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Data, Model, and Activation Partitioning

TL;DR: The recommended way of specifying partitions in T5X.

Partitioning is the process dividing and replicating machine learning model parameters, activations, and data across the accelerator devices (TPU/GPU) in order to:

  • Train and infer from models too large to fit in the memory of a single device
  • Use extremely large batch sizes
  • Train faster

How to Partition

Partitioning in T5X is configured in two steps:

  1. Specify logical axes names for parameter and activation array dimensions
  2. Map the logical names to the physical axes of the accelerator mesh

Let's take a closer look at each of these steps.

Note: In T5X, partitioning is primarily provided through the jax.pjit backend via PjitPartitioner using the Gin configuration framework.

Specify logical axis names

Logical axis names are a user-configured shorthand for grouping axes (aka dimensions) of either parameter or activation arrays in a model implementation.

For example, you could refer to the axes of the inputs to a model as ('batch', 'length', 'vocab'). If the parameters of the embedding matrix are labelled ('vocab', 'embed') then the activations following embedding should be named ('batch', 'length', 'embed').

Description Logical Axis Names
Inputs to model ('batch', 'length', 'vocab')
Embedding parameters ('vocab', 'embed')
Activations ('batch', 'length', 'embed')

How to configure logical axis names

Logical axis annotations can be provided through the utilities in flax.linen.partitioning.

Instead of calling self.param to create parameters within your model implementation, use the flax.linen.partitioning.param_with_axes API to communicate axis names for each parameter.

from flax.linen import partitioning

scale = partitioning.param_with_axes(
    'scale', self.scale_init, (features,), jnp.float32, axes=('embed',))

For an example in context, see layers.py.

Tip: We recommend you use the canonical logical axis names listed below.

To specify the logical axes for activation partitioning, provide the logical axes names to flax.linen.partitioning.with_sharding_constraint (instead of using jax.pjit.with_sharding_constraint or t5x.partitioning.with_sharding_constraint).

from flax.linen import partitioning

...
output = jnp.dot(x, embedding)
output = with_sharding_constraint(output, ('batch', 'length', 'embed'))
return output

Map logical names to device

For jax.pjit to know how to partition these arrays across the hardware, the logical axis names must be mapped to the physical axes of the accelerator mesh.

Note: A mesh is an n-dimensional array of TPU (or GPU) processors, connected by a network. The TPUv3 processor is limited to 2D meshes. The TPUv4 processor can handle 3D meshes.

In T5X, the two primary hardware axes are named 'data' and 'model', referring to the default mappings for data- and model-parallelism.

Note: You are actually free to map model parameters or activations across the 'data' axis. In fact, this is what is done in 2D parameter/activation sharding. To see how this works in practice, see:

Configuring PjitPartitioner

PjitPartitioner has three primary constructor arguments:

  • model_parallel_submesh
  • num_partitions
  • logical_axis_rules

The model_parallel_submesh and num_partitions arguments provide two mutually-exclusive methods of specifying the submesh of devices to use for model partitioning. As a rule of thumb:

  • Use model_parallel_submesh when you want to specify how the logical names are mapped to the device
  • Usenum_partitions for an automatic mapping

Using model_parallel_submesh

The PjitPartitioner constructor argument that provides the most control is:

model_parallel_submesh(Tuple[int, int, int, int])

It is a 4-tuple that specifies the (x, y, z, c) model-parallel submesh–an axis of accelerator parallelism orthogonal to data parallelism. Axes in a model's parameter or activation arrays can be sharded over this submesh using axis rules that map them to 'model'.

Note: The effective number of model subpartitions is equal to np.prod(model_parallel_submesh) and must evenly divide the total number of devices. Specifically:
jax.device_count() % np.prod(model_parallel_submesh) == 0.

The rest of the TPU mesh is the data parallel submesh, providing jax.device_count() // np.prod(model_parallel_submesh) partitions. It is used for data (aka batch) parallelism and to shard other array axes that are mapped to 'data'.

Using num_partitions

Alternatively,

num_partitions(int)

accepts an integer that specifies the size of the model parallel submesh to be automatically selected for the current topology.

Using logical_axis_rules

The third key argument is

logical_axis_rules(Sequence[Tuple[str, Optional[str]]])

This argument accepts a priority-ordered sequence of key-value (KV) tuples. These tuples map the logical axis names to hardware resources, using 'model' and 'data' as the two primary hardware axes. Specifically, each logical axis can be mapped to one of:

  • None to disable sharding, and thus be fully-replicated
  • 'model' to shard across the model-parallel submesh
  • 'data' to shard across the data-parallel submesh

The same key can be mapped to multiple values. For each array, mappings are applied in priority order. If a hardware resource has already been assigned in to a different axis and multiple keys exist, a latter mapping may be used.

For example, consider the following set of logical axis rules:

[
  ('head', 'model'),
  ('embed', 'model'),
  ('embed', 'data'),
  ('vocab', 'model'),
]

For an array with logical axes ('embed', 'head'), 'head' will first be mapped to 'model', since it comes first in the priority list. Next, 'embed' will be mapped to 'data', since 'model' has already been used. However, an array with logical axes ('vocab', 'embed') will receive the mapping (None, 'model') since 'embed' has a higher priority than 'vocab'.

T5X provides the t5x.partitioning.standard_logical_axis_rules() function to generate canonical logical axis rule sets depending on how many mesh dimensions you wish to shard. This assumes that you are using canonical logical axis names.

For details, see t5x.partitioning.standard_logical_axis_rules().

Other Stuff

Overriding axis names from an external codebase

You may wish to incorporate Flax modules from an external codebase into your model implementation that uses self.param instead of flax.linen.partitioning.param_with_axes, or that may use axis names that are incompatible with your codebase.

