code: def backward(self, indexes, ggx):
      y, gy = self.get_retained_inputs()
      ret = []
      exp_y = chainer.functions.exp(y)
      if 0 in indexes:
          gy_sum = chainer.functions.sum(gy, self.axis, True)
          gy_sum = chainer.functions.broadcast_to(gy_sum, gy.shape)
          g0 = -ggx[0] * exp_y * gy_sum
          ret.append(g0)
      if 1 in indexes:
          # TODO(Kenta Oono): implement it with double-backpropable F.matmul
          a = chainer.functions.sum(ggx[0] * exp_y, self.axis, True)
          a = chainer.functions.broadcast_to(a, gy.shape)
          g1 = ggx[0] - a
          ret.append(g1)
      return ret
  
imports: import chainer
  from chainer import backend
  from chainer.backends import cuda
  from chainer import function_node
  import chainer.functions
  from chainer.utils import type_check
  import chainerx
label_desc: Use image node_id 3 for calling the LogSoftmaxGrad obj's underlying member method code with example usage: obj.backward(indexes, ggx) and returns: ret