#
Performing gradient accumulation with Accelerate

Gradient accumulation is a technique where you can train on bigger batch sizes than your machine would normally be able to fit into memory. This is done by accumulating gradients over several batches, and only stepping the optimizer after a certain number of batches have been performed.

While technically standard gradient accumulation code would work fine in a distributed setup, it is not the most efficient method for doing so and you may experience considerable slowdowns!

In this tutorial you will see how to quickly setup gradient accumulation and perform it with the utilities provided in Accelerate, which can total to adding just one new line of code!

This example will use a very simplistic PyTorch training loop that performs gradient accumulation every two batches:

    device = "cuda"
    model.to(device)

    gradient_accumulation_steps = 2

    for index, batch in enumerate(training_dataloader):
        inputs, targets = batch
        inputs = inputs.to(device)
        targets = targets.to(device)
        outputs = model(inputs)
        loss = loss_function(outputs, targets)
        loss = loss / gradient_accumulation_steps
        loss.backward()
        if (index + 1) % gradient_accumulation_steps == 0:
            optimizer.step()
            scheduler.step()
            optimizer.zero_grad()

##
Converting it to Accelerate

First the code shown earlier will be converted to utilize Accelerate without the special gradient accumulation helper:

    + from accelerate import Accelerator
    + accelerator = Accelerator()

    + model, optimizer, training_dataloader, scheduler = accelerator.prepare(
    +     model, optimizer, training_dataloader, scheduler
    + )

      for index, batch in enumerate(training_dataloader):
          inputs, targets = batch
    -     inputs = inputs.to(device)
    -     targets = targets.to(device)
          outputs = model(inputs)
          loss = loss_function(outputs, targets)
          loss = loss / gradient_accumulation_steps
    +     accelerator.backward(loss)
          if (index+1) % gradient_accumulation_steps == 0:
              optimizer.step()
              scheduler.step()
              optimizer.zero_grad()

In its current state, this code is not going to perform gradient accumulation efficiently due to a process called gradient synchronization. Read more about that in the Concepts tutorial!

##
Letting Accelerate handle gradient accumulation

All that is left now is to let Accelerate handle the gradient accumulation for us. To do so you should pass in a `gradient_accumulation_steps` parameter to Accelerator, dictating the number of steps to perform before each call to `step()` and how to automatically adjust the loss during the call to backward():

      from accelerate import Accelerator
    - accelerator = Accelerator()
    + accelerator = Accelerator(gradient_accumulation_steps=2)

Alternatively, you can pass in a `gradient_accumulation_plugin` parameter to the Accelerator object’s `__init__`, which will allow you to further customize the gradient accumulation behavior. Read more about that in the GradientAccumulationPlugin docs.

From here you can use the accumulate() context manager from inside your training loop to automatically perform the gradient accumulation for you! You just wrap it around the entire training part of our code:

    - for index, batch in enumerate(training_dataloader):
    + for batch in training_dataloader:
    +     with accelerator.accumulate(model):
              inputs, targets = batch
              outputs = model(inputs)

You can remove all the special checks for the step number and the loss adjustment:

    - loss = loss / gradient_accumulation_steps
      accelerator.backward(loss)
    - if (index+1) % gradient_accumulation_steps == 0:
      optimizer.step()
      scheduler.step()
      optimizer.zero_grad()

As you can see the Accelerator is able to keep track of the batch number you are on and it will automatically know whether to step through the prepared optimizer and how to adjust the loss.

Typically with gradient accumulation, you would need to adjust the number of steps to reflect the change in total batches you are training on. Accelerate automagically does this for you by default. Behind the scenes we instantiate a `GradientAccumulationPlugin` configured to do this.

The state.GradientState is sync’d with the active dataloader being iterated upon. As such it assumes naively that when we have reached the end of the dataloader everything will sync and a step will be performed. To disable this, set `sync_with_dataloader` to be `False` in the `GradientAccumulationPlugin`:

    from accelerate import Accelerator
    from accelerate.utils import GradientAccumulationPlugin

    plugin = GradientAccumulationPlugin(sync_with_dataloader=False)
    accelerator = Accelerator(..., gradient_accumulation_plugin=plugin)

##
The finished code

Below is the finished implementation for performing gradient accumulation with Accelerate

    from accelerate import Accelerator
    accelerator = Accelerator(gradient_accumulation_steps=2)
    model, optimizer, training_dataloader, scheduler = accelerator.prepare(
        model, optimizer, training_dataloader, scheduler
    )
    for batch in training_dataloader:
        with accelerator.accumulate(model):
            inputs, targets = batch
            outputs = model(inputs)
            loss = loss_function(outputs, targets)
            accelerator.backward(loss)
            optimizer.step()
            scheduler.step()
            optimizer.zero_grad()

It’s important that only one forward/backward should be done inside the context manager `with accelerator.accumulate(model)`.

