onnx.proto

//
// WARNING: This file is automatically generated!  Please edit onnx.in.proto.
//


// SPDX-License-Identifier: Apache-2.0


syntax = "proto2";

package onnx;

// Overview
//
// ONNX is an open specification that is comprised of the following components:
//
// 1)  A definition of an extensible computation graph model.
// 2)  Definitions of standard data types.
// 3)  Definitions of built-in operators.
//
// This document describes the syntax of models and their computation graphs,
// as well as the standard data types. Together, they are referred to as the ONNX
// Intermediate Representation, or 'IR' for short.
//
// The normative semantic specification of the ONNX IR is found in docs/IR.md.
// Definitions of the built-in neural network operators may be found in docs/Operators.md.

// Notes
//
// Protobuf compatibility
//
// To simplify framework compatibility, ONNX is defined using the subset of protobuf
// that is compatible with both protobuf v2 and v3. This means that we do not use any
// protobuf features that are only available in one of the two versions.
//
// Here are the most notable contortions we have to carry out to work around
// these limitations:
//
//   - No 'map' (added protobuf 3.0). We instead represent mappings as lists
//     of key-value pairs, where order does not matter and duplicates
//     are not allowed.


// Versioning
//
// ONNX versioning is specified in docs/IR.md and elaborated on in docs/Versioning.md
//
// To be compatible with both proto2 and proto3, we will use a version number
// that is not defined by the default value but an explicit enum number.
enum Version {
  // proto3 requires the first enum value to be zero.
  // We add this just to appease the compiler.
  _START_VERSION = 0;
  // The version field is always serialized and we will use it to store the
  // version that the  graph is generated from. This helps us set up version
  // control.
  // For the IR, we are using simple numbers starting with 0x00000001,
  // which was the version we published on Oct 10, 2017.
  IR_VERSION_2017_10_10 = 0x0000000000000001;

  // IR_VERSION 2 published on Oct 30, 2017
  // - Added type discriminator to AttributeProto to support proto3 users
  IR_VERSION_2017_10_30 = 0x0000000000000002;

  // IR VERSION 3 published on Nov 3, 2017
  // - For operator versioning:
  //    - Added new message OperatorSetIdProto
  //    - Added opset_import in ModelProto
  // - For vendor extensions, added domain in NodeProto
  IR_VERSION_2017_11_3 = 0x0000000000000003;

  // IR VERSION 4 published on Jan 22, 2019
  // - Relax constraint that initializers should be a subset of graph inputs
  // - Add type BFLOAT16
  IR_VERSION_2019_1_22 = 0x0000000000000004;

  // IR VERSION 5 published on March 18, 2019
  // - Add message TensorAnnotation.
  // - Add quantization annotation in GraphProto to map tensor with its scale and zero point quantization parameters.
  IR_VERSION_2019_3_18 = 0x0000000000000005;

  // IR VERSION 6 published on Sep 19, 2019
  // - Add support for sparse tensor constants stored in model.
  //   - Add message SparseTensorProto
  //   - Add sparse initializers
  IR_VERSION_2019_9_19 = 0x0000000000000006;

  // IR VERSION 7 published on May 8, 2020
  // - Add support to allow function body graph to rely on multiple external opreator sets.
  // - Add a list to promote inference graph's initializers to global and
  //   mutable variables. Global variables are visible in all graphs of the
  //   stored models.
  // - Add message TrainingInfoProto to store initialization
  //   method and training algorithm. The execution of TrainingInfoProto
  //   can modify the values of mutable variables.
  // - Implicitly add inference graph into each TrainingInfoProto's algorithm.
  IR_VERSION_2020_5_8 = 0x0000000000000007;

  // IR VERSION 8 published on <TBD>
  // Introduce TypeProto.SparseTensor
  // Introduce TypeProto.Optional
  // Added a list of FunctionProtos local to the model
  // Deprecated since_version and operator status from FunctionProto
  IR_VERSION = 0x0000000000000008;

