native

ATen "native" functions are the modern mechanism for adding operators and functions to ATen. Native functions are declared in native_functions.yaml and have implementations defined in one of the cpp files in this directory.

Like all ATen methods/functions, native functions are made available from both ATen's C++ and Python APIs. In C++, they are made available either as methods on Tensor (t.mymeth()) and functions in the ATen namespace (at::myfunc()). In PyTorch, they are made available as methods on Variable or as functions on torch._C._FunctionBase. (It is the user's responsibility to re-export these functions in a more user-facing module.)

The rest of this document describes how to implement an ATen function.

Registering a function in native_functions.yaml

Every native function must have an entry in native_functions.yaml. The format can be summarized as:

- func: func_name(ArgType arg0[=default], ArgType arg1[=default], ...) -> Return
  variants: function, method
  dispatch:
    CPU: func_cpu
    CUDA: func_cuda

Each component is described in more detail below:

func

- func: func_name[.overload_name](ArgType arg0[=default], ArgType arg1[=default], ...) -> Return

The func entry is a string describing the name of the function and its type signature.

Argument types. These types are permissible as ArgType:

• Tensor. A Tensor argument translates into a C++ argument of type const Tensor& (except when the argument is "inplace"; in this case, it is simply Tensor&). A trailing ?, as in Tensor?, indicates that the tensor argument is optional and may be omitted by passing std::nullopt. When a function takes multiple Tensor arguments, these tensors are assumed to be the same type (e.g., if one argument is a FloatTensor, all other arguments are checked to be FloatTensors). Tensor or Tensor? must sometimes be annotated to indicate aliasing and mutability. In general annotations can be defined via the following situations:
  • Tensor(a) - a is a set of Tensors that may alias to the same data. The set could have a size of one.
  • Tensor(a!) - members of a may be written to thus mutating the underlying data.
  • Tensor(a! -> a|b) - Tensor is in set a, written to, and after the write is in set a AND b. For more details on when and why this needs to happen, please see the section on annotations.
• Tensor[]. A Tensor[] argument translates into a C++ argument of type ArrayRef<Tensor> (a.k.a. TensorList)
• int[]. int[] accepts an optional length specifier, e.g., int[2], which has no effect in C++ but extends our Python bindings to accept a bare number, which will be expanded into an appropriately sized list by repeating the number.
• int. Think about this like a Python int. This is translated into a C++ argument of type int64_t.
• float. Think about this like a Python float. It is translated into a C++ argument of type double.
• bool
• str. It is translated into a C++ argument of non-owning type std::string_view
• Scalar. Scalar supports binding to any numerical types from Python, including integral types, floating point types, and zero dimensional tensors. int and float bind to the corresponding Python numerical types. However, you probably don't want to use Scalar; float and int argument types should suffice for most algorithms (you should only use Scalar if the operator truly may accept either type).
• Generator?, the state for a random number generator,
• bool[N] (where N is 1-4).
• * is a special sentinel argument, which doesn't translate into an actual argument, but indicates that in the Python bindings, any subsequent arguments must be specified as keyword arguments (and cannot be provided positionally).
• ? is trailing question mark that annotates an argument to be an optional type. Grep for optional to find some example usages. In general, most functions will not need to use this, but there are some cases that we want to use optional for the different types:
  • You want to pass a None to an ATen function/method from Python and handle the None type on the C++ side. For example, clamp(Tensor self, Scalar? min=None, Scalar? max=None) can take None for its min and max parameter, but does not dispatch to different backends if one of the parameters is None. Optional type can accept a None type (nullopt in C++) from Python and use the C++ Optional class to interact with the parameters.
  • You want a default value, which is fine in Python, but would cause ambiguity in C++. For example, norm(Tensor self, Scalar p=2, int dim, bool keepdim=False) would cause ambiguity in C++ since its default args must be adjacent (p could not have a default value when dim does not). Therefore, we need to make p as a optional Scalar, and make p=2 when p is not passed in (nullopt).
  • You want a value to default to the same value as another argument (this cannot be expressed in C++ default arguments).

Functions with no tensor inputs are called factory functions, and are handled specially by code generation. If your function is behaving differently than another example, check first and see if one is a factory while another is not. In some rare cases, factory function might have a tensor argument. In this case mark it with category_override: factory explicitly.

Argument names. Argument names are meaningful; downstream binding code may make use of the specific argument name you provide, and a rename of an argument name is considered a BC-breaking change (e.g., you will probably need to update tools/autograd/derivatives.yaml at least, and it may affect Python keyword arguments). For more details please see the section on variants.

