Randomness

Randomness#

Random state in Flax NNX is radically simplified compared to systems like Haiku/Flax Linen in that it defines “random state as object state”. In essence, this means that random state is just another type of state, and is stored in Variables and help by the models themselves. The main characteristic of the RNG system in Flax NNX is that its explicit, its order-based, and uses dynamic counters. This is a bit different from Flax Linen’s RNG system which is (path + order)-based and uses a static counters.

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

Rngs, RngStream, and RngState#

Flax NNX provides the nnx.Rngs type a the main convenience API for managing random state. Following Flax Linen’s footsteps, Rngs has the ability to create multiple named RNG streams, each with its own state, for the purpose of tight control over randomness in the context of JAX transforms. Here’s a breakdown of the main RNG-related types in Flax NNX:

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

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

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

    • nnx.RngKey: Variable type for holding RNG keys, it includes a tag attribute containing the name of the stream.

    • nnx.RngCount: Variable type for holding RNG counts, it includes a tag attribute containing the name of the stream.

To create an Rngs object you can simply pass a 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 Variables contain the 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 a new keys are generated.

Standard stream names#

There are only two standard stream names used by Flax NNX’s built-in layers, shown in the table below:

Name

Description

params

Used for parameter initialization

dropout

Used by Dropout to create dropout masks

params is used my most of the standard layers (Linear, Conv, MultiHeadAttention, etc) during construction to initialize their parameters. dropout is used by the Dropout and MultiHeadAttention to generate dropout masks. Here’s a simple example of a model using params and dropout 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 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 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 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 default
key3 = rngs() # call default directly

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

nnx.display(rngs)

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

Note
For big 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 (RngState, RngKey, RngCount) or using strings corresponding to the stream names (see The 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 state
key_state = nnx.state(model, nnx.RngKey) # only 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 keys

nnx.display(params_key_state)

Reseeding#

In Haiku and Flax Linen, random state explicitly passed to apply each time before calling the model. This makes it easy to control the randomness of the model when needed e.g. for reproducibility. In Flax NNX there are two ways to approach this:

  1. By passing an Rngs object through the __call__ stack manually. Standard layers like Dropout and MultiHeadAttention accept an rngs argument in case 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.

reseed is a function that accepts an arbitrary graph node (this include pytrees of Flax NNX Modules) and some keyword arguments containing the new seed or key value for the RngStreams specified by the argument names. reseed will then traverse the graph and update the random state of the matching 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 using reseed to reset the random state of the 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 Rngs#

When interacting with transforms like vmap or 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 way, either by manually splitting a key before passing it to one of the Rngs streams, or using the nnx.split_rngs decorator which will automatically split the random state of any RngStreams found in the inputs of the function and automatically “lower” them once the function call ends. split_rngs is more convenient as it works nicely with transforms so we’ll show an example of that here:

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 that split_rngs allows passing a Filter to the only keyword argument to select the RngStreams that should be split when inside the function, in this case we only split the dropout stream.

Transforms#

As stated before, in Flax NNX random state is just another type of state, this means that there is nothing special about it regarding transforms. This means that you should be able to use the state handling APIs of each transform to get the results you want. In this section we will two examples of using random state in transforms, one with pmap where we’ll see how to split the RNG state, and another one with scan where we’ll see how to freeze the RNG state.

Data parallel dropout#

In the first example we’ll explore how to use pmap to call our Model in a data parallel context. Since Model uses Dropout we’ll need to split the random state of the dropout to ensure that each replica gets different dropout masks. StateAxes is passed to in_axes to specify that the model’s dropout stream will be parallelized across axis 0, and the rest of its state will be replicated. split_rngs is used to split the keys of the dropout 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 we will explore how to implement a RNNCell that uses recurrent dropout. To do this we will simply create a Dropout layer that will sample keys from a custom recurrent_dropout stream, and we will apply dropout to the hidden state h of the RNNCell. A initial_state method will be defined to create the initial state of the 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 we will use 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, to achieve this we’ll pass StateAxes to scan’s in_axes specifying that the cell’s recurrent_dropout stream will be broadcasted, and the rest of the cell’s state will be carried over. Also, the hidden state h will be the 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 'recurrent_dropout' RNG 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)
Contents