diff --git a/aten/src/ATen/native/native_functions.yaml b/aten/src/ATen/native/native_functions.yaml
index 88201a6170c2..b84c754b7efd 100644
--- a/aten/src/ATen/native/native_functions.yaml
+++ b/aten/src/ATen/native/native_functions.yaml
@@ -220,10 +220,14 @@
 - func: abs(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: abs
 
 - func: abs_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: abs_
 
 - func: abs.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -268,6 +272,8 @@
 - func: angle(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: angle
 
 - func: angle.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -276,10 +282,14 @@
 - func: view_as_real(Tensor(a) self) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: view_as_real
 
 - func: view_as_complex(Tensor(a) self) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: view_as_complex
 
 - func: sgn(Tensor self) -> Tensor
   use_c10_dispatcher: full
@@ -315,14 +325,20 @@
 - func: _conj(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: _conj
 
 - func: acos(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: acos
 
 - func: acos_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: acos_
 
 - func: acos.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -393,10 +409,14 @@
 - func: add.Scalar(Tensor self, Scalar other, Scalar alpha=1) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: add
 
 - func: add_.Scalar(Tensor(a!) self, Scalar other, Scalar alpha=1) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: add_
 
 - func: addmv(Tensor self, Tensor mat, Tensor vec, *, Scalar beta=1, Scalar alpha=1) -> Tensor
   use_c10_dispatcher: full
@@ -423,16 +443,24 @@
 - func: addr(Tensor self, Tensor vec1, Tensor vec2, *, Scalar beta=1, Scalar alpha=1) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: addr
 
 - func: addr_(Tensor(a!) self, Tensor vec1, Tensor vec2, *, Scalar beta=1, Scalar alpha=1) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: addr_
 
 - func: addr.out(Tensor self, Tensor vec1, Tensor vec2, *, Scalar beta=1, Scalar alpha=1, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: addr_out
 
 - func: affine_grid_generator(Tensor theta, int[] size, bool align_corners) -> Tensor
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: affine_grid_generator
 
 - func: affine_grid_generator_backward(Tensor grad, int[] size, bool align_corners) -> Tensor
   use_c10_dispatcher: full
@@ -511,10 +539,14 @@
 - func: acosh(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: acosh
 
 - func: acosh_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: acosh_
 
 - func: acosh.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -534,10 +566,14 @@
 - func: asinh(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: asinh
 
 - func: asinh_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: asinh_
 
 - func: asinh.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -557,10 +593,14 @@
 - func: atanh(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: atanh
 
 - func: atanh_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: atanh_
 
 - func: atanh.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -588,10 +628,14 @@
 - func: as_strided_(Tensor(a!) self, int[] size, int[] stride, int? storage_offset=None) -> Tensor(a!)
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: as_strided_
 
 - func: asin(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: asin
 
 - func: asin_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
@@ -619,10 +663,14 @@
 - func: atan(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: atan
 
 - func: atan_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: atan_
 
 - func: atan.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -709,6 +757,8 @@
 # Sample bernoulli with values in `self` as probability.
 - func: bernoulli(Tensor self, *, Generator? generator=None) -> Tensor
   variants: function, method
+  dispatch:
+    DefaultBackend: bernoulli
 
 - func: bernoulli.out(Tensor self, *, Generator? generator=None, Tensor(a!) out) -> Tensor(a!)
   variants: function
@@ -767,6 +817,8 @@
 - func: binary_cross_entropy_with_logits(Tensor self, Tensor target, Tensor? weight=None, Tensor? pos_weight=None, int reduction=Mean) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
   variants: function
+  dispatch:
+    DefaultBackend: binary_cross_entropy_with_logits
 
 - func: binary_cross_entropy_with_logits_backward(Tensor grad_output, Tensor self, Tensor target, Tensor? weight=None, Tensor? pos_weight=None, int reduction=Mean) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -879,8 +931,12 @@
 
 - func: cat(Tensor[] tensors, int dim=0) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: cat
 
 - func: cat.out(Tensor[] tensors, int dim=0, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: cat_out
 
 - func: cat.names(Tensor[] tensors, Dimname dim) -> Tensor
 
@@ -893,10 +949,14 @@
 - func: ceil(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: ceil
 
 - func: ceil_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: ceil_
 
 - func: ceil.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -934,6 +994,8 @@
 - func: clamp_(Tensor(a!) self, Scalar? min=None, Scalar? max=None) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: clamp_
 
 - func: clamp.out(Tensor self, Scalar? min=None, Scalar? max=None, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -942,10 +1004,14 @@
 - func: clamp_max(Tensor self, Scalar max) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: clamp_max
 
 - func: clamp_max_(Tensor(a!) self, Scalar max) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: clamp_max_
 
 - func: clamp_max.out(Tensor self, Scalar max, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -954,10 +1020,14 @@
 - func: clamp_min(Tensor self, Scalar min) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: clamp_min
 
 - func: clamp_min_(Tensor(a!) self, Scalar min) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: clamp_min_
 
 - func: clamp_min.out(Tensor self, Scalar min, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -980,6 +1050,8 @@
 - func: complex(Tensor real, Tensor imag) -> Tensor
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: complex
 
 - func: complex.out(Tensor real, Tensor imag, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -988,6 +1060,8 @@
 - func: polar(Tensor abs, Tensor angle) -> Tensor
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: polar
 
 - func: polar.out(Tensor abs, Tensor angle, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -996,6 +1070,8 @@
 - func: constant_pad_nd(Tensor self, int[] pad, Scalar value=0) -> Tensor
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: constant_pad_nd
 
 - func: contiguous(Tensor(a) self, *, MemoryFormat memory_format=contiguous_format) -> Tensor(a)
   use_c10_dispatcher: full
@@ -1006,9 +1082,13 @@
 
 - func: convolution_overrideable(Tensor input, Tensor weight, Tensor? bias, int[] stride, int[] padding, int[] dilation, bool transposed, int[] output_padding, int groups) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
+  dispatch:
+    DefaultBackend: convolution_overrideable
 