To learn more about what magic this wraps around, read the Gradient Synchronization concept guide

##
Self-contained example

Here is a self-contained example that you can run to see gradient accumulation in action with Accelerate:

    import torch
    import copy
    from accelerate import Accelerator
    from accelerate.utils import set_seed
    from torch.utils.data import TensorDataset, DataLoader

    # seed
    set_seed(0)

    # define toy inputs and labels
    x = torch.tensor([1., 2., 3., 4., 5., 6., 7., 8.])
    y = torch.tensor([2., 4., 6., 8., 10., 12., 14., 16.])
    gradient_accumulation_steps = 4
    per_device_batch_size = len(x) // gradient_accumulation_steps

    # define dataset and dataloader
    dataset = TensorDataset(x, y)
    dataloader = DataLoader(dataset, batch_size=per_device_batch_size)

    # define model, optimizer and loss function
    class SimpleLinearModel(torch.nn.Module):
        def __init__(self):
            super(SimpleLinearModel, self).__init__()
            self.weight = torch.nn.Parameter(torch.zeros((1, 1)))

        def forward(self, inputs):
            return inputs @ self.weight

    model = SimpleLinearModel()
    model_clone = copy.deepcopy(model)
    criterion = torch.nn.MSELoss()
    model_optimizer = torch.optim.SGD(model.parameters(), lr=0.02)
    accelerator = Accelerator(gradient_accumulation_steps=gradient_accumulation_steps)
    model, model_optimizer, dataloader = accelerator.prepare(model, model_optimizer, dataloader)
    model_clone_optimizer = torch.optim.SGD(model_clone.parameters(), lr=0.02)
    print(f"initial model weight is {model.weight.mean().item():.5f}")
    print(f"initial model weight is {model_clone.weight.mean().item():.5f}")
    for i, (inputs, labels) in enumerate(dataloader):
        with accelerator.accumulate(model):
            inputs = inputs.view(-1, 1)
            print(i, inputs.flatten())
            labels = labels.view(-1, 1)
            outputs = model(inputs)
            loss = criterion(outputs, labels)
            accelerator.backward(loss)
            model_optimizer.step()
            model_optimizer.zero_grad()
    loss = criterion(x.view(-1, 1) @ model_clone.weight, y.view(-1, 1))
    model_clone_optimizer.zero_grad()
    loss.backward()
    model_clone_optimizer.step()
    print(f"w/ accumulation, the final model weight is {model.weight.mean().item():.5f}")
    print(f"w/o accumulation, the final model weight is {model_clone.weight.mean().item():.5f}")

    initial model weight is 0.00000
    initial model weight is 0.00000
    0 tensor([1., 2.])
    1 tensor([3., 4.])
    2 tensor([5., 6.])
    3 tensor([7., 8.])
    w/ accumulation, the final model weight is 2.04000
    w/o accumulation, the final model weight is 2.04000

##
Gradient accumulation on training samples of variable size

As was pointed out in this blog-post, which points out a common error that occurs when performing gradient accumulation on training samples of variable size:

> […] for gradient accumulation across token-level tasks like causal LM training, the correct loss should be computed by the total loss across all batches in a gradient accumulation step divided by the total number of all non padding tokens in those batches. This is not the same as the average of the per-batch loss values.

In other words, some adjustments must be made on losses that operate on a token-level basis.

###
Skeleton code

    from accelerate import Accelerator
    import math
    import contextlib

    gradient_accumulation_steps = 2
    accelerator = Accelerator(gradient_accumulation_steps=gradient_accumulation_steps)
    model, optimizer, training_dataloader, scheduler = accelerator.prepare(
        model, optimizer, training_dataloader, scheduler
    )

    training_iterator = iter(training_dataloader)
    num_samples_in_epoch = len(training_dataloader)
    remainder = num_samples_in_epoch % gradient_accumulation_steps
    remainder = remainder if remainder != 0 else gradient_accumulation_steps
    total_updates = math.ceil(num_samples_in_epoch / gradient_accumulation_steps)

    total_batched_samples = 0
    for update_step in range(total_updates):
            # In order to correctly the total number of non-padded tokens on which we'll compute the cross-entropy loss
            # we need to pre-load the full local batch - i.e the next per_device_batch_size * accumulation_steps samples
            batch_samples = []
            num_batches_in_step = gradient_accumulation_steps if update_step != (total_updates - 1) else remainder
            for _ in range(num_batches_in_step):
                batch_samples += [next(training_iterator)]