}

// Attributes
//
// A named attribute containing either singular float, integer, string, graph,
// and tensor values, or repeated float, integer, string, graph, and tensor values.
// An AttributeProto MUST contain the name field, and *only one* of the
// following content fields, effectively enforcing a C/C++ union equivalent.
message AttributeProto {

  // Note: this enum is structurally identical to the OpSchema::AttrType
  // enum defined in schema.h.  If you rev one, you likely need to rev the other.
  enum AttributeType {
    UNDEFINED = 0;
    FLOAT = 1;
    INT = 2;
    STRING = 3;
    TENSOR = 4;
    GRAPH = 5;
    SPARSE_TENSOR = 11;
    TYPE_PROTO = 13;

    FLOATS = 6;
    INTS = 7;
    STRINGS = 8;
    TENSORS = 9;
    GRAPHS = 10;
    SPARSE_TENSORS = 12;
    TYPE_PROTOS = 14;
  }

  // The name field MUST be present for this version of the IR.
  optional string name = 1;           // namespace Attribute

  // if ref_attr_name is not empty, ref_attr_name is the attribute name in parent function.
  // In this case, this AttributeProto does not contain data, and it's a reference of attribute
  // in parent scope.
  // NOTE: This should ONLY be used in function (sub-graph). It's invalid to be used in main graph.
  optional string ref_attr_name = 21;

  // A human-readable documentation for this attribute. Markdown is allowed.
  optional string doc_string = 13;

  // The type field MUST be present for this version of the IR.
  // For 0.0.1 versions of the IR, this field was not defined, and
  // implementations needed to use has_field heuristics to determine
  // which value field was in use.  For IR_VERSION 0.0.2 or later, this
  // field MUST be set and match the f|i|s|t|... field in use.  This
  // change was made to accommodate proto3 implementations.
  optional AttributeType type = 20;   // discriminator that indicates which field below is in use

  // Exactly ONE of the following fields must be present for this version of the IR
  optional float f = 2;               // float
  optional int64 i = 3;               // int
  optional bytes s = 4;               // UTF-8 string
  optional TensorProto t = 5;         // tensor value
  optional GraphProto g = 6;          // graph
  optional SparseTensorProto sparse_tensor = 22;  // sparse tensor value
  // Do not use field below, it's deprecated.
  // optional ValueProto v = 12;         // value - subsumes everything but graph
  optional TypeProto tp = 14;          // type proto

  repeated float floats = 7;          // list of floats
  repeated int64 ints = 8;            // list of ints
  repeated bytes strings = 9;         // list of UTF-8 strings
  repeated TensorProto tensors = 10;  // list of tensors
  repeated GraphProto graphs = 11;    // list of graph
  repeated SparseTensorProto sparse_tensors = 23; // list of sparse tensors
  repeated TypeProto type_protos = 15;// list of type protos
}

// Defines information on value, including the name, the type, and
// the shape of the value.
message ValueInfoProto {
  // This field MUST be present in this version of the IR.
  optional string name = 1;     // namespace Value
  // This field MUST be present in this version of the IR for
  // inputs and outputs of the top-level graph.
  optional TypeProto type = 2;
  // A human-readable documentation for this value. Markdown is allowed.
  optional string doc_string = 3;
}

// Nodes
//
// Computation graphs are made up of a DAG of nodes, which represent what is
// commonly called a "layer" or "pipeline stage" in machine learning frameworks.
//
// For example, it can be a node of type "Conv" that takes in an image, a filter
// tensor and a bias tensor, and produces the convolved output.
message NodeProto {
  repeated string input = 1;    // namespace Value
  repeated string output = 2;   // namespace Value

  // An optional identifier for this node in a graph.
  // This field MAY be absent in ths version of the IR.
  optional string name = 3;     // namespace Node

  // The symbolic identifier of the Operator to execute.
  optional string op_type = 4;  // namespace Operator
  // The domain of the OperatorSet that specifies the operator named by op_type.
  optional string domain = 7;   // namespace Domain

