```python
from torchrec import _pin_and_move, gen_model_and_input, initialize_and_test_parameters, should_compute, _generate_dmps_and_batch, _setup_cpu_model_and_opt, calculate_shard_sizes_and_offsets, test_trace_and_script, _update_and_evict, seed_and_log, test_dataset_train_val_and_test_sets, test_should_compute, compute_and_output_dist, create_module_and_freeze, _calculate_cw_shard_sizes_and_offsets, _calculate_rw_shard_sizes_and_offsets, _shuffle_and_load_data_for_rank, _get_batch_inputs_and_shardable_parameters, convert_optimizer_type_and_kwargs, test_fx_and_shape
from torch.utils.data import DataLoader

def _get_random_dataloader(num_embeddings, batch_size, pin_memory):
    # Implementation of _get_random_dataloader function
    pass

def train(num_embeddings, embedding_dim, dense_architecture, over_architecture, learning_rate):
    # Implementation of train function
    pass

if __name__ == "__main__":
    train(num_embeddings=10, embedding_dim=64, dense_architecture=[128, 64], over_architecture=[256, 128], learning_rate=0.001)
```