Web Neural Network API

54 min read Original article ↗

1. Introduction

We’re working on this section. Meanwhile, please take a look at the explainer.

2. Use cases

2.1. Application Use Cases

This section illustrates application-level use cases for neural network inference hardware acceleration. All applications in those use cases can be built on top of pre-trained deep neural network (DNN) [models].

2.1.1. Person Detection

A user opens a web-based video conferencing application, but she temporarily leaves from her room. The application is watching whether she is in front of her PC by using object detection (for example, using object detection approaches such as [SSD] or [YOLO] that use a single DNN) to detect regions in a camera input frame that include persons.

When she comes back, the application automatically detects her and notifies other online users that she is active now.

2.1.2. Semantic Segmentation

A user joins a teleconference via a web-based video conferencing application at her desk since no meeting room in her office is available. During the teleconference, she does not wish that her room and people in the background are visible. To protect the privacy of the other people and the surroundings, the application runs a machine learning model such as [DeepLabv3+] or [MaskR-CNN] to semantically split an image into segments and replaces segments that represent other people and background with another picture.

2.1.3. Skeleton Detection

A web-based video conferencing application tracks a pose of user’s skeleton by running a machine learning model, which allows for real-time human pose estimation, such as [PoseNet] to recognize her gesture and body language. When she raises her hand, her microphone is automatically unmuted and she can start speaking on the teleconference.

2.1.4. Face Recognition

There are multiple people in the conference room and they join an online meeting using a web-based video conferencing application. The application detects faces of participants by using object detection (for example, using object detection approaches such as [SSD]) and checks whether each face was present at the previous meeting or not by running a machine learning model such as [FaceNet], which verifies whether two faces would be identical or not.

2.1.5. Facial Landmark Detection

A user wants to find new glasses that beautifully fits her on an online glasses store. The online store offers web-based try-on simulator that runs a machine learning model such as Face Alignment Network [FAN] to detect facial landmarks like eyes, nose, mouth, etc. When she chooses a pair of glasses, the simulator properly renders the selected glasses on the detected position of eyes on her facial image.

2.1.6. Style Transfer

A user is looking for cosmetics on an online store and wondering which color may fit her face. The online store shows sample facial makeup images of cosmetics, and offers makeup simulator that runs a machine learning model like [ContextualLoss] or [PairedCycleGAN] to transfer the makeup style of the sample makeup image to her facial image. She can check how the selected makeup looks like on her face by the simulator.

2.1.7. Super Resolution

A web-based video conferencing is receiving a video stream from its peer, but the resolution of the video becomes lower due to network congestion. To prevent degradation of the perceived video quality, the application runs a machine learning model for super-resolution such as [SRGAN] to generate higher-resolution video frames.

2.1.8. Image Captioning

For better accessibility, a web-based presentation application provides automatic image captioning by running a machine learning model such as [im2txt] which predicts explanatory words of the presentation slides.

2.1.9. Machine Translation

Multiple people from various countries are talking via a web-based real-time text chat application. The application translates their conversation by using a machine learning model such as [GNMT] or [OpenNMT], which translates every text into different language.

2.1.10. Emotion Analysis

A user is talking to her friend via a web-based real-time text chat application, and she is wondering how the friend feels because she cannot see the friend’s face. The application analyses the friend’s emotion by using a machine learning model such as [DeepMoji], which infers emotion from input texts, and displays an emoji that represents the estimated emotion.

2.1.11. Video Summarization

A web-based video conferencing application records received video streams, and it needs to reduce recorded video data to be stored. The application generates the short version of the recorded video by using a machine learning model for video summarization such as [Video-Summarization-with-LSTM].

2.1.12. Noise Suppression

A web-based video conferencing application records received audio streams, but usually the background noise is everywhere. The application leverages real-time noise suppression using Recurrent Neural Network such as [RNNoise] for suppressing background dynamic noise like baby cry or dog barking to improve audio experiences in video conferences.

2.2. Framework Use Cases

This section collects framework-level use cases for a dedicated low-level API for neural network inference hardware acceleration. It is expected that Machine Learning frameworks will be key consumers of the Web Neural Network API (WebNN API) and the low-level details exposed through the WebNN API are abstracted out from typical web developers. However, it is also expected that web developers with specific interest and competence in Machine Learning will want to interface with the WebNN API directly instead of a higher-level ML framework.

2.2.1. Custom Layer

A web application developer wants to run a DNN model on the WebNN API. However, she has found that some of activation functions like [LeakyReLU], [ELU], etc. are not included in the WebNN API. To address this issue, she constructs custom layers of the additional activation functions on top of the WebNN API. Note that the scope of custom layers may include convolution, normalization, etc. as well as activation.

2.2.2. Network Concatenation

A web application uses a DNN model, and its model data of upper convolutional layers and lower fully-connected layers are stored in separate files, since model data of the fully-connected layers are periodically updated due to fine tuning at the server side.

Therefore, the application downloads both partial model files at first and concatenates them into a single model. When the model is updated, the application downloads fine-tuned part of the model and replace only the fully-connected layers with it.

2.2.3. Performance Adaptation

A web application developer has a concern about performance of her DNN model on mobile devices. She has confirmed that it may run too slow on mobile devices which do not have GPU acceleration. To address this issue, her web application refers to the WebNN API to confirm whether acceleration is available or not, so that the application can display the warning for devices without acceleration.

After several weeks, she has developed a tiny DNN model that can even run on CPU. In order to accommodate CPU execution, she modifies the application so that the application loads the tiny model in the case of CPU-only devices.

2.2.4. Operation Level Execution

A JavaScript ML framework is responsible for loading, interpreting and executing a ML model. During the model execution phase, the framework iterates through the operations of the model and executes each operation on the hardware device, like CPU, GPU or ML accelerator. To avoid the unnecessary data copying across devices, the framework selects the same device to execute the operations. For a compute intensive operation, such as convolution 2D or matrix multiplication, the framework uses WebNN API to execute it with the ML-specific acceleration available on that selected device.

3. Security Considerations

This API is disabled by default in all cross-origin frames using the § 6.2.1 Permissions Policy Integration. This prevents third-party content from using this API unless the embedding page explicitly sets a policy that grants permission.

This API allows creation of an MLContext from a GPUDevice or WebGLRenderingContext defined by WebGPU and WebGL specifications respectively. See WebGPU Security Considerations and WebGL Security Consideration for more information regarding security characteristics of these contexts.

4. Privacy Considerations

This API enhances privacy compared to cloud-based inference, since input data such as locally sourced images or video streams stay within the browser’s sandbox.

This API exposes the minimum amount of information necessary to address the identified § 2 Use cases for the best performance and reliability of results.

No information from the underlying platform is exposed directly. An execution time analysis may reveal indirectly the performance of the underlying platform’s neural network hardware acceleration capabilities relative to another underlying platform.

Note: The group is soliciting further input on the proposed execution time analysis fingerprinting vector and will augment this section with more information and mitigations to inform the implementers of this API.

Implementers of this API are expected to be familiar with the WebGPU Privacy Considerations.

5. Programming Model

5.1. Device Selection

An MLContext interface represents a global state of neural network execution. One of the important context states is the underlying execution device that manages the resources and facilitates the compilation and the eventual execution of the neural network graph. An MLContext could be created from a specific GPU device such as GPUDevice or WebGLRenderingContext that is already in use by the application, in which case the corresponding GPUBuffer or WebGLBuffer resources used as graph constants, as well as the GPUTexture and WebGLTexture as graph inputs must also be created from the same device. In a multi-adapter configuration, the device used for MLContext must be created from the same adapter as the device used to allocate the resources referenced in the graph.

In a situation when a GPU context executes a graph with a constant or an input in the system memory as an ArrayBufferView, the input content is automatically uploaded from the system memory to the GPU memory, and downloaded back to the system memory of an ArrayBufferView output buffer at the end of the graph execution. This data upload and download cycles will only occur whenever the execution device requires the data to be copied out of and back into the system memory, such as in the case of the GPU. It doesn’t occur when the device is a CPU device. Additionally, the result of the graph execution is in a known layout format. While the execution may be optimized for a native memory access pattern in an intermediate result within the graph, the output of the last operation of the graph must convert the content back to a known layout format at the end of the graph in order to maintain the expected behavior from the caller’s perspective.

When an MLContext is created with MLContextOptions, the user agent selects and creates the underlying execution device by taking into account the application’s preference specified in the MLPowerPreference and the MLDevicePreference options:

  • The "gpu" device provides the broadest range of achievable performance across graphics hardware platforms from consumer devices to professional workstations.

