schedules.py 27.5 KB
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# coding=utf-8
# Copyright (c) 2020, NVIDIA CORPORATION.  All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

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from contextlib import contextmanager
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import torch
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from torch.autograd.variable import Variable
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from torch.nn.parallel.distributed import DistributedDataParallel as torchDDP
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from megatron import get_args
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from megatron import get_num_microbatches
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from megatron import get_timers
from megatron import mpu
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from megatron import p2p_communication
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from megatron.utils import unwrap_model
from megatron.model import DistributedDataParallel as LocalDDP
from megatron.model import Float16Module
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from megatron.model import ModelType

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def get_forward_backward_func():
    args = get_args()
    if mpu.get_pipeline_model_parallel_world_size() > 1:
        if args.virtual_pipeline_model_parallel_size is not None:
            forward_backward_func = forward_backward_pipelining_with_interleaving
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            assert get_num_microbatches() % args.pipeline_model_parallel_size == 0, \
                'number of microbatches is not divisible by pipeline-parallel ' \
                'size when using interleaved schedule'
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        else:
            forward_backward_func = forward_backward_pipelining_without_interleaving
    else:
        forward_backward_func = forward_backward_no_pipelining
    return forward_backward_func

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def deallocate_output_tensor(out):
    '''Pseudo-deallocate (i.e., set to scalar) the output tensor's '.data' field.
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    This method should be called right after the output tensor has been
    sent to the next pipeline stage. At this point, the output tensor is
    only useful for its '.grad_fn' field, and not its '.data'.
    '''
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    if out is None:
        return
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    assert isinstance(out, torch.Tensor), \
        "expected Tensor, found %s." % type(out).__name__
    assert out._base is None, \
        "counter-productive to free a view of another tensor."
    out.data = torch.empty(
        (1,),
        device = out.device,
        dtype = out.dtype,
    )
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def custom_backward(output, grad_output):
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    '''Directly call C++ autograd engine.

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    To make the 'deallocate_output_tensor' (above) optimization work, the C++
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    autograd engine must be called directly, bypassing Pytorch's
    torch.autograd.backward. Pytorch's 'backward' checks that the output and
    grad have the same shape, while C++'s 'backward' does not.
    '''
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    assert output.numel() == 1, \
        "output should be pseudo-'freed' in schedule, to optimize memory"
    assert isinstance(output, torch.Tensor), \
        "output == '%s'." % type(output).__name__
    assert isinstance(grad_output, (torch.Tensor, type(None))), \
        "grad_output == '%s'." % type(grad_output).__name__

    # Handle scalar output
    if grad_output is None:
        assert output.numel() == 1, "implicit grad requires scalar output."
        grad_output = torch.ones_like(
            output,
            memory_format = torch.preserve_format,
        )

    # Call c++ engine [ see torch/csrc/autograd/python_engine.cpp ]
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    Variable._execution_engine.run_backward(
        tensors = (output,),
        grad_tensors = (grad_output,),
        keep_graph = False,
        create_graph = False,
        inputs = tuple(),
        allow_unreachable=True,
        accumulate_grad=True,
    )
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def forward_step(forward_step_func, data_iterator, model, input_tensor, losses_reduced):
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    """Forward step for passed-in model.

    If first stage, input tensor is obtained from data_iterator, otherwise
    passed-in input_tensor is used.

    Returns output tensor."""
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    args = get_args()
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    timers = get_timers()

    timers('forward-compute').start()
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    unwrapped_model = unwrap_model(
        model, (torchDDP, LocalDDP, Float16Module))
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    unwrap_output_tensor = False
    if not isinstance(input_tensor, list):
        input_tensor = [input_tensor]
        unwrap_output_tensor = True

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    unwrapped_model.set_input_tensor(input_tensor)
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    output_tensor, loss_func = forward_step_func(data_iterator, model)
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    if mpu.is_pipeline_last_stage():
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        output_tensor = loss_func(output_tensor)
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        loss, loss_reduced = output_tensor
        output_tensor = loss / get_num_microbatches()
        losses_reduced.append(loss_reduced)
    timers('forward-compute').stop()

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    # If T5 model (or other model with encoder and decoder)
    # and in decoder stack, then send encoder_hidden_state
    # downstream as well.
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    if mpu.is_pipeline_stage_after_split() and \
            args.model_type == ModelType.encoder_and_decoder:
        return [output_tensor, input_tensor[-1]]
    if unwrap_output_tensor:
        return output_tensor
    return [output_tensor]
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def backward_step(optimizer, input_tensor, output_tensor, output_tensor_grad):
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    """Backward step through passed-in output tensor.

