code: def forward(self, x, importance=None):
      *_, b, group_size, dim = x.shape
      num_gates = self.num_gates
  
      if self.training:
          policy = self.second_policy_train
          threshold = self.second_threshold_train
          capacity_factor = self.capacity_factor_train
      else:
          policy = self.second_policy_eval
          threshold = self.second_threshold_eval
          capacity_factor = self.capacity_factor_eval
  
      raw_gates = torch.einsum("...bnd,...de->...bne", x, self.w_gating)
      raw_gates = raw_gates.softmax(dim=-1)
  
      # FIND TOP 2 EXPERTS PER POSITON
      # Find the top expert for each position. shape=[batch, group]
  
      gate_1, index_1 = top1(raw_gates)
      mask_1 = F.one_hot(index_1, num_gates).float()
      density_1_proxy = raw_gates
  
      if importance is not None:
          equals_one_mask = (importance == 1.0).float()
          mask_1 *= equals_one_mask[..., None]
          gate_1 *= equals_one_mask
          density_1_proxy = density_1_proxy * equals_one_mask[..., None]
          del equals_one_mask
  
      gates_without_top_1 = raw_gates * (1.0 - mask_1)
  
      gate_2, index_2 = top1(gates_without_top_1)
      mask_2 = F.one_hot(index_2, num_gates).float()
  
      if importance is not None:
          greater_zero_mask = (importance > 0.0).float()
          mask_2 *= greater_zero_mask[..., None]
          del greater_zero_mask
  
      # normalize top2 gate scores
      denom = gate_1 + gate_2 + self.eps
      gate_1 /= denom
      gate_2 /= denom
  
      # BALANCING LOSSES
      # shape = [batch, experts]
      # We want to equalize the fraction of the batch assigned to each expert
      density_1 = mask_1.mean(dim=-2)
      # Something continuous that is correlated with what we want to equalize.
      density_1_proxy = density_1_proxy.mean(dim=-2)
      loss = (density_1_proxy * density_1).mean() * float(
          num_gates**2
      )
  
      # Depending on the policy in the hparams, we may drop out some of the
      # second-place experts.
      if policy == "all":
          pass
      elif policy == "none":
          mask_2 = torch.zeros_like(mask_2)
      elif policy == "threshold":
          mask_2 *= (gate_2 > threshold).float()
      elif policy == "random":
          probs = torch.zeros_like(gate_2).uniform_(0.0, 1.0)
          mask_2 *= (
              (probs < (gate_2 / max(threshold, self.eps)))
              .float()
              .unsqueeze(-1)
          )
      else:
          raise ValueError(f"Unknown policy {policy}")
  
      # Each sequence sends (at most?) expert_capacity positions to each expert.
      # Static expert_capacity dimension is needed for expert batch sizes
      expert_capacity = min(
          group_size, int((group_size * capacity_factor) / num_gates)
      )
      expert_capacity = max(expert_capacity, MIN_EXPERT_CAPACITY)
      expert_capacity_f = float(expert_capacity)
  
      # COMPUTE ASSIGNMENT TO EXPERTS
      # [batch, group, experts]
      # This is the position within the expert's mini-batch for this sequence
      position_in_expert_1 = cumsum_exclusive(mask_1, dim=-2) * mask_1
      # Remove the elements that don't fit. [batch, group, experts]
      mask_1 *= (position_in_expert_1 < expert_capacity_f).float()
      # [batch, experts]
      # How many examples in this sequence go to this expert
      mask_1_count = mask_1.sum(dim=-2, keepdim=True)
      # [batch, group] - mostly ones, but zeros where something didn't fit
      mask_1_flat = mask_1.sum(dim=-1)
      # [batch, group]
      position_in_expert_1 = position_in_expert_1.sum(dim=-1)
      # Weight assigned to first expert.  [batch, group]
      gate_1 *= mask_1_flat
  
      position_in_expert_2 = (
          cumsum_exclusive(mask_2, dim=-2) + mask_1_count
      )
      position_in_expert_2 *= mask_2
      mask_2 *= (position_in_expert_2 < expert_capacity_f).float()
      mask_2_flat = mask_2.sum(dim=-1)
  
      position_in_expert_2 = position_in_expert_2.sum(dim=-1)
      gate_2 *= mask_2_flat
  
      # [batch, group, experts, expert_capacity]
      combine_tensor = (
          gate_1[..., None, None]
          * mask_1_flat[..., None, None]
          * F.one_hot(index_1, num_gates)[..., None]
          * safe_one_hot(position_in_expert_1.long(), expert_capacity)[
              ..., None, :
          ]
          + gate_2[..., None, None]
          * mask_2_flat[..., None, None]
          * F.one_hot(index_2, num_gates)[..., None]
          * safe_one_hot(position_in_expert_2.long(), expert_capacity)[
              ..., None, :
          ]
      )
  
      dispatch_tensor = combine_tensor.bool().to(combine_tensor)
      return dispatch_tensor, combine_tensor, loss
  
imports: import torch
  from torch import nn
  import torch.nn.functional
  import math
  from inspect import isfunction
label_desc: Use image node_id 2 for calling the Top2Gating obj's underlying member method code with example usage: obj.forward(x, importance) and returns: dispatch_tensor,  combine_tensor,  loss