As a convention we use 'out' to indicate an output argument. This aligns with the Python bindings. Even if a function might not be used in the Python bindings, we still advise to follow this convention. Check the generated code when making a change to make sure you're not breaking the API when renaming an argument name of an existing function.

Defaults. Any suffix of arguments can have a default value defined; these default values translate into C++/Python default values which are applied when those positional arguments are not specified.

Here are the supported default values:

• Numbers (e.g., 0 or 5.0 for int, float and int[] with an explicit length (e.g., int[2])--in the case of int[] a number is replicated to fill the length (e.g., int[2] x=2 is equivalent to int[2] x=[2,2]).
• Lists of numbers (e.g., [0, 0]) for IntList.
• Booleans (e.g., True) for bool.
• Empty initializer lists (e.g., []) for Tensor (this implicitly changes a Tensor argument to accept undefined tensors).
• None for pointer types (e.g., Generator?)

Returns. The following are permissible on Return:

Non-tuple return:

ReturnType [retarg0]

Tuple return:

(ReturnType [retarg0], ReturnType [retarg1], ...)

The following are permissible on ReturnType:

• Tensor and Tensor[], which translate into the C++ types Tensor and std::vector<Tensor>, respectively (unless the operation is in-place, in which case the return type is Tensor&.
• A tuple of any number of Tensor, e.g., (Tensor, Tensor), translating into the C++ std::tuple<Tensor, Tensor>.

If you need a type that is not listed in this list, it may be possible to extend ATen's code generation to support it. ATen's philosophy on types to support is that it supports only simple, universal types, as well as a handful of fundamental Tensor structures (e.g., Tensor and Generator?), because these types can be easily ported to any language bound to ATen (in practice, C++ and Python.)

Return also supports specifying (optional) return argument names. These serve two functions:

• They let you easily write derivatives in terms of return arguments in tools/autograd/derivatives.yaml

• They correspond to the named field the output can be referred to from Python. (This means that changing a return argument name is BC-breaking, be careful!)

Note that argument type modifiers such as defaults and optional are not currently supported on Return.

Overloads. You can register multiple functions with the same name and different function signatures if you give them unique overload names. An overload name is specified after the function name, separated by a dot.

Overload names do not have to be globally unique, but must be unique in the set of all overloads for the same function. Overload names cannot be changed for backwards compatibility reasons. Please try to make overload names semantically meaningful. An overload name that just enumerates all the argument types isn't helpful. In many cases, a semantic name is clear from what the overload is doing differently. As a fallback, you can use the name or type of the first differing argument as an overload name.

If you add a new overload to an existing function, please leave the existing overload names as they are (for backwards compatibility), but give the new overload a new, unique name. Although overload names are not directly used by the Python or C++ APIs, they are public API surface for external backends (who register to specific overload names) and deployed mobile models (which use overload names as part of the serialization format.)

Not specifying an overload name is equivalent to specifying an empty overload name. If you add a new function with multiple overloads, give them unique overload names, at most one overload is allowed to have an empty overload name.

The declarations also support the following attributes.

Namespaces. User can register operators in different namespaces than aten, by simply putting custom namespaces before the function name. Currently nested namespace is not supported for function name. If not specified, all the functions will be registered in aten namespace.

For example, suppose we are registering my_op into custom namespace, we can have:

- func: custom::my_op(Tensor(a) self, ...) -> Tensor(a)
  variants: function, method
  dispatch:
    CPU: my_op_cpu
    CUDA: my_op_cuda

Note that we have a one-off TORCH_LIBRARY APIs to achieve the same goal of registering an operator in a custom namespace. Comparing with that API, having custom namespace in native_functions.yaml is useful in cases where the function does not really belong to ATen but is also widely used and it is preferred to have a shared place to register it.

variants

variants: function, method

Controls whether Tensor method (t.foo()) or namespace Function (at::foo()) is generated as a result of this declaration. If the declaration is a method, you must have an argument Tensor self at some position in the method; in the method variant this argument will be elided from the argument list. For example, given the declaration where(BoolTensor cond, Tensor self, Tensor other), this generates the function at::where(cond, self, other) and the method self.where(cond, other).

By default, ATen generates only the function variant for a native function. When should you also generate a method variant? Tensor operations as methods are appropriate for "core" Tensor operations (e.g., add, sub, etc.), but not for more complicated neural network layers (e.g., conv2d) and internal functions designed specifically for binding (e.g., cudnn_convolution).