 - func: convolution_backward_overrideable(Tensor grad_output, Tensor input, Tensor weight, int[] stride, int[] padding, int[] dilation, bool transposed, int[] output_padding, int groups, bool[3] output_mask) -> (Tensor grad_input, Tensor grad_weight, Tensor grad_bias)
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: convolution_backward_overrideable
 
 - func: _convolution(Tensor input, Tensor weight, Tensor? bias, int[] stride, int[] padding, int[] dilation, bool transposed, int[] output_padding, int groups, bool benchmark, bool deterministic, bool cudnn_enabled, bool allow_tf32) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -1033,6 +1113,8 @@
 
 - func: conv_tbc(Tensor self, Tensor weight, Tensor bias, int pad=0) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: conv_tbc
 
 - func: conv_tbc_backward(Tensor self, Tensor input, Tensor weight, Tensor bias, int pad) -> (Tensor, Tensor, Tensor)
   use_c10_dispatcher: full
@@ -1051,6 +1133,8 @@
   use_c10_dispatcher: full
   variants: method
   device_guard: False
+  dispatch:
+    DefaultBackend: copy_
 
 - func: _copy_from(Tensor self, Tensor dst, bool non_blocking=False) -> Tensor
   use_c10_dispatcher: full
@@ -1059,10 +1143,14 @@
 - func: cos(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cos
 
 - func: cos_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cos_
 
 - func: cos.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1071,10 +1159,14 @@
 - func: cosh(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cosh
 
 - func: cosh_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cosh_
 
 - func: cosh.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1092,6 +1184,8 @@
 - func: count_nonzero(Tensor self, int? dim=None) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: count_nonzero
 
 - func: cudnn_affine_grid_generator(Tensor theta, int N, int C, int H, int W) -> Tensor grid
   use_c10_dispatcher: full
@@ -1191,8 +1285,12 @@
 - func: cummax(Tensor self, int dim) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cummax
 
 - func: cummax.out(Tensor self, int dim, *, Tensor(a!) values, Tensor(b!) indices) -> (Tensor(a!) values, Tensor(b!) indices)
+  dispatch:
+    DefaultBackend: cummax_out
 
 - func: cummax.dimname(Tensor self, Dimname dim) -> (Tensor values, Tensor indices)
   variants: function, method
@@ -1208,8 +1306,12 @@
 - func: cummin(Tensor self, int dim) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cummin
 
 - func: cummin.out(Tensor self, int dim, *, Tensor(a!) values, Tensor(b!) indices) -> (Tensor(a!) values, Tensor(b!) indices)
+  dispatch:
+    DefaultBackend: cummin_out
 
 - func: cummin.dimname(Tensor self, Dimname dim) -> (Tensor values, Tensor indices)
   variants: function, method
@@ -1230,8 +1332,12 @@
 - func: cumprod(Tensor self, int dim, *, ScalarType? dtype=None) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cumprod
 
 - func: cumprod.out(Tensor self, int dim, *, ScalarType? dtype=None, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: cumprod_out
 
 - func: cumprod.dimname(Tensor self, Dimname dim, *, ScalarType? dtype=None) -> Tensor
   variants: function, method
@@ -1246,8 +1352,12 @@
 - func: cumsum(Tensor self, int dim, *, ScalarType? dtype=None) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: cumsum
 
 - func: cumsum.out(Tensor self, int dim, *, ScalarType? dtype=None, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: cumsum_out
 
 - func: cumsum.dimname(Tensor self, Dimname dim, *, ScalarType? dtype=None) -> Tensor
   variants: function, method
@@ -1284,6 +1394,8 @@
 - func: diagonal(Tensor(a) self, int offset=0, int dim1=0, int dim2=1) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: diagonal
 
 - func: diagonal.Dimname(Tensor(a) self, *, Dimname outdim, Dimname dim1, Dimname dim2, int offset=0) -> Tensor(a)
   variants: function, method
@@ -1320,10 +1432,14 @@
 - func: div.Scalar(Tensor self, Scalar other) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: div
 
 - func: div_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: div_
 
 # divide, alias for div
 - func: divide.Tensor(Tensor self, Tensor other) -> Tensor
@@ -1371,6 +1487,8 @@
     CUDA: dot_cuda
 
 - func: dot.out(Tensor self, Tensor tensor, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: dot_out
 
 - func: vdot(Tensor self, Tensor other) -> Tensor
   use_c10_dispatcher: full
@@ -1380,12 +1498,16 @@
     CUDA: vdot_cuda
 
 - func: vdot.out(Tensor self, Tensor other, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: vdot_out
 
 - func: einsum(str equation, Tensor[] tensors) -> Tensor
   use_c10_dispatcher: full
 
 - func: embedding(Tensor weight, Tensor indices, int padding_idx=-1, bool scale_grad_by_freq=False, bool sparse=False) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: embedding
 
 - func: embedding_backward(Tensor grad, Tensor indices, int num_weights, int padding_idx, bool scale_grad_by_freq, bool sparse) -> Tensor
   use_c10_dispatcher: full
@@ -1524,10 +1646,14 @@
 - func: erf(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: erf
 
 - func: erf_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: erf_
 
 - func: erf.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1536,10 +1662,14 @@
 - func: erfc(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: erfc
 
 - func: erfc_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: erfc_
 
 - func: erfc.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1548,10 +1678,14 @@
 - func: exp(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: exp
 
 - func: exp_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: exp_
 
 - func: exp.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1560,10 +1694,14 @@
 - func: exp2(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: exp2
 
 - func: exp2_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: exp2_
 
 - func: exp2.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1572,10 +1710,14 @@
 - func: expm1(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: expm1
 
 - func: expm1_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: expm1_
 
 - func: expm1.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1585,6 +1727,8 @@
   use_c10_dispatcher: full
   variants: method  # This is method-only to match the previous tensor API. In the future we could make this a function too.
   device_guard: False
+  dispatch:
+    DefaultBackend: expand
 
 - func: expand_as(Tensor(a) self, Tensor other) -> Tensor(a)
   use_c10_dispatcher: full
@@ -1629,18 +1773,26 @@
 - func: fill_.Scalar(Tensor(a!) self, Scalar value) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: fill_
 
 - func: fill_.Tensor(Tensor(a!) self, Tensor value) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: fill_
 