    If last stage, output_tensor_grad is None, otherwise gradient of loss
    with respect to stage's output tensor.

    Returns gradient of loss with respect to input tensor (None if first
    stage)."""
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    # NOTE: This code currently can handle at most one skip connection. It
    # needs to be modified slightly to support arbitrary numbers of skip
    # connections.
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    args = get_args()

    timers = get_timers()
    timers('backward-compute').start()

    # Retain the grad on the input_tensor.
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    unwrap_input_tensor_grad = False
    if not isinstance(input_tensor, list):
        input_tensor = [input_tensor]
        unwrap_input_tensor_grad = True
    for x in input_tensor:
        if x is not None:
            x.retain_grad()

    if not isinstance(output_tensor, list):
        output_tensor = [output_tensor]
    if not isinstance(output_tensor_grad, list):
        output_tensor_grad = [output_tensor_grad]
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    # Backward pass.
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    if output_tensor_grad[0] is None:
        output_tensor = optimizer.scale_loss(output_tensor[0])
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    custom_backward(output_tensor[0], output_tensor_grad[0])
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    # Collect the grad of the input_tensor.
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    input_tensor_grad = [None]
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    if input_tensor is not None:
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        input_tensor_grad = []
        for x in input_tensor:
            if x is None:
                input_tensor_grad.append(None)
            else:
                input_tensor_grad.append(x.grad)

    # Handle single skip connection if it exists (encoder_hidden_state in
    # model with encoder and decoder).
    if mpu.get_pipeline_model_parallel_world_size() > 1 and \
            mpu.is_pipeline_stage_after_split() and \
            args.model_type == ModelType.encoder_and_decoder:
        if output_tensor_grad[1] is not None:
            input_tensor_grad[-1].add_(output_tensor_grad[1])
    if unwrap_input_tensor_grad:
        input_tensor_grad = input_tensor_grad[0]
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    timers('backward-compute').stop()

    return input_tensor_grad


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@contextmanager
def dummy_handler():
    try:
        yield
    finally:
        pass


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def forward_backward_no_pipelining(forward_step_func, data_iterator, model,
                                   optimizer, timers, forward_only):
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    """Run forward and backward passes with no pipeline parallelism
    (no inter-stage communication).

    Returns dictionary with losses."""
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    assert len(model) == 1
    model = model[0]

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    context_handler = dummy_handler
    if isinstance(model, torchDDP):
        context_handler = model.no_sync

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    losses_reduced = []
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    input_tensor, output_tensor_grad = None, None
    with context_handler():
        for i in range(get_num_microbatches() - 1):
            output_tensor = forward_step(forward_step_func, data_iterator, model,
                                         input_tensor, losses_reduced)
            if not forward_only:
                backward_step(optimizer, input_tensor, output_tensor,
                              output_tensor_grad)

    # Run computation for last microbatch out of context handler (want to
    # synchronize gradients).
    output_tensor = forward_step(forward_step_func, data_iterator, model,
                                 input_tensor, losses_reduced)
    if not forward_only:
        backward_step(optimizer, input_tensor, output_tensor, output_tensor_grad)
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    return losses_reduced


def forward_backward_pipelining_with_interleaving(forward_step_func, data_iterator, model,
                                                  optimizer, timers, forward_only):
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    """Run interleaved 1F1B schedule (model split into model chunks), with
    communication between pipeline stages as needed.

    Returns dictionary with losses if the last stage, empty dict otherwise."""
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    input_tensors = [[] for _ in range(len(model))]
    output_tensors = [[] for _ in range(len(model))]
    losses_reduced = []
    if not forward_only:
        output_tensor_grads = [[] for _ in range(len(model))]

    pipeline_parallel_size = mpu.get_pipeline_model_parallel_world_size()
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    pipeline_parallel_rank = mpu.get_pipeline_model_parallel_rank()
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    args = get_args()
    tensor_shape = (args.seq_length, args.micro_batch_size, args.hidden_size)