  • The "cpu" device provides the broadest reach of software compute availability, but with limited scalability of execution performance on the more complex neural networks.

  • When the device preference is not specified ("default"), the user agent selects the most suitable device to use.

The following table summarizes the types of resource supported by the device selected.

Device Type ArrayBufferView GPUBuffer GPUTexture WebGLBuffer WebGLTexture
GPUDevice Yes Yes Yes No No
WebGLRenderingContext Yes No No Yes Yes
default Yes No No No No
gpu Yes No No No No
cpu Yes No No No No

6. API

6.1. navigator.ml

A ML object is available in the Window and DedicatedWorkerGlobalScope contexts through the Navigator and WorkerNavigator interfaces respectively and is exposed via navigator.ml:

interface mixin NavigatorML {
  [SecureContext, SameObject] readonly attribute ML ml;
};
Navigator includes NavigatorML;
WorkerNavigator includes NavigatorML;

6.2. ML

enum MLDevicePreference {
  "default",
  "gpu",
  "cpu"
};

enum MLPowerPreference {
  // Let the user agent select the most suitable behavior.
  "default",

  // Prioritizes execution speed over power consumption.
  "high-performance",
  
  // Prioritizes power consumption over other considerations such as execution speed.
  "low-power"
};

dictionary MLContextOptions {
  // Preferred kind of device used
  MLDevicePreference devicePreference = "default";

  // Preference as related to power consumption
  MLPowerPreference powerPreference = "default";
};

[SecureContext, Exposed=(Window, DedicatedWorker)]
interface ML {
  // Create a context with options
  MLContext createContext(optional MLContextOptions options = {});

  // Create a context from WebGL rendering context
  MLContext createContext(WebGLRenderingContext glContext);

  // Create a context from WebGPU device
  MLContext createContext(GPUDevice gpuDevice);
};
======= The createContext() method steps are:

  1. If the responsible document is not allowed to use the webnn feature, then throw a "SecurityError" DOMException and abort these steps.

  2. Let context be a new MLContext object.

  3. Switch on the method’s first argument:

    MLContextOptions
    Set context’s context type to default.
    WebGLRenderingContext
    Set context’s context type to webgl.
    GPUDevice
    Set context’s context type to webgpu.
    Otherwise
    Set context’s context type to default.

  4. Return context.

6.2.1. Permissions Policy Integration

This specification defines a policy-controlled feature identified by the string "webnn". Its default allowlist is 'self'.

6.3. MLContext

The MLContext interface represents a global state of neural network compute workload and execution processes. 
[SecureContext, Exposed=(Window, DedicatedWorker)]
interface MLContext {};

The context type for an MLContext is either "default", "webgl" or "webgpu".

6.4. MLOperandDescriptor

enum MLInputOperandLayout {
  "nchw",
  "nhwc"
};

enum MLOperandType {
  "float32",
  "float16",
  "int32",
  "uint32",
  "int8",
  "uint8"
};

dictionary MLOperandDescriptor {
  // The operand type.
  required MLOperandType type;

  // The dimensions field is only required for tensor operands.
  // The negative value means an unknown dimension.
  sequence<long> dimensions;
};

6.5. MLOperand

[SecureContext, Exposed=(Window, DedicatedWorker)]
interface MLOperand {};

6.6. MLGraphBuilder

The MLGraphBuilder interface defines a set of operations as identified by the § 2 Use cases that can be composed into a computational graph. It also represents the intermediate state of a graph building session.

typedef record<DOMString, MLOperand> MLNamedOperands;

dictionary MLBufferResourceView {
  required (WebGLBuffer or GPUBuffer) resource;
  unsigned long long offset = 0;
  unsigned long long size;
};

typedef (ArrayBufferView or MLBufferResourceView) MLBufferView;

[SecureContext, Exposed=(Window, DedicatedWorker)]
interface MLGraphBuilder {
  // Construct the graph builder from the context.
  constructor(MLContext context);

  // Create an operand for a graph input.
  MLOperand input(DOMString name, MLOperandDescriptor desc);

  // Create an operand for a graph constant.
  MLOperand constant(MLOperandDescriptor desc, MLBufferView bufferView);

  // Create a single-value operand from the specified number of the specified type.
  MLOperand constant(double value, optional MLOperandType type = "float32");

  // Compile the graph up to the specified output operands
  MLGraph build(MLNamedOperands outputs);
};

6.6.1. batchNormalization

Normalize the tensor values of input features across the batch dimension using [Batch-Normalization]. For each input feature, the mean and variance values of that feature supplied in this calculation as parameters are previously computed across the batch dimension of the input during the model training phrase of this operation. 
dictionary MLBatchNormalizationOptions {
  MLOperand scale;
  MLOperand bias;
  long axis = 1;
  float epsilon = 1e-5;
};

partial interface MLGraphBuilder {
  MLOperand batchNormalization(MLOperand input, MLOperand mean, MLOperand variance,
                             optional MLBatchNormalizationOptions options = {});
};

Arguments:

  • input: an MLOperand. The input N-D tensor.

  • mean: an MLOperand. The 1-D tensor of the mean values of the input features across the batch whose length is equal to the size of the input dimension denoted by options.axis.

  • variance: an MLOperand. The 1-D tensor of the variance values of the input features across the batch whose length is equal to the size of the input dimension denoted by options.axis.

  • options: an optional MLBatchNormalizationOptions. The optional parameters of the operation.

    • scale: an MLOperand. The 1-D tensor of the scaling values whose length is equal to the size of the input dimension denoted by options.axis.

    • bias: an MLOperand. The 1-D tensor of the bias values whose length is equal to the size of the input dimension denoted by options.axis.

    • axis: a long scalar. The index to the feature count dimension of the input shape for which the mean and variance values are. When it’s not specified, the default value is 1.

    • epsilon: a float scalar. A small value to prevent computational error due to divide-by-zero. The default value is 0.00001 when not specified.

Returns: an MLOperand. The batch-normalized N-D tensor of the same shape as the input tensor.

When input is a 4-D tensor of the "nchw" or "nhwc" layout, options.axis should be set to 1 or 3 respectively. The axis value designates the feature or channel count dimension of the input tensor.

The behavior of this operation when the input tensor is 4-D of the "nchw" layout can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

const shape = [1,-1,1,1];
return builder.add(
    builder.mul(
      builder.reshape(options.scale, shape),
      builder.div(
        builder.sub(input, builder.reshape(mean, shape)),
        builder.pow(
          builder.add(builder.reshape(variance, shape), builder.constant(options.epsilon)),
          builder.constant(0.5))
        )
      ),
    builder.reshape(options.bias, shape)
  );

6.6.2. clamp

Clamp the input tensor element-wise within a range specified by the minimum and maximum values. 
dictionary MLClampOptions {
  MLOperand minValue;
  MLOperand maxValue;
};

partial interface MLGraphBuilder {
  MLOperand clamp(MLOperand x, optional MLClampOptions options = {});
};

Arguments:

  • x: an MLOperand. The input tensor.

  • options: an optional MLClampOptions. The optional parameters of the operation.

    • minValue: an MLOperand. Specifies the minimum values of the range. It is either a scalar, or of the shape that is unidirectionally broadcastable to the shape of x according to [numpy-broadcasting-rule]. When it is not specified, the clamping is not performed on the lower limit of the range.

    • maxValue: an MLOperand. Specifies the maximum values of the range. It is either a scalar, or of the shape that is unidirectionally broadcastable to the shape of x according to [numpy-broadcasting-rule]. When it is not specified, the clamping is not performed on the upper limit of the range.

Returns: an MLOperand. The output tensor of the same shape as x.

Clamp the input tensor element-wise within a range specified by minValue and maxValue. The calculation follows the expression min(max(x, minValue), maxValue). When minValue is not specified, the clamping is not performed on the lower limit. When maxValue is not specified, the clamping is not performed on the upper limit.

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

if (options.minValue === undefined) {
  if (options.maxValue === undefined) {
    return x;
  } else {
    return builder.min(x, options.maxValue);
  }
} else {
  if (options.maxValue === undefined) {
    return builder.max(x, options.minValue);
  } else {
    return builder.min(builder.max(x, options.minValue), options.maxValue);
  }
}

6.6.3. concat

Concatenates the input tensors along a given axis. 
partial interface MLGraphBuilder {
  MLOperand concat(sequence<MLOperand> inputs, long axis);
};

Arguments:

  • inputs: a sequence of MLOperand. All input tensors must have the same shape, except for the size of the dimension to concatenate on.