  // Additional named attributes.
  repeated AttributeProto attribute = 5;

  // A human-readable documentation for this node. Markdown is allowed.
  optional string doc_string = 6;
}

// Training information
// TrainingInfoProto stores information for training a model.
// In particular, this defines two functionalities: an initialization-step
// and a training-algorithm-step. Initialization resets the model
// back to its original state as if no training has been performed.
// Training algorithm improves the model based on input data.
//
// The semantics of the initialization-step is that the initializers
// in ModelProto.graph and in TrainingInfoProto.algorithm are first
// initialized as specified by the initializers in the graph, and then
// updated by the "initialization_binding" in every instance in
// ModelProto.training_info.
//
// The field "algorithm" defines a computation graph which represents a
// training algorithm's step. After the execution of a
// TrainingInfoProto.algorithm, the initializers specified by "update_binding"
// may be immediately updated. If the targeted training algorithm contains
// consecutive update steps (such as block coordinate descent methods),
// the user needs to create a TrainingInfoProto for each step.
message TrainingInfoProto {
  // This field describes a graph to compute the initial tensors
  // upon starting the training process. Initialization graph has no input
  // and can have multiple outputs. Usually, trainable tensors in neural
  // networks are randomly initialized. To achieve that, for each tensor,
  // the user can put a random number operator such as RandomNormal or
  // RandomUniform in TrainingInfoProto.initialization.node and assign its
  // random output to the specific tensor using "initialization_binding".
  // This graph can also set the initializers in "algorithm" in the same
  // TrainingInfoProto; a use case is resetting the number of training
  // iteration to zero.
  //
  // By default, this field is an empty graph and its evaluation does not
  // produce any output. Thus, no initializer would be changed by default.
  optional GraphProto initialization = 1;

  // This field represents a training algorithm step. Given required inputs,
  // it computes outputs to update initializers in its own or inference graph's
  // initializer lists. In general, this field contains loss node, gradient node,
  // optimizer node, increment of iteration count.
  //
  // An execution of the training algorithm step is performed by executing the
  // graph obtained by combining the inference graph (namely "ModelProto.graph")
  // and the "algorithm" graph. That is, the actual the actual
  // input/initializer/output/node/value_info/sparse_initializer list of
  // the training graph is the concatenation of
  // "ModelProto.graph.input/initializer/output/node/value_info/sparse_initializer"
  // and "algorithm.input/initializer/output/node/value_info/sparse_initializer"
  // in that order. This combined graph must satisfy the normal ONNX conditions.
  // Now, let's provide a visualization of graph combination for clarity.
  // Let the inference graph (i.e., "ModelProto.graph") be
  //    tensor_a, tensor_b -> MatMul -> tensor_c -> Sigmoid -> tensor_d
  // and the "algorithm" graph be
  //    tensor_d -> Add -> tensor_e
  // The combination process results
  //    tensor_a, tensor_b -> MatMul -> tensor_c -> Sigmoid -> tensor_d -> Add -> tensor_e
  //
  // Notice that an input of a node in the "algorithm" graph may reference the
  // output of a node in the inference graph (but not the other way round). Also, inference
  // node cannot reference inputs of "algorithm". With these restrictions, inference graph
  // can always be run independently without training information.
  //
  // By default, this field is an empty graph and its evaluation does not
  // produce any output. Evaluating the default training step never
  // update any initializers.
  optional GraphProto algorithm = 2;

  // This field specifies the bindings from the outputs of "initialization" to
  // some initializers in "ModelProto.graph.initializer" and
  // the "algorithm.initializer" in the same TrainingInfoProto.
  // See "update_binding" below for details.
  //
  // By default, this field is empty and no initializer would be changed
  // by the execution of "initialization".
  repeated StringStringEntryProto initialization_binding = 3;

