legacy_backward.yaml

- backward_op : add_double_grad
  forward : add_grad (Tensor x, Tensor y, Tensor grad_out, int axis = -1) -> Tensor(grad_x), Tensor(grad_y)
  args : (Tensor y, Tensor grad_out, Tensor grad_x_grad, Tensor grad_y_grad, int axis = -1)
  output : Tensor(grad_out_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [grad_out]
  kernel :
    func : add_double_grad
  optional : grad_x_grad, grad_y_grad
  backward : add_triple_grad
  inplace : (grad_x_grad -> grad_out_grad)
  composite : add_double_grad(y, grad_out, grad_x_grad, grad_y_grad, axis, grad_out_grad)

- backward_op : add_grad
  forward : add (Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad, int axis = -1)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : add_grad
  no_need_buffer : x, y
  composite : add_grad(x, y, out_grad, axis, x_grad, y_grad)
  backward : add_double_grad
  inplace : (out_grad -> x_grad)

- backward_op : add_triple_grad
  forward : add_double_grad (Tensor y, Tensor grad_out, Tensor grad_grad_x, Tensor grad_grad_y, int axis = -1) -> Tensor(grad_grad_out)
  args : (Tensor grad_grad_x, Tensor grad_grad_y, Tensor grad_grad_out_grad, int axis = -1)
  output : Tensor(grad_grad_x_grad), Tensor(grad_grad_y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [grad_grad_x, grad_grad_y]
  kernel :
    func : add_triple_grad
  inplace : (grad_grad_out_grad -> grad_grad_x_grad)

- backward_op : amax_grad
  forward: amax (Tensor x,  int64_t[] axis={},  bool keepdim=false) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, int64_t[] axis={},  bool keepdim=false, bool reduce_all=false)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : amax_grad

- backward_op : amin_grad
  forward: amin (Tensor x,  int64_t[] axis={},  bool keepdim=false) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, int64_t[] axis={},  bool keepdim=false, bool reduce_all=false)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : amin_grad

- backward_op : assign_grad
  forward : assign (Tensor x) -> Tensor(out)
  args : (Tensor out_grad)
  output : Tensor(x_grad)
  composite: assign_grad(out_grad, x_grad)
  invoke : assign(out_grad)

- backward_op : assign_out__grad
  forward : assign_out_ (Tensor x, Tensor output) -> Tensor(out)
  args : (Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
  kernel :
    func : assign
  inplace : (out_grad -> x_grad)

- backward_op : batch_norm_double_grad
  forward : batch_norm_grad (Tensor x, Tensor scale, Tensor bias, Tensor out_mean, Tensor out_variance, Tensor saved_mean, Tensor saved_variance, Tensor reserve_space, Tensor grad_out, float momentum, float epsilon, str data_layout, bool is_test, bool use_global_stats, bool trainable_statistics) -> Tensor(grad_x), Tensor(grad_scale), Tensor(grad_bias)
  args : (Tensor x, Tensor scale, Tensor out_mean, Tensor out_variance, Tensor saved_mean, Tensor saved_variance, Tensor grad_out,  Tensor grad_x_grad, Tensor grad_scale_grad, Tensor grad_bias_grad, float momentum, float epsilon, str data_layout, bool is_test, bool use_global_stats, bool trainable_statistics)
  output : Tensor(x_grad), Tensor(scale_grad), Tensor(grad_out_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x, scale, x]
  kernel :
    func : batch_norm_double_grad
    data_type : x
  optional : out_mean, out_variance, grad_x_grad, grad_scale_grad, grad_bias_grad
  inplace : (grad_out -> grad_out_grad)

- backward_op : batch_norm_grad
  forward : batch_norm (Tensor x, Tensor mean, Tensor variance, Tensor scale, Tensor bias, bool is_test, float momentum, float epsilon, str data_layout, bool use_global_stats, bool trainable_statistics) -> Tensor(out), Tensor(mean_out), Tensor(variance_out), Tensor(saved_mean), Tensor(saved_variance), Tensor(reserve_space)
  args : (Tensor x, Tensor scale, Tensor bias, Tensor mean_out, Tensor variance_out, Tensor saved_mean, Tensor saved_variance, Tensor reserve_space, Tensor out_grad, float momentum, float epsilon, str data_layout, bool is_test, bool use_global_stats, bool trainable_statistics)
  output : Tensor(x_grad), Tensor(scale_grad), Tensor(bias_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x, scale, bias]
  kernel :
    func : batch_norm_grad
    data_type : out_grad
  optional : mean_out, variance_out, reserve_space
  composite: batch_norm_grad(x, scale, bias, mean_out, variance_out, saved_mean, saved_variance, reserve_space, out_grad, momentum, epsilon, data_layout, is_test, use_global_stats, trainable_statistics)
  backward : batch_norm_double_grad

