code: def hardness_metric(batch, num_classes):
      """Hardness metric of an episode, as defined in [1].
  
      Parameters
      ----------
      batch : dict
          The batch of tasks over which the metric is computed. The batch of tasks
          is a dictionary containing the keys `train` (or `support`) and `test`
          (or `query`). This is typically the output of `BatchMetaDataLoader`.
  
      num_classes : int
          The number of classes in the classification task. This corresponds to
          the number of ways in an `N`-way classification problem.
  
      Returns
      -------
      metric : `torch.FloatTensor` instance
          Values of the hardness metric for each task in the batch.
  
      References
      ----------
      .. [1] Dhillon, G. S., Chaudhari, P., Ravichandran, A. and Soatto S. (2019).
             A Baseline for Few-Shot Image Classification. (https://arxiv.org/abs/1909.02729)
      """
      if ("train" not in batch) and ("support" not in batch):
          raise ValueError(
              "The tasks do not contain any training/support set. "
              'Make sure the tasks contain either the "train" or the '
              '"support" key.'
          )
      if ("test" not in batch) and ("query" not in batch):
          raise ValueError(
              "The tasks do not contain any test/query set. Make "
              'sure the tasks contain either the "test" of the '
              '"query" key.'
          )
  
      train = "train" if ("train" in batch) else "support"
      test = "test" if ("test" in batch) else "query"
  
      with torch.no_grad():
          # Load a pre-trained backbone Resnet-152 model from PyTorch Hub
          backbone = torch.hub.load(
              "pytorch/vision:v0.5.0",
              "resnet152",
              pretrained=True,
              verbose=False,
          )
          backbone.eval()
  
          train_inputs, train_targets = batch[train]
          test_inputs, test_targets = batch[test]
          batch_size, num_images, num_channels = train_inputs.shape[:3]
          num_test_images = test_inputs.size(1)
  
          backbone.to(device=train_inputs.device)
  
          if num_channels != 3:
              raise ValueError("The images must be RGB images.")
  
          # Pad the images so that they are compatible with the pre-trained model
          padded_train_inputs = _pad_images(
              train_inputs, size=(224, 224), mode="constant", value=0.0
          )
          padded_test_inputs = _pad_images(
              test_inputs, size=(224, 224), mode="constant", value=0.0
          )
  
          # Compute the features from the logits returned by the pre-trained
          # model on the train/support examples. These features are z(x, theta)_+,
          # averaged for each class
          train_logits = backbone(
              padded_train_inputs.view(-1, 3, 224, 224)
          )
          train_logits = F.relu(
              train_logits.view(batch_size, num_images, -1)
          )
          train_features = get_prototypes(
              train_logits, train_targets, num_classes
          )
  
          # Get the weights by normalizing the features
          weights = F.normalize(train_features, p=2, dim=2)
  
          # Compute and normalize the logits of the test/query examples
          test_logits = backbone(
              padded_test_inputs.view(-1, 3, 224, 224)
          )
          test_logits = test_logits.view(
              batch_size, num_test_images, -1
          )
          test_logits = F.normalize(test_logits, p=2, dim=2)
  
          # Compute the log probabilities of the test/query examples
          test_logits = torch.bmm(weights, test_logits.transpose(1, 2))
          test_log_probas = -F.cross_entropy(
              test_logits, test_targets, reduction="none"
          )
  
          # Compute the log-odds ratios for each image of the test/query set
          log_odds_ratios = (
              torch.log1p(-test_log_probas.exp()) - test_log_probas
          )
  
      return torch.mean(log_odds_ratios, dim=1)
  
imports: import torch
  import torch.nn.functional
  from torchmeta.utils.prototype import get_prototypes
label_desc: Use image node_id 2 for calling a global function with example usage: hardness_metric(batch, num_classes) and returns: torch