  • axis: a long scalar. The axis that the inputs concatenate along, with the value in the interval [0, N) where N is the rank of all the inputs.

Returns: an MLOperand. The concatenated tensor of all the inputs along the axis. The output tensor has the same shape except on the dimension that all the inputs concatenated along. The size of that dimension is computed as the sum of all the input sizes of the same dimension.

6.6.4. conv2d

Compute a 2-D convolution given 4-D input and filter tensors 
enum MLFilterOperandLayout {
  "oihw",
  "hwio",
  "ohwi",
  "ihwo"
};

enum MLAutoPad {
  "explicit",
  "same-upper",
  "same-lower"
};

dictionary MLConv2dOptions {
  sequence<long> padding;
  sequence<long> strides;
  sequence<long> dilations;
  sequence<long> outputPadding;
  sequence<long> outputSizes;
  MLAutoPad autoPad = "explicit";
  boolean transpose = false;
  long groups = 1;
  MLInputOperandLayout inputLayout = "nchw";
  MLFilterOperandLayout filterLayout = "oihw";
};

partial interface MLGraphBuilder {
  MLOperand conv2d(MLOperand input, MLOperand filter, optional MLConv2dOptions options = {});
};

Arguments:

  • input: an MLOperand. The input 4-D tensor. The logical shape is interpreted according to the value of options.layout.

  • filter: an MLOperand. The filter 4-D tensor. The logical shape is interpreted according to the value of options.layout and options.groups.

  • options: an optional MLConv2dOptions. The optional parameters of the operation.

    • padding: a sequence of long of length 4. The additional rows and columns added to the beginning and ending of each spatial dimension of input, [beginning_height, ending_height, beginning_width, ending_width]. If not present, the values are assumed to be [0,0,0,0].

    • strides: a sequence of long of length 2. The stride of the sliding window for each spatial dimension of input, [stride_height, stride_width]. If not present, the values are assumed to be [1,1].

    • dilations: a sequence of long of length 2. The dilation factor for each spatial dimension of input, [dilation_height, dilation_width]. If not present, the values are assumed to be [1,1].

    • outputPadding: a sequence of long of length 2. The padding values applied to each spatial dimension of the output tensor when options.transpose is set to true. This explicit padding values are needed to disambiguate the output tensor shape for transposed convolution when the value of the options.strides is greater than 1. Note that these values are only used to disambiguate output shape when needed; it does not necessarily cause any padding value to be written to the output tensor. If not specified, the values are assumed to be [0,0].

    • outputSizes: a sequence of long of length 2. The sizes of the last two dimensions of the output tensor when options.transpose is set to true. When the output sizes are explicitly specified, the output padding values in options.outputPadding are ignored. If not specified, the output sizes are automatically computed.

    • autoPad: an MLAutoPad. The automatic input padding options. By default, this argument is set to "explicit", which means that the values in the options.padding array should be used for input padding. When the option is set other than "explicit", the values in the options.padding array are ignored. With the "same-upper" option, the padding values are automatically computed such that the additional ending padding of the spatial input dimensions would allow all of the input values in the corresponding dimension to be filtered. The "same-lower" option is similar but padding is applied to the beginning padding of the spatial input dimensions instead of the ending one.

    • transpose: a boolean indicating that a transposed convolution operation is performed. Transposed convolution is used in upsampling networks to increase the resolution of a feature as opposed to the typical convolution process that reduces the feature’s resolution. When transposed convolution is performed, options.outputPadding may be needed to disambiguate the output tensor shape. If not present, this option is assumed to be false.

    • groups: a long scalar. The number of groups that input channels and output channels are divided into, default to 1.

    • inputLayout: an MLInputOperandLayout. The default value is "nchw". This option specifies the layout format of the input and output tensor as follow:

      "nchw":

      • input tensor: [batches, input_channels, height, width]

      • output tensor: [batches, output_channels, height, width]

      "nhwc":

      • input tensor: [batches, height, width, input_channels]

      • output tensor: [batches, height, width, output_channels]

    • filterLayout: a MLFilterOperandLayout. The default value is "oihw". This option specifies the layout format of the filter tensor as follow:

      "oihw":

      • [output_channels, input_channels/groups, height, width]

      "hwio":

      • [height, width, input_channels/groups, output_channels]

      "ohwi":

      • [output_channels, height, width, input_channels/groups]

      "ihwo":

      • [input_channels/groups, height, width, output_channels]

Returns: an MLOperand. The output 4-D tensor that contains the convolution result. The output shape is interpreted according to the options.layout value. More specifically the sizes of the last two dimensions of the output tensor, the spatial dimensions, for the convolution operation can be calculated as follow:

output size = 1 + (input size - filter size + beginning padding + ending padding) / stride

Whereas for the transposed convolution case with options.transpose set to true, unless the options.outputSizes values are explicitly specified, the options.outputPadding may be needed to compute the spatial dimension values of the output tensor as follow:

output size = (input size - 1) * stride + filter size - beginning padding - ending padding + output padding

A depthwise conv2d operation is a variant of grouped convolution, used in models like the MobileNet, where the options.groups = input_channels = output_channels and the shape of filter tensor is [options.groups, 1, height, width] for "oihw" layout, [height, width, 1, options.groups] for "hwio" layout, [options.groups, height, width, 1] for "ohwi" layout and [1, height, width, options.groups] for "ihwo" layout.

6.6.5. element-wise binary operations

Compute the element-wise binary addition, subtraction, multiplication, division, maximum and minimum of the two input tensors. 
partial interface MLGraphBuilder {
  MLOperand add(MLOperand a, MLOperand b);
  MLOperand sub(MLOperand a, MLOperand b);
  MLOperand mul(MLOperand a, MLOperand b);
  MLOperand div(MLOperand a, MLOperand b);
  MLOperand max(MLOperand a, MLOperand b);
  MLOperand min(MLOperand a, MLOperand b);
  MLOperand pow(MLOperand a, MLOperand b);
};

Arguments:

Returns: an MLOperand. The output tensor that contains the result of element-wise binary operation of the two input tensors.

The element-wise binary operation will be broadcasted according to [numpy-broadcasting-rule]. The rank of the output tensor is the maximum rank of the input tensors. For each dimension of the output tensor, its size is the maximum size along that dimension of the input tensors.

Operation types:

  • add: Add the values of the two input tensors, element-wise.

  • sub: Subtract the values of the second input tensor from the values of the first input tensor, element-wise.

  • mul: Multiply the values of the two input tensors, element-wise.

  • div: Divide the values of the first input tensor with the values of the second tensor, element-wise.

  • max: Select the greater values of the two input tensors, element-wise.

  • min: Select the lesser values of the two input tensors, element-wise.

  • pow: Compute the values of the values of the first input tensor to the power of the values of the second input tensor, element-wise.

6.6.6. element-wise unary operations

Compute the element-wise unary operation for input tensor. 
partial interface MLGraphBuilder {
  MLOperand abs(MLOperand x);
  MLOperand ceil(MLOperand x);
  MLOperand cos(MLOperand x);
  MLOperand exp(MLOperand x);
  MLOperand floor(MLOperand x);
  MLOperand log(MLOperand x);
  MLOperand neg(MLOperand x);
  MLOperand relu(MLOperand x);
  MLOperand sigmoid(MLOperand x);
  MLOperand sin(MLOperand x);
  MLOperand tan(MLOperand x);
  MLOperand tanh(MLOperand x);
};

Arguments:

Returns: an MLOperand. The output tensor that contains the result of element-wise unary operation of the input tensor. The shape of the output tensor is the same as the shape of input tensor.

Operation types:

  • abs: Compute the absolute value of the input tensor, element-wise.

  • ceil: Compute the ceiling of the input tensor, element-wise.

  • cos: Compute the cosine of the input tensor, element-wise.

  • exp: Compute the exponential of the input tensor, element-wise.

  • floor: Compute the floor of the input tensor, element-wise.

  • log: Compute the natural logarithm of the input tensor, element-wise.

  • neg: Compute the numerical negative value of the input tensor, element-wise.

  • relu: Compute the rectified linear function of the input tensor, element-wise.

    The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

    return builder.max(builder.constant(0), x);

  • sigmoid: Compute the sigmoid function of the input tensor, element-wise.

  • sin: Compute the sine of the input tensor, element-wise.

  • tan: Compute the tangent of the input tensor, element-wise.

  • tanh: Compute the hyperbolic tangent of the input tensor, element-wise.