- backward_op : cast_grad
  forward : cast (Tensor x, DataType dtype) -> Tensor(out)
  args : (Tensor x, Tensor out_grad)
  output : Tensor(x_grad)
  invoke : cast (out_grad, x.dtype())
  composite: cast_grad(x, out_grad, x_grad)
  no_need_buffer : x

- backward_op : channel_shuffle_grad
  forward : channel_shuffle (Tensor x, int groups, str data_format="NCHW") -> Tensor(out)
  args : (Tensor out_grad, int groups, str data_format="NCHW")
  output : Tensor(x_grad)
  infer_meta :
    func : ChannelShuffleGradInferMeta
  kernel :
    func : channel_shuffle_grad

- backward_op : concat_double_grad
  forward : concat_grad (Tensor[] x, Tensor grad_out, Scalar axis) -> Tensor[](grad_x)
  args : (Tensor[] grad_x_grad, Scalar axis = 0)
  output : Tensor(grad_out_grad)
  invoke : concat(grad_x_grad, axis)

- backward_op : concat_grad
  forward : concat (Tensor[] x, Scalar axis) -> Tensor(out)
  args : (Tensor[] x, Tensor out_grad, Scalar axis = 0)
  output : Tensor[](x_grad){x.size()}
  infer_meta :
    func : UnchangedMultiInferMeta
    param : [x]
  kernel :
    func : concat_grad
  composite : concat_grad(x, out_grad, axis, x_grad)
  no_need_buffer : x
  backward : concat_double_grad

- backward_op : conv2d_transpose_double_grad
  forward : conv2d_transpose_grad(Tensor x, Tensor filter, Tensor grad_out, int[] strides, int[] paddings, int[] output_padding, IntArray output_size, str padding_algorithm, int groups, int[] dilations, str data_format) -> Tensor(grad_x), Tensor(grad_filter)
  args : (Tensor x, Tensor filter, Tensor grad_out, Tensor grad_x_grad, Tensor grad_filter_grad, int[] strides, int[] paddings, int[] output_padding, IntArray output_size, str padding_algorithm, int groups, int[] dilations, str data_format)
  output : Tensor(x_grad), Tensor(filter_grad), Tensor(grad_out_grad)
  infer_meta :
    func : Conv2dTransposeDoubleGradInferMeta
  kernel :
    func : conv2d_transpose_double_grad

- backward_op : conv2d_transpose_grad
  forward : conv2d_transpose(Tensor x, Tensor filter, int[] strides, int[] paddings, int[] output_padding, IntArray output_size, str padding_algorithm, int groups, int[] dilations, str data_format) -> Tensor(out)
  args : (Tensor x, Tensor filter, Tensor out_grad, int[] strides, int[] paddings, int[] output_padding, IntArray output_size, str padding_algorithm, int groups, int[] dilations, str data_format)
  output : Tensor(x_grad), Tensor(filter_grad)
  infer_meta :
    func : Conv2dTransposeGradInferMeta
  kernel :
    func : conv2d_transpose_grad
  backward : conv2d_transpose_double_grad

- backward_op : conv3d_transpose_grad
  forward : conv3d_transpose(Tensor x, Tensor filter, int[] strides, int[] paddings, int[] output_padding, int[] output_size, str padding_algorithm, int groups, int[] dilations, str data_format) -> Tensor(out)
  args : (Tensor x, Tensor filter, Tensor out_grad, int[] strides, int[] paddings, int[] output_padding, int[] output_size, str padding_algorithm, int groups, int[] dilations, str data_format)
  output : Tensor(x_grad), Tensor(filter_grad)
  infer_meta :
    func : ConvTransposeGradInferMeta
  kernel :
    func : conv3d_transpose_grad

- backward_op : cumsum_grad
  forward : cumsum(Tensor x, Scalar axis, bool flatten, bool exclusive, bool reverse) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, Scalar axis, bool flatten, bool exclusive, bool reverse)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : cumsum_grad
    data_type: x
  composite: cumsum_grad(x, out_grad, axis, flatten, exclusive, reverse, x_grad)

