code: import argparse
  import math
  import os
  import time
  
  from .benchmark_dataset import BenchmarkLMDataset, collate_sentences_lm
  import torch
  from torch.distributed import rpc
  import torch.nn as nn
  from torch.utils.data import DataLoader
  
  from torch.distributed.pipeline.sync import Pipe
  from torch.testing._internal.distributed.pipeline.utils import convert_to_balance
  from torch.optim import Adam  # type: ignore
  
  def sizeof_fmt(num, suffix='B'):
      for unit in ['', 'Ki', 'Mi', 'Gi', 'Ti']:
          if abs(num) < 1024.0:
              return "%3.2f%sB" % (num, unit)
          num /= 1024.0
  
  
  def init_random_seed(seed: int):
      import numpy
  
      torch.manual_seed(seed)
      torch.cuda.manual_seed(seed)
      numpy.random.seed(seed)
  
  
  iteration_count = 0
  
  
  class EmbeddingLayer(nn.Embedding):
      def __init__(self, ntoken, ninp, initrange):
          super().__init__(ntoken, ninp)
          self.ninp = ninp
          self.weight.data.uniform_(-initrange, initrange)
  
      def forward(self, src):
          return super().forward(src) * math.sqrt(self.ninp)
  
  
  class PositionalEncodingLayer(nn.Module):
      def __init__(self, d_model, dropout=0.1, max_len=5000):
          super(PositionalEncodingLayer, self).__init__()
          self.dropout = nn.Dropout(p=dropout)
  
          pe = torch.zeros(max_len, d_model)
          position = torch.arange(0, max_len, dtype=torch.float).unsqueeze(1)
          div_term = torch.exp(torch.arange(0, d_model, 2).float() * (-math.log(10000.0) / d_model))
          pe[:, 0::2] = torch.sin(position * div_term)
          pe[:, 1::2] = torch.cos(position * div_term)
          pe = pe.unsqueeze(0).transpose(0, 1)
          self.register_buffer("pe", pe)
  
      def forward(self, x):
          x = x + self.pe[: x.size(0), :]
          return self.dropout(x)
  
  
  class TransformerDecoderLayer(nn.TransformerEncoderLayer):
      """Though this class inherits from torch.nn.TransformerEncoderLayer,
      it functions as a decoder in this model"""
  
      def __init__(self, ninp, nhead, nhid, droupout):
          super().__init__(ninp, nhead, nhid, droupout)
          self.src_mask = None
  
      def _generate_square_subsequent_mask(self, sz):
          mask = (torch.triu(torch.ones(sz, sz)) == 1).transpose(0, 1)
          mask = mask.float().masked_fill(mask == 0, float("-inf")).masked_fill(mask == 1, float(0.0))
          return mask
  
      def forward(self, src):
          global iteration_count
          iteration_count += 1
  
          if self.src_mask is None or self.src_mask.size(0) != len(src):
              device = src.device
              mask = self._generate_square_subsequent_mask(len(src)).to(device)
              self.src_mask = mask
  
          return super().forward(src, self.src_mask)
  
  
  class LinearLayer(nn.Linear):
      def __init__(self, ninp, ntoken, initrange):
          super().__init__(ninp, ntoken)
          self.bias.data.zero_()
          self.weight.data.uniform_(-initrange, initrange)
  
  
  class TransformerLMSequential(nn.Sequential):
      """A small language model based on the design of GPT-2 using nn.Sequential
      for compatibility with Pipe"""
  
      def __init__(self, ntokens, ninp, nhead, nhid, dropout, initrange, ndecoder):
          layers = [
              EmbeddingLayer(ntokens, ninp, initrange),
              PositionalEncodingLayer(ninp, dropout),
          ]
          for _ in range(ndecoder):
              layers.append(TransformerDecoderLayer(ninp, nhead, nhid, dropout))
  
          layers.append(LinearLayer(ninp, ntokens, initrange))
          super(TransformerLMSequential, self).__init__(*layers)
  
  
  def make_model(args, device, ntokens):
      ninp = 2048  # embedding dimension
      nhid = 2048  # the dimension of the feedforward network model in nn.TransformerEncoder
      nhead = 32  # the number of heads in the multiheadattention models
      dropout = 0
      initrange = 0.1
      ndecoder = args.num_decoder_layers
  
      model = TransformerLMSequential(ntokens, ninp, nhead, nhid, dropout, initrange, ndecoder).to(device)
  
      criterion = nn.CrossEntropyLoss()
      lr = 0.01  # learning rate
  
      def make_adam(model):
          return Adam(model.parameters(), lr=lr)
  
      optimizer = make_adam
  
      return model, criterion, optimizer
  
  
  def train(lm_dataloader, model, criterion, optimizer, vocab_size, args):
      model.train()
  