As we progress along our schema unification of the func schema with the JIT signature schema, we must introduce features that allow us to increase compliance. One of these features are Tensor annotations. As of now we use naming conventions to indicate whether an argument of a function is going to be mutated and returned.

annotations

There are two typical situations in which we mutate the memory of an argument in the Python frontend: a) For an inplace operations such as self.abs_() b) for a function with an output keyword argument such as torch.abs(input, out=None).

In order to provide implementations for these Python functions the legacy schema requires C++ implementations for three situations abs(Tensor self) -> Tensor, abs_(Tensor self) -> Tensor and abs_out(Tensor out, Tensor self) -> Tensor.

Now, as we move towards the unification, we start to use a different syntax to represent this by using annotations. In the end we still translate to the legacy schema for the downstream consumers such as the C++ code generation, but this will soon change.

If two Tensors carry the same annotation, they both may represent the same memory. A write annotation, as indicated by an exclamation mark, indicates that they both may also be written to.

Let's revisit the previous native function declarations and see the conventions of adding annotations.

• abs(Tensor self) -> Tensor stays the same as it will always allocate new memory.
• abs_(Tensor(a!) self) -> Tensor(a!) self may be written to and returned. Further, the annotation indicates that the return value may alias the input. This indicates an inplace function and by convention ends in a single '_'.
• abs(Tensor self, *, Tensor(a!) out) -> Tensor(a!) In the Python frontend out can be passed as a keyword argument and may be written to. In this case it indicates the schema for a function that must accept out as this does not provide a default argument. The idea behind representing this as a optional argument is to document the intended usage. This maps to the legacy abs_out(Tensor out, Tensor self) -> Tensor. As with the legacy _out function you must call the argument Tensor out or Tensor out0, Tensor out1 in the context of multiple arguments.

There is also another situation in which we use annotations, namely views.

• transpose(Tensor(a) self, int dim0, int dim1) -> Tensor(a) An alias to the memory represented by self may be also returned, however it is not mutated.

When a Tensor views are contained in a Tensor list, we need to represent that the output list contains Tensors that alias the input.

• func: chunk(Tensor(a -> *) self, int chunks, int dim=0) -> Tensor(a)[] We assume lists contain memory which aliases the heap, so in order to correctly set up the aliasing relationship between the output and input, we annotate that the input Tensor enters the wildcard set (a -> *). For more details, see the JIT README.

We have some asserts to check whether a developer uses these annotations correctly and throw asserts if she doesn't. For example, any out function must use the (a!) annotation as described above. If this causes a lot of confusion please add @cpuhrsch to your PR.

dispatch

dispatch:
    CPU: func_cpu
    CUDA: func_cuda

This specifies the actual name of the function you want to dispatch to, so you can dispatch to different functions depending on which backend the passed tensors belong to. Notice that custom namespaces is supported on these names, it's useful when the native function listed lives in a namespace other than the default at::native. Currently we support nested namespace with maximum level of 2. For example:

dispatch:
    CPU: custom::ns::func_cpu

The example above hinted the native function can be found under custom::ns::native namespace (the trailing ::native is added automatically).

If the dispatch table is omitted, we assume a default dispatch table:

# overload is ignored
func: func.overload(...) -> ...
dispatch:
    CompositeImplicitAutograd: func

# overload is ignored, but out functions get suffixed with _out in their name
# (NB: no out functions in PyTorch today actually support autograd, but if they
# did, you could call them here and autograd would be inferred)
func: func.out_overload(...) -> ...
dispatch:
    CompositeImplicitAutograd: func_out

If two backends have the same dispatch function, you can write CPU, CUDA: func to reuse the same function name in both cases.

Available backend options can be found by searching dispatch_keys in codegen. There are also three special "generic" backends:

• CompositeExplicitAutograd (previously known as DefaultBackend): implementations of kernels that work for all backends, but require an explicit definition of backward function in derivatives.yaml to support autograd. The most typical use of this key are for delegating functions; i.e., functions that do a very small amount of work and then delegate to another operator to do the actual heavy lifting. Under the hood, registering a kernel to CompositeExplicitAutograd is equivalent to registering that kernel to every backend (e.g., CPU, CUDA). Note: kernels which call DispatchStub should NOT be registered as CompositeExplicitAutograd, as DispatchStub only works for CPU, CUDA)

• CompositeExplicitAutogradNonFunctional: Similar to CompositeExplicitAutograd, but this key should be used if: (1) Your kernel is written for a non-aliasing operator. (2) and it calls internally into an aliasing operator. An example of this is select_backward, which is non-aliasing, but decomposes into select. We would like to distinguish between "ordinary" CompositeExplicitAutograd kernels and these kernels, because some backends would not like to decompose an non-aliasing op into an aliasing op. LazyTensor + XLA are the two current examples of this - since they operate on a functional IR, they would prefer to directly implement a non-aliasing operator with their own kernel, instead of using a decomposition that results in more aliasing operators.

