ONNX Shape Inference

ONNX provides an optional implementation of shape inference on ONNX graphs. This implementation covers each of the core operators, as well as provides an interface for extensibility. Therefore, you may choose to invoke the existing shape inference functionality on your graphs, or to define shape inference implementations to go along with your custom operators (or both!). Shape inference functions are stored as a member of the OpSchema objects.

In ONNX 1.10 release, symbol generation and propagation along with shape data propagation was added to ONNX graph level shape inference. Detailed proposal is here


Please see this section of IR.md for a review of static tensor shapes. In particular, a static tensor shape (represented by a TensorShapeProto) is distinct from a runtime tensor shape. This feature is commonly used when the exact runtime tensor shape is not known statically (that is, at compile time).

  • A Tensor with an undefined shape field is used to represent a tensor of unknown rank.

  • A Tensor with a defined shape represents a tensor of known rank.

  • Each Dimension of a TensorShapeProto can have a known integer value (represented by the dim_value field) or it can have an unknown value represented by a symbolic identified (the dim_param field) or it may have neither field defined (in which case it represents an anonymous unknown value).

Invoking Shape Inference

Shape inference can be invoked either via C++ or Python. The Python API is described, with example, here.

The C++ API consists of a single function

    ModelProto& m,
    const ISchemaRegistry* schema_registry);

The first argument is a ModelProto to perform shape inference on, which is annotated in-place with shape information. The second argument is optional.


Shape inference is not guaranteed to be complete. In particular, some dynamic behaviors block the flow of shape inference, for example a Reshape to a dynamically-provide shape. Also, all operators are not required to have a shape inference implementation.

Shape inference works only with constants and simple variables. It does not support arithmetic expressions containing variables. For example, Concat on tensors of shapes (5, 2) and (7, 2) can be inferred to produce a result of shape (12, 2), but Concat on tensors of shapes (5, 2) and (N, 2) will simply produce (M, 2), rather than containing a representation of N+5. Note that differing unknown symbolic values will be propagated, so the M here represents an unknown quantity that is the same as other occurrences of M.

These limitations are a property of the current implementation, not fundamental constraints - if you are in need of something more advanced, do let us know!

Implementing Shape Inference For Operators

You can add a shape inference function to your operator’s Schema with

OpSchema& Opschema::TypeAndShapeInferenceFunction(InferenceFunction inferenceFunction);

InferenceFunction is defined in shape_inference.h, along with the core interface struct InferenceContext and an assortment of helper methods. InferenceContext is the core struct which is provided to your inference function. It allows accessing information about the operator’s inputs, and also allows writing out inferred information.

To see numerous examples, search for occurrences of TypeAndShapeInferenceFunction in the codebase. One that is relatively involved is the implementation for Concat, in onnx/defs/tensor/defs.cc.

Please note the following points when implementing the shape-inference method for operators to avoid common errors:

  • Before accessing the shape of any input, the code must check that the shape is available. If unavailable, it should be treated as a dynamic tensor whose rank is unknown and handled appropriately. Usually, the shape-inference logic is guarded by a call to hasInputShape or hasNInputShapes.

  • Before accessing the dim_value or dim_param of any dimension, the code must check if these fields have a value. In particular, the code must handle the possibility that the dimension may not have a statically known value.

There are several utility functions in shape_inference.h to handle various common situations.

  • Use checkInputRank for inputs that must have a fixed rank. (See the inference for RoiAlign as an example.)

  • unifyInputDim and unifyDim and updateOutputShape can be used when multiple input dims are expected to be the same, and when input dimensions are propagated to specific output dimensions. (See the inference for RoiAlign for an example.)

  • Overloaded operators * and / can be used on symbolic dimensions when output dimensions are computed from input dimensions using arithmetic. (See the inference for SpaceToDepth for an example.)

These utilities handle missing shapes and dimensions safely.

Example: Consider a simple matrix-multiplication op that expects inputs of shape [M,K] and [K,N] and returns an output of shape [M,N]. This can be coded up as below:

   // Check that input 0 has rank 2 (if its rank is known).
   checkInputRank(ctx, 0, 2);
   // Check that input 1 has rank 2 (if its rank is known).
   checkInputRank(ctx, 1, 2);
   Dim M, K, N;
   // Check various dimensions, handling missing dimensions/shapes safely.
   unifyInputDim(ctx, 0, 0, M);
   unifyInputDim(ctx, 0, 1, K);
   unifyInputDim(ctx, 1, 0, K);
   unifyInputDim(ctx, 1, 1, N);
   updateOutputShape(ctx, 0, {M. N});