  // Gradient-based training is usually an iterative procedure. In one gradient
  // descent iteration, we apply
  //
  // x = x - r * g
  //
  // where "x" is the optimized tensor, "r" stands for learning rate, and "g" is
  // gradient of "x" with respect to a chosen loss. To avoid adding assignments
  // into the training graph, we split the update equation into
  //
  // y = x - r * g
  // x = y
  //
  // The user needs to save "y = x - r * g" into TrainingInfoProto.algorithm. To
  // tell that "y" should be assigned to "x", the field "update_binding" may
  // contain a key-value pair of strings, "x" (key of StringStringEntryProto)
  // and "y" (value of StringStringEntryProto).
  // For a neural network with multiple trainable (mutable) tensors, there can
  // be multiple key-value pairs in "update_binding".
  //
  // The initializers appears as keys in "update_binding" are considered
  // mutable variables. This implies some behaviors
  // as described below.
  //
  //  1. We have only unique keys in all "update_binding"s so that two
  //     variables may not have the same name. This ensures that one
  //     variable is assigned up to once.
  //  2. The keys must appear in names of "ModelProto.graph.initializer" or
  //     "TrainingInfoProto.algorithm.initializer".
  //  3. The values must be output names of "algorithm" or "ModelProto.graph.output".
  //  4. Mutable variables are initialized to the value specified by the
  //     corresponding initializer, and then potentially updated by
  //     "initializer_binding"s and "update_binding"s in "TrainingInfoProto"s.
  //
  // This field usually contains names of trainable tensors
  // (in ModelProto.graph), optimizer states such as momentums in advanced
  // stochastic gradient methods (in TrainingInfoProto.graph),
  // and number of training iterations (in TrainingInfoProto.graph).
  //
  // By default, this field is empty and no initializer would be changed
  // by the execution of "algorithm".
  repeated StringStringEntryProto update_binding = 4;
}

// Models
//
// ModelProto is a top-level file/container format for bundling a ML model and
// associating its computation graph with metadata.
//
// The semantics of the model are described by the associated GraphProto's.
message ModelProto {
  // The version of the IR this model targets. See Version enum above.
  // This field MUST be present.
  optional int64 ir_version = 1;

  // The OperatorSets this model relies on.
  // All ModelProtos MUST have at least one entry that
  // specifies which version of the ONNX OperatorSet is
  // being imported.
  //
  // All nodes in the ModelProto's graph will bind against the operator
  // with the same-domain/same-op_type operator with the HIGHEST version
  // in the referenced operator sets.
  repeated OperatorSetIdProto opset_import = 8;

  // The name of the framework or tool used to generate this model.
  // This field SHOULD be present to indicate which implementation/tool/framework
  // emitted the model.
  optional string producer_name = 2;

  // The version of the framework or tool used to generate this model.
  // This field SHOULD be present to indicate which implementation/tool/framework
  // emitted the model.
  optional string producer_version = 3;

  // Domain name of the model.
  // We use reverse domain names as name space indicators. For example:
  // `com.facebook.fair` or `com.microsoft.cognitiveservices`
  //
  // Together with `model_version` and GraphProto.name, this forms the unique identity of
  // the graph.
  optional string domain = 4;

  // The version of the graph encoded. See Version enum below.
  optional int64 model_version = 5;

  // A human-readable documentation for this model. Markdown is allowed.
  optional string doc_string = 6;

  // The parameterized graph that is evaluated to execute the model.
  optional GraphProto graph = 7;

  // Named metadata values; keys should be distinct.
  repeated StringStringEntryProto metadata_props = 14;

  // Training-specific information. Sequentially executing all stored
  // `TrainingInfoProto.algorithm`s and assigning their outputs following
  // the corresponding `TrainingInfoProto.update_binding`s is one training
  // iteration. Similarly, to initialize the model
  // (as if training hasn't happened), the user should sequentially execute
  // all stored `TrainingInfoProto.initialization`s and assigns their outputs
  // using `TrainingInfoProto.initialization_binding`s.
  //
  // If this field is empty, the training behavior of the model is undefined.
  repeated TrainingInfoProto training_info = 20;

