- backward_api : matmul_grad
  forward : matmul (Tensor x, Tensor y, bool transpose_x=false, bool transpose_y=false) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad, bool transpose_x=false, bool transpose_y=false)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : matmul_grad

- backward_api : matmul_double_grad
  forward : matmul_grad (Tensor x, Tensor y, Tensor out_grad, bool transpose_x, bool transpose_y) -> Tensor(dx), Tensor(dy)
  args : (Tensor x, Tensor y, Tensor out_grad, Tensor dx_grad, Tensor dy_grad, bool transpose_x, bool transpose_y)
  output : Tensor(d2x), Tensor(d2y), Tensor(dout_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x, y, out_grad]
  kernel :
    func : matmul_double_grad
  optional : dx_grad, dy_grad

- backward_api : scale_grad
  forward : scale (Tensor x, Scalar scale, float bias, bool bias_after_scale) -> Tensor(out)
  args : (Tensor out_grad, Scalar scale, float bias=0.0, bool bias_after_scale=true)
  output : Tensor(x_grad)
  invoke : scale(out_grad, scale, bias, bias_after_scale)

- backward_api : digamma_grad
  forward : digamma (Tensor x) -> Tensor(out)
  args : (Tensor x, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : digamma_grad

- backward_api : abs_grad
  forward : abs (Tensor x) -> Tensor(out)
  args : (Tensor x, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : abs_grad

- backward_api : trunc_grad
  forward : trunc (Tensor x) -> Tensor(out)
  args : (Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out_grad]
  kernel :
    func : trunc_grad

# - backward_api : norm_grad
#   forward : norm (Tensor x, int axis, float epsilon, bool is_test) -> Tensor(out), Tensor(norm)
#   args : (Tensor x, Tensor norm, Tensor out_grad, int axis, float epsilon, bool is_test)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : norm_grad

- backward_api : diagonal_grad
  forward : diagonal (Tensor x, int offset, int axis1, int axis2) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int offset = 0, int axis1 = 0, int axis2 = 1)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : diagonal_grad

# - backward_api : split_grad
#   forward : split (Tensor x, ScalarArray num_or_sections, Scalar axis) -> Tensor[](out)
#   args : (Tensor[] out_grad, Scalar axis)
#   output : Tensor(x_grad)    
#   invoke : concat( out_grad, axis)
# TODO(zhangyunfei) The config of double grad and triple grad will be supported in the future.

# - backward_api : matmul_triple_grad
#   forward : matmul_double_grad (Tensor x, Tensor y, Tensor out_grad, Tensor dx_grad, Tensor dy_grad, bool transpose_x, bool transpose_y) -> Tensor(d2x), Tensor(d2y), Tensor(dout_grad)
#   args : (Tensor x, Tensor y, Tensor out_grad, Tensor dx_grad, Tensor dy_grad, Tensor d2x_grad, Tensor d2y_grad, Tensor dout_grad_grad, bool transpose_x, bool transpose_y)
#   output : Tensor(d3x), Tensor(d3y), Tensor(d2out_grad), Tensor(ddx_grad), Tensor(ddy_grad)
#   infer_meta :
#     func : MatmulTripleGradInferMeta
#   kernel :
#     func : matmul_triple_grad

- backward_api : softmax_grad
  forward : softmax (Tensor x, int axis) -> Tensor(out)
  args : (Tensor out, Tensor out_grad, int axis)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : softmax_grad

# - backward_api : maxout_grad
#   forward : maxout (Tensor x, int groups, int axis) -> Tensor(out)
#   args : (Tensor x, Tensor out, Tensor out_grad, int groups, int axis)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : maxout_grad


# output is optional 如何处理
- backward_api : put_along_axis_grad
  forward : put_along_axis (Tensor x, Tensor index, Tensor value, int axis, str reduce) -> Tensor(out)
  args : (Tensor x, Tensor index, Tensor out_grad, int axis, str reduce)
  output : Tensor(x_grad), Tensor(value_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, index]
  kernel :
    func : put_along_axis_grad

- backward_api : take_along_axis_grad
  forward : take_along_axis (Tensor x, Tensor index, int axis) -> Tensor(out)
  args : (Tensor x, Tensor index, Tensor out_grad, int axis)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : take_along_axis_grad

- backward_api : matrix_power_grad
  forward : matrix_power (Tensor x, int n) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, int n)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : matrix_power_grad
  
- backward_api : eigh_grad
  forward : eigh (Tensor x, str uplo) -> Tensor(out_w), Tensor(out_v)
  args : (Tensor out_w, Tensor out_v, Tensor out_w_grad, Tensor out_v_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out_v]
  kernel :
    func : eigh_grad

- backward_api : segment_pool_grad
  forward : segment_pool (Tensor x, Tensor segment_ids, str pooltype) -> Tensor(out), Tensor(summed_ids)
  args : (Tensor x, Tensor segment_ids, Tensor out, Tensor summed_ids, Tensor out_grad, str pooltype)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : segment_pool_grad