 - func: floor(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: floor
 
 - func: floor_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: floor_
 
 - func: floor.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1676,10 +1828,14 @@
 - func: frac(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: frac
 
 - func: frac_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: frac_
 
 - func: frac.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -1758,6 +1914,8 @@
 # See NOTE [ grid_sample CPU fallback ]
 - func: _grid_sampler_2d_cpu_fallback(Tensor input, Tensor grid, int interpolation_mode, int padding_mode, bool align_corners) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _grid_sampler_2d_cpu_fallback
 
 - func: _grid_sampler_2d_cpu_fallback_backward(Tensor grad_output, Tensor input, Tensor grid, int interpolation_mode, int padding_mode, bool align_corners) -> (Tensor, Tensor)
   use_c10_dispatcher: full
@@ -1865,6 +2023,8 @@
 - func: index_copy_(Tensor(a!) self, int dim, Tensor index, Tensor source) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: index_copy_
 
 - func: index_copy(Tensor self, int dim, Tensor index, Tensor source) -> Tensor
   use_c10_dispatcher: full
@@ -1878,6 +2038,8 @@
 
 - func: index_put_(Tensor(a!) self, Tensor?[] indices, Tensor values, bool accumulate=False) -> Tensor(a!)
   variants: function, method
+  dispatch:
+    DefaultBackend: index_put_
   # NB: The following functions are declared in aten/src/ATen/templates/TensorBody.h and defined in aten/src/ATen/TensorIndexing.cpp:
   # - Tensor & Tensor::index_put_(ArrayRef<TensorIndex> indices, Tensor const & rhs)
   # - Tensor & Tensor::index_put_(ArrayRef<TensorIndex> indices, Scalar v)
@@ -1899,8 +2061,12 @@
 - func: inverse(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: inverse
 
 - func: inverse.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: inverse_out
 
 - func: _inverse_helper(Tensor self) -> Tensor
   use_c10_dispatcher: full
@@ -1957,6 +2123,8 @@
 
 - func: kl_div(Tensor self, Tensor target, int reduction=Mean, *, bool log_target=False) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: kl_div
 
 - func: kl_div_backward(Tensor grad_output, Tensor self, Tensor target, int reduction=Mean, *, bool log_target=False) -> Tensor
   use_c10_dispatcher: full
@@ -1967,6 +2135,8 @@
 - func: kthvalue(Tensor self, int k, int dim=-1, bool keepdim=False) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: kthvalue
 
 - func: kthvalue.values(Tensor self, int k, int dim=-1, bool keepdim=False, *, Tensor(a!) values, Tensor(b!) indices) -> (Tensor(a!) values, Tensor(b!) indices)
   dispatch:
@@ -1996,12 +2166,18 @@
 - func: nan_to_num(Tensor self, float? nan=None, float? posinf=None, float? neginf=None) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: nan_to_num
 
 - func: nan_to_num_(Tensor(a!) self, float? nan=None, float? posinf=None, float? neginf=None) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: nan_to_num_
 
 - func: nan_to_num.out(Tensor self, float? nan=None, float? posinf=None, float? neginf=None, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: nan_to_num_out
 
 - func: linear(Tensor input, Tensor weight, Tensor? bias=None) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -2048,10 +2224,14 @@
 - func: log(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log
 
 - func: log_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log_
 
 - func: log.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2060,10 +2240,14 @@
 - func: log10(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log10
 
 - func: log10_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log10_
 
 - func: log10.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2072,6 +2256,8 @@
 - func: log1p(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log1p
 
 - func: log1p_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
@@ -2088,10 +2274,14 @@
 - func: log2(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log2
 
 - func: log2_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: log2_
 
 - func: log2.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2104,6 +2294,8 @@
 - func: logaddexp(Tensor self, Tensor other) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: logaddexp
 
 - func: logaddexp2.out(Tensor self, Tensor other, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2112,10 +2304,14 @@
 - func: logaddexp2(Tensor self, Tensor other) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: logaddexp2
 
 - func: logdet(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: logdet
 
 - func: logspace(Scalar start, Scalar end, int? steps=None, float base=10.0, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -2159,8 +2355,12 @@
 - func: logcumsumexp(Tensor self, int dim) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: logcumsumexp
 
 - func: logcumsumexp.out(Tensor self, int dim, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: logcumsumexp_out
 
 - func: logcumsumexp.dimname(Tensor self, Dimname dim) -> Tensor
   variants: function, method
@@ -2170,8 +2370,12 @@
 - func: logsumexp(Tensor self, int[1] dim, bool keepdim=False) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: logsumexp
 
 - func: logsumexp.out(Tensor self, int[1] dim, bool keepdim=False, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: logsumexp_out
 
 - func: logsumexp.names(Tensor self, Dimname[1] dim, bool keepdim=False) -> Tensor
   variants: function, method
@@ -2229,6 +2433,8 @@
 - func: max.dim(Tensor self, int dim, bool keepdim=False) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: max
 
 - func: max.dim_max(Tensor self, int dim, bool keepdim=False, *, Tensor(a!) max, Tensor(b!) max_values) -> (Tensor(a!) values, Tensor(b!) indices)
   dispatch:
@@ -2247,6 +2453,8 @@
 - func: amax(Tensor self, int[1] dim=[], bool keepdim=False) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: amax
 
 - func: amax.out(Tensor self, int[1] dim=[], bool keepdim=False, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2321,6 +2529,8 @@
 - func: median.dim(Tensor self, int dim, bool keepdim=False) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: median
 
 - func: median.dim_values(Tensor self, int dim, bool keepdim=False, *, Tensor(a!) values, Tensor(b!) indices) -> (Tensor(a!) values, Tensor(b!) indices)
   dispatch:
@@ -2342,6 +2552,8 @@
 - func: nanmedian.dim(Tensor self, int dim, bool keepdim=False) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: nanmedian
 
 - func: nanmedian.dim_values(Tensor self, int dim, bool keepdim=False, *, Tensor(a!) values, Tensor(b!) indices) -> (Tensor(a!) values, Tensor(b!) indices)
   dispatch:
@@ -2356,6 +2568,8 @@
 - func: min.dim(Tensor self, int dim, bool keepdim=False) -> (Tensor values, Tensor indices)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: min
 