- backward_op : deformable_conv_grad
  forward : deformable_conv(Tensor x, Tensor offset, Tensor filter, Tensor mask, int[] strides, int[] paddings, int[] dilations, int deformable_groups, int groups, int im2col_step) -> Tensor(out)
  args : (Tensor x, Tensor offset, Tensor filter, Tensor mask, Tensor out_grad, int[] strides, int[] paddings, int[] dilations, int deformable_groups, int groups, int im2col_step)
  output : Tensor(x_grad), Tensor(offset_grad), Tensor(filter_grad), Tensor(mask_grad)
  infer_meta :
    func : DeformableConvGradInferMeta
  kernel :
    func : deformable_conv_grad
    data_type : x
  optional : mask

- backward_op : depthwise_conv2d_transpose_grad
  forward : depthwise_conv2d_transpose(Tensor x, Tensor filter, int[] strides, int[] paddings, int[] output_padding, IntArray output_size, str padding_algorithm, int groups, int[] dilations, str data_format) -> Tensor(out)
  args : (Tensor x, Tensor filter, Tensor out_grad, int[] strides, int[] paddings, int[] output_padding, IntArray output_size, str padding_algorithm, int groups, int[] dilations, str data_format)
  output : Tensor(x_grad), Tensor(filter_grad)
  infer_meta :
    func : Conv2dTransposeGradInferMeta
  kernel :
    func : depthwise_conv2d_transpose_grad

- backward_op : divide_double_grad
  forward : divide_grad (Tensor x, Tensor y, Tensor out, Tensor grad_out, int axis = -1) -> Tensor(grad_x), Tensor(grad_y)
  args : (Tensor y, Tensor out, Tensor grad_x, Tensor grad_x_grad, Tensor grad_y_grad, int axis = -1)
  output : Tensor(y_grad), Tensor(out_grad), Tensor(grad_out_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [y, grad_x, grad_x]
  kernel :
    func : divide_double_grad
    data_type : out
  optional : grad_x_grad, grad_y_grad
  inplace : (grad_x_grad -> grad_out_grad)

- backward_op : divide_grad
  forward : divide (Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out, Tensor out_grad, int axis = -1)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : divide_grad
  composite : divide_grad(x, y, out, out_grad, axis, x_grad, y_grad)
  backward : divide_double_grad

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

- backward_op : einsum_grad
  forward : einsum (Tensor[] x, str equation) -> Tensor(out), Tensor[](inner_cache), Tensor[](x_shape)
  args : (Tensor[] x_shape, Tensor[] inner_cache, Tensor out_grad, str equation)
  output : Tensor[](x_grad){x_shape.size()}
  infer_meta :
    func : UnchangedMultiInferMeta
    param : [x_shape]
  kernel :
    func : einsum_grad

- backward_op : elementwise_pow_grad
  forward : elementwise_pow(Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param: [x, y]
  composite : elementwise_pow_grad(x, y, out_grad, axis, x_grad, y_grad)
  kernel :
    func : elementwise_pow_grad

- backward_op : embedding_grad
  forward : embedding (Tensor x, Tensor weight, int64_t padding_idx=-1, bool sparse=false) -> Tensor(out)
  args : (Tensor x, Tensor weight, Tensor out_grad, int64_t padding_idx=-1, bool sparse=false)
  output : Tensor(weight_grad)
  invoke : embedding_grad_impl(x, weight, out_grad, padding_idx, sparse, weight_grad)
  no_need_buffer : weight

- backward_op : expand_double_grad
  forward : expand_grad (Tensor x, Tensor grad_out, IntArray shape) -> Tensor(grad_x)
  args : (Tensor grad_x_grad, IntArray shape)
  output : Tensor(grad_out_grad)
  invoke : expand(grad_x_grad, shape)

- backward_op : expand_grad
  forward : expand (Tensor x, IntArray shape) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, IntArray shape)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : expand_grad
  no_need_buffer : x
  backward : expand_double_grad
  composite: expand_grad(x, out_grad, shape, x_grad)

- backward_op : exponential__grad
  forward : exponential_ (Tensor x, float lam) -> Tensor(out)
  args : (Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
  invoke : zeros_like(out_grad)

- backward_op : fill_grad
  forward : fill (Tensor x, Scalar value) -> Tensor(out)
  args : (Tensor out_grad, Scalar value)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out_grad]
  kernel :
    func : fill_grad
  inplace : (out_grad -> x_grad)

- backward_op : fmax_grad
  forward : fmax(Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param: [x, y]
  kernel :
    func : fmax_grad

- backward_op : fmin_grad
  forward : fmin(Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param: [x, y]
  kernel :
    func : fmin_grad

- backward_op : frobenius_norm_grad
  forward : frobenius_norm(Tensor x, int64_t[] axis,  bool keep_dim,  bool reduce_all) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, int64_t[] axis,  bool keep_dim,  bool reduce_all)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : frobenius_norm_grad