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    # Compute number of warmup and remaining microbatches.
    num_model_chunks = len(model)
    num_microbatches = get_num_microbatches() * num_model_chunks
    all_warmup_microbatches = False
    if forward_only:
        num_warmup_microbatches = num_microbatches
    else:
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        # Run all forward passes and then all backward passes if number of
        # microbatches is just the number of pipeline stages.
        # Otherwise, perform (num_model_chunks-1)*pipeline_parallel_size on
        # all workers, followed by more microbatches after depending on
        # stage ID (more forward passes for earlier stages, later stages can
        # immediately start with 1F1B).
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        if get_num_microbatches() == pipeline_parallel_size:
            num_warmup_microbatches = num_microbatches
            all_warmup_microbatches = True
        else:
            num_warmup_microbatches = \
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                (pipeline_parallel_size - pipeline_parallel_rank - 1) * 2
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            num_warmup_microbatches += (
                num_model_chunks - 1) * pipeline_parallel_size
            num_warmup_microbatches = min(num_warmup_microbatches,
                                          num_microbatches)
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    num_microbatches_remaining = \
        num_microbatches - num_warmup_microbatches

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    def get_model_chunk_id(microbatch_id, forward):
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        """Helper method to get the model chunk ID given the iteration number."""
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        microbatch_id_in_group = microbatch_id % (pipeline_parallel_size * num_model_chunks)
        model_chunk_id = microbatch_id_in_group // pipeline_parallel_size
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        if not forward:
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            model_chunk_id = (num_model_chunks - model_chunk_id - 1)
        return model_chunk_id
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    def forward_step_helper(microbatch_id):
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        """Helper method to run forward step with model split into chunks
        (run set_virtual_pipeline_model_parallel_rank() before calling
        forward_step())."""
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        model_chunk_id = get_model_chunk_id(microbatch_id, forward=True)
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        mpu.set_virtual_pipeline_model_parallel_rank(model_chunk_id)

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        # forward step
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        if mpu.is_pipeline_first_stage():
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            if len(input_tensors[model_chunk_id]) == \
                    len(output_tensors[model_chunk_id]):
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                input_tensors[model_chunk_id].append(None)
        input_tensor = input_tensors[model_chunk_id][-1]
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        output_tensor = forward_step(forward_step_func,
                                     data_iterator[model_chunk_id],
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                                     model[model_chunk_id],
                                     input_tensor, losses_reduced)
        output_tensors[model_chunk_id].append(output_tensor)

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        # if forward-only, no need to save tensors for a backward pass
        if forward_only:
            input_tensors[model_chunk_id].pop()
            output_tensors[model_chunk_id].pop()

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        return output_tensor

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    def backward_step_helper(microbatch_id):
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        """Helper method to run backward step with model split into chunks
        (run set_virtual_pipeline_model_parallel_rank() before calling
        backward_step())."""
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        model_chunk_id = get_model_chunk_id(microbatch_id, forward=False)
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        mpu.set_virtual_pipeline_model_parallel_rank(model_chunk_id)

        if mpu.is_pipeline_last_stage():
            if len(output_tensor_grads[model_chunk_id]) == 0:
                output_tensor_grads[model_chunk_id].append(None)
        input_tensor = input_tensors[model_chunk_id].pop(0)
        output_tensor = output_tensors[model_chunk_id].pop(0)
        output_tensor_grad = output_tensor_grads[model_chunk_id].pop(0)
        input_tensor_grad = \
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            backward_step(optimizer,
                          input_tensor,
                          output_tensor,
                          output_tensor_grad)
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        return input_tensor_grad