To deal with this situation, we provide the utils.override_params_axes_names helper function. This helper can be called at the end of Model.get_initial_variables to apply a priority-ordered mapping from regex patterns (fully matching parameter names) to tuples containing string logical axis names to replace model-derived names.

For example, the following configuration provides logical axis names for an external module called 'external_mlp' used in every layer of the model's encoder, without modifying any other modules:

class MyCustomEncoderDecoderModel(models.EncoderDecoderModel):

  def get_initial_variables():
    self,
    rng: jnp.ndarray,
    input_shapes: Mapping[str, Array],
    input_types: Optional[Mapping[str, jnp.dtype]] = None
  ) -> flax_scope.FrozenVariableDict:
    initial_variables = super().get_initial_variables(
        rng=rng, input_shapes=input_shapes, input_types=input_types)
    return utils.override_params_axes_names(
        initial_variables,
        params_axes_names_override=[
            ('encoder/layer_\\d/external_mlp/kernel':, ('embed', 'mlp')),
            ('encoder/layer_\\d/external_mlp/bias':, ('mlp',)),
        ])

Note: It is not possible to add or modify activation partitioning in an external module.

Canonical logical axis names

Use the following logical axis names to be compatible with t5x.partitioning.standard_logical_axis_rules:

Logical Axis Name Description
"embed" The common "activation_dim" in the network, first
: : emitted by the embedding layer. :
"heads" Number of heads for attention/relative position
: : biases. :
"kv" For query/key/value hidden dimensions of each head.
"joined_kv" For "heads * kv" fused dimension of attention
: : matrices, when the kernel is reshaped such that :
: : "heads" and "kv" are packed in the same dimension. :
"mlp" Intermediate dimension of the feed-forward layer.
"vocab" For embeddings, the input/output vocabulary size.
"mlp_activations" For fused MLP matrices that have a dimension for the
: : activation function index. :
"stack" For KV and QKV fused attention implementations, the
: : manual parameter-fusion stacked dimension. :
"abspos_buckets" / The dimension for positional bias buckets.
: "relpos_buckets" : :

If you wish to use a non-canonical axis name, you will need to pass a custom set of axis rules to the PjitPartitioner.

Example configurations

Automatic - Full 2D partitioning

You can override the default 1D sharding configuration by modifying the arguments to t5x.partitioning.standard_logical_axis_rules. For example, for full parameter and activation 2D partitioning you can set:

from t5x import partitioning

train_script.train:
  partitioner = @partitioning.PjitPartitioner()

partitioning.PjitPartitioner:
  num_partitions = 1
  logical_axis_rules= @partitioning.standard_logical_axis_rules()

partitioning.standard_logical_axis_rules:
  activation_partitioning_dims = 2
  parameter_partitioning_dims = 2

Manual configurations

Alternatively, you can manually set the rules, experimenting with some of the following options:

Data-only parallelism

partitioning.PjitPartitioner.logical_axis_rules = [
    ('batch', 'data'),
    ('vocab', None),
    ('embed', None),
    ('mlp', None),
    ('heads', None),
    ('kv', None),
    ('joined_kv', None),
    ('relpos_buckets', None),
    ('abspos_buckets', None),
    ('length', None),
    ('layers', None),
    ('stack', None),
    ('mlp_activations', None),
]

Data parallel with parameter gather

An example of 2D parameter partitioning with trival MP submesh, such as ZeRO-3.

partitioning.PjitPartitioner.logical_axis_rules = [
    ('batch', 'data'),
    # all weight matrices have this axis; activations already shard it along 'data'
    ('embed', 'data'),
    ('vocab', None),
    ('mlp', None),
    ('heads', None),
    ('kv', None),
    ('joined_kv', None),
    ('relpos_buckets', None),
    ('abspos_buckets', None),
    ('length', None),
    ('layers', None),
    ('stack', None),
    ('mlp_activations', None),
]

Data and model parallel with replicated activations

An example of 1D parameter partitioning, such as Megatron.

partitioning.PjitPartitioner.logical_axis_rules = [
    ('batch', 'data'),
    ('mlp', 'model'),
    ('heads', 'model'),
    ('vocab', 'model'),
    ('embed', None),
    ('kv', None),
    ('joined_kv', None),
    ('relpos_buckets', None),
    ('abspos_buckets', None),
    ('length', None),
    ('layers', None),
    ('stack', None),
    ('mlp_activations', None),
]

Data and model parallel with sharded activations

An example of 1D parameter partitioning with 2D activation partitioning, such as Optimus.

partitioning.PjitPartitioner.logical_axis_rules = [
    ('batch', 'data'),
    ('mlp', 'model'),
    ('heads', 'model'),
    ('vocab', 'model'),
    # shard remaining activations; weight matrices already have axes mapped to 'model'
    ('embed', 'model'),
    ('kv', None),
    ('joined_kv', None),
    ('relpos_buckets', None),
    ('abspos_buckets', None),
    ('length', None),
    ('layers', None),
    ('stack', None),
    ('mlp_activations', None),
]

Full 2D sharding

An example of 2D parameter and activation partitioning, such as GShard.

partitioning.PjitPartitioner.logical_axis_rules = [
    ('batch', 'data'),
    ('mlp', 'model'),
    ('heads', 'model'),
    ('vocab', 'model'),
    # shard both activations and weight matrices on the remaining available axis
    ('embed', 'model'),
    ('embed', 'data'),
    ('kv', None),
    ('joined_kv', None),
    ('relpos_buckets', None),
    ('abspos_buckets', None),
    ('length', None),
    ('layers', None),
    ('stack', None),
    ('mlp_activations', None),
]