code: def train_linear_model(
      model: FeedForward, per_layer_scaling=False
  ) -> FeedForward:
      criterion = torch.nn.BCEWithLogitsLoss()
      optimizer = torch.optim.SGD(model.parameters(), lr=0.001)
  
      x_train, y_train = load_data("linear_model")
      num_epochs = 2
      model.train()
  
      layers_to_scale = (
          {"fc1": 1024, "fc2": 512, "fc3": 1024}
          if per_layer_scaling
          else {}
      )
      layer_scaler = LayerwiseGradientScaler(model, layers_to_scale)
  
      for _ in range(num_epochs):
          optimizer.zero_grad()
  
          # scale the gradients
          layer_scaler.scale()
  
          with autocast():
              # forward pass
              y_pred = model(x_train)
              # compute loss
              loss = criterion(y_pred.squeeze(), y_train)
  
          loss.backward()
  
          # unscale the gradients
          layer_scaler.unscale()
  
          # update weights and scaling factor
          layer_scaler.step(optimizer)
  
      return model
  
imports: import logging
  import os
  from typing import Any, List, Tuple, Union
  import numpy
  import pytest
  from sklearn.datasets import make_blobs
  import torch
  from torch.cuda.amp.autocast_mode import autocast
  import torch.nn
  from torch.utils.data import DataLoader
  import torchvision
  import torchvision.transforms
  from fairscale.fair_dev.common_paths import DATASET_CACHE_ROOT
  from fairscale.fair_dev.testing.testing import skip_a_test_if_in_CI
  from fairscale.optim.layerwise_gradient_scaler import LayerwiseGradientScaler
label_desc: Use image node_id 4 for calling a global function with example usage: train_linear_model(model, per_layer_scaling) and returns: model