  // A list of function protos local to the model.
  //
  // Name of the function "FunctionProto.name" should be unique within the domain "FunctionProto.domain".
  // In case of any conflicts the behavior (whether the model local functions are given higher priority,
  // or standard opserator sets are given higher priotity or this is treated as error) is defined by
  // the runtimes.
  //
  // The operator sets imported by FunctionProto should be compatible with the ones
  // imported by ModelProto and other model local FunctionProtos.
  // Example, if same operator set say 'A' is imported by a FunctionProto and ModelProto
  // or by 2 FunctionProtos then versions for the operator set may be different but,
  // the operator schema returned for op_type, domain, version combination
  // for both the versions should be same for every node in the function body.
  //
  // One FunctionProto can reference other FunctionProto in the model, however, recursive reference
  // is not allowed.
  repeated FunctionProto functions = 25;
};

// StringStringEntryProto follows the pattern for cross-proto-version maps.
// See https://developers.google.com/protocol-buffers/docs/proto3#maps
message StringStringEntryProto {
  optional string key = 1;
  optional string value = 2;
};

message TensorAnnotation {
  optional string tensor_name = 1;
  // <key, value> pairs to annotate tensor specified by <tensor_name> above.
  // The keys used in the mapping below must be pre-defined in ONNX spec.
  // For example, for 8-bit linear quantization case, 'SCALE_TENSOR', 'ZERO_POINT_TENSOR' will be pre-defined as
  // quantization parameter keys.
  repeated StringStringEntryProto quant_parameter_tensor_names = 2;
}



// Graphs
//
// A graph defines the computational logic of a model and is comprised of a parameterized
// list of nodes that form a directed acyclic graph based on their inputs and outputs.
// This is the equivalent of the "network" or "graph" in many deep learning
// frameworks.
message GraphProto {
  // The nodes in the graph, sorted topologically.
  repeated NodeProto node = 1;

  // The name of the graph.
  optional string name = 2;   // namespace Graph

  // A list of named tensor values, used to specify constant inputs of the graph.
  // Each initializer (both TensorProto as well SparseTensorProto) MUST have a name.
  // The name MUST be unique across both initializer and sparse_initializer,
  // but the name MAY also appear in the input list.
  repeated TensorProto initializer = 5;

  // Initializers (see above) stored in sparse format.
  repeated SparseTensorProto sparse_initializer = 15;

  // A human-readable documentation for this graph. Markdown is allowed.
  optional string doc_string = 10;

  // The inputs and outputs of the graph.
  repeated ValueInfoProto input = 11;
  repeated ValueInfoProto output = 12;

  // Information for the values in the graph. The ValueInfoProto.name's
  // must be distinct. It is optional for a value to appear in value_info list.
  repeated ValueInfoProto value_info = 13;

  // This field carries information to indicate the mapping among a tensor and its
  // quantization parameter tensors. For example:
  // For tensor 'a', it may have {'SCALE_TENSOR', 'a_scale'} and {'ZERO_POINT_TENSOR', 'a_zero_point'} annotated,
  // which means, tensor 'a_scale' and tensor 'a_zero_point' are scale and zero point of tensor 'a' in the model.
  repeated TensorAnnotation quantization_annotation = 14;

  reserved 3, 4, 6 to 9;
  reserved "ir_version", "producer_version", "producer_tag", "domain";
}

// Tensors
//
// A serialized tensor value.
message TensorProto {
  enum DataType {
    UNDEFINED = 0;
    // Basic types.
    FLOAT = 1;   // float
    UINT8 = 2;   // uint8_t
    INT8 = 3;    // int8_t
    UINT16 = 4;  // uint16_t
    INT16 = 5;   // int16_t
    INT32 = 6;   // int32_t
    INT64 = 7;   // int64_t
    STRING = 8;  // string
    BOOL = 9;    // bool