• CompositeImplicitAutograd (previously known as Math): implementations of kernels that work for all backends, and also can implicitly support autograd, because all of the operations it calls support autograd. Direct use of this key should be rare: if you provide no dispatch table, we default to registering your kernel as CompositeImplicitAutograd. Explicitly adding this key to an existing dispatch table may be useful if you have specialized CPU and CUDA implementations, but you might want to provide a fallback lowering for external backends that may not have a specialized implementation.

Functions registered to composite backends should work for any backend, if the nested functions they call work for those backends.

For example, suppose my_op can be implemented in the following way:

at::Tensor my_op(const Tensor& self, const Tensor& other) {
  return self + 2 * other;
}

If we already know inference kernels and derivative formulas for operators + and * in our system, you can just register my_op to CompositeImplicitAutograd and both inference & autograd will just work. Although it seems we only write down the inference formula here, PyTorch autograd system would correctly set up the backward for my_op using the chain formula and derivatives of + & * operators. In other words d_out/d_self = 1; d_out/d_other = 2 can be derived automatically from the my_op inference kernel. Of course if we don't have derivative formula defined for either + or *, backward of my_op can no longer be derived automatically.

Whether to use implicit or explicit autograd for your kernel can be decided by the following steps:

1. If you can, always start with a CompositeImplicitAutograd kernel that's composable from existing operators.
2. If you don't want to use the derived gradient formula from CompositeImplicitAutograd kernel for autograd, either to get better performance or better numerical stability, you should register the kernel with CompositeExplicitAutograd so that it's only used in inference. Later for autograd, depending on whether your autograd kernel works for all backends or not, you can put them in alias Autograd or specific keys like AutogradCPU.
3. If you prefer to write backend-specific kernels, use reserved dispatch keys for your backend instead, e.g. CPU/AutogradCPU.

Important: because a CompositeImplicitAutograd kernel is implicitly registered for ops with no dispatch: section, when you add a backend-specific kernel (and hence a dispatch: section) to one of these, you must also add a CompositeImplicitAutograd: entry that names the old kernel implementation (it's named after the op, with _ added if applicable), so that it's still available for other backends to use.

If you implemented a native function in C++ and want to find out which dispatch keyword should be used in native_functions.yaml, please follow steps in dispatch keywords

Composite Compliance

Definition: a "composite function" is an Operator registered as CompositeImplicitAutograd or a (Python or C++) function that consists of PyTorch operations. Examples of the latter include backward formulas and forward-mode AD formulas.

Composite functions defined in the PyTorch library MUST work for most, if not all, backends/subclasses. This means that we impose a set of constraints that make it more difficult to write composite functions inside PyTorch library code than users writing PyTorch code.

If you wish to do something that is banned (you may wish to do this for perf reasons), please write a backwards formula for your function so it is no longer hide parts of the function in a new aten operator that is not CompositeImplicitAutograd.

Composite functions may not:

• call resize_ or moral equivalents. These are tricky to handle for many backends, like vmap and meta.
• call out= operations. These are impossible to handle for vmap and can cause dispatch-to-python objects to lose their subclassing.
• Change the metadata of a Tensor without performing dispatches. Examples of these operations are directly accessing the TensorImpl API to modify the sizes/strides/metadata of a Tensor.
• In the same vein as the last point, data_ptr access or item access are not allowed. These operations do not go through the dispatcher.
• copy_ is a marginal case. If you're able to rewrite your operation without copy_ you should definitely do so; this should be trivial if you're not copy-ing into a view. Otherwise, it is fine to leave the code as-is.

We have CompositeImplicitAutograd compliance tests in test/test_ops.py. These tests aren't perfect (it's pretty difficult to check for all of the above) so if something looks wrong please shout.

device_guard

device_guard: False

By default, ATen code generation will generate a DeviceGuard invocation, which will ensure that kernel code will run with the current device set to match the device of the first Tensor argument (or first tensor of the first Tensor[] argument, if the function takes a list of tensors). For the most part, this means kernel authors do not have to worry about setting devices.