 - func: min.dim_min(Tensor self, int dim, bool keepdim=False, *, Tensor(a!) min, Tensor(b!) min_indices) -> (Tensor(a!) values, Tensor(b!) indices)
   dispatch:
@@ -2369,6 +2583,8 @@
 - func: amin(Tensor self, int[1] dim=[], bool keepdim=False) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: amin
 
 - func: amin.out(Tensor self, int[1] dim=[], bool keepdim=False, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2376,6 +2592,8 @@
 
 - func: mkldnn_convolution(Tensor self, Tensor weight, Tensor? bias, int[] padding, int[] stride, int[] dilation, int groups) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
+  dispatch:
+    DefaultBackend: mkldnn_convolution
 
 - func: mkldnn_convolution_backward_input(int[] self_size, Tensor grad_output, Tensor weight, int[] padding, int[] stride, int[] dilation, int groups, bool bias_defined) -> Tensor
   use_c10_dispatcher: full
@@ -2385,6 +2603,8 @@
 
 - func: mkldnn_convolution_backward(Tensor self, Tensor grad_output, Tensor weight, int[] padding, int[] stride, int[] dilation, int groups, bool[3] output_mask) -> (Tensor, Tensor, Tensor)
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: mkldnn_convolution_backward
 
 - func: miopen_batch_norm(Tensor input, Tensor weight, Tensor? bias, Tensor? running_mean, Tensor? running_var, bool training, float exponential_average_factor, float epsilon) -> (Tensor, Tensor, Tensor)
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -2497,6 +2717,8 @@
     CPU, CUDA: mode
 
 - func: mode.values(Tensor self, int dim=-1, bool keepdim=False, *, Tensor(a!) values, Tensor(b!) indices) -> (Tensor(a!) values, Tensor(b!) indices)
+  dispatch:
+    DefaultBackend: mode_out
 
 - func: mode.dimname(Tensor self, Dimname dim, bool keepdim=False) -> (Tensor values, Tensor indices)
   variants: function, method
@@ -2530,10 +2752,14 @@
 - func: mul.Scalar(Tensor self, Scalar other) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: mul
 
 - func: mul_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: mul_
 
 # multiply, alias for mul
 - func: multiply.Tensor(Tensor self, Tensor other) -> Tensor
@@ -2562,14 +2788,20 @@
     SparseCPU, SparseCUDA: mv_sparse
 
 - func: mv.out(Tensor self, Tensor vec, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: mv_out
 
 - func: mvlgamma(Tensor self, int p) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: mvlgamma
 
 - func: mvlgamma_(Tensor(a!) self, int p) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: mvlgamma_
 
 - func: narrow_copy(Tensor self, int dim, int start, int length) -> Tensor
   use_c10_dispatcher: full
@@ -2655,6 +2887,8 @@
 - func: _nnpack_spatial_convolution(Tensor input, Tensor weight, Tensor? bias, int[2] padding, int[2] stride=1) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
   variants: function
+  dispatch:
+    DefaultBackend: _nnpack_spatial_convolution
 
 - func: _nnpack_spatial_convolution_backward(Tensor input, Tensor grad_output, Tensor weight, int[2] padding, bool[3] output_mask) -> (Tensor, Tensor, Tensor)
   use_c10_dispatcher: full
@@ -2687,6 +2921,8 @@
 
 - func: _euclidean_dist(Tensor x1, Tensor x2) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _euclidean_dist
 
 - func: _cdist_forward(Tensor x1, Tensor x2, float p, int? compute_mode) -> Tensor
   use_c10_dispatcher: full
@@ -2718,6 +2954,8 @@
 - func: permute(Tensor(a) self, int[] dims) -> Tensor(a)
   use_c10_dispatcher: full
   variants: method  # This is method-only to match the previous tensor API. In the future we could make this a function too.
+  dispatch:
+    DefaultBackend: permute
 
 - func: movedim.intlist(Tensor(a) self, int[] source, int[] destination) -> Tensor(a)
   use_c10_dispatcher: full
@@ -2766,22 +3004,34 @@
 - func: rad2deg(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: rad2deg
 
 - func: rad2deg_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: rad2deg_
 
 - func: rad2deg.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: rad2deg_out
 
 - func: deg2rad(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: deg2rad
 
 - func: deg2rad_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: deg2rad_
 
 - func: deg2rad.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: deg2rad_out
 
 - func: scalar_tensor(Scalar s, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -2876,10 +3126,14 @@
 - func: reciprocal(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: reciprocal
 
 - func: reciprocal_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: reciprocal_
 
 - func: reciprocal.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -2888,6 +3142,8 @@
 - func: neg(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: neg
 
 - func: neg_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
@@ -2915,6 +3171,8 @@
 - func: repeat(Tensor self, int[] repeats) -> Tensor
   use_c10_dispatcher: full
   variants: method  # This is method-only to match the previous tensor API. In the future we could make this a function too.
+  dispatch:
+    DefaultBackend: repeat
 
 - func: repeat_interleave.Tensor(Tensor repeats) -> Tensor
   use_c10_dispatcher: full
@@ -2950,10 +3208,14 @@
 - func: round(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: round
 
 - func: round_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: round_
 
 - func: round.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3029,10 +3291,14 @@
 - func: rsqrt(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: rsqrt
 
 - func: rsqrt_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: rsqrt_
 
 - func: rsqrt.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3046,6 +3312,8 @@
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: select
 
 - func: select_backward(Tensor grad, int[] input_sizes, int dim, int index) -> Tensor
   use_c10_dispatcher: full
@@ -3060,17 +3328,25 @@
 
 - func: celu(Tensor self, Scalar alpha=1.0) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: celu
 
 - func: celu_(Tensor(a!) self, Scalar alpha=1.0) -> Tensor(a!)
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: celu_
 
 - func: silu(Tensor self) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: silu
 
 - func: silu_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: silu_
 
 - func: silu.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   python_module: nn
@@ -3119,10 +3395,14 @@
 - func: sin(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sin
 
 - func: sin_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sin_
 
 - func: sin.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3131,10 +3411,14 @@
 - func: sinh(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sinh
 