- backward_op : gather_grad
  forward : gather(Tensor x, Tensor index, Scalar axis=0) -> Tensor(out)
  args : (Tensor x, Tensor index, Tensor out_grad, Scalar axis=0)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    data_type: x
    func : gather_grad
  composite : gather_grad(x, index, out_grad, axis, x_grad)
  no_need_buffer : x

- backward_op : hardswish_grad
  forward : hardswish (Tensor x) -> Tensor(out)
  args : (Tensor x, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : hardswish_grad
  inplace : (out_grad -> x_grad)

- backward_op : heaviside_grad
  forward : heaviside (Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : heaviside_grad

- backward_op : hsigmoid_loss_grad
  forward : hsigmoid_loss (Tensor x, Tensor label, Tensor w, Tensor bias, Tensor path, Tensor code, int num_classes, bool is_sparse) -> Tensor(out), Tensor(pre_out), Tensor(w_out)
  args : (Tensor x, Tensor w, Tensor label, Tensor path, Tensor code, Tensor bias, Tensor pre_out, Tensor out_grad, int num_classes, bool is_sparse)
  output : Tensor(x_grad), Tensor(w_grad), Tensor(bias_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x ,w, bias]
  optional: path, code, bias
  kernel :
    func : hsigmoid_loss_grad

- backward_op : logsumexp_grad
  forward : logsumexp(Tensor x, int64_t[] axis,  bool keepdim,  bool reduce_all) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, int64_t[] axis,  bool keepdim,  bool reduce_all)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : logsumexp_grad

- backward_op : matmul_double_grad
  forward : matmul_grad (Tensor x, Tensor y, Tensor grad_out, bool transpose_x=false, bool transpose_y=false) -> Tensor(grad_x), Tensor(grad_y)
  args : (Tensor x, Tensor y, Tensor grad_out, Tensor grad_x_grad, Tensor grad_y_grad, bool transpose_x=false, bool transpose_y=false)
  output : Tensor(x_grad), Tensor(y_grad), Tensor(grad_out_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x, y, grad_out]
  kernel :
    func : matmul_double_grad
  composite : matmul_double_grad(x, y, grad_out, grad_x_grad, grad_y_grad, transpose_x=false, transpose_y=false)
  optional : grad_x_grad, grad_y_grad

- backward_op : 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 : matmul_double_grad

- backward_op : max_grad
  forward: max (Tensor x,  IntArray axis={},  bool keepdim=false) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, IntArray axis={}, bool keepdim=false, bool reduce_all=false)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : max_grad
  composite : max_grad(x, out, out_grad, axis, keepdim, reduce_all, x_grad)

- backward_op : maximum_grad
  forward : maximum(Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param: [x, y]
  kernel :
    func : maximum_grad
  composite : maximum_grad(x, y, out_grad, axis, x_grad, y_grad)

- backward_op : mean_double_grad
  forward: mean_grad (Tensor x, Tensor grad_out, IntArray axis={},  bool keepdim=false, bool reduce_all = false) -> Tensor(grad_x)
  args : (Tensor grad_x_grad, IntArray axis={},  bool keepdim=false)
  output : Tensor(grad_out_grad)
  invoke : mean(grad_x_grad, axis, keepdim)

- backward_op : mean_grad
  forward: mean (Tensor x,  IntArray axis={},  bool keepdim=false) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, IntArray axis={},  bool keepdim=false, bool reduce_all=false)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : mean_grad
  backward : mean_double_grad
  no_need_buffer : x

- backward_op : min_grad
  forward: min (Tensor x,  IntArray axis={},  bool keepdim=false) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, IntArray axis={}, bool keepdim=false, bool reduce_all=false)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : min_grad

- backward_op : minimum_grad
  forward : minimum(Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param: [x, y]
  kernel :
    func : minimum_grad
  composite : minimum_grad(x, y, out_grad, axis, x_grad, y_grad)

- backward_op : mish_grad
  forward : mish (Tensor x, float threshold) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, float threshold)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : mish_grad
  inplace : (out_grad -> x_grad)

- backward_op : multiply_double_grad
  forward : multiply_grad (Tensor x, Tensor y, Tensor grad_out, int axis = -1) -> Tensor(grad_x), Tensor(grad_y)
  args : (Tensor x, Tensor y, Tensor grad_out, Tensor grad_x_grad, Tensor grad_y_grad, int axis = -1)
  output : Tensor(x_grad), Tensor(y_grad), Tensor(grad_out_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x, y, grad_out]
  kernel :
    func : multiply_double_grad
  optional : grad_x_grad, grad_y_grad
  inplace : (grad_x_grad -> grad_out_grad)
  backward : multiply_triple_grad
  composite : multiply_double_grad(x, y, grad_out, grad_x_grad, grad_y_grad, axis, x_grad, y_grad, grad_out_grad)

