//               = x_n y_n - X_n y_n - x_n Y_{n-1} + X_n Y_{n-1}
    //               = (x_n - X_n) (y_n - Y_{n-1})
    xStats.add(x);
    if (isFinite(x) && isFinite(y)) {
      if (xStats.count() > 1) {
        sumOfProductsOfDeltas += (x - xStats.mean()) * (y - yStats.mean());
      }
    } else {
      sumOfProductsOfDeltas = NaN;
    }
    yStats.add(y);
  }

  /**

    //               = x_n y_n - X_n y_n - x_n Y_{n-1} + X_n Y_{n-1}
    //               = (x_n - X_n) (y_n - Y_{n-1})
    xStats.add(x);
    if (isFinite(x) && isFinite(y)) {
      if (xStats.count() > 1) {
        sumOfProductsOfDeltas += (x - xStats.mean()) * (y - yStats.mean());
      }
    } else {
      sumOfProductsOfDeltas = NaN;
    }
    yStats.add(y);
  }

  /**

                std::vector<Output>* grad_outputs) {
  // AddN doesn't support broadcasting, so all the inputs must be the
  // same shape.
  // Note:
  // dy/dx_k = d(x_1 + x_2 + ... + x_n)/dx_k = 1 for all x_k
  // hence dx_k = dy for all x_k
  // So the gradient for AddN just transfers the incoming gradient to
  // all outgoing gradients.
  auto incoming = Identity(scope, grad_inputs[0]);