 - func: sinh_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sinh_
 
 - func: sinh.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3154,6 +3438,8 @@
 - func: detach(Tensor(a) self) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: detach
 
 # Like `detach()`, but modifies this `Variable` in-place. This method may
 # only be called on non-view `Variable`s. You can use `is_view()` to check
@@ -3161,6 +3447,8 @@
 - func: detach_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: detach_
 
 - func: size.int(Tensor self, int dim) -> int
   use_c10_dispatcher: full
@@ -3175,6 +3463,8 @@
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: slice
 
 - func: slice_backward(Tensor grad, int[] input_sizes, int dim, int start, int end, int step) -> Tensor
   use_c10_dispatcher: full
@@ -3184,6 +3474,8 @@
 - func: slogdet(Tensor self) -> (Tensor sign, Tensor logabsdet)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: slogdet
 
 - func: smm(Tensor self, Tensor mat2) -> Tensor
   use_c10_dispatcher: full
@@ -3214,31 +3506,43 @@
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: unsafe_split
 
 - func: split.Tensor(Tensor(a) self, int split_size, int dim=0) -> Tensor(a)[]
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: split
 
 - func: unsafe_split_with_sizes(Tensor self, int[] split_sizes, int dim=0) -> Tensor[]
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: unsafe_split_with_sizes
 
 - func: split_with_sizes(Tensor(a) self, int[] split_sizes, int dim=0) -> Tensor(a)[]
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: split_with_sizes
 
 - func: squeeze(Tensor(a) self) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: squeeze
 
 - func: squeeze.dim(Tensor(a) self, int dim) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: squeeze
 
 - func: squeeze.dimname(Tensor(a) self, Dimname dim) -> Tensor(a)
   variants: function, method
@@ -3248,11 +3552,15 @@
   use_c10_dispatcher: full
   variants: method
   device_guard: False
+  dispatch:
+    DefaultBackend: squeeze_
 
 - func: squeeze_.dim(Tensor(a!) self, int dim) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
   device_guard: False
+  dispatch:
+    DefaultBackend: squeeze_
 
 - func: squeeze_.dimname(Tensor(a!) self, Dimname dim) -> Tensor(a!)
   variants: method
@@ -3271,8 +3579,12 @@
 
 - func: stack(Tensor[] tensors, int dim=0) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: stack
 
 - func: stack.out(Tensor[] tensors, int dim=0, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: stack_out
 
 - func: hstack(Tensor[] tensors) -> Tensor
   use_c10_dispatcher: full
@@ -3355,10 +3667,14 @@
 - func: sqrt(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sqrt
 
 - func: sqrt_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sqrt_
 
 - func: sqrt.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3433,19 +3749,27 @@
   use_c10_dispatcher: full
   device_guard: False
   variants: function, method
+  dispatch:
+    DefaultBackend: t
 
 - func: t_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   device_guard: False
   variants: method
+  dispatch:
+    DefaultBackend: t_
 
 - func: tan(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: tan
 
 - func: tan_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: tan_
 
 - func: tan.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3461,6 +3785,8 @@
 - func: tanh_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: tanh_
 
 - func: tanh.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3502,6 +3828,8 @@
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: transpose
 
 - func: transpose.Dimname(Tensor(a) self, Dimname dim0, Dimname dim1) -> Tensor(a)
   variants: function, method
@@ -3517,6 +3845,8 @@
   use_c10_dispatcher: full
   variants: method
   device_guard: False
+  dispatch:
+    DefaultBackend: transpose_
 
 - func: _mkldnn_transpose_(Tensor(a!) self, int dim0, int dim1) -> Tensor(a!)
   use_c10_dispatcher: full
@@ -3556,6 +3886,8 @@
 - func: rot90(Tensor self, int k=1, int[] dims=[0,1]) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: rot90
 
 - func: trapz.x(Tensor y, Tensor x, *, int dim=-1) -> Tensor
   use_c10_dispatcher: full
@@ -3565,6 +3897,8 @@
 
 - func: _trilinear(Tensor i1, Tensor i2, Tensor i3, int[] expand1, int[] expand2, int[] expand3, int[] sumdim, int unroll_dim=1) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _trilinear
 
 - func: triplet_margin_loss(Tensor anchor, Tensor positive, Tensor negative, float margin=1.0, float p=2, float eps=1e-06, bool swap=False, int reduction=Mean) -> Tensor
   use_c10_dispatcher: full
@@ -3572,10 +3906,14 @@
 - func: trunc(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: trunc
 
 - func: trunc_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: trunc_
 
 - func: trunc.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3641,16 +3979,22 @@
 
 - func: _unsafe_view(Tensor self, int[] size) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _unsafe_view
 
 - func: unsqueeze(Tensor(a) self, int dim) -> Tensor(a)
   use_c10_dispatcher: full
   variants: function, method
   device_guard: False
+  dispatch:
+    DefaultBackend: unsqueeze
 
 - func: unsqueeze_(Tensor(a!) self, int dim) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
   device_guard: False
+  dispatch:
+    DefaultBackend: unsqueeze_
 
 - func: vander(Tensor x, int? N=None, bool increasing=False) -> Tensor
   use_c10_dispatcher: full
@@ -3819,6 +4163,8 @@
 
 - func: _sparse_sum.dim(Tensor self, int[1] dim) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _sparse_sum
 
 - func: _sparse_sum.dim_dtype(Tensor self, int[1] dim, *, ScalarType dtype) -> Tensor
   use_c10_dispatcher: full
@@ -3870,18 +4216,26 @@
 - func: norm.ScalarOpt_dtype(Tensor self, Scalar? p, *, ScalarType dtype) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: norm
 
 - func: norm.Scalar(Tensor self, Scalar p=2) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: norm
 
 - func: norm.ScalarOpt_dim_dtype(Tensor self, Scalar? p, int[1] dim, bool keepdim, *, ScalarType dtype) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: norm
 
 - func: norm.ScalarOpt_dim(Tensor self, Scalar? p, int[1] dim, bool keepdim=False) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: norm
 
 - func: norm.dtype_out(Tensor self, Scalar? p, int[1] dim, bool keepdim, *, ScalarType dtype, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -3938,6 +4292,8 @@
 - func: resize_as_(Tensor(a!) self, Tensor the_template, *, MemoryFormat? memory_format=None) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: resize_as_
 