- backward_op : multiply_grad
  forward : multiply (Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad, int axis = -1)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : multiply_grad
  composite: multiply_grad(x, y, out_grad, axis, x_grad, y_grad)
  backward : multiply_double_grad

- backward_op : multiply_triple_grad
  forward : multiply_double_grad (Tensor x, Tensor y, Tensor fwd_grad_out, Tensor fwd_grad_grad_x, Tensor fwd_grad_grad_y, int aixs = -1) -> Tensor(grad_x), Tensor(grad_y), Tensor(grad_grad_out)
  args : (Tensor x, Tensor y, Tensor fwd_grad_out, Tensor fwd_grad_grad_x, Tensor fwd_grad_grad_y, Tensor grad_x_grad, Tensor grad_y_grad, Tensor grad_grad_out_grad, int axis = -1)
  output : Tensor(x_grad), Tensor(y_grad), Tensor(fwd_grad_out_grad), Tensor(fwd_grad_grad_x_grad), Tensor(fwd_grad_grad_y_grad)
  infer_meta :
    func : GeneralQuinaryGradInferMeta
    param : [x, y, fwd_grad_out, fwd_grad_grad_x, fwd_grad_grad_y]
  kernel :
    func : multiply_triple_grad
  optional : fwd_grad_grad_x, fwd_grad_grad_y, grad_x_grad, grad_y_grad, grad_grad_out_grad

- backward_op : 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_op : pad_double_grad
  forward : pad_grad(Tensor x, Tensor grad_out, int[] paddings, Scalar pad_value) -> Tensor(grad_x)
  args : (Tensor grad_x_grad, int[] paddings, Scalar pad_value)
  output : Tensor(grad_out_grad)
  infer_meta :
    func : PadInferMeta
  kernel :
    func : pad

- backward_op : pad_grad
  forward : pad(Tensor x, int[] paddings, Scalar pad_value) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int[] paddings, Scalar pad_value)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : pad_grad
    param: [out_grad, paddings, pad_value]
  no_need_buffer : x
  composite : pad_grad(x, out_grad, paddings, pad_value, x_grad)
  backward : pad_double_grad

- backward_op : pool2d_double_grad
  forward : pool2d_grad(Tensor x, Tensor out, Tensor grad_out, IntArray kernel_size, int[] strides, int[] paddings, bool ceil_mode, bool exclusive, str data_format, str pooling_type, bool global_pooling, bool adaptive, str padding_algorithm) -> Tensor(grad_x)
  args : (Tensor x, Tensor grad_x_grad, IntArray kernel_size, int[] strides, int[] paddings, bool ceil_mode, bool exclusive, str data_format, str pooling_type, bool global_pooling, bool adaptive, str padding_algorithm)
  output : Tensor(grad_out_grad)
  infer_meta :
    func : Pool2DInferMeta
    param : [grad_x_grad, kernel_size, strides, paddings, ceil_mode, exclusive, data_format, pooling_type, global_pooling, adaptive, padding_algorithm]
  kernel :
    func : pool2d_double_grad
    param : [grad_x_grad, kernel_size, strides, paddings, ceil_mode, exclusive, data_format, pooling_type, global_pooling, adaptive, padding_algorithm]
  no_need_buffer : x

- backward_op : pool2d_grad
  forward : pool2d(Tensor x, IntArray kernel_size, int[] strides, int[] paddings, bool ceil_mode, bool exclusive, str data_format, str pooling_type, bool global_pooling, bool adaptive, str padding_algorithm) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, IntArray kernel_size, int[] strides, int[] paddings, bool ceil_mode, bool exclusive, str data_format, str pooling_type, bool global_pooling, bool adaptive, str padding_algorithm)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : pool2d_grad
    param : [x, out, out_grad, kernel_size, strides, paddings, ceil_mode, exclusive, data_format, pooling_type, global_pooling, adaptive, padding_algorithm]
  backward : pool2d_double_grad

- backward_op : pool3d_grad
  forward : pool3d(Tensor x, int[] kernel_size, int[] strides, int[] paddings, bool ceil_mode, bool exclusive, str data_format, str pooling_type, bool global_pooling, bool adaptive, str padding_algorithm) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, int[] kernel_size, int[] strides, int[] paddings, bool ceil_mode, bool exclusive, str data_format, str pooling_type, bool global_pooling, bool adaptive, str padding_algorithm)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param: [x]
  kernel :
    func : pool3d_grad
    param : [x, out, out_grad, kernel_size, strides, paddings, ceil_mode, exclusive, data_format, pooling_type, global_pooling, adaptive, padding_algorithm]

