class_docstr: Pairwise likelihood using probit function
  
  Given two items v and u with utilities f(v) and f(u), the probability that we
  prefer v over u with probability std_normal_cdf((f(v) - f(u))/sqrt(2)). Note
  that this formulation implicitly assume the noise term is fixed at 1.
code: def negative_log_gradient_sum(
      self, utility: Tensor, D: Tensor
  ) -> Tensor:
      # Compute the sum over of grad. of negative Log-LH wrt utility f.
      # Original grad should be of dimension m x n, as in (6) from
      # [Chu2005preference]_. The sum over the m dimension of grad. of
      # negative log likelihood with respect to the utility
      z = self._calc_z(utility, D)
      _, _, h = self._calc_z_derived(z)
      h_factor = h / math.sqrt(2)
      grad = (h_factor.unsqueeze(-2) @ (-D)).squeeze(-2)
      return grad
  
imports: from __future__ import annotations
  import math
  from abc import ABC, abstractmethod
  from typing import Any, Tuple
  import torch
  from botorch.utils.probability.utils import log_ndtr, log_phi, standard_normal_log_hazard
  from gpytorch.likelihoods import Likelihood
  from torch import Tensor
  from torch.distributions import Bernoulli
label_desc: Use image node_id 4 for calling the PairwiseProbitLikelihood obj's underlying member method code with example usage: obj.negative_log_gradient_sum(utility, D) and returns: grad