6.6.7. gemm

Calculate the general matrix multiplication of the Basic Linear Algebra Subprograms. The calculation follows the expression alpha * A * B + beta * C, where A is a 2-D tensor with shape [M, K] or [K, M], B is a 2-D tensor with shape [K, N] or [N, K], and C is broadcastable to the shape [M, N]. A and B may optionally be transposed prior to the calculation. 
dictionary MLGemmOptions {
  MLOperand c;
  float alpha = 1.0;
  float beta = 1.0;
  boolean aTranspose = false;
  boolean bTranspose = false;
};

partial interface MLGraphBuilder {
  MLOperand gemm(MLOperand a, MLOperand b, optional MLGemmOptions options = {});
};

Arguments:

  • a: an MLOperand. The first input 2-D tensor with shape [M, K] if aTranspose is false, or [K, M] if aTranspose is true.

  • b: an MLOperand. The second input 2-D tensor with shape [K, N] if bTranspose is false, or [N, K] if bTranspose is true.

  • options: an optional MLGemmOptions. The optional parameters of the operation.

    • c: an MLOperand. The third input tensor. It is either a scalar, or of the shape that is unidirectionally broadcastable to the shape [M, N] according to [numpy-broadcasting-rule]. When it is not specified, the computation is done as if c is a scalar 0.0.

    • alpha: a float scalar multiplier for the first input, default to 1.0.

    • beta: a float scalar multiplier for the third input, default to 1.0.

    • aTranspose: a boolean indicating if the first input should be transposed prior to calculating the output, default to false.

    • bTranspose: a boolean indicating if the second input should be transposed prior to calculating the output, default to false.

Returns: an MLOperand. The output 2-D tensor of shape [M, N] that contains the calculated product of all the inputs.

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

if (options.aTranspose)
  a = builder.transpose(a);

if (options.bTranspose)
  b = builder.transpose(b);

let ab = builder.matmul(builder.mul(builder.constant(options.alpha), a), b);
return (c ? builder.add(ab, builder.mul(builder.constant(options.beta), c)) : ab);

6.6.8. gru

Gated Recurrent Unit [GRU] recurrent network using an update gate and a reset gate to compute the hidden state that rolls into the output across the temporal sequence of the Network 
enum MLRecurrentNetworkWeightLayout {
  "zrn",  // update-reset-new gate ordering
  "rzn"   // reset-update-new gate ordering
};

enum MLRecurrentNetworkActivation {
  "relu",
  "sigmoid",
  "tanh"
};

enum MLRecurrentNetworkDirection {
  "forward",
  "backward",
  "both"
};

dictionary MLGruOptions {
  MLOperand bias;
  MLOperand recurrentBias;
  MLOperand initialHiddenState;
  boolean resetAfter = true;
  boolean returnSequence = false;
  MLRecurrentNetworkDirection direction = "forward";
  MLRecurrentNetworkWeightLayout layout = "zrn";
  sequence<MLRecurrentNetworkActivation> activations;
};

partial interface MLGraphBuilder {
  sequence<MLOperand> gru(MLOperand input, MLOperand weight, MLOperand recurrentWeight, 
                        long steps, long hiddenSize, optional MLGruOptions options = {});
};

Arguments:

  • input: an MLOperand. The input 3-D tensor of shape [steps, batch_size, input_size].

  • weight: an MLOperand. The 3-D input weight tensor of shape [num_directions, 3 * hidden_size, input_size]. The ordering of the weight vectors in the second dimension of the tensor shape is specified according to the layout argument.

  • recurrentWeight: an MLOperand. The 3-D recurrent weight tensor of shape [num_directions, 3 * hidden_size, hidden_size]. The ordering of the weight vectors in the second dimension of the tensor shape is specified according to the layout argument.

  • steps: a long scalar. The number of time steps in the recurrent network. The value must be greater than 0.

  • hiddenSize: a long scalar. The value of the third dimension of the cell output tensor shape. It indicates the number of features in the hidden state.

  • options: an optional MLGruOptions. The optional parameters of the operation.

    • bias: an MLOperand. The 2-D input bias tensor of shape [num_directions, 3 * hidden_size]. The ordering of the bias vectors in the second dimension of the tensor shape is specified according to the options.layout argument.

    • recurrentBias: an MLOperand. The 2-D recurrent bias tensor of shape [num_directions, 3 * hidden_size]. The ordering of the bias vectors in the second dimension of the tensor shape is specified according to the options.layout argument.

    • initialHiddenState: an MLOperand. The 3-D initial hidden state tensor of shape [num_directions, batch_size, hidden_size]. When not specified, it’s assumed to be a tensor filled with zero.

    • resetAfter: a boolean indicating whether to apply the reset gate after or before matrix multiplication. Default to true.

    • returnSequence: a boolean indicating whether to also return the entire sequence with every cell output from each time step in it in addition to the cell output of the last time step. Default to false.

    • direction: a MLRecurrentNetworkDirection. The processing direction of the input sequence. When set to "both", the size of the first dimension of the weight and the bias tensor shapes must be 2, and the input is processed in both directions.

    • layout: a MLRecurrentNetworkWeightLayout. The ordering of the weight and bias vectors for the internal gates of GRU, specifically the update (z), reset (r), and new (n) gate, as indicated in the second dimension of the weight and bias tensor shape. When not specified, the default layout is "zrn".

    • activations: a sequence of MLRecurrentNetworkActivation. A pair of activation functions with the first function used for the update and reset gate, and the second used for the new gate. When not specified, it’s assumed to be the sigmoid ("sigmoid") and the hyperbolic tangent ("tanh") function respectively.

Returns: a sequence of MLOperand. The first element of the sequence is a 3-D tensor of shape [num_directions, batch_size, hidden_size], the cell output from the last time step of the network. Additionally, if returnSequence is set to true, the second element is the 4-D output tensor of shape [steps, num_directions, batch_size, hidden_size] containing every cell outputs from each time step in the temporal sequence.

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

const numDirections = (options.direction == "both" ? 2 : 1);
let hiddenState = options.initialHiddenState;

if (!hiddenState) {
  const desc = { type: 'float32', dimensions: [numDirections, 1, hiddenSize] };
  const totalSize = numDirections * hiddenSize;
  hiddenState = builder.constant(desc, new Float32Array(totalSize).fill(0));
}

let sequence = null;
let cellWeight = [];
let cellRecurrentWeight = [];
let cellBias = [];
let cellRecurrentBias = [];

for (let slot = 0; slot < numDirections; ++slot) {
  cellWeight.push(builder.squeeze(builder.slice(weight, [slot, 0, 0], [1, -1, -1]), { axes: [0] }));
  cellRecurrentWeight.push(builder.squeeze(builder.slice(recurrentWeight, [slot, 0, 0], [1, -1, -1]), { axes: [0] }));
  cellBias.push(options.bias ? (builder.squeeze(builder.slice(options.bias, [slot, 0], [1, -1]), { axes: [0] })) : null);
  cellRecurrentBias.push(options.recurrentBias ? 
    (builder.squeeze(builder.slice(options.recurrentBias, [slot, 0], [1, -1]), { axes: [0] })) : null);
}

for (let step = 0; step < steps; ++step) {
  let cellHidden = [];
  let cellOutput = null;

  for (let slot = 0; slot < numDirections; ++slot) {
    cellHidden.push(builder.squeeze(builder.slice(hiddenState, [slot, 0, 0], [1, -1, -1]), { axes: [0] }));
  }

  for (let slot = 0; slot < numDirections; ++slot) {
    let slice = (slot == 1 || options.direction == "backward" ? steps - step - 1 : step);
    let cellInput = builder.squeeze(builder.slice(input, [slice, 0, 0], [1, -1, -1]), { axes: [0] });

    let result = builder.reshape(
      builder.gruCell(
        cellInput, cellWeight[slot], cellRecurrentWeight[slot],
        cellHidden[slot], hiddenSize, { bias: cellBias[slot],
        recurrentBias: cellRecurrentBias[slot], resetAfter: options.resetAfter,
        layout: options.layout, activations: options.activations }),
      [1, -1, hiddenSize]);

    cellOutput = (cellOutput ? builder.concat([cellOutput, result], 0) : result);
  }

  hiddenState = cellOutput;

  if (options.returnSequence) {
    cellOutput = builder.reshape(cellOutput, [1, numDirections, -1, hiddenSize]);
    sequence = (sequence ? builder.concat([sequence, cellOutput], 0) : cellOutput);
  }
}

return (sequence ? [hiddenState, sequence] : [hiddenState]);

6.6.9. gruCell

A single time step of the Gated Recurrent Unit [GRU] recurrent network using an update gate and a reset gate to compute the hidden state that rolls into the output across the temporal sequence of a recurrent network. 
dictionary MLGruCellOptions {
  MLOperand bias;
  MLOperand recurrentBias;
  boolean resetAfter = true;
  MLRecurrentNetworkWeightLayout layout = "zrn";
  sequence<MLRecurrentNetworkActivation> activations;
};

partial interface MLGraphBuilder {
  MLOperand gruCell(MLOperand input, MLOperand weight, MLOperand recurrentWeight, 
                  MLOperand hiddenState, long hiddenSize, optional MLGruCellOptions options = {});
};

Arguments:

  • input: an MLOperand. The input 2-D tensor of shape [batch_size, input_size].