- backward_op : prod_grad
  forward : prod (Tensor x, IntArray dims, bool keep_dim, bool reduce_all) -> Tensor(out)
  args : (Tensor x, Tensor out, Tensor out_grad, IntArray dims,  bool keep_dim, bool reduce_all)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : prod_grad
  composite: prod_grad(x, out, out_grad, dims, keep_dim, reduce_all, x_grad)

- backward_op : psroi_pool_grad
  forward : psroi_pool (Tensor x, Tensor boxes, Tensor boxes_num, int pooled_height, int pooled_width, int output_channels, float spatial_scale) -> Tensor(out)
  args : (Tensor x, Tensor boxes, Tensor boxes_num, Tensor out_grad, int pooled_height, int pooled_width, int output_channels, float spatial_scale)
  output : Tensor(x_grad)
  infer_meta :
    func : GeneralUnaryGradInferMeta
    param : [x]
  kernel :
    func : psroi_pool_grad
    data_type : x
  optional : boxes_num

- backward_op : relu6_grad
  forward : relu6 (Tensor x) -> Tensor(out)
  args : (Tensor out, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out]
  kernel :
    func : relu6_grad
  inplace : (out_grad -> x_grad)

- backward_op : repeat_interleave_grad
  forward : repeat_interleave(Tensor x, int repeats, int axis) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int repeats, int axis)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : repeat_interleave_grad

- backward_op : repeat_interleave_with_tensor_index_grad
  forward : repeat_interleave_with_tensor_index(Tensor x, Tensor repeats, int axis) -> Tensor(out)
  args : (Tensor x, Tensor repeats, Tensor out_grad, int axis)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : repeat_interleave_with_tensor_index_grad
    data_type : x

- backward_op : reshape_double_grad
  forward : reshape_grad (Tensor xshape, Tensor grad_out) -> Tensor(grad_x)
  args : (Tensor grad_out, Tensor grad_x_grad)
  output : Tensor(grad_out_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [grad_out]
  kernel :
    func : reshape_double_grad
  no_need_buffer : grad_out
  inplace : (grad_x_grad -> grad_out_grad)

- backward_op : reshape_grad
  forward : reshape (Tensor x, IntArray shape) -> Tensor(out), Tensor(xshape)
  args : (Tensor xshape, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : KernelWithXShapeInferMeta
    param : [xshape]
  kernel :
    func : reshape_grad
    param : [out_grad]
    data_type: out_grad
    backend: out_grad
    layout: out_grad
  backward : reshape_double_grad
  inplace : (out_grad -> x_grad)

- backward_op : rnn_grad
  forward : rnn (Tensor x, Tensor[] pre_state, Tensor[] weight_list, Tensor sequence_length, Tensor dropout_state_in, float dropout_prob, bool is_bidirec, int input_size, int hidden_size, int num_layers, str mode, int seed, bool is_test) -> Tensor(out), Tensor(dropout_state_out), Tensor[](state), Tensor(reserve)
  args : (Tensor x, Tensor[] pre_state, Tensor[] weight_list, Tensor sequence_length, Tensor out, Tensor dropout_state_out, Tensor reserve, Tensor out_grad, Tensor[] state_grad, float dropout_prob, bool is_bidirec, int input_size, int hidden_size, int num_layers, str mode, int seed, bool is_test)
  output : Tensor(x_grad), Tensor[](pre_state_grad){pre_state.size()}, Tensor[](weight_list_grad){weight_list.size()}
  infer_meta :
    func : RnnGradInferMeta
    param : [x, pre_state, weight_list]
  kernel :
    func : rnn_grad
    data_type: out_grad
  optional : sequence_length

- backward_op : roi_align_grad
  forward : roi_align (Tensor x, Tensor boxes, Tensor boxes_num, int pooled_height, int pooled_width, float spatial_scale, int sampling_ratio, bool aligned) -> Tensor(out)
  args : (Tensor x, Tensor boxes, Tensor boxes_num, Tensor out_grad, int pooled_height, int pooled_width, float spatial_scale, int sampling_ratio, bool aligned)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : roi_align_grad
    data_type : boxes
  no_need_buffer : x
  optional : boxes_num