However, in some cases, setting the device is unnecessary, because, e.g., you call a function already manages device guard setting, or you're a function that simply does not interact with any devices. In that case, code generation of the device guard can be disabled by adding device_guard: False to your function definition.

device_check

device_check: NoCheck

By default, ATen code generation will generate device check, which will ensure all the tensor parameters passed to kernel are on the same device.

However, in some cases, checking the device is unnecessary, because, e.g., you call a function allows to work on multiple devices. In that case, code generation of the device check can be disabled by adding device_check: NoCheck to your function definition.

manual_kernel_registration

manual_kernel_registration: True

With this flag set, we will not generate code to automatically register the C++ operator implementation to TypeDefault (catchAll dispatch key) with the dispatcher. It doesn't make sense to have both dispatch section and manual_kernel_registration: True for the same op. You can find the manual registrations in torch/csrc/autograd/VariableTypeManual.cpp. Currently ops have this field set to True should match MANUAL_CATCHALL in tools/autograd/gen_variable_type.py (It can be a superset of MANUAL_CATCHALL but we don't have a use case for it). This field should only be used rarely.

use_const_ref_for_mutable_tensors

use_const_ref_for_mutable_tensors: True

With this flag set, we will generate arguments for Tensors whose underlying data may change as const Tensor& (or similar), just like we would for other Tensors. Previously, we generated these as Tensor &, which 1) allowed changing which TensorImpl the Tensor itself referred to and 2) was not necessary to allow the underlying data to change. (This was like using T * const when we wanted const T*.)

autogen

- func: my_op_(Tensor(a!) self) -> Tensor(a!)
...
  autogen: my_op, my_op.out

autogen keyword is being used to specify which native function the codegen system should generate implementations for.

• For an in-place variant of a native function (op name ends with an _), we will generate a functional variant and an out= variant.
• If a functional variant is given, we generate an out= variant.
• We don't support autogen for view ops, ops that bypass the dispatcher as well as composite ops.

We also generate kernels for generated ops, which merely copy and return the result from the base ops. These generated kernels can be found in <gen-out>/aten/src/ATen/CompositeViewCopyKernels.cpp.

Also notice that for new operators being added to native_functions.yaml, if they satisfy the requirements mentioned above, they should include autogen keyword, since functionalization depends on it. We will enforce this in codegen.

Writing an implementation in C++

Implementations of native functions go in an appropriate C++ file in the native/ directory (they are organized roughly by topic, but there is no semantic meaning to their organization aside for the cuda directory, which is the only place the build system knows how to build cu files.) To write a native function, you only need to write a C++ implementation (no header necessary) with a matching signature to the generated header from the ATen metadata. There are many simple native functions; take a look at some of them to see what to do.

Although writing an ATen function is mostly writing the algorithm you want to implement, there are some less obvious details you should also consider.

Will your function be automatically differentiable?

If you are writing a pair of functions foo and foo_backward, with the intent that foo_backward implements the derivative of foo, then your implementation of foo is probably not automatically differentiable: it might make use of functions like data_ptr() or it dispatches differently depending on if it's operating on CPU or CUDA tensors. Once you write these two functions, you will have to write an entry correlating them together in tools/autograd/derivatives.yaml.

However, in some situations, you can write a function in ATen and it will be automatically differentiated! This can be the case if the function implementation only calls other operations which are themselves differentiable. In this case, you don't have to write an entry in tools/autograd/derivatives.yaml.

Choosing the right dispatch keyword

After writing a native function in C++, it's important to think about which dispatch keyword to use in native_functions.yaml as it gives the dispatcher information about backend and autograd support of the implementation.

Here're steps to follow to decide the right dispatch keyword:

1. Think about inference: does your kernel work for all backends?

   • No: you're likely providing different kernels for different backends, e.g. backend-dependent logic is used in the implementation or it's implemented through DispatchStub. DispatchStub only support a backend if you explicitly provide a kernel through REGISTER_DISPATCH. Typically it only supports a few in-tree backends like CPU, CUDA, QuantizedCPU etc but not out-of-tree backends like XLA. Write a dispatch section, enumerate all supported backends and point them to the implementations.

     dispatch:
       CPU: kernel_cpu
       CUDA: kernel_cuda
       QuantizedCPU: kernel_quantized_cpu
     

     You're done. Now this op will be called in CPU/CUDA/QuantizedCPU backend inference!

