class_docstr: This function takes in
  
      - the kernel interpolation term K_ZZ^{-1/2} k_ZX
      - the natural parameters of the variational distribution
  
  and returns
  
      - the predictive distribution mean/covariance
      - the inducing KL divergence KL( q(u) || p(u))
  
  However, the gradients will be with respect to the **cannonical parameters**
  of the variational distribution, rather than the **natural parameters**.
  This corresponds to performing natural gradient descent on the variational distribution.
code: def backward(
      ctx: FunctionCtx,
      interp_mean_grad: torch.Tensor,
      interp_var_grad: torch.Tensor,
      kl_div_grad: torch.Tensor,
  ) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, None]:
      # Get the saved terms
      (
          interp_term,
          s_times_interp_term,
          interp_mean,
          natural_vec,
          expec_vec,
          prec,
      ) = ctx.saved_tensors
  
      # Expand data-depenedent gradients
      interp_mean_grad = interp_mean_grad.unsqueeze(-2)
      interp_var_grad = interp_var_grad.unsqueeze(-2)
  
      # Compute gradient of interp term (K^{-1/2} k)
      # interp_mean component: m
      # interp_var component: S K^{-1/2} k
      # kl component: 0
      interp_term_grad = (interp_var_grad * s_times_interp_term).mul(
          2.0
      ) + (interp_mean_grad * expec_vec.unsqueeze(-1))
  
      # Compute gradient of expected vector (m)
      # interp_mean component: K^{-1/2} k
      # interp_var component: (k^T K^{-1/2} m) K^{-1/2} k
      # kl component: S^{-1} m
      expec_vec_grad = (
          (interp_var_grad * interp_mean.unsqueeze(-2) * interp_term)
          .sum(dim=-1)
          .mul(-2)
          + (interp_mean_grad * interp_term).sum(dim=-1)
          + (kl_div_grad.unsqueeze(-1) * natural_vec)
      )
  
      # Compute gradient of expected matrix (mm^T + S)
      # interp_mean component: 0
      # interp_var component: K^{-1/2} k k^T K^{-1/2}
      # kl component: 1/2 ( I - S^{-1} )
      eye = torch.eye(
          expec_vec.size(-1),
          device=expec_vec.device,
          dtype=expec_vec.dtype,
      )
      expec_mat_grad = torch.add(
          (interp_var_grad * interp_term)
          @ interp_term.transpose(-1, -2),
          (
              kl_div_grad.unsqueeze(-1).unsqueeze(-1)
              * (eye - prec).mul(0.5)
          ),
      )
  
      # We're done!
      return interp_term_grad, expec_vec_grad, expec_mat_grad, None
  
imports: from typing import Optional, Tuple
  import torch
  from linear_operator import to_linear_operator
  from linear_operator.operators import DiagLinearOperator, LinearOperator, MatmulLinearOperator, SumLinearOperator
  from linear_operator.utils import linear_cg
  from torch import Tensor
  from torch.autograd.function import FunctionCtx
  from ..None import settings
  from ..distributions import Delta, Distribution, MultivariateNormal
  from ..module import Module
  from ..utils.memoize import cached
  from ._variational_strategy import _VariationalStrategy
  from .natural_variational_distribution import NaturalVariationalDistribution
label_desc: Use image node_id 2 for calling the _NgdInterpTerms obj's underlying member method code with example usage: obj.backward(ctx, interp_mean_grad, interp_var_grad, kl_div_grad) and returns: interp_term_grad,  expec_vec_grad,  expec_mat_grad,  None