- backward_op : roi_pool_grad
  forward : roi_pool (Tensor x, Tensor boxes, Tensor boxes_num, int pooled_height, int pooled_width, float spatial_scale) -> Tensor(out), Tensor(arg_max)
  args : (Tensor x, Tensor boxes, Tensor boxes_num, Tensor arg_max, Tensor out_grad, int pooled_height, int pooled_width, float spatial_scale)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : roi_pool_grad
    data_type : x
  optional : boxes_num

- backward_op : rrelu_grad
  forward : rrelu (Tensor x, float lower, float upper, bool is_test) -> Tensor(out), Tensor(noise)
  args : (Tensor x, Tensor noise, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : RReluGradInferMeta
    param : [out_grad, noise]
  kernel :
    func : rrelu_grad
    data_type : x

- backward_op : slice_double_grad
  forward : slice_grad (Tensor input, Tensor grad_out, int64_t[] axes, IntArray starts, IntArray ends, int64_t[] infer_flags, int64_t[] decrease_axis) -> Tensor(grad_input)
  args : (Tensor grad_input_grad, int64_t[] axes, IntArray starts, IntArray ends, int64_t[] infer_flags, int64_t[] decrease_axis)
  output : Tensor(grad_out_grad)
  invoke : slice(grad_input_grad, axes, starts, ends, infer_flags, decrease_axis)

- backward_op : slice_grad
  forward : slice (Tensor input, int64_t[] axes, IntArray starts, IntArray ends, int64_t[] infer_flags, int64_t[] decrease_axis) -> Tensor(out)
  args : (Tensor input, Tensor out_grad, int64_t[] axes, IntArray starts, IntArray ends, int64_t[] infer_flags, int64_t[] decrease_axis)
  output : Tensor(input_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [input]
  kernel :
    func : slice_grad
  composite: slice_grad(input, out_grad, axes, starts, ends, infer_flags, decrease_axis, input_grad)
  backward : slice_double_grad
  no_need_buffer : input

- backward_op : 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
  composite : softmax_grad(out, out_grad, axis, x_grad)

- backward_op : split_grad
  forward : split (Tensor x, IntArray num_or_sections, Scalar axis) -> Tensor[](out)
  args : (Tensor[] out_grad, Scalar axis = -1)
  output : Tensor(x_grad)
  invoke : concat( out_grad, axis)
  composite : split_grad(out_grad, axis, x_grad)

- backward_op : split_with_num_grad
  forward : split_with_num (Tensor x, int num, Scalar axis) -> Tensor[](out)
  args : (Tensor[] out_grad, Scalar axis = -1)
  output : Tensor(x_grad)
  invoke : concat( out_grad, axis)
  composite : split_grad(out_grad, axis, x_grad)

- backward_op : strided_slice_grad
  forward : strided_slice (Tensor x, int[] axes, IntArray starts, IntArray ends, IntArray strides) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int[] axes, IntArray starts, IntArray ends, IntArray strides)
  output : Tensor(x_grad)
  infer_meta :
    func : GeneralUnaryGradInferMeta
    param : [x]
  kernel :
    func : strided_slice_grad
  no_need_buffer : x

- backward_op : subtract_double_grad
  forward : subtract_grad (Tensor x, Tensor y, Tensor grad_out, int axis = -1) -> Tensor(grad_x), Tensor(grad_y)
  args : (Tensor y, Tensor grad_out, Tensor grad_x_grad, Tensor grad_y_grad, int axis = -1)
  output : Tensor(grad_out_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [grad_out]
  kernel :
    func : subtract_double_grad
  optional : grad_x_grad, grad_y_grad
  no_need_buffer : y, grad_out
  inplace : (grad_x_grad -> grad_out_grad)
  composite : subtract_double_grad(y, grad_out, grad_x_grad, grad_y_grad, axis, grad_out_grad)

- backward_op : subtract_grad
  forward : subtract (Tensor x, Tensor y) -> Tensor(out)
  args : (Tensor x, Tensor y, Tensor out_grad, int axis = -1)
  output : Tensor(x_grad), Tensor(y_grad)
  infer_meta :
    func : GeneralBinaryGradInferMeta
    param : [x, y]
  kernel :
    func : subtract_grad
  no_need_buffer : x, y
  composite : subtract_grad(x, y, out_grad, axis, x_grad, y_grad)
  backward : subtract_double_grad
  inplace : (out_grad -> x_grad)

- backward_op : sum_double_grad
  forward : sum_grad (Tensor x, Tensor grad_out, IntArray axis, bool keepdim, bool reduce_all=false) -> Tensor(grad_x)
  args : (Tensor grad_x_grad, IntArray axis={}, bool keepdim=false)
  output : Tensor(grad_out_grad)
  invoke : sum(grad_x_grad, axis, grad_x_grad.dtype(), keepdim)

