Adding an Operator to Relay

In this document we will go over the steps needed to register a new TVM operator in Relay. We will be following this PR which adds a cumulative product operation as an example. The PR itself builds upon another PR which adds a cumulative sum operation.

Registering a new operator requires a few steps:

  1. Add an attribute node declaring fixed arguments which are known at compile time

  2. Write a type relation for your operation to integrate into Relay’s type system.

  3. Use the RELAY_REGISTER_OP macro in C++ to register the operator’s arity, type, and other hints for the compiler

  4. Write how the operator is computed

  5. Register the compute, schedule with the relay operator

  6. Define a C++ function to produce a call node for the operator and registering a Python API hook for the function

  7. Wrapping the above Python API hook in a neater interface

  8. Writing tests for the new relay operator

1. Defining an Attribute Node

Attributes are fixed arguments which are supposed to be known at compile time. The stride and dilation of a convolution operator would be an appropriate example of fields which might belong in an attribute node for a convolution operator.

Attributes should be defined in a file within the folder include/tvm/relay/attrs/.

Ultimately we want to create an operator whose interface can be seen clearly in the final python interface:

def cumprod(data, axis=None, dtype=None, exclusive=None):
    """Numpy style cumprod op. Return the cumulative inclusive product of the elements along
    a given axis.
    data : relay.Expr
        The input data to the operator.
    axis : int, optional
        Axis along which the cumulative product is computed. The default (None) is to compute
        the cumprod over the flattened array.
    dtype : string, optional
        Type of the returned array and of the accumulator in which the elements are multiplied.
        If dtype is not specified, it defaults to the dtype of data.
    exclusive : bool, optional
        If true will return exclusive product in which the first element is not
        included. In other terms, if true, the j-th output element would be
        the product of the first (j-1) elements. Otherwise, it would be the product of
        the first j elements. The product of zero elements will be 1.
    result : relay.Expr
        The result has the same size as data, and the same shape as data if axis is not None.
        If axis is None, the result is a 1-d array.

A similiar interface exists for cumsum().

Therefore, when defining our attributes in include/tvm/relay/attrs/transform.h we choose the axis, accumulation dtype, and exclusivity of the operation as appropriate fields for the struct.

/*! \brief Attributes used in cumsum and cumprod operator */
struct ScanopAttrs : public tvm::AttrsNode<ScanopAttrs> {
  Integer axis;
  DataType dtype;
  Bool exclusive = Bool(false);
  TVM_DECLARE_ATTRS(ScanopAttrs, "relay.attrs.ScanopAttrs") {
    TVM_ATTR_FIELD(axis).describe("The axis to operate over").set_default(NullValue<Integer>());
    TVM_ATTR_FIELD(dtype).describe("Output data type").set_default(NullValue<DataType>());
        .describe("The first element is not included")

2. Writing a Type Relation

To allow for flexibility in registering operators and greater expressivity and granularity in expressing types in Relay, operators are typed using relations between input and output types. These relations are represented as functions that take in a list of input types and output types (any of these types may be incomplete) and return a list of input and output types that satisfies the relation. This includes shape information which can be determined statically at compile time. Essentially, a relation for an operator can enforce all the necessary typing rules (namely by inspecting the input types) in addition to computing the output type.

Type relation for the cumulative product and sum operators can be found in src/relay/op/tensor/

bool ScanopRel(const Array<Type>& types, int num_inputs, const Attrs& attrs, const TypeReporter& reporter) {
    // types: [data, output]
    ICHECK_EQ(types.size(), 2) << "Expects two types, one for the input and another for the output";
    const auto* data = types[0].as<TensorTypeNode>();
    if (data == nullptr) {
        << "Scanop: expect input type to be TensorType but get " << types[0];
        return false;

    const auto* param =<ScanopAttrs>();

    auto dtype = param->dtype;
    if (dtype.is_void()) {
        dtype = data->dtype;

    if (param->axis.defined()) {
        reporter->Assign(types[1], TensorType(data->shape, dtype));
    } else {
        auto prod = data->shape[0];
        for (size_t i = 1; i < data->shape.size(); ++i) {
            prod = prod * data->shape[i];
        reporter->Assign(types[1], TensorType({prod}, dtype));

    return true;

3. Relating the Arity and Attributes to an Operation

We then register the name of our new ops and annotate them with the calling interface. The RELAY_REGISTER_OP macro in C++ allows a developer to specify the following information about an operator in Relay:

  • Arity (number of arguments)

  • Names and descriptions for positional arguments

  • Support level (1 indicates an internal intrinsic; higher numbers indicate less integral or externally supported operators)

  • A type relation for the operator

  • Other annotations useful when optimizing the operation.