- backward_api : cos_grad
  forward : cos (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : cos_grad

- backward_api : tanh_grad
  forward : tanh (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : tanh_grad

- backward_api : acos_grad
  forward : acos (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : acos_grad

- backward_api : sin_grad
  forward : sin (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : sin_grad

- backward_api : asin_grad
  forward : asin (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : asin_grad

- backward_api : atan_grad
  forward : atan (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : atan_grad
  
- backward_api : sinh_grad
  forward : sinh (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : sinh_grad

- backward_api : cosh_grad
  forward : cosh (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : cosh_grad

- backward_api : asinh_grad
  forward : asinh (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : asinh_grad

- backward_api : acosh_grad
  forward : acosh (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : acosh_grad
  
- backward_api : atanh_grad
  forward : atanh (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : atanh_grad

- backward_api : relu_grad
  forward : relu (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : relu_grad

- backward_api : sigmoid_grad
  forward : sigmoid (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : sigmoid_grad

- backward_api : argsort_grad
  forward : argsort (Tensor x, int axis, bool descending) -> Tensor(out), Tensor(indices)
  args : (Tensor indices, Tensor x, Tensor out_grad, int axis, bool descending)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : argsort_grad


# - backward_api : batch_norm_grad
#   forward : batch_norm (Tensor x, Tensor scale, Tensor bias, Tensor mean, Tensor variance, float momentum, float epsilon, str data_layout, bool is_test, bool use_global_stats, bool trainable_statistics, bool fuse_with_relu) -> Tensor(out), Tensor(mean_out), Tensor(variance_out), Tensor(saved_mean), Tensor(saved_variance), Tensor(reserve_space)
#   args : (Tensor indices, Tensor x, Tensor out_grad, int axis, bool descending)
#   output : Tensor(x_grad), Tensor(scale_grad), Tensor(bias_grad)
#   infer_meta :
#     func : GeneralTernaryGradInferMeta
#     param : [x, scale, bias]
#   kernel :
#     func : batch_norm_grad

# - backward_api : bilinear_tensor_product_grad
#   forward : bilinear_tensor_product (Tensor x, Tensor y, Tensor weight, Tensor bias) -> Tensor(out)
#   args : (Tensor x, Tensor y, Tensor weight, Tensor out_grad)
#   output : Tensor(x_grad), Tensor(y_grad), Tensor(weight_grad), Tensor(bias_grad)
#   infer_meta :
#     func : FourXXXXInferMeta
#     param : [x, y, weight, bias]
#   kernel :
#     func : bilinear_tensor_product_grad
#   optional : bias

# - backward_api : broadcast_tensor_grad
#   forward : broadcast_tensors (Tensor[] x) -> Tensor [] (out)
#   args : (Tensor [] out_grad)
#   output : Tensor [] (x_grad)
#   infer_meta :
#     func : XXXXInferMeta
#     param : [out_grad]
#   kernel :
#     func : broadcast_tensor_grad

- backward_api : cholesky_grad
  forward : cholesky (Tensor x, bool upper) -> Tensor(out)
  args : (Tensor out, Tensor out_grad, bool upper)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : cholesky_grad

- backward_api : cholesky_solve_grad
  forward : cholesky (Tensor x, Tensor y, bool upper) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out, Tensor out_grad, bool upper)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : cholesky_solve_grad

# - backward_api : dropout_grad
#   forward : dropout (Tensor x, Tensor seed_tensor, float p, bool is_test, str mode, int seed, bool fix_seed) -> Tensor(out), Tensor(mask)
#   args : (Tensor mask, Tensor out_grad, float p, bool is_test, str mode)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [out_grad]
#   kernel :
#     func : dropout_grad


- backward_api : erf_grad
  forward : erf (Tensor x) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : erf_grad
  
- backward_api : erfinv_grad
  forward : erf (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : erfinv_grad

# - backward_api : expand_as_grad
#   forward : expand_as (Tensor x, Tensor y, int[] target_shape) -> Tensor(out)
#   args : (Tensor x, Tensor out_grad, int[] target_shape)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedGradInferMeta
#     param : [x]
#   kernel :
#     func : expand_as_grad

# - backward_api : expand_grad
#   forward : expand (Tensor x, ScalarArray shape) -> Tensor(out)
#   args : (Tensor x, Tensor out_grad, ScalarArray shape)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedGradInferMeta
#     param : [x]
#   kernel :
#     func : expand_grad

# - backward_api : graph_send_recv_grad
#   forward : graph_send_recv (Tensor x, Tensor src_index, Tensor dst_index, str pool_type) -> Tensor(out), Tensor(dst_count)
#   args : (Tensor out_grad, Tensor x, Tensor out, Tensor src_index, Tensor dst_index, Tensor dst_count, str pool_type)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : graph_send_recv_grad