     Note: to support training, you're required to write a formula in derivatives.yaml since your backend implementations don't support autograd.

   • Yes: you're likely calling other at:: ops in the implementation. Go to step 2.

2. Think about training: does your kernel support autograd? check autograd support

   • Yes: in other words, you're providing a CompositeImplicitAutograd kernel which supports both inference and autograd. To use autograd support for training, simply skip adding a dispatch section and you're done. This will allow this op to be correctly registered for both inference and training.

   • Yes, but you still want to provide a numerically stable gradient formula instead of using autograd, write

     dispatch:
       CompositeExplicitAutograd: kernel
     

     You're done. This op will be called in inference for all backends.

     Note: to support training you're required to add an autograd formula, or it'll error out in backward pass when calling with a Tensor has requires_grad=True.

   • No: ops in this category are mainly using _out boilerplate where its out version doesn't have a derivative formula defined. For example:

     Tensor& sign_out(Tensor& result, const Tensor& self) { return unary_op_impl_out(result, self, sign_stub); }
     Tensor sign(const Tensor& self) { return unary_op_impl(self, at::sign_out); }
     Tensor& sign_(Tensor& self) { return unary_op_impl_(self, at::sign_out); }
     

     sign_out uses DispatchStub so the supported backends are enumerated in its dispatch section. For sign and sign_, write

     dispatch:
       CompositeExplicitAutograd: kernel
     

     You're done. This op will be called in inference for all backends.

     Note: to support training you're required to add an autograd formula for sign, or it'll error out in backward pass when calling with a Tensor has requires_grad=True.

     Note: current plan on record for ops using this boilerplate is to replace at:: with at::native in the implementations and add dispatch section with device keywords instead.

3. Validate the computed dispatch table matches what you want. You can use PythonDispatcher provided in torch/_python_dispatcher.py. It shows for a certain operator, what the computed dispatch table looks like after your registrations.

   dispatcher = PythonDispatcher()
   dispatcher.register(["CPU", "XLA", "AutogradCPU", "CompositeImplicitAutograd"])
   print(dispatcher.dispatchTable()) # Tells you exactly which kernel is used for certain backend.
   

4. TODO: AutogradCPUOrCUDA

Note that in native_functions.yaml you can mix using backend keywords and alias keywords above for one op:

• direct registration to backend always has higher precedence than alias
• DO NOT provide multiple alias keywords to the same op: alias keywords have precedence CompositeExplicitAutograd > CompositeImplicitAutograd, e.g. adding both CompositeImplicitAutograd and CompositeExplicitAutograd kernels for one op will completely ignore CompositeImplicitAutograd kernel for both inference and training. Thus this will trigger an error when native_functions.yaml is parsed.

Will this function be exposed to python? What are the namespaces?

We don't generate python bindings for all functions. There're certain patterns in function name that we skip in python binding generation, e.g. *_backward. Check tools/autograd/gen_python_functions.py for the latest rules.

The generated bindings are either exposed as methods on python_variable or functions on the torch._C._nn (marked with python_module: nn), torch._C._fft (marked with python_module: fft), torch._C._linalg (marked with python_module: linalg) objects, torch._C._sparse (marked with python_module: sparse) objects, torch._C._special (marked with python_module: special) objects, or torch._C._nested (marked with python_module: nested) objects.

Undefined tensor conventions

By default, Tensor arguments to ATen functions are always defined, unless you explicitly specified that an undefined tensor was permissible by writing Tensor? or Tensor? x=[], the latter one is needed when you have to assign a default value in C++ (e.g. in the middle of other parameters with default values).

The rules for returning undefined Tensors are a bit more subtle, but there is only one case you have to remember:

• If the function in question is a backward function which accepts a std::array<bool,N> output_mask argument, you MUST return an undefined Tensor at every tuple position i for which output_mask[i] is false, otherwise

• You MUST NOT return an undefined tensor.

The most common situations where you might be tempted to return undefined tensors are when:

• You have a forward function that may return a buffer if training is enabled, but does not return the buffer in inference mode. In this case, just return an appropriately typed zero-size tensor.

• You have a backward function where the gradient for an input is zero. In this case, you are expected to create a zero-filled tensor of appropriate size to return for this input. To get the shape, it may be helpful to take a TensorGeometry of the input to use.

Debugging tips

If you build ATen and get a linker error, that probably means you copy-pasted the C++ definition of your function incorrectly. Double check your Tensor arguments, and make sure you wrote const Tensor& in your signature.