 - func: zero_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
@@ -3970,10 +4326,14 @@
 - func: sub.Scalar(Tensor self, Scalar other, Scalar alpha=1) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sub
 
 - func: sub_.Scalar(Tensor(a!) self, Scalar other, Scalar alpha=1) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: sub_
 
 # subtract, alias for sub
 - func: subtract.out(Tensor self, Tensor other, *, Scalar alpha=1, Tensor(a!) out) -> Tensor(a!)
@@ -4016,11 +4376,15 @@
 - func: rsub.Scalar(Tensor self, Scalar other, Scalar alpha=1) -> Tensor
   use_c10_dispatcher: full
   variants: function
+  dispatch:
+    DefaultBackend: rsub
 
 # Functionally the same as addmm, but we give it a different derivative formula
 # that doesn't propagate gradients to non-present entries on sparse.
 - func: _sparse_addmm(Tensor self, Tensor sparse, Tensor dense, *, Scalar beta=1, Scalar alpha=1) -> Tensor
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _sparse_addmm
 
 - func: addmm.out(Tensor self, Tensor mat1, Tensor mat2, *, Scalar beta=1, Scalar alpha=1, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -4323,6 +4687,8 @@
 - func: unbind.int(Tensor(a) self, int dim=0) -> Tensor(a)[]
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: unbind
 
 - func: unbind.Dimname(Tensor(a) self, Dimname dim) -> Tensor(a)[]
   variants: function, method
@@ -4664,6 +5030,8 @@
 # PackedSequence utilities
 - func: _pack_padded_sequence(Tensor input, Tensor lengths, bool batch_first) -> (Tensor, Tensor)
   use_c10_dispatcher: full
+  dispatch:
+    DefaultBackend: _pack_padded_sequence
 
 - func: _pack_padded_sequence_backward(Tensor grad, int[] input_size, Tensor batch_sizes, bool batch_first) -> Tensor
   use_c10_dispatcher: full
@@ -4862,10 +5230,14 @@
 - func: eq_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: eq_
 
 - func: eq_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: eq_
 
 - func: bitwise_and.Tensor_out(Tensor self, Tensor other, *, Tensor(a!) out) -> Tensor(a!)
   variants: function
@@ -5159,6 +5531,8 @@
 - func: addcdiv_(Tensor(a!) self, Tensor tensor1, Tensor tensor2, *, Scalar value=1) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: addcdiv_
 
 - func: random_.from(Tensor(a!) self, int from, int? to, *, Generator? generator=None) -> Tensor(a!)
   variants: method
@@ -5210,6 +5584,8 @@
 - func: diag(Tensor self, int diagonal=0) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: diag
 
 - func: diag_backward(Tensor grad, int[] input_sizes, int diagonal) -> Tensor
   use_c10_dispatcher: full
@@ -5234,6 +5610,8 @@
 - func: triu(Tensor self, int diagonal=0) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: triu
 
 - func: tril.out(Tensor self, int diagonal=0, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -5243,6 +5621,8 @@
 - func: tril(Tensor self, int diagonal=0) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: tril
 
 - func: tril_indices(int row, int col, int offset=0, *, ScalarType? dtype=long, Layout? layout=None, Device? device=None, bool? pin_memory=None) -> Tensor
   use_c10_dispatcher: hacky_wrapper_for_legacy_signatures
@@ -5295,10 +5675,14 @@
 - func: ne_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: ne_
 
 - func: ne_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: ne_
 
 # not_equal, alias for torch.ne
 - func: not_equal.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)
@@ -5372,10 +5756,14 @@
 - func: ge_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: ge_
 
 - func: ge_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: ge_
 
 # greater_equal, alias for torch.ge
 - func: greater_equal.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)
@@ -5425,10 +5813,14 @@
 - func: le_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: le_
 
 - func: le_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: le_
 
 # less_equal, alias for torch.le
 - func: less_equal.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)
@@ -5478,10 +5870,14 @@
 - func: gt_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: gt_
 
 - func: gt_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: gt_
 
 #  greater, alias for torch.gt
 - func: greater.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)
@@ -5531,10 +5927,14 @@
 - func: lt_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: lt_
 
 - func: lt_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: lt_
 
 #  less, alias for torch.lt
 - func: less.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)
@@ -5662,10 +6062,14 @@
 - func: addcmul(Tensor self, Tensor tensor1, Tensor tensor2, *, Scalar value=1) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: addcmul
 
 - func: addcmul_(Tensor(a!) self, Tensor tensor1, Tensor tensor2, *, Scalar value=1) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: addcmul_
 
 - func: addcdiv.out(Tensor self, Tensor tensor1, Tensor tensor2, *, Scalar value=1, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -5674,6 +6078,8 @@
 - func: addcdiv(Tensor self, Tensor tensor1, Tensor tensor2, *, Scalar value=1) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: addcdiv
 
 - func: lstsq.X(Tensor self, Tensor A, *, Tensor(a!) X, Tensor(b!) qr) -> (Tensor(a!) solution, Tensor(b!) QR)
   dispatch:
@@ -5688,10 +6094,14 @@
     CUDA: legacy::cuda::_th_gels
 
 - func: triangular_solve.X(Tensor self, Tensor A, bool upper=True, bool transpose=False, bool unitriangular=False, *, Tensor(a!) X, Tensor(b!) M) -> (Tensor(a!) solution, Tensor(b!) cloned_coefficient)
+  dispatch:
+    DefaultBackend: triangular_solve_out
 
 - func: triangular_solve(Tensor self, Tensor A, bool upper=True, bool transpose=False, bool unitriangular=False) -> (Tensor solution, Tensor cloned_coefficient)
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: triangular_solve
 
 - func: _triangular_solve_helper(Tensor self, Tensor A, bool upper, bool transpose, bool unitriangular) -> (Tensor, Tensor)
   use_c10_dispatcher: full
@@ -5701,10 +6111,14 @@
     CUDA: _triangular_solve_helper_cuda
 