Once again we add this to src/relay/op/tensor/

        R"doc(Return the cumulative sum of the elements along a given axis.)doc" TVM_ADD_FILELINE)
    .add_argument("data", "Tensor", "The input tensor.")
    .add_type_rel("Cumsum", ScanopRel)
    .set_attr<TOpPattern>("TOpPattern", kOpaque);

        R"doc(Return the cumulative product of the elements along a given axis.)doc" TVM_ADD_FILELINE)
    .add_argument("data", "Tensor", "The input tensor.")
    .add_type_rel("Cumprod", ScanopRel)
    .set_attr<TOpPattern>("TOpPattern", kOpaque);

In this case the TOpPattern is a hint to the compiler on the pattern of computation the operator does, which might be useful for fusing operators. kOpaque tells TVM to not bother trying to fuse this operator.

4. Defining the Compute of the Operation

While we’ve now defined the interface for our operations we still need to define how to perform the actual calculations for cumulative sum and product.

Writing this code is outside the scope of the tutorial. For now, we assume we have a well tested implementation for the operation’s compute. For more details on how to do this, we recommend looking up the tutorials on tensor expressions, TVM’s operator inventory (topi) and looking at the example cumulative sum and product implementations found in python/tvm/topi/ and the gpu versions in python/tvm/topi/cuda/ In the case of our cumulative sum and product operations we write things directly in TIR which is the representation where tensor expressions and topi will lower into.

5. Hooking up Compute and Strategy with Relay

After you have implemented your compute function we now need to glue it to our relay operation. Within TVM this means not only defining the computation, but also the schedule for an operation. A strategy is a method which picks which computation and which schedule to use. For example, for 2D convolutions we might recognize we are doing a depthwise convolution and dispatch to a more efficient computation and schedule as a result. In our case however we have no such need except for dispatching between our CPU and GPU implementations. In python/tvm/relay/op/strategy/ and python/tvm/relay/op/strategy/ we add the following strategies:

def wrap_compute_scanop(topi_compute):
    """Wrap scanop style topi compute"""

    def _compute_scanop(attrs, inputs, _):
        return [topi_compute(inputs[0], attrs.axis, attrs.dtype, attrs.exclusive)]

    return _compute_scanop

def cumsum_strategy(attrs, inputs, out_type, target):
    """cumsum generic strategy"""
    strategy = _op.OpStrategy()
    return strategy

def cumprod_strategy(attrs, inputs, out_type, target):
    """cumprod generic strategy"""
    strategy = _op.OpStrategy()
    return strategy

@cumsum_strategy.register(["cuda", "gpu"])
def cumsum_strategy_cuda(attrs, inputs, out_type, target):
    """cumsum cuda strategy"""
    strategy = _op.OpStrategy()
    return strategy

@cumprod_strategy.register(["cuda", "gpu"])
def cumprod_strategy_cuda(attrs, inputs, out_type, target):
    """cumprod cuda strategy"""
    strategy = _op.OpStrategy()
    return strategy

Where in each strategy we define the compute we wrote and the schedule to use within add_implementation(). We finally link the strategy and compute with the defined relay operator in python/tvm/relay/op/

# cumsum
def compute_cumsum(attrs, inputs, output_type):
    """Compute definition of cumsum"""
    return [topi.cumsum(inputs[0], attrs.axis, attrs.dtype, attrs.exclusive)]

_reg.register_strategy("cumsum", strategy.cumsum_strategy)
_reg.register_shape_func("cumsum", False, elemwise_shape_func)

# cumprod
def compute_cumprod(attrs, inputs, output_type):
    """Compute definition of cumprod"""
    return [topi.cumprod(inputs[0], attrs.axis, attrs.dtype, attrs.exclusive)]

_reg.register_strategy("cumprod", strategy.cumprod_strategy)
_reg.register_shape_func("cumprod", False, elemwise_shape_func)

The shape functions are used for determining output shape given a dynamically shaped tensor. In this case we tell TVM the output shape will be the same as the input shape.

6. Creating a Relay Call Node and Exposing a Python Hook

We now have a working operation and now just need to properly call it via a Relay Call Node. This step requires simply writing a function that takes the arguments to the operator (as Relay expressions) and returning a call node to the operator (i.e., the node that should be placed into the Relay AST where the call to the operator is intended).

At present call attributes and type arguments (the last two fields) are not supported, so it suffices to use Op::Get to fetch the operator’s information from the operator registry and pass in the arguments to the call node, as below. In src/relay/op/tensor/

Expr MakeCumsum(Expr data, Integer axis, DataType dtype, Bool exclusive) {
    auto attrs = make_object<ScanopAttrs>();
    attrs->dtype = dtype;
    attrs->axis = axis;
    attrs->exclusive = exclusive;
    static const Op& op = Op::Get("cumsum");
    return Call(op, {data}, Attrs(attrs), {});


Expr MakeCumprod(Expr data, Integer axis, DataType dtype, Bool exclusive) {
    auto attrs = make_object<ScanopAttrs>();
    attrs->dtype = dtype;
    attrs->axis = axis;
    attrs->exclusive = exclusive;
    static const Op& op = Op::Get("cumprod");
    return Call(op, {data}, Attrs(attrs), {});


Where TVM_REGISTER_GLOBAL exposes the MakeCumsum and MakeCumprod functions in Python via relay.op._make.cumsum(...) and relay.op._make.cumprod(...).