            # get local num items in batch
            num_items_in_batch = sum([(batch["labels"].ne(-100)).sum() for batch in batch_samples])
            # to compute it correctly in a multi-device DDP training, we need to gather the total number of items in the full batch.
            num_items_in_batch = accelerator.gather(num_items_in_batch).sum().item()

            for i, batch in enumerate(batch_samples):
                # if we perform gradient accumulation in a multi-devices set-up, we want to avoid unnecessary communications when accumulating
                # cf: https://muellerzr.github.io/blog/gradient_accumulation.html
                if (i < len(batch_samples) - 1 and accelerator.num_processes > 1):
                    ctx = model.no_sync
                else:
                    ctx = contextlib.nullcontext

                total_batched_samples += 1

                with ctx():
                    inputs, targets = batch
                    outputs = model(inputs)
                    loss = loss_function(outputs, targets) # the loss function should sum over samples rather than averaging

                    # We multiply by num_processes because the DDP calculates the average gradient across all devices whereas dividing by num_items_in_batch already takes into account all devices
                    # Same reason for gradient_accumulation_steps, but this times it's Accelerate that calculate the average gradient across the accumulated steps
                    loss = (loss * gradient_accumulation_steps * accelerator.num_processes) / num_items_in_batch

                    accelerator.backward(loss)

            # Sync gradients and perform optimization steps once every gradient_accumulation_steps
            optimizer.step()
            scheduler.step()
            optimizer.zero_grad()

###
Self-contained causal LM example

    import torch
    import copy
    from accelerate import Accelerator
    from accelerate.utils import set_seed
    from accelerate.logging import  get_logger
    from torch.utils.data import Dataset, DataLoader
    import math
    import contexlib

    # seed
    set_seed(0)
    logger = get_logger(__name__)

    class MyDataset(Dataset):
        def __init__(self, num_samples):
            super().__init__()
            self.len = num_samples

        def __getitem__(self, index):
            input_ids = torch.arange(1, index+2, dtype=torch.float32)
            labels = torch.remainder(input_ids, 2)
            return {"input_ids": input_ids, "labels": labels}

        def __len__(self):
            return self.len

    def collate_fn(features):
        input_ids = torch.nn.utils.rnn.pad_sequence([f["input_ids"] for f in features], batch_first=True, padding_value=-100)
        labels = torch.nn.utils.rnn.pad_sequence([f["labels"] for f in features], batch_first=True, padding_value=-100)
        return {"input_ids": input_ids[..., None], "labels": labels[..., None]}

    # define toy inputs and labels
    gradient_accumulation_steps = 2
    per_device_batch_size = 4

    # define accelerator
    accelerator = Accelerator(gradient_accumulation_steps=gradient_accumulation_steps)

    # define dataset and dataloader
    # for this toy example, we'll compute gradient descent over one single global batch
    dataset = MyDataset(per_device_batch_size*gradient_accumulation_steps*accelerator.num_processes)
    dataloader = DataLoader(dataset, batch_size=per_device_batch_size, collate_fn=collate_fn)

    # define model, model_optimizer and loss function
    model = torch.nn.Linear(1, 2, bias=False)
    model_clone = copy.deepcopy(model)
    criterion = torch.nn.CrossEntropyLoss(reduction="sum") # must sum over samples rather than averaging
    model_optimizer = torch.optim.SGD(model.parameters(), lr=0.08)

    logger.warning(f"initial model weight is {model.weight.detach().cpu().squeeze()}")
    logger.warning(f"initial model clone weight is {model_clone.weight.detach().cpu().squeeze()}")

    # prepare artifacts - accelerator handles device placement and dataloader splitting
    model, model_optimizer = accelerator.prepare(model, model_optimizer)
    dataloader = accelerator.prepare_data_loader(dataloader, device_placement=True)
    training_iterator = iter(dataloader)

    num_samples_in_epoch = len(dataloader)
    remainder = num_samples_in_epoch % gradient_accumulation_steps
    remainder = remainder if remainder != 0 else gradient_accumulation_steps
    total_gradient_updates = math.ceil(num_samples_in_epoch / gradient_accumulation_steps)

    total_batched_samples = 0
    for update_step in range(total_gradient_updates):
            # In order to correctly the total number of non-padded tokens on which we'll compute the cross-entropy loss
            # we need to pre-load the full local batch - i.e the next per_device_batch_size * accumulation_steps samples
            batch_samples = []
            num_batches_in_step = gradient_accumulation_steps if update_step != (total_gradient_updates - 1) else remainder
            for _ in range(num_batches_in_step):
                batch_samples += [next(training_iterator)]