 - func: symeig.e(Tensor self, bool eigenvectors=False, bool upper=True, *, Tensor(a!) e, Tensor(b!) V) -> (Tensor(a!) eigenvalues, Tensor(b!) eigenvectors)
+  dispatch:
+    DefaultBackend: symeig_out
 
 - func: symeig(Tensor self, bool eigenvectors=False, bool upper=True) -> (Tensor eigenvalues, Tensor eigenvectors)
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: symeig
 
 - func: _symeig_helper(Tensor self, bool eigenvectors, bool upper) -> (Tensor, Tensor)
   use_c10_dispatcher: full
@@ -5726,10 +6140,14 @@
     CUDA: legacy::cuda::_th_eig
 
 - func: svd.U(Tensor self, bool some=True, bool compute_uv=True, *, Tensor(a!) U, Tensor(b!) S, Tensor(c!) V) -> (Tensor(a!) U, Tensor(b!) S, Tensor(c!) V)
+  dispatch:
+    DefaultBackend: svd_out
 
 - func: svd(Tensor self, bool some=True, bool compute_uv=True) -> (Tensor U, Tensor S, Tensor V)
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: svd
 
 - func: _svd_helper(Tensor self, bool some, bool compute_uv) -> (Tensor, Tensor, Tensor)
   use_c10_dispatcher: full
@@ -5739,10 +6157,14 @@
     CUDA: _svd_helper_cuda
 
 - func: cholesky.out(Tensor self, bool upper=False, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: cholesky_out
 
 - func: cholesky(Tensor self, bool upper=False) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: cholesky
 
 - func: _cholesky_helper(Tensor self, bool upper) -> Tensor
   use_c10_dispatcher: full
@@ -5752,10 +6174,14 @@
     CUDA: _cholesky_helper_cuda
 
 - func: cholesky_solve.out(Tensor self, Tensor input2, bool upper=False, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: cholesky_solve_out
 
 - func: cholesky_solve(Tensor self, Tensor input2, bool upper=False) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: cholesky_solve
 
 - func: _cholesky_solve_helper(Tensor self, Tensor A, bool upper) -> Tensor
   use_c10_dispatcher: full
@@ -5767,8 +6193,12 @@
 - func: solve(Tensor self, Tensor A) -> (Tensor solution, Tensor LU)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: solve
 
 - func: solve.solution(Tensor self, Tensor A, *, Tensor(a!) solution, Tensor(b!) lu) -> (Tensor(a!) solution, Tensor(b!) LU)
+  dispatch:
+    DefaultBackend: solve_out
 
 - func: _solve_helper(Tensor self, Tensor A) -> (Tensor, Tensor)
   use_c10_dispatcher: full
@@ -5790,10 +6220,14 @@
     CUDA: legacy::cuda::_th_potri
 
 - func: qr.Q(Tensor self, bool some=True, *, Tensor(a!) Q, Tensor(b!) R) -> (Tensor(a!) Q, Tensor(b!) R)
+  dispatch:
+    DefaultBackend: qr_out
 
 - func: qr(Tensor self, bool some=True) -> (Tensor Q, Tensor R)
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: qr
 
 - func: _qr_helper(Tensor self, bool some) -> (Tensor, Tensor)
   use_c10_dispatcher: full
@@ -5842,10 +6276,14 @@
     CUDA: _lu_with_info_cuda
 
 - func: lu_solve.out(Tensor self, Tensor LU_data, Tensor LU_pivots, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: lu_solve_out
 
 - func: lu_solve(Tensor self, Tensor LU_data, Tensor LU_pivots) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: lu_solve
 
 - func: _lu_solve_helper(Tensor self, Tensor LU_data, Tensor LU_pivots) -> Tensor
   use_c10_dispatcher: full
@@ -5905,6 +6343,8 @@
 - func: polygamma(int n, Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: polygamma
 
 - func: erfinv(Tensor self) -> Tensor
   use_c10_dispatcher: full
@@ -5927,10 +6367,14 @@
 - func: i0(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: i0
 
 - func: i0_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: i0_
 
 - func: i0.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -5939,10 +6383,14 @@
 - func: sign(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: sign
 
 - func: sign_(Tensor(a!) self) -> Tensor(a!)
   use_c10_dispatcher: full
   variants: method
+  dispatch:
+    DefaultBackend: sign_
 
 - func: sign.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -5960,6 +6408,8 @@
 - func: dist(Tensor self, Tensor other, Scalar p=2) -> Tensor
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: dist
 
 - func: atan2.out(Tensor self, Tensor other, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -6043,6 +6493,8 @@
 
 - func: hypot_(Tensor(a!) self, Tensor other) -> Tensor(a!)
   variants: method
+  dispatch:
+    DefaultBackend: hypot_
 
 - func: nextafter.out(Tensor self, Tensor other, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -6056,6 +6508,8 @@
 
 - func: nextafter_(Tensor(a!) self, Tensor other) -> Tensor(a!)
   variants: method
+  dispatch:
+    DefaultBackend: nextafter_
 
 - func: remainder.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)
   dispatch:
@@ -6302,6 +6756,8 @@
 - func: alias(Tensor(a) self) -> Tensor(a)
   use_c10_dispatcher: full
   variants: method, function
+  dispatch:
+    DefaultBackend: alias
 
 - func: _index_copy_(Tensor(a!) self, int dim, Tensor index, Tensor source) -> Tensor(a!)
   use_c10_dispatcher: full
@@ -6694,10 +7150,14 @@
 
 - func: l1_loss.out(Tensor self, Tensor target, int reduction=Mean, *, Tensor(a!) out) -> Tensor(a!)
   python_module: nn
+  dispatch:
+    DefaultBackend: l1_loss_out
 
 - func: l1_loss(Tensor self, Tensor target, int reduction=Mean) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: l1_loss
 
 - func: l1_loss_backward.grad_input(Tensor grad_output, Tensor self, Tensor target, int reduction, *, Tensor(a!) grad_input) -> Tensor(a!)
   python_module: nn
@@ -6707,6 +7167,8 @@
 - func: l1_loss_backward(Tensor grad_output, Tensor self, Tensor target, int reduction) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: l1_loss_backward
 