  • weight: an MLOperand. The 2-D input weight tensor of shape [3 * hidden_size, input_size]. The ordering of the weight vectors in the first dimension of the tensor shape is specified according to the layout argument.

  • recurrentWeight: an MLOperand. The 2-D recurrent weight tensor of shape [3 * hidden_size, hidden_size]. The ordering of the weight vectors in the first dimension of the tensor shape is specified according to the layout argument.

  • hiddenState: an MLOperand. The 2-D input hidden state tensor of shape [batch_size, hidden_size].

  • hiddenSize: a long scalar. The value of the second dimension of the output tensor shape. It indicates the number of features in the hidden state.

  • options: an optional MLGruCellOptions. The optional parameters of the operation.

    • bias: an MLOperand. The 1-D input bias tensor of shape [3 * hidden_size]. The ordering of the bias vectors in the first dimension of the tensor shape is specified according to the options.layout argument.

    • recurrentBias: an MLOperand. The 1-D recurrent bias tensor of shape [3 * hidden_size]. The ordering of the bias vectors in the first dimension of the tensor shape is specified according to the options.layout argument.

    • resetAfter: a boolean indicating whether to apply the reset gate after or before matrix multiplication. Default to true.

    • layout: a MLRecurrentNetworkWeightLayout. The ordering of the weight and bias vectors for the internal gates of GRU, specifically the update (z), reset (r), and new (n) gate, as indicated in the first dimension of the weight and bias tensor shapes. When not specified, the default layout is "zrn".

    • activations: a sequence of MLRecurrentNetworkActivation. A pair of activation functions with the first function used for the update and reset gate, and the second used for the new gate. When not specified, it’s default to the sigmoid ("sigmoid") and the hyperbolic tangent ("tanh") function respectively.

Returns: an MLOperand. The 2-D tensor of shape [batch_size, hidden_size], the cell output hidden state of a single time step of the recurrent network.

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

const one = builder.constant(1);
const zero = builder.constant(0);

// update gate
let z = builder.sigmoid(
  builder.add(
    builder.add(
      (options.bias ? builder.slice(options.bias, [0], [hiddenSize]) : zero), 
      (options.recurrentBias ? builder.slice(options.recurrentBias, [0], [hiddenSize]) : zero)
      ),
    builder.add(
      builder.matmul(
        input, 
        builder.transpose(builder.slice(weight, [0, 0], [hiddenSize, -1]))
        ),
      builder.matmul(
        hiddenState,
        builder.transpose(builder.slice(recurrentWeight, [0, 0], [hiddenSize, -1]))
        )
      )
    )
  );

// reset gate
let r = builder.sigmoid(
  builder.add(
    builder.add(
      (options.bias ? builder.slice(options.bias, [hiddenSize], [hiddenSize]) : zero),
      (options.recurrentBias ? builder.slice(options.recurrentBias, [hiddenSize], [hiddenSize]) : zero)
      ),
    builder.add(
      builder.matmul(
        input, 
        builder.transpose(builder.slice(weight, [hiddenSize, 0], [hiddenSize, -1]))
        ),
      builder.matmul(
        hiddenState, 
        builder.transpose(builder.slice(recurrentWeight, [hiddenSize, 0], [hiddenSize, -1]))
        )
      )
    )
  );

// new gate
let n;
if (resetAfter) {
  n = builder.tanh(
    builder.add(
      (options.bias ? builder.slice(options.bias, [2 * hiddenSize], [hiddenSize]) : zero),
      builder.add(
        builder.matmul(
          input, 
          builder.transpose(builder.slice(weight, [2 * hiddenSize, 0], [hiddenSize, -1]))
          ),
        builder.mul(
          r,
          builder.add(
            (options.recurrentBias ? builder.slice(options.recurrentBias, [2 * hiddenSize], [hiddenSize]) : zero),
            builder.matmul(
              hiddenState, 
              builder.transpose(builder.slice(recurrentWeight, [2 * hiddenSize, 0], [hiddenSize, -1]))
              )
            )
          )
        )
      )
    );
}
else {
  n = builder.tanh(
    builder.add(
      builder.add(
        (options.bias ? builder.slice(options.bias, [2 * hiddenSize], [hiddenSize]) : zero),
        (options.recurrentBias ? builder.slice(options.recurrentBias, [2 * hiddenSize], [hiddenSize]) : zero)
        ),
      builder.add(
        builder.matmul(
          input, 
          builder.transpose(builder.slice(weight, [2 * hiddenSize, 0], [hiddenSize, -1]))
          ),
        builder.matmul(
          builder.mul(r, hiddenState),
          builder.transpose(builder.slice(recurrentWeight, [2 * hiddenSize, 0], [hiddenSize, -1]))
          )
        )
      )
    );
}

// compute the new hidden state
return builder.add(builder.mul(z, hiddenState), builder.mul(n, builder.sub(one, z)));

6.6.10. instanceNormalization

Normalize the input features using [Instance-Normalization]. Unlike § 6.6.1 batchNormalization where the mean and variance values used in the calculation are previously computed across the batch dimension during the model training phrase, the mean and variance values used in the calculation of an instance normalization are computed internally on the fly per input feature. 
dictionary MLInstanceNormalizationOptions {
  MLOperand scale;
  MLOperand bias;
  float epsilon = 1e-5;
  MLInputOperandLayout layout = "nchw";
};

partial interface MLGraphBuilder {
  MLOperand instanceNormalization(MLOperand input, 
                                optional MLInstanceNormalizationOptions options = {});
};

Arguments:

  • input: an MLOperand. The input 4-D tensor.

  • options: an optional MLInstanceNormalizationOptions. The optional parameters of the operation.

    • scale: an MLOperand. The 1-D tensor of the scaling values whose length is equal to the size of the feature dimension of the input e.g. for the input tensor with nchw layout, the feature dimension is 1.

    • bias: an MLOperand. The 1-D tensor of the bias values whose length is equal to the size of the feature dimension of the input e.g. for the input tensor with nchw layout, the feature dimension is 1.

    • epsilon: a float scalar. A small value to prevent computational error due to divide-by-zero. The default value is 0.00001 when not specified.

    • layout: an MLInputOperandLayout. This option specifies the layout format of the input. The default value is "nchw".

Returns: an MLOperand. The instance-normalized 4-D tensor of the same shape as the input tensor.

The behavior of this operation when the input tensor is 4-D of the "nchw" layout can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

// The mean reductions happen over the spatial dimensions of the input
// e.g. axis 2 and 3 of the input tensor.
const reduceOptions = { axes: [2,3], keepDimensions: true };
const mean = builder.reduceMean(input, reduceOptions);
const variance = builder.reduceMean(
  builder.pow(
    builder.sub(input, mean), 
    buider.constant(2)),
  reduceOptions
  );

// The scale and bias values are applied per input feature
// e.g. axis 1 of the input tensor.
const shape = [1,-1,1,1];
return builder.add(
  builder.mul(
    builder.reshape(options.scale, shape),
    builder.div(
      builder.sub(input, mean),
      buidler.pow(
        builder.add(variance, options.epsilon), 
        builder.constant(0.5))
      )
    ),
  builder.reshape(options.bias, shape)
  );

6.6.11. leakyRelu

dictionary MLLeakyReluOptions {
  float alpha = 0.01;
};

partial interface MLGraphBuilder {
  MLOperand leakyRelu(MLOperand x, optional MLLeakyReluOptions options = {});
};

Arguments:

  • x: an MLOperand. The input tensor.

  • options: an optional MLLeakyReluOptions. The optional parameters of the operation.

    • alpha: a float scalar multiplier, default to 0.01.

Returns: an MLOperand. The output tensor of the same shape as x.

Calculate the leaky version of rectified linear function on the input tensor element-wise. The calculation follows the expression max(0, x) + alpha ∗ min(0, x).