    # Run warmup forward passes.
    mpu.set_virtual_pipeline_model_parallel_rank(0)
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    input_tensors[0].append(
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        p2p_communication.recv_forward(tensor_shape, timers=timers))
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    for k in range(num_warmup_microbatches):
        output_tensor = forward_step_helper(k)
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        # Determine if tensor should be received from previous stage.
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        next_forward_model_chunk_id = get_model_chunk_id(k+1, forward=True)
        recv_prev = True
        if mpu.is_pipeline_first_stage(ignore_virtual=True):
            if next_forward_model_chunk_id == 0:
                recv_prev = False
        if k == (num_microbatches - 1):
            recv_prev = False
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        # Don't send tensor downstream if on last stage.
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        if mpu.is_pipeline_last_stage():
            output_tensor = None
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        # Send and receive tensors as appropriate (send tensors computed
        # in this iteration; receive tensors for next iteration).
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        if k == (num_warmup_microbatches - 1) and not forward_only and \
                not all_warmup_microbatches:
            input_tensor_grad = None
            recv_next = True
            if mpu.is_pipeline_last_stage(ignore_virtual=True):
                recv_next = False
            input_tensor, output_tensor_grad = \
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                p2p_communication.send_forward_backward_recv_forward_backward(
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                        output_tensor, input_tensor_grad,
                        recv_prev=recv_prev, recv_next=recv_next,
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                        tensor_shape=tensor_shape,
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                        timers=timers)
            output_tensor_grads[num_model_chunks-1].append(output_tensor_grad)
        else:
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            input_tensor = \
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                p2p_communication.send_forward_recv_forward(
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                    output_tensor, recv_prev=recv_prev,
                    tensor_shape=tensor_shape,
                    timers=timers)
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        input_tensors[next_forward_model_chunk_id].append(input_tensor)
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        deallocate_output_tensor(output_tensor)
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    # Run 1F1B in steady state.
    for k in range(num_microbatches_remaining):
        # Forward pass.
        forward_k = k + num_warmup_microbatches
        output_tensor = forward_step_helper(forward_k)

        # Backward pass.
        backward_k = k
        input_tensor_grad = backward_step_helper(backward_k)

        # Send output_tensor and input_tensor_grad, receive input_tensor
        # and output_tensor_grad.

        # Determine if current stage has anything to send in either direction,
        # otherwise set tensor to None.
        forward_model_chunk_id = get_model_chunk_id(forward_k, forward=True)
        mpu.set_virtual_pipeline_model_parallel_rank(forward_model_chunk_id)
        if mpu.is_pipeline_last_stage():
            output_tensor = None

        backward_model_chunk_id = get_model_chunk_id(backward_k, forward=False)
        mpu.set_virtual_pipeline_model_parallel_rank(backward_model_chunk_id)
        if mpu.is_pipeline_first_stage():
            input_tensor_grad = None

        # Determine if peers are sending, and where in data structure to put
        # received tensors.
        recv_prev = True
        if mpu.is_pipeline_first_stage(ignore_virtual=True):
            # First stage is ahead of last stage by (pipeline_parallel_size - 1).
            next_forward_model_chunk_id = get_model_chunk_id(
                forward_k - (pipeline_parallel_size - 1), forward=True)
            if next_forward_model_chunk_id == (num_model_chunks - 1):
                recv_prev = False
            next_forward_model_chunk_id += 1
        else:
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            next_forward_model_chunk_id = get_model_chunk_id(forward_k + 1,
                                                             forward=True)
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        recv_next = True
        if mpu.is_pipeline_last_stage(ignore_virtual=True):
            # Last stage is ahead of first stage by (pipeline_parallel_size - 1).
            next_backward_model_chunk_id = get_model_chunk_id(
                backward_k - (pipeline_parallel_size - 1), forward=False)
            if next_backward_model_chunk_id == 0:
                recv_next = False
            next_backward_model_chunk_id -= 1
        else:
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            next_backward_model_chunk_id = get_model_chunk_id(backward_k + 1,
                                                              forward=False)
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        # If last iteration, don't receive; we already received one extra
        # before the start of the for loop.
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        if k == (num_microbatches_remaining - 1):
            recv_prev = False

        # Communicate tensors.
        input_tensor, output_tensor_grad = \
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            p2p_communication.send_forward_backward_recv_forward_backward(
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                    output_tensor, input_tensor_grad,
                    recv_prev=recv_prev, recv_next=recv_next,
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                    tensor_shape=tensor_shape, timers=timers)
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        deallocate_output_tensor(output_tensor)
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        # Put input_tensor and output_tensor_grad in data structures in the
        # right location.
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        if recv_prev:
            input_tensors[next_forward_model_chunk_id].append(input_tensor)
        if recv_next:
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            output_tensor_grads[next_backward_model_chunk_id].append(
                output_tensor_grad)
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    # Run cooldown backward passes (flush out pipeline).
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    if not forward_only:
        if all_warmup_microbatches:
            output_tensor_grads[num_model_chunks-1].append(
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                p2p_communication.recv_backward(tensor_shape, timers=timers))
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        for k in range(num_microbatches_remaining, num_microbatches):
            input_tensor_grad = backward_step_helper(k)
            next_backward_model_chunk_id = get_model_chunk_id(k+1, forward=False)
            recv_next = True
            if mpu.is_pipeline_last_stage(ignore_virtual=True):
                if next_backward_model_chunk_id == (num_model_chunks - 1):
                    recv_next = False
            if k == (num_microbatches - 1):
                recv_next = False
            output_tensor_grads[next_backward_model_chunk_id].append(
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                p2p_communication.send_backward_recv_backward(
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                    input_tensor_grad, recv_next=recv_next,
                    tensor_shape=tensor_shape,
                    timers=timers))
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    return losses_reduced


