code: def forward(self, x: torch.Tensor) -> torch.Tensor:
      batch_size = x.shape[0]
      current_nodes = torch.zeros(
          (batch_size,), dtype=torch.long, device=x.device
      )
      all_nodes = torch.zeros(
          (batch_size, self.depth + 1),
          dtype=torch.long,
          device=x.device,
      )
      all_logits = torch.empty(
          (batch_size, self.depth + 1),
          dtype=torch.float,
          device=x.device,
      )
  
      x_coordinates = torch.arange(
          batch_size, dtype=torch.long, device=x.device
      ).repeat(
          self.input_width
      )  # (batch_size * self.input_width,)
      y_coordinate_offsets = torch.arange(
          self.input_width, dtype=torch.long, device=x.device
      ).unsqueeze(
          0
      )  # (1, input_width)
  
      for i in range(self.depth + 1):
          all_nodes[:, i] = current_nodes
          y_coordinate_bases = (
              current_nodes * self.input_width
          ).unsqueeze(
              -1
          )  # (batch_size, 1)
          y_coordinates = (
              y_coordinate_bases + y_coordinate_offsets
          )  # (batch_size, input_width)
          indices = torch.stack(
              (x_coordinates, y_coordinates.flatten()), dim=0
          )  # (2, batch_size * input_width)
          x_sparse = torch.sparse_coo_tensor(
              indices=indices,
              values=x.flatten(),
              size=(batch_size, self.n_nodes * self.input_width),
              device=x.device,
          )  # (batch_size, self.n_nodes * self.input_width)
          logits = torch.sparse.mm(x_sparse, self.w1s).squeeze(
              -1
          )  # (batch_size,)
  
          all_logits[:, i] = logits  # (batch_size,)
          plane_choices = (logits >= 0).long()  # (batch_size,)
  
          current_nodes = (
              current_nodes * 2 + plane_choices + 1
          )  # (batch_size,)
  
      all_logits = torch.nn.functional.gelu(
          all_logits
      )  # (batch_size, self.depth)
  
      x_coordinates = torch.arange(
          batch_size, dtype=torch.long, device=x.device
      ).repeat(
          self.depth + 1
      )  # (batch_size * (self.depth+1),)
      indices = torch.stack(
          (x_coordinates, all_nodes.flatten()), dim=0
      )  # (2, batch_size * (self.depth+1))
      hidden_sparse = torch.sparse_coo_tensor(
          indices=indices,
          values=all_logits.flatten(),
          size=(batch_size, self.n_nodes),
          device=x.device,
      )  # (batch_size, self.n_nodes)
      new_logits = torch.sparse.mm(
          hidden_sparse, self.w2s
      )  # (batch_size, self.output_width)
  
      return new_logits
  
imports: import torch
  from torch import nn
  import math
label_desc: Use image node_id 2 for calling the FFF_Sparse obj's underlying member method code with example usage: obj.forward(x) and returns: new_logits