# - backward_api : label_smooth_grad
#   forward : label_smooth (Tensor label, Tensor prior_dist, float epsilon) -> Tensor(out)
#   args : (Tensor out_grad, float epsilon)
#   output : Tensor(label_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [out_grad]
#   kernel :
#     func : label_smooth_grad
  
- backward_api : log_loss_grad
  forward : log_loss (Tensor input, Tensor label, float epsilon) -> Tensor(out)
  args : (Tensor input, Tensor label, Tensor out_grad, float epsilon)
  output : Tensor(input_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [input]
  kernel :
    func : log_loss_grad

# - backward_api : masked_selecte_grad
#   forward : masked_select (Tensor x, Tensor mask) -> Tensor(out)
#   args : (Tensor out_grad, Tensor x, Tensor mask)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : masked_selecte_grad

# - backward_api : multi_dot_grad
#   forward : multi_dot (Tensor[] x) -> Tensor(out)
#   args : (Tensor out_grad, Tensor[] x)
#   output : Tensor[] (x_grad)
#   infer_meta :
#     func : XXXXInferMeta
#     param : [x]
#   kernel :
#     func : multi_dot_grad

# - backward_api : nll_loss_grad
#   forward : nll_loss (Tensor x, Tensor label, Tensor weight, int64 ignore_index, str reduction) -> Tensor(out), Tensor(total_weight)
#   args : (Tensor x, Tensor label, Tensor total_weight, Tensor weight, Tensor out_grad, int64 ignore_index, str reduction)
#   output : Tensor[] (x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : nll_loss_grad
  
# - backward_api : pad_grad
#   forward : pad (Tensor x, int[] paddings, float pad_value) -> Tensor(out)
#   args : (Tensor out_grad, int[] paddings, float pad_value)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : XXXXXInferMeta
#     param : [x]
#   kernel :
#     func : pad_grad

# - backward_api : pixel_shuffle_grad
#   forward : pixel_shuffle (Tensor x, int upscale_factor, str data_format) -> Tensor(out)
#   args : (Tensor out_grad, int upscale_factor, str data_format)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : XXXXXInferMeta
#     param : [x]
#   kernel :
#     func : pixel_shuffle_grad

# - backward_api : poisson_grad
#   forward : poisson (Tensor x) -> Tensor(out)
#   args : ()
#   output : Tensor(x_grad)
#   infer_meta :
#     func : XXXXXInferMeta
#     param : [x]
#   kernel :
#     func : poisson_grad

# - backward_api : psroi_pool_grad
#   forward : psroi_pool (Tensor x, Tensor rois, Tensor rois_num, int pooled_weight, int pooled_width, int output_channels, float spatial_scale ) -> Tensor(out)
#   args : (Tensor x, Tensor rois, Tensor rois_num, Tensor out_grad, int pooled_weight, int pooled_width, int output_channels, float spatial_scale)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : psroi_pool_grad
#   optional : rois_num

- backward_api : selu_grad
  forward : selu (Tensor x, float scale, float alpha) -> Tensor(out)
  args : (Tensor out, Tensor out_grad, float scale, float alpha)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : selu_grad

- backward_api : sigmoid_cross_entropy_with_logits_grad
  forward : sigmoid_cross_entropy_with_logits (Tensor x, Tensor label, bool normalize, int ignore_index) -> Tensor(out)
  args : (Tensor x, Tensor label, Tensor out_grad, bool normalize, int ignore_index)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : sigmoid_cross_entropy_with_logits_grad

- backward_api : tile_grad
  forward : tile (Tensor x, ScalarArray repeat_times) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, ScalarArray repeat_times)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : tile_grad

# # forward backward type not match
# - backward_api : top_k_grad 
#   forward : top_k (Tensor x, Scalar k, int axis, bool largest, bool sorted) -> Tensor(out), Tensor(indices)
#   args : (Tensor out_grad, Tensor x, Tensor indices, int k, index axis, bool largest, bool sorted)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : top_k_grad


- backward_api : trace_grad 
  forward : trace (Tensor x, int offset, int axis1, int axis2) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int offset, int axis1, int axis2)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : trace_grad

- backward_api : unfold_grad 
  forward : unfold (Tensor x, int[] kernel_sizes, int[] strides, int[] paddings, int[] dilations) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int[] kernel_sizes, int[] strides, int[] paddings, int[] dilations)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : unfold_grad

# - backward_api : where_index_grad 
#   forward : where_index (Tensor condition) -> Tensor(out)
#   args : (Tensor out_grad, Tensor x, int offset, int axis1, int axis2)
#   output : Tensor(x_grad)
#   infer_meta :
#     func : UnchangedInferMeta
#     param : [x]
#   kernel :
#     func : where_index_grad