7. Including a Cleaner Python API Hook

It is generally the convention in Relay, that functions exported through TVM_REGISTER_GLOBAL should be wrapped in a separate Python function rather than called directly in Python. For our operators we expose this cleaner interface in python/tvm/relay/op/

def cumsum(data, axis=None, dtype=None, exclusive=None):
    return _make.cumsum(data, axis, dtype, exclusive)

def cumprod(data, axis=None, dtype=None, exclusive=None):
    return _make.cumprod(data, axis, dtype, exclusive)

Note that these Python wrappers might also be good opportunities to provide an easier interface to the operator. For example, the concat operator is registered as taking only one operator, namely a tuple with the tensors to be concatenated, but the Python wrapper takes the tensors as arguments and combines them into a tuple before producing the call node:

def concat(*args):
    """Concatenate the input tensors along the zero axis.

    args: list of Tensor

    tensor: The concatenated tensor.
    tup = Tuple(list(args))
    return _make.concat(tup)

8. Writing Unit Tests!

This is self explanatory! Some example unit tests can be found in tests/python/relay/ for our cumulative sum and product operators.

Other Topics

Gradient Operators

Gradient operators are important for writing differentiable programs in Relay. While it is the case that Relay’s autodiff algorithm can differentiate first-class language constructs, operators are opaque. Because Relay can’t look into the implementation, an explicit differentiation rule must be provided.

Both Python and C++ can be used to write gradient operators, but we focus our examples on Python, as it is more commonly used.

Adding a Gradient in Python

A collection of Python gradient operators can be found in python/tvm/relay/op/ We will walk through two representative examples: sigmoid and multiply.

def sigmoid_grad(orig, grad):
    """Returns [grad * sigmoid(x) * (1 - sigmoid(x))]."""
    return [grad * orig * (ones_like(orig) - orig)]

The inputs here are the original operator orig and a gradient grad to accumulate into. What we return is a list, where the element at the i’th index is the derivative of the operator with respect to the operator’s i’th input. In general, the gradient will return a list with as many elements as there are inputs to the base operator.

Before we further analyze this definition, first we should recall the derivative of the sigmoid function: \(\frac{\partial \sigma}{\partial x} = \sigma(x)(1 - \sigma(x))\). The definition above looks similar to the mathematical definition, but there is one important addition, which we describe below.

The term orig * (ones_like(orig) - orig) directly matches the derivative, because orig here is the sigmoid function, but we’re not just interested in how to compute the gradient of this function. We’re interested in composing this gradient with other gradients, so we can accumulate the gradient across an entire program. This is where the grad term comes in. In the expression grad * orig * (ones_like(orig) - orig), multiplying by grad specifies how to compose the derivative with the gradient thus far.

Now, we consider multiply, a slightly more interesting example:

def multiply_grad(orig, grad):
    """Returns [grad * y, grad * x]"""
    x, y = orig.args
    return [collapse_sum_like(grad * y, x),
            collapse_sum_like(grad * x, y)]

In this example, there are two elements in the returned list, because multiply is a binary operator. And to recall, if \(f(x, y) = xy\), the partial derivatives are \(\frac{\partial f}{\partial x} = y\) and \(\frac{\partial f}{\partial y} = x\).

There is one required step for multiply that is not required for sigmoid, because multiply has broadcasting semantics. Since the shape of grad might not match the shape of the inputs, we use collapse_sum_like to take the contents of the grad * <var> terms and make the shape match the shape of the input we’re differentiating with respect to.

Adding a Gradient in C++

Adding a gradient in C++ is similar to adding one in Python, but the interface for registering is slightly different.

First, make sure src/relay/transforms/pattern_utils.h is included. It provides helper functions for creating nodes in the Relay AST. Then, define the gradient in a similar fashion as in the Python example:

tvm::Array<Expr> MultiplyGrad(const Expr& orig_call, const Expr& output_grad) {
    const Call& call = orig_call.Downcast<Call>();
    return { CollapseSumLike(Multiply(output_grad, call.args[1]), call.args[0]),
             CollapseSumLike(Multiply(output_grad, call.args[0]), call.args[1]) };

Notice that in C++ we can’t use the same operator overloading that we have in Python, and we need to downcast, so the implementation is more verbose. Even so, we can easily verify that this definition mirrors the earlier example in Python.

Now, instead of using a Python decorator, we need to tack a set_attr call for “FPrimalGradient” onto the end of the base operator’s registration, in order to register the gradient.

    // ...
    // Set other attributes
    // ...
    .set_attr<FPrimalGradient>("FPrimalGradient", MultiplyGrad);