and uses static 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.

Let’ start with some necessary imports:

from flax import nnx
import jax
from jax import random, numpy as jnp

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.

Standard PRNG key stream names#

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

  • params is used by most of the standard layers (such as nnx.Linear, nnx.Conv, nnx.MultiHeadAttention, and so on) during the construction to initialize their parameters.

  • dropout is used by nnx.Dropout and nnx.MultiHeadAttention to generate dropout masks.

Below is a simple example of a model that uses params and dropout PRNG key streams:

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)

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.

# Test with the `Model` that uses `params` and `dropout`.
model = Model(rngs)
y = model(jnp.ones((1, 20)))

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.

Filtering random state#

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_params_state = nnx.state(model, 'params') # Only `params`.
rng_dropout_state = nnx.state(model, 'dropout') # Only `dropout`.
params_key_state = nnx.state(model, nnx.All('params', nnx.RngKey)) # `Params` PRNG keys.

nnx.display(params_key_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. Standard layers like nnx.Dropout and nnx.MultiHeadAttention accept the rngs argument if you want to have tight control over the random state.

  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

Splitting PRNG keys#

When interacting with Flax NNX transforms like nnx.vmap or nnx.pmap, it is often necessary to split the random state such that each replica has its own unique state. This can be done in two ways:

  • By manually splitting a key before passing it to one of the nnx.Rngs streams; or

  • By using the nnx.split_rngs decorator which will automatically split the random state of any nnx.RngStreams found in the inputs of the function, and automatically “lower” them once the function call ends.

It is more convenient to use nnx.split_rngs, since it works nicely with Flax NNX transforms, so here’s one example:

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

@nnx.split_rngs(splits=5, only='dropout')
def f(rngs: nnx.Rngs):
  print('Inside:')
  # rngs.dropout() # ValueError: fold_in accepts a single key...
  nnx.display(rngs)

f(rngs)

print('Outside:')
rngs.dropout() # works!
nnx.display(rngs)

Inside:

Outside:

Note: nnx.split_rngs allows passing an NNX Filter to the only keyword argument in order to select the nnx.RngStreams that should be split when inside the function. In such a case, you only need to split the dropout PRNG key stream.

Transforms#

As stated before, in Flax NNX the random state is just another type of state. This means that there is nothing special about it when it comes to Flax NNX transforms, which means that you should be able to use the Flax NNX state handling APIs of each transform to get the results you want.

In this section, you will go through two examples of using the random state in Flax NNX transforms - one with nnx.pmap, where you will learn how to split the PRNG state, and another one with nnx.scan, where you will freeze the PRNG state.

Data parallel dropout#

In the first example, you’ll explore how to use nnx.pmap to call the nnx.Model in a data parallel context.

  • Since the nnx.Model uses nnx.Dropout, you’ll need to split the random state of the dropout to ensure that each replica gets different dropout masks.

  • nnx.StateAxes is passed to in_axes to specify that the model’s dropout PRNG key stream will be parallelized across axis 0, and the rest of its state will be replicated.

  • nnx.split_rngs is used to split the keys of the dropout PRNG key streams into N unique keys, one for each replica.

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

num_devices = jax.local_device_count()
x = jnp.ones((num_devices, 16, 20))
state_axes = nnx.StateAxes({'dropout': 0, ...: None})

@nnx.split_rngs(splits=num_devices, only='dropout')
@nnx.pmap(in_axes=(state_axes, 0), out_axes=0)
def forward(model: Model, x: jnp.ndarray):
  return model(x)

y = forward(model, x)
print(y.shape)

(1, 16, 10)

Recurrent dropout#

Next, let’s explore how to implement an RNNCell that uses a recurrent dropout. To do this:

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

  • You will 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 += 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, you will 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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