    // IEEE754 half-precision floating-point format (16 bits wide).
    // This format has 1 sign bit, 5 exponent bits, and 10 mantissa bits.
    FLOAT16 = 10;

    DOUBLE = 11;
    UINT32 = 12;
    UINT64 = 13;
    COMPLEX64 = 14;     // complex with float32 real and imaginary components
    COMPLEX128 = 15;    // complex with float64 real and imaginary components

    // Non-IEEE floating-point format based on IEEE754 single-precision
    // floating-point number truncated to 16 bits.
    // This format has 1 sign bit, 8 exponent bits, and 7 mantissa bits.
    BFLOAT16 = 16;

    // Future extensions go here.
  }

  // The shape of the tensor.
  repeated int64 dims = 1;

  // The data type of the tensor.
  // This field MUST have a valid TensorProto.DataType value
  optional int32 data_type = 2;

  // For very large tensors, we may want to store them in chunks, in which
  // case the following fields will specify the segment that is stored in
  // the current TensorProto.
  message Segment {
    optional int64 begin = 1;
    optional int64 end = 2;
  }
  optional Segment segment = 3;

  // Tensor content must be organized in row-major order.
  //
  // Depending on the data_type field, exactly one of the fields below with
  // name ending in _data is used to store the elements of the tensor.

  // For float and complex64 values
  // Complex64 tensors are encoded as a single array of floats,
  // with the real components appearing in odd numbered positions,
  // and the corresponding imaginary component appearing in the
  // subsequent even numbered position. (e.g., [1.0 + 2.0i, 3.0 + 4.0i]
  // is encoded as [1.0, 2.0 ,3.0 ,4.0]
  // When this field is present, the data_type field MUST be FLOAT or COMPLEX64.
  repeated float float_data = 4 [packed = true];

  // For int32, uint8, int8, uint16, int16, bool, and float16 values
  // float16 values must be bit-wise converted to an uint16_t prior
  // to writing to the buffer.
  // When this field is present, the data_type field MUST be
  // INT32, INT16, INT8, UINT16, UINT8, BOOL, or FLOAT16
  repeated int32 int32_data = 5 [packed = true];

  // For strings.
  // Each element of string_data is a UTF-8 encoded Unicode
  // string. No trailing null, no leading BOM. The protobuf "string"
  // scalar type is not used to match ML community conventions.
  // When this field is present, the data_type field MUST be STRING
  repeated bytes string_data = 6;

  // For int64.
  // When this field is present, the data_type field MUST be INT64
  repeated int64 int64_data = 7 [packed = true];

  // Optionally, a name for the tensor.
  optional string name = 8; // namespace Value

  // A human-readable documentation for this tensor. Markdown is allowed.
  optional string doc_string = 12;

  // Serializations can either use one of the fields above, or use this
  // raw bytes field. The only exception is the string case, where one is
  // required to store the content in the repeated bytes string_data field.
  //
  // When this raw_data field is used to store tensor value, elements MUST
  // be stored in as fixed-width, little-endian order.
  // Floating-point data types MUST be stored in IEEE 754 format.
  // Complex64 elements must be written as two consecutive FLOAT values, real component first.
  // Complex128 elements must be written as two consecutive DOUBLE values, real component first.
  // Boolean type MUST be written one byte per tensor element (00000001 for true, 00000000 for false).
  //
  // Note: the advantage of specific field rather than the raw_data field is
  // that in some cases (e.g. int data), protobuf does a better packing via
  // variable length storage, and may lead to smaller binary footprint.
  // When this field is present, the data_type field MUST NOT be STRING or UNDEFINED
  optional bytes raw_data = 9;