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def get_tensor_shapes(rank, model_type):
    # Determine right tensor sizes (based on position of rank with respect to split
    # rank) and model size.
    # Send two tensors if model is T5 and rank is in decoder stage:
    #     first tensor is decoder (pre-transpose),
    #     second tensor is encoder (post-transpose).
    # If model is T5 and rank is at the boundary:
    #     send one tensor (post-transpose from encoder).
    # Otherwise, send one tensor (pre-transpose).
    args = get_args()
    tensor_shapes = []
    if model_type == ModelType.encoder_and_decoder:
        if mpu.is_pipeline_stage_before_split(rank):
            # If next rank is after split, then need transpose for encoder_hidden_state.
            if mpu.is_pipeline_stage_before_split(rank+1):
                tensor_shapes.append((args.seq_length, args.micro_batch_size, args.hidden_size))
            else:
                tensor_shapes.append((args.micro_batch_size, args.seq_length, args.hidden_size))
        else:
            tensor_shapes.append((args.decoder_seq_length, args.micro_batch_size, args.hidden_size))
            tensor_shapes.append((args.micro_batch_size, args.seq_length, args.hidden_size))
    else:
        tensor_shapes.append((args.seq_length, args.micro_batch_size, args.hidden_size))
    return tensor_shapes


def recv_forward(tensor_shapes, timers):
    input_tensors = []
    for tensor_shape in tensor_shapes:
        if tensor_shape is None:
            input_tensors.append(None)
        else:
            input_tensors.append(p2p_communication.recv_forward(tensor_shape,
                                                                timers=timers))
    return input_tensors


def recv_backward(tensor_shapes, timers):
    output_tensor_grads = []
    for tensor_shape in tensor_shapes:
        if tensor_shape is None:
            output_tensor_grads.append(None)
        else:
            output_tensor_grads.append(p2p_communication.recv_backward(tensor_shape,
                                                                       timers=timers))
    return output_tensor_grads


def send_forward(output_tensors, tensor_shapes, timers):
    if not isinstance(output_tensors, list):
        output_tensors = [output_tensors]
    for (output_tensor, tensor_shape) in zip(output_tensors, tensor_shapes):
        if tensor_shape is None:
            continue
        p2p_communication.send_forward(output_tensor, tensor_shape, timers=timers)


def send_backward(input_tensor_grads, tensor_shapes, timers):
    if not isinstance(input_tensor_grads, list):
        input_tensor_grads = [input_tensor_grads]
    for (input_tensor_grad, tensor_shape) in zip(input_tensor_grads, tensor_shapes):
        if tensor_shape is None:
            continue
        p2p_communication.send_backward(input_tensor_grad, tensor_shape, timers=timers)


def send_forward_recv_backward(output_tensors, tensor_shapes, timers):
    if not isinstance(output_tensors, list):
        output_tensors = [output_tensors]
    output_tensor_grads = []
    for (output_tensor, tensor_shape) in zip(output_tensors, tensor_shapes):
        if tensor_shape is None:
            output_tensor_grads.append(None)
            continue
        output_tensor_grad = p2p_communication.send_forward_recv_backward(
                output_tensor, tensor_shape, timers=timers)
        output_tensor_grads.append(output_tensor_grad)
    return output_tensor_grads


def send_backward_recv_forward(input_tensor_grads, tensor_shapes, timers):
    if not isinstance(input_tensor_grads, list):
        input_tensor_grads = [input_tensor_grads]
    input_tensors = []
    for (input_tensor_grad, tensor_shape) in zip(input_tensor_grads, tensor_shapes):
        if tensor_shape is None:
            input_tensors.append(None)
            continue
        input_tensor = p2p_communication.send_backward_recv_forward(
                input_tensor_grad, tensor_shape, timers=timers)
        input_tensors.append(input_tensor)
    return input_tensors


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def forward_backward_pipelining_without_interleaving(forward_step_func, data_iterator,
                                                     model, optimizer, timers,
                                                     forward_only):
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    """Run non-interleaved 1F1B schedule, with communication between pipeline
    stages.

