 ```python
import torch
import torchrec
from torchrec.datasets import DataLoader, RandomDataLoader
from torchrec.modules. DylanEmbeddingBag import DylanEmbeddingBag
from torchrec.modules. Embedding import Embedding
from torchrec.modules. FusedDense import FusedDense
from torchrec.modules. FusedLinear import FusedLinear
from torchrec.sparse.JaggedTensor import JaggedTensor, pack_jagged_tensor
from torchrec.sparse.PartitionedEmbeddingBag import PartitionedEmbeddingBag
from torchrec.sparse.PartitionedEmbedding import PartitionedEmbedding
from torchrec.sparse.SparseFeatureExtractor import SparseFeatureExtractor
from torchrec.sparse.SparseTensor import SparseTensor
from torchrec.sparse.TrianularSparseTensor import TriangularSparseTensor
from torchrec.utils import get_process_group, device_type, device_index, backend

def _get_random_dataloader(num_embeddings, batch_size, pin_memory):
    return DataLoader(
        RandomDataLoader(num_embeddings, batch_size),
        batch_size=batch_size,
        pin_memory=pin_memory,
    )

def train(num_embeddings, embedding_dim, dense_arch, over_arch, learning_rate):
    torch.distributed.init_process_group(backend)
    device = device_type(device_index())
    rank = torch.distributed.get_rank()

    sparse_feature_extractor = SparseFeatureExtractor(
        [
            Embedding(num_embeddings[0], embedding_dim, sparse=True),
            Embedding(num_embeddings[1], embedding_dim, sparse=True),
            Embedding(num_embeddings[2], embedding_dim, sparse=True),
            Embedding(num_embeddings[3], embedding_dim, sparse=True),
            Embedding(num_embeddings[4], embedding_dim, sparse=True),
        ]
    )

    dense_layers = [
        FusedDense(in_features, out_features)
        for in_features, out_features in zip(
            [embedding_dim] + dense_arch[:-1], dense_arch
        )
    ]

    over_layers = [
        FusedLinear(in_features, out_features)
        for in_features, out_features in zip(
            dense_arch + [dense_arch[-1]], over_arch
        )
    ]

    model = DLRMModel(
        sparse_feature_extractor,
        dense_layers,
        over_layers,
        embedding_dim,
    ).to(device)

    model = torch.nn.parallel.DistributedDataParallel(
        model, device_ids=[rank], output_device=rank
    )

    optimizer = torch.optim.AdamW(model.parameters(), lr=learning_rate)

    train_iterator = _get_random_dataloader(num_embeddings, 128, True)

    for epoch in range(10):
        for batch in train_iterator:
            input_sparse, input_dense, target = batch

            input_sparse = input_sparse.to(device)
            input_dense = input_dense.to(device)
            target = target.to(device)

            optimizer.zero_grad()

            output = model(input_sparse, input_dense)

            loss = torch.nn.functional.binary_cross_entropy_with_logits(
                output, target
            )

            loss.backward()

            optimizer.step()

if __name__ == "__main__":
    train(
        num_embeddings=[10000, 10000, 10000, 10000, 10000],
        embedding_dim=128,
        dense_arch=[128, 128, 128],
        over_arch=[128, 128],
        learning_rate=0.001,
    )
```