 - func: multi_margin_loss.out(Tensor self, Tensor target, Scalar p=1, Scalar margin=1, Tensor? weight=None, int reduction=Mean, *, Tensor(a!) out) -> Tensor(a!)
   python_module: nn
@@ -6854,20 +7316,30 @@
 - func: smooth_l1_loss_backward(Tensor grad_output, Tensor self, Tensor target, int reduction, float beta) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: smooth_l1_loss_backward
 
 - func: soft_margin_loss.out(Tensor self, Tensor target, int reduction=Mean, *, Tensor(a!) out) -> Tensor(a!)
   python_module: nn
+  dispatch:
+    DefaultBackend: soft_margin_loss_out
 
 - func: soft_margin_loss(Tensor self, Tensor target, int reduction=Mean) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: soft_margin_loss
 
 - func: soft_margin_loss_backward.grad_input(Tensor grad_output, Tensor self, Tensor target, int reduction, *, Tensor(a!) grad_input) -> Tensor(a!)
   python_module: nn
+  dispatch:
+    DefaultBackend: soft_margin_loss_backward_out
 
 - func: soft_margin_loss_backward(Tensor grad_output, Tensor self, Tensor target, int reduction) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: soft_margin_loss_backward
 
 - func: elu.out(Tensor self, Scalar alpha=1, Scalar scale=1, Scalar input_scale=1, *, Tensor(a!) out) -> Tensor(a!)
   python_module: nn
@@ -6894,6 +7366,8 @@
 - func: elu_(Tensor(a!) self, Scalar alpha=1, Scalar scale=1, Scalar input_scale=1) -> Tensor(a!)
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: elu_
 
 - func: glu.out(Tensor self, int dim=-1, *, Tensor(a!) out) -> Tensor(a!)
   python_module: nn
@@ -7073,6 +7547,8 @@
 - func: rrelu_with_noise_backward(Tensor grad_output, Tensor self, Tensor noise, Scalar lower, Scalar upper, bool training, bool self_is_result) -> Tensor
   use_c10_dispatcher: full
   python_module: nn
+  dispatch:
+    DefaultBackend: rrelu_with_noise_backward
 
 - func: rrelu_with_noise_(Tensor(a!) self, Tensor noise, Scalar lower=0.125, Scalar upper=0.3333333333333333, bool training=False, Generator? generator=None) -> Tensor(a!)
   python_module: nn
@@ -8293,6 +8769,8 @@
 - func: det(Tensor self) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: det
 
 # torch.outer, alias for torch.ger
 - func: outer(Tensor self, Tensor vec2) -> Tensor
@@ -8304,8 +8782,12 @@
 - func: ger(Tensor self, Tensor vec2) -> Tensor
   use_c10_dispatcher: full
   variants: function, method
+  dispatch:
+    DefaultBackend: ger
 
 - func: ger.out(Tensor self, Tensor vec2, *, Tensor(a!) out) -> Tensor(a!)
+  dispatch:
+    DefaultBackend: ger_out
 
 - func: linalg_norm(Tensor self, Scalar? ord=None, int[1]? dim=None, bool keepdim=False, *, ScalarType? dtype=None) -> Tensor
   python_module: linalg
diff --git a/tools/autograd/gen_variable_type.py b/tools/autograd/gen_variable_type.py
index a1f162f91471..9cca7b1319f8 100644
--- a/tools/autograd/gen_variable_type.py
+++ b/tools/autograd/gen_variable_type.py
@@ -748,6 +748,12 @@ def gen_variable_type_shard(out, aten_declarations, template_path, suffix, heade
 
         # See Note [Manual catchAll kernels]
         assert (declaration['name'] in MANUAL_CATCHALL) == declaration['manual_kernel_registration']
+        # If you want to register a kernel to Autograd, you must make the op abstract.
+        # In other words, this op must have dispatch section in native_functions.yaml.
+        if declaration['name'] in MANUAL_AUTOGRAD_AND_TRACER or declaration['derivative']:
+            msg = (f'Did you add a formula for {declaration["name"]}(or its functional variant) in derivatives.yaml?'
+                   f'If so please add a dispatch section for it with DefaultBackend in native_functions.yaml.')
+            assert declaration['abstract'], msg
 
         # Emit TraceType code
         if declaration['name'] not in MANUAL_TRACER:
diff --git a/tools/codegen/gen.py b/tools/codegen/gen.py
index 69e1aae3a014..785cab06a589 100644
--- a/tools/codegen/gen.py
+++ b/tools/codegen/gen.py
@@ -155,6 +155,9 @@ def cpp_string(s: str) -> str:
 # code we want.
 Target = Enum('Target', ('DEFINITION', 'DECLARATION', 'REGISTRATION'))
 
+# Dispatch keywords in native_functions.yaml that support all backends.
+KEYWORD_ALL_BACKENDS = ('DefaultBackend', 'Math')
+
 # Generates {dispatch}Type.cpp and {dispatch}Type.h (e.g., CPUType.cpp
 # and CPUType.h).  This function is also reused to implement per-operator
 # registration.  It also generates TypeDefault.cpp and TypeDefault.h when
@@ -273,7 +276,7 @@ def func(f: NativeFunction) -> Optional[str]:
             assert returns_type == dispatcher.returns_type(f.func.returns)
             dispatcher_args = dispatcher.arguments(f.func)
             dispatcher_args_types_str = ', '.join(map(lambda a: a.type, dispatcher_args))
-            if dispatch is None or dispatch == 'Math' or dispatch == 'DefaultBackend':
+            if dispatch is None or dispatch in KEYWORD_ALL_BACKENDS:
                 type_name = f'TypeDefault::{name}'
             else:
                 type_name = f'{dispatch}Type::{name}'
@@ -901,7 +904,7 @@ def compute_registration_declarations(f: NativeFunction) -> str:
     comment_data : Dict[str, str] = {
         'schema': f'aten::{f.func}',
         'dispatch': str(f.dispatch is not None),
-        'math': str(f.dispatch is not None and 'Math' in f.dispatch)
+        'default': str(f.dispatch is not None and any(k in f.dispatch for k in KEYWORD_ALL_BACKENDS))
     }
     return f"""{returns_type} {name}({args_str}); // {json.dumps(comment_data)}
 """