- backward_op : sum_grad
  forward : sum (Tensor x, IntArray axis={}, DataType dtype=DataType::UNDEFINED, bool keepdim=false) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, IntArray axis, bool keepdim, bool reduce_all=false)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : sum_grad
  composite : sum_grad(x, out_grad, axis, keepdim, reduce_all, x_grad)
  no_need_buffer : x
  backward : sum_double_grad

- backward_op : swish_grad
  forward : swish (Tensor x) -> Tensor(out)
  args : (Tensor x, Tensor out_grad)
  output : Tensor(x_grad)
  infer_meta :
    func : GeneralUnaryGradInferMeta
    param : [x]
  kernel :
    func : swish_grad
  inplace : (out_grad -> x_grad)

- backward_op : sync_batch_norm_grad
  forward : sync_batch_norm_ (Tensor x, Tensor mean, Tensor variance, Tensor scale, Tensor bias, bool is_test, float momentum, float epsilon, str data_layout, bool use_global_stats, bool trainable_statistics) -> Tensor(out), Tensor(mean_out), Tensor(variance_out), Tensor(saved_mean), Tensor(saved_variance), Tensor(reserve_space)
  args : (Tensor x, Tensor scale, Tensor bias, Tensor saved_mean, Tensor saved_variance, Tensor reserve_space, Tensor out_grad, float momentum, float epsilon, str data_layout, bool is_test, bool use_global_stats, bool trainable_statistics)
  output : Tensor(x_grad), Tensor(scale_grad), Tensor(bias_grad)
  infer_meta :
    func : GeneralTernaryGradInferMeta
    param : [x, scale, bias]
  kernel :
    func : sync_batch_norm_grad
    data_type : out_grad
  optional : reserve_space

- backward_op : tile_double_grad
  forward : tile_grad (Tensor x, Tensor grad_out, IntArray repeat_times) -> Tensor(grad_x)
  args : (Tensor grad_x_grad, IntArray repeat_times)
  output : Tensor(grad_out_grad)
  invoke : tile(grad_x_grad, repeat_times)

- backward_op : tile_grad
  forward : tile (Tensor x, IntArray repeat_times) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, IntArray repeat_times)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [x]
  kernel :
    func : tile_grad
  no_need_buffer : x
  composite : tile_grad(x, outgrad, repeat_times, x_grad)
  backward : tile_double_grad

- backward_op : trans_layout_grad
  forward : trans_layout (Tensor x, int[] perm) -> Tensor(out)
  args : (Tensor x, Tensor out_grad, int[] perm)
  output : Tensor(x_grad)
  infer_meta :
    func : TransLayoutGradInferMeta
  kernel :
    func : trans_layout_grad

- backward_op : transpose_double_grad
  forward : transpose_grad (Tensor grad_out, int[] perm) -> Tensor(grad_x)
  args : (Tensor grad_x_grad, int[] perm)
  output : Tensor(grad_out_grad)
  invoke : transpose(grad_x_grad, perm)

- backward_op : transpose_grad
  forward : transpose (Tensor x, int[] perm) -> Tensor(out)
  args : (Tensor out_grad, int[] perm)
  output : Tensor(x_grad)
  infer_meta :
    func : TransposeGradInferMeta
    param : [out_grad, perm]
  kernel :
    func : transpose_grad
  backward : transpose_double_grad
  composite: transpose_grad(out_grad, perm, x_grad)

- backward_op : tril_grad
  forward : tril(Tensor x,  int diagonal) -> Tensor(out)
  args : (Tensor out_grad,  int diagonal)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out_grad]
  kernel :
    func : tril_grad

- backward_op : triu_grad
  forward : triu(Tensor x,  int diagonal) -> Tensor(out)
  args : (Tensor out_grad,  int diagonal)
  output : Tensor(x_grad)
  infer_meta :
    func : UnchangedInferMeta
    param : [out_grad]
  kernel :
    func : triu_grad

- backward_op: unpool_grad
  forward: unpool (Tensor x, Tensor indices, int[] ksize, int[] strides, int[] padding,  IntArray output_size, str data_format) -> Tensor(out)
  args: (Tensor x, Tensor indices, Tensor out, Tensor out_grad, int[] ksize, int[] strides, int[] padding, IntArray output_size, str data_format)
  output: Tensor(x_grad)
  infer_meta:
    func: UnchangedInferMeta
    param : [x]
  kernel:
    func: unpool_grad
    data_type: x