    Returns dictionary with losses if the last stage, empty dict otherwise."""
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    args = get_args()
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    timers = get_timers()

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    assert len(model) == 1
    model = model[0]

    # Compute number of warmup microbatches.
    num_microbatches = get_num_microbatches()
    num_warmup_microbatches = \
        (mpu.get_pipeline_model_parallel_world_size() -
         mpu.get_pipeline_model_parallel_rank() - 1)
    num_warmup_microbatches = min(
        num_warmup_microbatches,
        num_microbatches)
    num_microbatches_remaining = \
        num_microbatches - num_warmup_microbatches

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    unwrapped_model = unwrap_model(
        model, (torchDDP, LocalDDP, Float16Module))
    model_type = unwrapped_model.model_type
    rank = mpu.get_pipeline_model_parallel_rank()
    recv_tensor_shapes = get_tensor_shapes(rank-1, model_type)
    send_tensor_shapes = get_tensor_shapes(rank, model_type)

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    # Input, output tensors only need to be saved when doing backward passes
    input_tensors = None
    output_tensors = None
    if not forward_only:
        input_tensors = []
        output_tensors = []
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    losses_reduced = []

    # Run warmup forward passes.
    for i in range(num_warmup_microbatches):
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        input_tensor = recv_forward(recv_tensor_shapes, timers=timers)
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        output_tensor = forward_step(forward_step_func, data_iterator, model,
                                     input_tensor, losses_reduced)
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        send_forward(output_tensor, send_tensor_shapes, timers=timers)
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        if not forward_only:
            input_tensors.append(input_tensor)
            output_tensors.append(output_tensor)
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            deallocate_output_tensor(output_tensor[0])
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    # Before running 1F1B, need to receive first forward tensor.
    # If all microbatches are run in warmup / cooldown phase, then no need to
    # receive this tensor here.
    if num_microbatches_remaining > 0:
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        input_tensor = recv_forward(recv_tensor_shapes, timers=timers)
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    # Run 1F1B in steady state.
    for i in range(num_microbatches_remaining):
        last_iteration = (i == (num_microbatches_remaining - 1))

        output_tensor = forward_step(forward_step_func, data_iterator, model,
                                     input_tensor, losses_reduced)
        if forward_only:
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            send_forward(output_tensor, send_tensor_shapes, timers=timers)
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            if not last_iteration:
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                input_tensor = recv_forward(recv_tensor_shapes, timers=timers)
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        else:
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            output_tensor_grad = \
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                send_forward_recv_backward(output_tensor,
                                           send_tensor_shapes,
                                           timers=timers)
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            # Add input_tensor and output_tensor to end of list.
            input_tensors.append(input_tensor)
            output_tensors.append(output_tensor)
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            deallocate_output_tensor(output_tensor[0])
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            # Pop input_tensor and output_tensor from the start of the list for
            # the backward pass.
            input_tensor = input_tensors.pop(0)
            output_tensor = output_tensors.pop(0)
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            input_tensor_grad = \
                backward_step(optimizer, input_tensor, output_tensor,
                              output_tensor_grad)

            if last_iteration:
                input_tensor = None
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                send_backward(input_tensor_grad, recv_tensor_shapes, timers=timers)
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            else:
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                input_tensor = \
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                    send_backward_recv_forward(
                        input_tensor_grad, recv_tensor_shapes, timers=timers)
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    # Run cooldown backward passes.
    if not forward_only:
        for i in range(num_warmup_microbatches):
            input_tensor = input_tensors.pop(0)
            output_tensor = output_tensors.pop(0)

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            output_tensor_grad = recv_backward(send_tensor_shapes, timers=timers)
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            input_tensor_grad = \
                backward_step(optimizer, input_tensor, output_tensor,
                              output_tensor_grad)

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            send_backward(input_tensor_grad, recv_tensor_shapes, timers=timers)
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    return losses_reduced