      vocab_size = 10000
      total_loss = 0.0
      start_time = time.time()
      word_counter = 0
  
      optimizer = optimizer(model)
  
      def get_first_device(model):
          if model.devices:
              return model.devices[0]
          else:
              return torch.cuda.current_device()
  
      def get_last_device(model):
          if model.devices:
              return model.devices[-1]
          else:
              return torch.cuda.current_device()
  
  
      print('Number of parameters for model: {}'.format(sum(p.numel() for p in model.parameters())))
      for i, batch in enumerate(lm_dataloader):
          bi = batch["input"]
          if args.max_batch and i > args.max_batch:
              break
          optimizer.zero_grad()
          try:
              tmp = batch["input"].to(get_first_device(model))
              output = model(tmp).local_value()
          except Exception as e:
              raise RuntimeError(f"training failed on {torch.distributed.get_rank()}") from e
  
          target = batch["target"].to(get_last_device(model))
          output = output.to(target.device)
  
          loss = criterion(output.view(-1, vocab_size), target.view(-1))
          loss.backward()
          del target
          del output
  
          torch.nn.utils.clip_grad_value_(model.parameters(), 0.05)
          optimizer.step()
  
          total_loss += loss.item()
          log_interval = 1
          word_counter += batch["ntokens"]
          if i % log_interval == 0 and i > 0:
              cur_loss = total_loss / log_interval
              elapsed = time.time() - start_time
              print(
                  "| batch {:5d} | wps {:5.2f} | loss {:5.2f} | ppl {:8.2f}".format(
                      i, word_counter / elapsed, cur_loss, math.exp(cur_loss)
                  )
              )
              word_counter = 0
              total_loss = 0
              start_time = time.time()
  
      print('Peak memory usage for GPUs: ', end='')
      for i in range(len(model.devices)):
          print("cuda:{}: {}, ".format(
              i,
              sizeof_fmt(torch.cuda.memory_stats(i)["allocated_bytes.all.peak"])), end='')
      print()
  
  
  def generate_balance(num_devices, num_layers):
      balance = []
      layers_assigned = 0
      for i in range(num_devices):
          x = (num_layers - layers_assigned) / (num_devices - i)
          if x.is_integer():
              balance.append(int(x))
              layers_assigned += x
          else:
              balance.append(math.ceil(x))
              layers_assigned += math.ceil(x)
      return balance
  
  
  def make_model_and_data(args, device):
      device = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")
      vocab_size = 10000
      model, criterion, optimizer = make_model(args, device, vocab_size)
      lm_dataset = BenchmarkLMDataset()
      lm_dataloader = DataLoader(
          lm_dataset, batch_size=args.batch_size, shuffle=True, num_workers=0, collate_fn=collate_sentences_lm
      )
      return {
          "model": model,
          "criterion": criterion,
          "optimizer": optimizer,
          "data": lm_dataloader,
          "vocab_size": vocab_size,
      }
  
  
  def bench_single_process(args):
      os.environ.update({"MASTER_ADDR" : args.host})
      os.environ.update({"MASTER_PORT" : "10638"})
  
      rpc.init_rpc(
          "worker",
          rank=0,
          world_size=1,
      )
  
      num_devices = torch.cuda.device_count() if torch.cuda.is_available() else 1
      num_devices = min(args.num_devices, num_devices)
      assert num_devices > 0
      init_random_seed(0)
      device = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")
  
      blob = make_model_and_data(args, None)
      model = blob["model"]
  
      balance = generate_balance(num_devices, len(model))
      model = convert_to_balance(model, balance)
      p = Pipe(
          model, chunks=args.chunks, checkpoint=args.checkpoint
      )
      del model
      del blob["model"]
  
      train(blob["data"], p, blob["criterion"], blob["optimizer"], blob["vocab_size"], args)
  
  parser = argparse.ArgumentParser(description="benchmark")
  parser.add_argument("--host", "-o", type=str, default="localhost", help="hostname")
  parser.add_argument("--chunks", type=int, default=4, help="number of microbatches per batch")
  parser.add_argument("--batch-size", type=int, default=8, help="size of a batch")
  parser.add_argument("--max-batch", type=int, default=10, help="Max number of batches")
  parser.add_argument("--num-decoder-layers", type=int, default=10, help="Number of decoder layers in the model")
  parser.add_argument(
      "--checkpoint", default="except_last", choices=["always", "except_last", "never"],
      help="Checkpointing strategy for pipe"
  )
  parser.add_argument(
      "--num-devices", type=int, default=4, help="Number of GPU devices to use"
  )
  
  if __name__ == "__main__":
      args = parser.parse_args()
      print(f"Running benchmark with args: {args}")
      bench_single_process(args)
  