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

return builder.add(builder.max(builder.constant(0), x),
          builder.mul(builder.constant(options.alpha), builder.min(builder.constant(0), x)));

6.6.12. matmul

Compute the matrix product of two input tensors. 
partial interface MLGraphBuilder {
  MLOperand matmul(MLOperand a, MLOperand b);
};

Arguments:

  • a: an MLOperand. The first input N-D tensor.

  • b: an MLOperand. The second input N-D tensor.

Returns: an MLOperand. The output N-D tensor that contains the matrix product of two input tensors.

Compute the matrix product of two input tensors. It behaves as following:

  • If both a and b are 2-D, they are multiplied like conventional matrices and produce a 2-D tensor as the output.

  • If either a or b is N-D, N > 2, it is treated as a stack of matrices with dimensions corresponding to the last two indices. The matrix multiplication will be broadcasted accordingly by following [numpy-broadcasting-rule]. The output is a N-D tensor whose rank is the maximum rank of the input tensors. For each dimension, except the last two, of the output tensor, its size is the maximum size along that dimension of the input tensors.

  • If a is 1-D, it is converted to a 2-D tensor by prepending a 1 to its dimensions.

  • If b is 1-D, it is converted to a 2-D tensor by by appending a 1 to its dimensions.

  • If both a and b are 1-D, the operation is a vector dot-product, which produces a scalar output.

6.6.13. pad

Inflate the tensor with constant or mirrored values on the edges. 
enum MLPaddingMode {
  "constant",
  "edge",
  "reflection",
  "symmetric"
};

dictionary MLPadOptions {
  MLPaddingMode mode = "constant";
  float value = 0;
};

partial interface MLGraphBuilder {
  MLOperand pad(MLOperand input, MLOperand padding, optional MLPadOptions options = {});
};

Arguments:

  • input: an MLOperand. The input tensor.

  • padding: an MLOperand. The 2-D Tensor of integer values indicating the number of padding values to add at the beginning and end of each input dimensions. The tensor has shape [n, 2] where n is the rank of the input tensor. For each dimension D of input, padding[D, 0] indicates how many values to add before the content in that dimension, and padding[D, 1] indicates how many values to add after the content in that dimension.

  • options: an optional MLPadOptions. The optional parameters of the operation.

    • mode: a MLPaddingMode. The different ways to pad the tensor. When not set, it’s assumed to be "constant".

    • value: a float. The pad value when the options.mode is set to "constant". When not set, it’s assumed to be 0.

Returns: an MLOperand. The padded output tensor.

// input: [[1,2,3], [4,5,6]]
const input = builder.constant(
  { type: 'float32', dimensions: [2,3] }, new Float32Array([1,2,3,4,5,6]));

// padding: [[1,1], [2,2]]
const padding = builder.constant(
  { type: 'float32', dimensions: [2,2] }, new Float32Array([1,1,2,2]));

// "constant" padded:
//    [[0,0,0,0,0,0,0],
//     [0,0,1,2,3,0,0],
//     [0,0,4,5,6,0,0],
//     [0,0,0,0,0,0,0]]
builder.pad(input, padding);

// "edge" padded:
//    [[1,1,1,2,3,3,3],
//     [1,1,1,2,3,3,3],
//     [4,4,4,5,6,6,6],
//     [4,4,4,5,6,6,6]]
builder.pad(input, padding, { mode: "edge" });

// "reflection" padded:
//    [[6,5,4,5,6,5,4],
//     [3,2,1,2,3,2,1],
//     [6,5,4,5,6,5,4],
//     [3,2,1,2,3,2,1]]
builder.pad(input, padding, { mode: "reflection" });

// "symmetric" padded:
//    [[2,1,1,2,3,3,2],
//     [2,1,1,2,3,3,2],
//     [5,4,4,5,6,6,5],
//     [5,4,4,5,6,6,5]]
builder.pad(input, padding, { mode: "symmetric" });

6.6.14. pooling operations

Compute a mean, L2 norm, or max reduction operation across all the elements within the moving window over the input tensor. See the description of each type of reduction in § 6.6.15 reduction operations. 
dictionary MLPool2dOptions {
  sequence<long> windowDimensions;
  sequence<long> padding;
  sequence<long> strides;
  sequence<long> dilations;
  MLAutoPad autoPad = "explicit";
  MLInputOperandLayout layout = "nchw";
};

partial interface MLGraphBuilder {
  MLOperand averagePool2d(MLOperand input, optional MLPool2dOptions options = {});
  MLOperand l2Pool2d(MLOperand input, optional MLPool2dOptions options = {});
  MLOperand maxPool2d(MLOperand input, optional MLPool2dOptions options = {});
};

Arguments:

  • input: an MLOperand. The input 4-D tensor. The logical shape is interpreted according to the value of options.layout.

  • options: an optional MLPool2dOptions. The optional parameters of the operation.

    • windowDimensions: a sequence of long of length 2. The dimensions of the sliding window, [window_height, window_width]. If not present, the window dimensions are assumed to be the height and width dimensions of the input shape.

    • padding: a sequence of long of length 4. The additional rows and columns added to the beginning and ending of each spatial dimension of input, [beginning_height, ending_height, beginning_width, ending_width]. If not present, the values are assumed to be [0,0,0,0].

    • strides: a sequence of long of length 2. The stride of the sliding window for each spatial dimension of input, [stride_height, stride_width]. If not present, the values are assumed to be [1,1].

    • dilations: a sequence of long of length 2. The dilation factor for each spatial dimension of input, [dilation_height, dilation_width]. If not present, the values are assumed to be [1,1].

    • autoPad: an MLAutoPad. The automatic input padding options. By default, this argument is set to "explicit", which means that the values in the options.padding array should be used for input padding. When the option is set other than "explicit", the values in the options.padding array are ignored. With the "same-upper" option, the padding values are automatically computed such that the additional ending padding of the spatial input dimensions would allow all of the input values in the corresponding dimension to be filtered. The "same-lower" option is similar but padding is applied to the beginning padding of the spatial input dimensions instead of the ending one.

    • layout: an MLInputOperandLayout. The default value is "nchw". This option specifies the layout format of the input and output tensor as follow:

      "nchw":

      • input tensor: [batches, channels, height, width]

      • output tensor: [batches, channels, height, width]

      "nhwc":

      • input tensor: [batches, height, width, channels]

      • output tensor: [batches, height, width, channels]

Returns: an MLOperand. The output 4-D tensor that contains the result of the reduction. The logical shape is interpreted according to the value of layout.

A global pooling operation such as one for the max pooling operation is a variant of pooling where the window dimensions is the spatial dimensions (last two dimensions) of the input shape, as follow. 

// 'global' max pooling
builder.maxPool2d(input);

6.6.15. reduction operations

Reduce the input along the dimensions given in axes. 
dictionary MLReduceOptions {
  sequence<long> axes = null;
  boolean keepDimensions = false;
};

partial interface MLGraphBuilder {
  MLOperand reduceL1(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceL2(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceLogSum(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceLogSumExp(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceMax(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceMean(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceMin(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceProduct(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceSum(MLOperand input, optional MLReduceOptions options = {});
  MLOperand reduceSumSquare(MLOperand input, optional MLReduceOptions options = {});
};

Arguments:

  • input: an MLOperand. The input tensor.

  • options: an optional MLReduceOptions. The optional parameters of the operation.

    • axes: a sequence of long. The dimensions to reduce where -1 means the last dimension. If not present, all dimensions are reduced.

    • keepDimensions: a boolean. If true, retains reduced dimensions with size of 1. The default value is false.

Returns: an MLOperand. The reduced output tensor.

Reduction types:

  • L1: Compute the L1 norm of all the input values along the axes.

  • L2: Compute the L2 norm of all the input values along the axes.

  • LogSum: Compute the log value of the sum of all the input values along the axes.

  • LogSumExp: Compute the log value of the sum of the exponent of all the input values along the axes.

  • Max: Compute the maximum value of all the input values along the axes.

  • Mean: Compute the average value of all the input values along the axes.

  • Min: Compute the minimum value of all the input values along the axes.

  • Product: Compute the product of all the input values along the axes.

  • Sum: Compute the sum of all the input values along the axes.

  • SumSquare: Compute the sum of the square of all the input values along the axes.

6.6.16. resample

Resample the tensor values from the source to the destination dimensions according to the scaling factors. 
enum MLInterpolationMode {
  "nearest-neighbor",
  "linear"
};

dictionary MLResampleOptions {
  MLInterpolationMode mode = "nearest-neighbor";
  sequence<float> scales;
  sequence<long> sizes;
};

partial interface MLGraphBuilder {
  MLOperand resample(MLOperand input, optional MLResampleOptions options = {});
};

Arguments:

  • input: an MLOperand. The input 4-D tensor.