  // Data can be stored inside the protobuf file using type-specific fields or raw_data.
  // Alternatively, raw bytes data can be stored in an external file, using the external_data field.
  // external_data stores key-value pairs describing data location. Recognized keys are:
  // - "location" (required) - POSIX filesystem path relative to the directory where the ONNX
  //                           protobuf model was stored
  // - "offset" (optional) - position of byte at which stored data begins. Integer stored as string.
  //                         Offset values SHOULD be multiples 4096 (page size) to enable mmap support.
  // - "length" (optional) - number of bytes containing data. Integer stored as string.
  // - "checksum" (optional) - SHA1 digest of file specified in under 'location' key.
  repeated StringStringEntryProto external_data = 13;

  // Location of the data for this tensor. MUST be one of:
  // - DEFAULT - data stored inside the protobuf message. Data is stored in raw_data (if set) otherwise in type-specified field.
  // - EXTERNAL - data stored in an external location as described by external_data field.
  enum DataLocation {
    DEFAULT = 0;
    EXTERNAL = 1;
  }

  // If value not set, data is stored in raw_data (if set) otherwise in type-specified field.
  optional DataLocation data_location = 14;

  // For double
  // Complex128 tensors are encoded as a single array of doubles,
  // with the real components appearing in odd numbered positions,
  // and the corresponding imaginary component appearing in the
  // subsequent even numbered position. (e.g., [1.0 + 2.0i, 3.0 + 4.0i]
  // is encoded as [1.0, 2.0 ,3.0 ,4.0]
  // When this field is present, the data_type field MUST be DOUBLE or COMPLEX128
  repeated double double_data = 10 [packed = true];

  // For uint64 and uint32 values
  // When this field is present, the data_type field MUST be
  // UINT32 or UINT64
  repeated uint64 uint64_data = 11 [packed = true];
}

// A serialized sparse-tensor value
message SparseTensorProto {
  // The sequence of non-default values are encoded as a tensor of shape [NNZ].
  // The default-value is zero for numeric tensors, and empty-string for string tensors.
  // values must have a non-empty name present which serves as a name for SparseTensorProto
  // when used in sparse_initializer list.
  optional TensorProto values = 1;

  // The indices of the non-default values, which may be stored in one of two formats.
  // (a) Indices can be a tensor of shape [NNZ, rank] with the [i,j]-th value
  // corresponding to the j-th index of the i-th value (in the values tensor).
  // (b) Indices can be a tensor of shape [NNZ], in which case the i-th value
  // must be the linearized-index of the i-th value (in the values tensor).
  // The linearized-index can be converted into an index tuple (k_1,...,k_rank)
  // using the shape provided below.
  // The indices must appear in ascending order without duplication.
  // In the first format, the ordering is lexicographic-ordering:
  // e.g., index-value [1,4] must appear before [2,1]
  optional TensorProto indices = 2;

  // The shape of the underlying dense-tensor: [dim_1, dim_2, ... dim_rank]
  repeated int64 dims = 3;
}

// Defines a tensor shape. A dimension can be either an integer value
// or a symbolic variable. A symbolic variable represents an unknown
// dimension.
message TensorShapeProto {
  message Dimension {
    oneof value {
      int64 dim_value = 1;
      string dim_param = 2;   // namespace Shape
    };
    // Standard denotation can optionally be used to denote tensor
    // dimensions with standard semantic descriptions to ensure
    // that operations are applied to the correct axis of a tensor.
    // Refer to https://github.com/onnx/onnx/blob/main/docs/DimensionDenotation.md#denotation-definition
    // for pre-defined dimension denotations.
    optional string denotation = 3;
  };
  repeated Dimension dim = 1;
}

// Types
//
// The standard ONNX data types.
message TypeProto {

  message Tensor {
    // This field MUST NOT have the value of UNDEFINED
    // This field MUST have a valid TensorProto.DataType value
    // This field MUST be present for this version of the IR.
    optional int32 elem_type = 1;
    optional TensorShapeProto shape = 2;
  }

  // repeated T
  message Sequence {
    // The type and optional shape of each element of the sequence.
    // This field MUST be present for this version of the IR.
    optional TypeProto elem_type = 1;
  };

