Toy network

Training on Multiple GPUs

Scaling beyond one GPU

A single GPU can train ResNet on ImageNet — slowly. Modern large models need many GPUs. Three ways to split work:

• Network partitioning — different layers on different GPUs. Hard to balance; rarely used alone today.
• Layerwise partitioning — split each layer’s parameters across GPUs (model parallelism). For giant models whose weights don’t fit on one GPU.
• Data parallelism — replicate the model on every GPU; each processes a different minibatch chunk; gradients averaged across GPUs.

Data parallelism is the default for everyday training.

Strategies side by side

Original, network partitioning, layerwise partitioning, data parallelism.

Data parallelism

Each GPU computes a forward + backward pass on its slice of the minibatch. After the backward pass, gradients are averaged across GPUs (all_reduce). Optimizer step then runs identically on every GPU, keeping replicas in sync.

Data-parallel SGD on 2 GPUs: split data, compute gradients independently, all-reduce, then update.

%matplotlib inline
from d2l import torch as d2l
import torch
from torch import nn
from torch.nn import functional as F

Tiny LeNet for the demo — small enough to fit on each GPU many times over:

# Initialize model parameters
scale = 0.01
W1 = torch.randn(size=(20, 1, 3, 3)) * scale
b1 = torch.zeros(20)
W2 = torch.randn(size=(50, 20, 5, 5)) * scale
b2 = torch.zeros(50)
W3 = torch.randn(size=(800, 128)) * scale
b3 = torch.zeros(128)
W4 = torch.randn(size=(128, 10)) * scale
b4 = torch.zeros(10)
params = [W1, b1, W2, b2, W3, b3, W4, b4]

# Define the model
def lenet(X, params):
    h1_conv = F.conv2d(input=X, weight=params[0], bias=params[1])
    h1_activation = F.relu(h1_conv)
    h1 = F.avg_pool2d(input=h1_activation, kernel_size=(2, 2), stride=(2, 2))
    h2_conv = F.conv2d(input=h1, weight=params[2], bias=params[3])
    h2_activation = F.relu(h2_conv)
    h2 = F.avg_pool2d(input=h2_activation, kernel_size=(2, 2), stride=(2, 2))
    h2 = h2.reshape(h2.shape[0], -1)
    h3_linear = torch.mm(h2, params[4]) + params[5]
    h3 = F.relu(h3_linear)
    y_hat = torch.mm(h3, params[6]) + params[7]
    return y_hat

# Cross-entropy loss function
loss = nn.CrossEntropyLoss(reduction='none')

Distribute parameters

Replicate the parameter list onto each device:

def get_params(params, device):
    new_params = [p.to(device) for p in params]
    for p in new_params:
        p.requires_grad_()
    return new_params

new_params = get_params(params, d2l.try_gpu(0))
print('b1 weight:', new_params[1])
print('b1 grad:', new_params[1].grad)

b1 weight: tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       device='cuda:0', requires_grad=True)
b1 grad: None

all_reduce

Sum vectors across GPUs and broadcast the result back — the gradient-averaging primitive of data-parallel SGD. NCCL implements this efficiently in production:

def allreduce(data):
    for i in range(1, len(data)):
        data[0][:] += data[i].to(data[0].device)
    for i in range(1, len(data)):
        data[i][:] = data[0].to(data[i].device)

data = [torch.ones((1, 2), device=d2l.try_gpu(i)) * (i + 1) for i in range(2)]
print('before allreduce:\n', data[0], '\n', data[1])
allreduce(data)
print('after allreduce:\n', data[0], '\n', data[1])

before allreduce:
 tensor([[1., 1.]], device='cuda:0') 
 tensor([[2., 2.]], device='cuda:1')
after allreduce:
 tensor([[3., 3.]], device='cuda:0') 
 tensor([[3., 3.]], device='cuda:1')

Distribute the minibatch

Split a tensor evenly across devices:

data = torch.arange(20).reshape(4, 5)
devices = [torch.device('cuda:0'), torch.device('cuda:1')]
split = nn.parallel.scatter(data, devices)
print('input :', data)
print('load into', devices)
print('output:', split)

input : tensor([[ 0,  1,  2,  3,  4],
        [ 5,  6,  7,  8,  9],
        [10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19]])
load into [device(type='cuda', index=0), device(type='cuda', index=1)]
output: (tensor([[0, 1, 2, 3, 4],
        [5, 6, 7, 8, 9]], device='cuda:0'), tensor([[10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19]], device='cuda:1'))

def split_batch(X, y, devices):
    """Split `X` and `y` into multiple devices."""
    assert X.shape[0] == y.shape[0]
    return (nn.parallel.scatter(X, devices),
            nn.parallel.scatter(y, devices))

One step of multi-GPU training

Forward + backward on each replica → all_reduce gradients → update parameters identically:

def train_batch(X, y, device_params, devices, lr):
    X_shards, y_shards = split_batch(X, y, devices)
    # Loss is calculated separately on each GPU
    ls = [loss(lenet(X_shard, device_W), y_shard).sum()
          for X_shard, y_shard, device_W in zip(
              X_shards, y_shards, device_params)]
    for l in ls:  # Backpropagation is performed separately on each GPU
        l.backward()
    # Sum all gradients from each GPU and broadcast them to all GPUs
    with torch.no_grad():
        for i in range(len(device_params[0])):
            allreduce([device_params[c][i].grad for c in range(len(devices))])
    # The model parameters are updated separately on each GPU
    for param in device_params:
        d2l.sgd(param, lr, X.shape[0]) # Here, we use a full-size batch

def train(num_gpus, batch_size, lr):
    train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
    devices = [d2l.try_gpu(i) for i in range(num_gpus)]
    # Copy model parameters to `num_gpus` GPUs
    device_params = [get_params(params, d) for d in devices]
    num_epochs = 10
    animator = d2l.Animator('epoch', 'test acc', xlim=[1, num_epochs])
    timer = d2l.Timer()
    for epoch in range(num_epochs):
        timer.start()
        for X, y in train_iter:
            # Perform multi-GPU training for a single minibatch
            train_batch(X, y, device_params, devices, lr)
            torch.cuda.synchronize()
        timer.stop()
        # Evaluate the model on GPU 0
        animator.add(epoch + 1, (d2l.evaluate_accuracy_gpu(
            lambda x: lenet(x, device_params[0]), test_iter, devices[0]),))
    print(f'test acc: {animator.Y[0][-1]:.2f}, {timer.avg():.1f} sec/epoch '
          f'on {str(devices)}')

Single-GPU baseline

train(num_gpus=1, batch_size=256, lr=0.2)

test acc: 0.83, 1.7 sec/epoch on [device(type='cuda', index=0)]

This gives the wall-clock reference point: one model copy, one minibatch stream, no gradient synchronization.

Two GPUs

Per-epoch time roughly halves; per-step iteration count drops because each GPU sees half the minibatch:

train(num_gpus=2, batch_size=256, lr=0.2)

test acc: 0.84, 2.3 sec/epoch on [device(type='cuda', index=0), device(type='cuda', index=1)]

Recap

• Data parallelism is the default: replicate model, split minibatch, all-reduce gradients, identical optimizer step on every GPU.
• all_reduce is the workhorse — implemented as a ring reduction in NCCL; bandwidth-optimal for k GPUs.
• Model parallelism is for huge models that don’t fit on a single GPU; tensor / pipeline parallelism are modern variants.