  • options: an optional MLResampleOptions. The optional parameters of the operation.

    • mode: an MLInterpolationMode. The interpolation algorithm used to fill the output tensor values. If not set, it is assumed to be the Nearest Neighbor interpolation.

    • scales: a sequence of float of length 4. Each value represents the scaling factor used to scale in each input dimensions.

    • sizes: a sequence of long of length 4. The target sizes for each input dimensions. When the target sizes are specified, the options.scales argument is ignored as the scaling factor values are derived from the target sizes of each input dimension.

Returns: an MLOperand. The output 4-D tensor.

6.6.17. reshape

Alter the shape of a tensor to a new shape. Reshape does not copy or change the content of the tensor. It just changes the tensor’s logical dimensions for the subsequent operations. 
partial interface MLGraphBuilder {
  MLOperand reshape(MLOperand input, sequence<long> newShape);
};

Arguments:

  • input: an MLOperand. The input tensor.

  • newShape: a sequence of long. The shape of the output tensor. The number of elements implied by newShape must be the same as the number of elements in the input tensor. Only one component of newShape can be the special value of -1. The size of the dimension with the value -1 is computed so that the total size remains constant.

Returns: an MLOperand. The output tensor. The values of the output tensor are the same as values of the input tensor. The shape of the output tensor is specified by the newShape argument.

6.6.18. slice

Produce a slice of the input tensor. 
dictionary MLSliceOptions {
  sequence<long> axes;
};

partial interface MLGraphBuilder {
  MLOperand slice(MLOperand input, sequence<long> starts, sequence<long> sizes,
                optional MLSliceOptions options = {});
};

Arguments:

  • input: an MLOperand. The input tensor.

  • starts: a sequence of long. The starting indices to slice of the corresponding axes of the input shape. A negative index value is interpreted as counting back from the end. For example, the value -1

  • sizes: a sequence of long. The lengths to slice of the corresponding axes of the input shape. The length value of -1 selects all the remaining elements from the starting index of the given axis.

  • options: an optional MLSliceOptions. The optional parameters of the operation.

    • axes: a sequence of long. The dimensions of the input shape to which starts and sizes apply. The values in the sequence are either within the [0, r-1] range where r is the input tensor rank, or the [-r, -1] range where negative values mean counting back from the end of the input shape. When not specified, the sequence is assumed to be [0,1,..r-1].

Returns: an MLOperand. The output tensor of the same rank as the input tensor with tensor values stripped to the specified starting and ending indices in each dimension.

6.6.19. softmax

Compute the softmax values of the 2-D input tensor along axis 1. 
partial interface MLGraphBuilder {
  MLOperand softmax(MLOperand x);
};

Arguments:

Returns: an MLOperand. The output 2-D tensor that contains the softmax results, of the same shape as the input tensor.

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

// This sample deploys a well-known implementation trick [1] to compute the
// exponentials of the distances to the max value, instead of the exponentials
// of the input values itself, in order to increase the numerical stability of
// the result.
// [1]: https://cs231n.github.io/linear-classify/#softmax
const max_x = builder.reduceMax(x, { axes: [1], keepDimensions: true });
const exp_x = builder.exp(builder.sub(x, max));
return builder.div(exp_x, builder.reduceSum(exp_x, { axes: [1], keepDimensions: true }));

6.6.20. split

Split the input tensor into a number of sub tensors along the given axis. 
dictionary MLSplitOptions {
  long axis = 0;
};

partial interface MLGraphBuilder {
  sequence<MLOperand> split(MLOperand input,
                          (unsigned long or sequence<unsigned long>) splits,
                          optional MLSplitOptions options = {});
};

Arguments:

  • input: an MLOperand. The input tensor.

  • splits: an unsigned long or a sequence of unsigned long. If an unsigned long, it specifies the number of output tensors along the axis. The number must evenly divide the dimension size of input along options.axis. If a sequence of unsigned long, it specifies the sizes of each output tensor along the options.axis. The sum of sizes must equal to the dimension size of input along options.axis.

  • options: an optional MLSplitOptions. The optional parameters of the operation.

    • axis: a long. The dimension along which to split. Default to 0. A negative value is interpreted as counting back from the end.

Returns: a sequence of MLOperand. The splitted output tensors. If splits is an unsigned long, the length of the output sequence equals to splits. The shape of each output tensor is the same as input except the dimension size of axis equals to the quotient of dividing the dimension size of input along axis by splits. If splits is a sequence of unsigned long, the length of the output sequence equals to the length of splits. The shape of the i-th output tensor is the same as as input except along axis where the dimension size is splits[i].

The behavior of this operation can be generically emulated from the usage of other operations as follow. However, user agents typically have a more efficient implementation for it, therefore its usage is encouraged from the performance standpoint. 

// This sample shows the case that the splits parameter is an array.
const outputs = [];
let start = 0;
for (const size of splits) {
  outputs.push(builder.slice(input, [start], [size], { axis: [options.axis] }));
  start += size;
}
return outputs;

6.6.21. squeeze

Reduce the rank of a tensor by eliminating dimensions with size 1 of the tensor shape. Squeeze only affects the tensor’s logical dimensions. It does not copy or change the content in the tensor. 
dictionary MLSqueezeOptions {
  sequence<long> axes;
};

partial interface MLGraphBuilder {
  MLOperand squeeze(MLOperand input, optional MLSqueezeOptions options = {});
};

Arguments:

  • input: an MLOperand. The input tensor.

  • options: an optional MLSqueezeOptions. The optional parameters of the operation.

    • axes: a sequence of long. Indices to the shape dimensions of size 1 to eliminate. When not specified, every shape dimensions of size 1 in the tensor are eliminated.

Returns: an MLOperand. The output tensor of the same or reduced rank with the shape dimensions of size 1 eliminated.

6.6.22. transpose

Permute the dimensions of the input tensor according to the permutation argument. 
dictionary MLTransposeOptions {
  sequence<long> permutation;
};

partial interface MLGraphBuilder {
  MLOperand transpose(MLOperand input, optional MLTransposeOptions options = {});
};

Arguments:

  • input: an MLOperand. The input N-D tensor.

  • options: an optional MLTransposeOptions. The optional parameters of the operation.

    • permutation: a sequence of long values. The values used to permute the output shape. When it’s not specified, it’s set to [N-1...0], where N is the rank of the input tensor. These default values cause the output to become a transposed tensor of the input. When specified, the number of values in the sequence must be the same as the rank of the input tensor, and the values in the sequence must be within the range from 0 to N-1 with no two or more same values found in the sequence.

Returns: an MLOperand. The permuted or transposed N-D tensor.

6.7. MLGraph

The MLGraph interface represents a compiled computational graph. A compiled graph once constructed is immutable and cannot be subsequently changed. 
typedef (MLBufferView or WebGLTexture or GPUTexture) MLResource;

dictionary MLInput {
  required MLResource resource;
  required sequence<long> dimensions;
};

typedef record<DOMString, (MLResource or MLInput)> MLNamedInputs;
typedef record<DOMString, MLResource> MLNamedOutputs;

[SecureContext, Exposed=(Window, DedicatedWorker)]
interface MLGraph {
  undefined compute(MLNamedInputs inputs, MLNamedOutputs outputs);
};

MLGraph has the following internal slots:

[[context]] of type MLContext

The context of type MLContext associated with this MLGraph.

[[inputDescriptors]] of type record<DOMString, MLOperandDescriptor>

Maps the name of an input MLOperand to its MLOperandDescriptor for all input MLOperands of this MLGraph.

[[outputNames]] of type sequence<DOMString>

Contains the names of all output MLOperands of this MLGraph.

[[implementation]]

The underlying implemenation provided by the User Agent.

compute(inputs, outputs)

Compute the MLGraph given MLNamedInputs and MLNamedOutputs. Return once the compute has completed and the results in MLNamedOutputs are ready to be consumed.

Called on: MLGraph this.

Arguments:

Arguments for the MLGraph.compute(inputs, outputs) method.
Parameter Type Nullable Optional Description
inputs MLNamedInputs ✘ ✘ an MLNamedInputs. The resources and optional dimensions of inputs for the compute.
outputs MLNamedOutputs ✘ ✘ an MLNamedOutputs. The pre-allocated resources of required outputs for the compute.

Returns: undefined.

  1. If any of the following requirements are unmet, then throw a DataError DOMException and stop.

    1. For each key -> value of inputs:

      1. this.[[inputDescriptors]][key] must exist.