            # get local num items in batch
            local_num_items_in_batch = sum([(batch["labels"].ne(-100)).sum() for batch in batch_samples])
            logger.warning(f"Step {update_step} - Device {accelerator.process_index} - num items in the local batch {local_num_items_in_batch}", main_process_only=False)

            # to compute it correctly in a multi-device DDP training, we need to gather the total number of items in the full batch.
            num_items_in_batch = accelerator.gather(local_num_items_in_batch).sum().item()
            logger.warning(f"Total num items {num_items_in_batch}")

            for i, batch in enumerate(batch_samples):
                inputs, labels = batch["input_ids"], batch["labels"]
                total_batched_samples += 1
                # if we perform gradient accumulation in a multi-devices set-up, we want to avoid unnecessary communications when accumulating
                # cf: https://muellerzr.github.io/blog/gradient_accumulation.html
                if (i < len(batch_samples) - 1 and accelerator.num_processes > 1):
                    ctx = model.no_sync
                else:
                    ctx = contextlib.nullcontext
                with ctx():

                    outputs = model(inputs)
                    loss = criterion(outputs.view(-1, 2), labels.view(-1).to(torch.int64))

                    # We multiply by num_processes because the DDP calculates the average gradient across all devices whereas dividing by num_items_in_batch already takes into account all devices
                    # Same reason for gradient_accumulation_steps, but this times it's Accelerate that calculate the average gradient across the accumulated steps
                    loss = (loss * gradient_accumulation_steps * accelerator.num_processes) / num_items_in_batch
                    accelerator.backward(loss)
            model_optimizer.step()
            model_optimizer.zero_grad()

    logger.warning(f"Device {accelerator.process_index} - w/ accumulation, the final model weight is {accelerator.unwrap_model(model).weight.detach().cpu().squeeze()}", main_process_only=False)

    # We know do the same operation but on a single device and without gradient accumulation

    if accelerator.is_main_process:
        # prepare one single entire batch
        dataloader = DataLoader(dataset, batch_size=len(dataset), collate_fn=collate_fn)
        full_batch_without_accum = next(iter(dataloader))
        total_inputs, total_labels = full_batch_without_accum["input_ids"], full_batch_without_accum["labels"]
        model_clone_optimizer = torch.optim.SGD(model_clone.parameters(), lr=0.08)

        # train the cloned model
        loss = torch.nn.CrossEntropyLoss(reduction="mean")(model_clone(total_inputs).view(-1, 2), total_labels.view(-1).to(torch.int64))
        model_clone_optimizer.zero_grad()
        loss.backward()
        model_clone_optimizer.step()

        # We should have the same final weights.
        logger.warning(f"w/o accumulation, the final model weight is {model_clone.weight.detach().cpu().squeeze()}")

Results on a single device - gradient accumulation steps set to 1 and batch_size set to 8:

    initial model weight is tensor([-0.0075,  0.5364])
    initial model clone weight is tensor([-0.0075,  0.5364])
    Step 0 - Device 0 - num items in the local batch 36
    Total num items 36
    Device 0 - w/ accumulation, the final model weight is tensor([0.0953, 0.4337])
    w/o accumulation, the final model weight is tensor([0.0953, 0.4337])

Results on a two devices set-up - gradient accumulation steps set to 2 and batch_size set to 4.

    initial model weight is tensor([-0.0075,  0.5364])
    initial model clone weight is tensor([-0.0075,  0.5364])
    Step 0 - Device 0 - num items in the local batch 52
    Step 0 - Device 1 - num items in the local batch 84
    Total num items 136
    Device 1 - w/ accumulation, the final model weight is tensor([0.2117, 0.3172])
    Device 0 - w/ accumulation, the final model weight is tensor([0.2117, 0.3172])
    w/o accumulation, the final model weight is tensor([0.2117, 0.3172])

###
To go further:

Please find a complete example script on a real world training run in the examples folder at the path `accelerate/examples/by_feature/gradient_accumulation_for_autoregressive_models.py`.

Running it on several training configurations with constant global batch size equal to 32 gives the following graph:

Note that the training losses are exactly the same up to training step 20. The small deviation after this training step occurs at the very end of the first epoch, because, by default, the dataloader duplicates the samples at the beginning of the dataset when the total batch size doesn’t exactly divide the dataset.

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