code: def _f_corrected_default(self, f, g, y, adj_y, requires_grad):
      g_columns = [
          g_column.squeeze(dim=-1) for g_column in g.split(1, dim=-1)
      ]
      dg_g_jvp = sum(
          [
              misc.jvp(
                  outputs=g_column,
                  inputs=y,
                  grad_inputs=g_column,
                  allow_unused=True,
                  create_graph=True,
              )[0]
              for g_column in g_columns
          ]
      )
      # Double Stratonovich correction.
      f = f - dg_g_jvp
      vjp_y_and_params = misc.vjp(
          outputs=f,
          inputs=[y] + self.params,
          grad_outputs=adj_y,
          allow_unused=True,
          retain_graph=True,
          create_graph=requires_grad,
      )
      # Convert the adjoint Stratonovich SDE to Itô form.
      extra_vjp_y_and_params = []
      for g_column in g_columns:
          (a_dg_vjp,) = misc.vjp(
              outputs=g_column,
              inputs=y,
              grad_outputs=adj_y,
              allow_unused=True,
              retain_graph=True,
              create_graph=requires_grad,
          )
          extra_vjp_y_and_params_column = misc.vjp(
              outputs=g_column,
              inputs=[y] + self.params,
              grad_outputs=a_dg_vjp,
              allow_unused=True,
              retain_graph=True,
              create_graph=requires_grad,
          )
          extra_vjp_y_and_params.append(extra_vjp_y_and_params_column)
      vjp_y_and_params = misc.seq_add(
          vjp_y_and_params, *extra_vjp_y_and_params
      )
      if not requires_grad:
          # See corresponding note in _f_uncorrected.
          f = f.detach()
      return misc.flatten((-f, *vjp_y_and_params)).unsqueeze(0)
  
imports: import torch
  from .None import base_sde
  from .None import misc
  from ..settings import NOISE_TYPES, SDE_TYPES
  from ..types import Sequence, TensorOrTensors
label_desc: Use image node_id 4 for calling the AdjointSDE obj's underlying member method code with example usage: obj._f_corrected_default(f, g, y, adj_y, requires_grad) and returns: misc