  // map<K,V>
  message Map {
    // This field MUST have a valid TensorProto.DataType value
    // This field MUST be present for this version of the IR.
    // This field MUST refer to an integral type ([U]INT{8|16|32|64}) or STRING
    optional int32 key_type = 1;
    // This field MUST be present for this version of the IR.
    optional TypeProto value_type = 2;
  };

  // wrapper for Tensor, Sequence, or Map
  message Optional {
    // The type and optional shape of the element wrapped.
    // This field MUST be present for this version of the IR.
    // Possible values correspond to OptionalProto.DataType enum
    optional TypeProto elem_type = 1;
  };


  message SparseTensor {
    // This field MUST NOT have the value of UNDEFINED
    // This field MUST have a valid TensorProto.DataType value
    // This field MUST be present for this version of the IR.
    optional int32 elem_type = 1;
    optional TensorShapeProto shape = 2;
  }


  oneof value {
    // The type of a tensor.
    Tensor tensor_type = 1;

    // NOTE:  DNN-only implementations of ONNX MAY elect to not support non-tensor values
    //        as input and output to graphs and nodes. These types are needed to naturally
    //        support classical ML operators.  DNN operators SHOULD restrict their input
    //        and output types to tensors.

    // The type of a sequence.
    Sequence sequence_type = 4;

    // The type of a map.
    Map map_type = 5;

    // The type of an optional.
    Optional optional_type = 9;


    // Type of the sparse tensor
    SparseTensor sparse_tensor_type = 8;

  }

  // An optional denotation can be used to denote the whole
  // type with a standard semantic description as to what is
  // stored inside. Refer to https://github.com/onnx/onnx/blob/main/docs/TypeDenotation.md#type-denotation-definition
  // for pre-defined type denotations.
  optional string denotation = 6;
}

// Operator Sets
//
// OperatorSets are uniquely identified by a (domain, opset_version) pair.
message OperatorSetIdProto {
  // The domain of the operator set being identified.
  // The empty string ("") or absence of this field implies the operator
  // set that is defined as part of the ONNX specification.
  // This field MUST be present in this version of the IR when referring to any other operator set.
  optional string domain = 1;

  // The version of the operator set being identified.
  // This field MUST be present in this version of the IR.
  optional int64 version = 2;
}

// Operator/function status.
enum OperatorStatus {
    EXPERIMENTAL = 0;
    STABLE = 1;
}

message FunctionProto {
  // The name of the function, similar usage of op_type in OperatorProto.
  // Combined with FunctionProto.domain, this forms the unique identity of
  // the FunctionProto.
  optional string name = 1;

  // Deprecated since IR Version 8
  // optional int64 since_version = 2;
  reserved 2;
  reserved "since_version";

  // Deprecated since IR Version 8
  // optional OperatorStatus status = 3;
  reserved 3;
  reserved "status";

  // The inputs and outputs of the function.
  repeated string input = 4;
  repeated string output = 5;

  // The attributes of the function.
  repeated string attribute = 6;

  // The nodes in the function.
  repeated NodeProto node = 7;
  // A human-readable documentation for this function. Markdown is allowed.
  optional string doc_string = 8;

  // The OperatorSets this function body (graph) relies on.
  //
  // All nodes in the function body (graph) will bind against the operator
  // with the same-domain/same-op_type operator with the HIGHEST version
  // in the referenced operator sets. This means at most one version can be relied
  // for one domain.
  //
  // The operator sets imported by FunctionProto should be compatible with the ones
  // imported by ModelProto. Example, if same operator set say 'A' is imported by FunctionProto
  // and ModelProto then versions for the operator set may be different but,
  // the operator schema returned for op_type, domain, version combination
  // for both the versions should be same.

  repeated OperatorSetIdProto opset_import = 9;

  // The domain which this function belongs to. Combined with FunctionProto.name, this forms the unique identity of
  // the FunctionProto.
  optional string domain = 10;
}


// For using protobuf-lite
option optimize_for = LITE_RUNTIME;