def backward(ctx, grad_output: torch.Tensor) -> torch.Tensor:
        """A backward pass for the KL Divergence Loss.

        Args:
            ctx: Torch autograd context
            grad_output (torch.Tensor): The gradient of the loss with respect to the output.

        Returns:
            tuple[torch.Tensor, None, None, None, None]: The gradient of the loss with respect to the inputs and None for the other arguments of the forward method.
        """
        (y_true,) = ctx.saved_tensors

        new_grads = torch.empty_like(y_true)

        derivative = kldiv_backward_triton(y_true, grad_output, new_grads, ctx.log_target)

        if ctx.reduction == "batchmean":
            derivative = derivative / y_true.shape[0]
        elif ctx.reduction == "sum" or ctx.reduction == "none":
            pass
        elif ctx.reduction == "mean":
            derivative = derivative / (y_true.shape[0] * y_true.shape[1])

        return (
            derivative,
            None,
            None,
            None,
            None,
        )
A backward pass for the KL Divergence Loss.

        Args:
            ctx: Torch autograd context
            grad_output (torch.Tensor): The gradient of the loss with respect to the output.

        Returns:
            tuple[torch.Tensor, None, None, None, None]: The gradient of the loss with respect to the inputs and None for the other arguments of the forward method.
        
src/liger_kernel/ops/kl_div.py