      2. Let inputDesc be this.[[inputDescriptors]][key].

      3. Let inputSize be 1.

      4. If value is an MLInput, then:

        1. The length of value.dimensions must be the same as the length of inputDesc.dimensions.

        2. Let i be 0.

        3. While true:

          1. Let dimension be value.dimensions[i].

          2. dimension must be greater than 0.

          3. If inputDesc.dimensions[i] is greater than 0, then dimension must be equal to inputDesc.dimensions[i].

          4. Set inputSize to the product of inputSize and dimension.

          5. Increment i by 1.

          6. If i if equal to the length of value.dimensions, then break.

      5. Else:

        1. For each dimension of inputDesc.dimensions:

          1. The value of dimension must be greater than 0.

          2. Set inputSize to the product of inputSize and dimension.

      6. If value is an MLInput, then let resource be value.resource.

      7. If value is an MLResource, then let resource be value.

      8. If resource is an ArrayBufferView, then:

        1. The kind of resource must be compatible with inputDesc.type according to this table.

        2. The length of resource must be the same as inputSize.

    2. For each key -> value of outputs:

      1. this.[[outputNames]][key] must exist.

  2. For each key -> value of inputs:

    1. Let inputDesc be this.[[inputDescriptors]][key].

    2. Let inputTensor be a new tensor for this.[[implementation]] of data type that is compatible with inputDesc.type.

    3. If value is an MLInput, then:

      1. Set the dimensions of inputTensor to value.dimensions.

    4. Else:

      1. Set the dimensions of inputTensor to inputDesc.dimensions.

    5. If value is an MLInput, then:

      1. Set the values of inputTensor to the values of value.resource.

    6. If value is an MLResource, then:

      1. Set the values of inputTensor to the values of value.

    7. Set the input of this.[[implementation]] that is associated with key to inputTensor.

  3. For each key -> value of outputs:

    1. Issue a compute request for output of this.[[implementation]] that is associated with key.

    2. Wait for the compute request to be completed.

    3. If there is an error returned by this.[[implementation]], then:

      1. Throw an OperationError DOMException and stop.

    4. Else:

      1. Let outputTensor be the output tensor returned by this.[[implementation]].

      2. If the kind of value is not compatible with the value type of outputTensor, then throw a DataError DOMException and stop.

      3. Let outputSize be 1.

      4. For each dimension of dimensions of outputTensor:

        1. Set outputSize to the product of outputSize and dimension.

      5. If outputSize is greater than the length of value, then:

        1. Throw a DataError DOMException and stop.

      6. Else:

        1. Set the values of value to the values of outputTensor.

  4. Return undefined.

Describe the algorithm steps for this.[[context]] created from WebGLRenderingContext and GPUDevice.

6.7.1. Examples

The following code showcases the computation with dynamic input dimensions. 

function sizeOfShape(array) {
  return array.reduce(
      (accumulator, currentValue) => accumulator * currentValue);
}

const context = navigator.ml.createContext();

// Create a graph with dynamic shaped inputs.
const builder = new MLGraphBuilder(context);
const descA = {type: 'float32', dimensions: [-1, 4]};
const a = builder.input('a', descA);
const descB = {type: 'float32', dimensions: [4, -1]};
const b = builder.input('b', descB);
const c = builder.matmul(a, b);
const graph = builder.build({'c': c});

function allocateAndCompute(shapeA, shapeB, shapeC) {
  const bufferA = new Float32Array(sizeOfShape(shapeA)).fill(0.5);
  const bufferB = new Float32Array(sizeOfShape(shapeB)).fill(0.5);
  const bufferC = new Float32Array(sizeOfShape(shapeC));

  // Specify the shape of inputs when computing.
  const inputs = {
    'a': {resource: bufferA, dimensions: shapeA},
    'b': {resource: bufferB, dimensions: shapeB},
  };
  const outputs = {'c': bufferC};
  graph.compute(inputs, outputs);
  console.log(`values: ${bufferC}`);
}

allocateAndCompute([3, 4], [4, 3], [3, 3]);
allocateAndCompute([4, 4], [4, 4], [4, 4]);
allocateAndCompute([5, 4], [4, 5], [5, 5]);

The following code showcases the computation with optional outputs. 

const context = navigator.ml.createContext();

// Build a graph with two outputs.
const builder = new MLGraphBuilder(context);
const descA = {type: 'float32', dimensions: [3, 4]};
const a = builder.input('a', descA);
const descB = {type: 'float32', dimensions: [4, 3]};
const bufferB = new Float32Array(sizeOfShape(descB.dimensions)).fill(0.5);
const b = builder.constant(descB, bufferB);
const descC = {type: 'float32', dimensions: [3, 3]};
const bufferC = new Float32Array(sizeOfShape(descC.dimensions)).fill(1);
const c = builder.constant(descC, bufferC);
const d = builder.matmul(a, b);
const e = builder.add(d, c);
const graph = builder.build({'d': d, 'e': e});

const bufferA = new Float32Array(sizeOfShape(descA.dimensions)).fill(0.5);
const inputs = {'a': bufferA};

// Compute d.
const bufferD = new Float32Array(sizeOfShape([3, 3]));
graph.compute(inputs, {'d': bufferD});
console.log(`values: ${bufferD}`);

// Compute e.
const bufferE = new Float32Array(sizeOfShape([3, 3]));
graph.compute(inputs, {'e': bufferE});
console.log(`values: ${bufferE}`);

7. Examples

The following code gets the MLContext object. 

const context = navigator.ml.createContext({powerPreference: 'low-power'});

The following code builds a graph as: 

constant1 ---+
             +--- Add ---> intermediateOutput1 ---+
input1    ---+                                    |
                                                  +--- Mul---> output
constant2 ---+                                    |
             +--- Add ---> intermediateOutput2 ---+
input2    ---+

// Use tensors in 4 dimensions.
const TENSOR_DIMS = [1, 2, 2, 2];
const TENSOR_SIZE = 8;

const builder = new MLGraphBuilder(context);

// Create MLOperandDescriptor object.
const desc = {type: 'float32', dimensions: TENSOR_DIMS};

// constant1 is a constant MLOperand with the value 0.5.
const constantBuffer1 = new Float32Array(TENSOR_SIZE).fill(0.5);
const constant1 = builder.constant(desc, constantBuffer1);

// input1 is one of the input MLOperands. Its value will be set before execution.
const input1 = builder.input('input1', desc);

// constant2 is another constant MLOperand with the value 0.5.
const constantBuffer2 = new Float32Array(TENSOR_SIZE).fill(0.5);
const constant2 = builder.constant(desc, constantBuffer2);

// input2 is another input MLOperand. Its value will be set before execution.
const input2 = builder.input('input2', desc);

// intermediateOutput1 is the output of the first Add operation.
const intermediateOutput1 = builder.add(constant1, input1);

// intermediateOutput2 is the output of the second Add operation.
const intermediateOutput2 = builder.add(constant2, input2);

// output is the output MLOperand of the Mul operation.
const output = builder.mul(intermediateOutput1, intermediateOutput2);

Compile the graph up to the output operand. 

// Compile the constructed graph.
const graph = builder.build({'output': output});

The following code executes the compiled graph. 

// Setup the input buffers with value 1.
const inputBuffer1 = new Float32Array(TENSOR_SIZE).fill(1);
const inputBuffer2 = new Float32Array(TENSOR_SIZE).fill(1);
const outputBuffer = new Float32Array(TENSOR_SIZE);

// Execute the compiled graph with the specified inputs.
const inputs = {
  'input1': inputBuffer1,
  'input2': inputBuffer2,
};
const outputs = {'output': outputBuffer};
graph.compute(inputs, outputs);

console.log('Output value: ' + outputBuffer);
// Output value: 2.25,2.25,2.25,2.25,2.25,2.25,2.25,2.25

8. Appendices

8.1. MLOperandType and ArrayBufferView compatibility

MLOperandType ArrayBufferView
float32 Float32Array
int32 Int32Array
uint32 Uint32Array
int8 Int8Array
uint8 Uint8Array

clarify the usage of ArrayBufferView for float16. <https://github.com/webmachinelearning/webnn/issues/127>

9. Acknowledgements

This specification follows the concepts of the Android Neural Networks API C API.

Thanks to Tomoyuki Shimizu, Ningxin Hu, Zhiqiang Yu and Belem Zhang for the use cases.

Thanks to Nikhil Thorat, Daniel Smilkov, Ganesan Ramalingam, Rafael Cintron and Benjamin Poulain for their contributions to the API specification.