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1. Neural Network Extension
1.1. Acknowledgements
This specification would not be possible without the contributions from this partial list of the following individuals from the Khronos Working Group and the companies that they represented at the time:

Radhakrishna Giduthuri  Intel

Frank Brill  Cadence Design Systems

Thierry Lepley  Cadence Design Systems

Kari Pulli  Intel

Mostafa Hagog  Intel

Tomer Schwartz  Intel

Victor Eruhimov  Itseez3D

Chuck Pilkington  Synopsis

Jesse Villarreal  Texas Instruments

Xin Wang  Verisilicon
1.2. Background and Terminology
Deep Learning using Neural Networks techniques is being increasingly used to perform vision classification and recognition tasks. Deep Neural Networks have significantly improved image recognition capabilities over previous technologies. The Neural Network extension for OpenVX is intended to enable the implementation of Deep Neural Network in the OpenVX framework. It is well known that the Deep learning domain for vision, has two fundamental stages. At first the network topology is designed and trained given a collection of labelled data. The network topology is represented as a graph of several nodes comprising Neural Network building block. The trained data represents the problem to be addressed. During the training Phase, the parameters (also referred to as weights/biasses or coefficients) are determined for the given network topology. The network topology solution can then be deployed.
In Deployment the network topology as well as parameters are fixed which allow optimizing in hardware and software. In certain scenarios an additional intermediate step is performed to optimize the parameters to a certain target hardware. As an example, using fixed point calculations. When Deployed, the Neural Network is used for inferences on input data. The main objective of the Neural Network Extension for OpenVX is to enable the deployment phase (in other words inferences).
This section provides the definition of the basic terminology to be used across the document, in an attempt to address the various use and different naming in the academy as well as the industry. Those names refer to the same fundamental concept of Deep Neural Networks in the deep learning domain. We refer to the term Deep Neural Network to the network topology of the deep learning network, that is composed of multiple layers in which one of the main layer is Convolution. Other names used in the academia and industry to refer to the same type of network topologies are CNN (Convolutional Neural Networks) and ConvNets. Throughout this document we will use the Deep Neural Network to refer to the Neural Network, CNN and ConvNet.
Weights  Will use the term Weights to refer to the parameters or coefficients that are the result of training the Deep Neural Network. Weights can be shared or non shared. Or have local connectivity.
Biasses  Will use the term Biasses to refer to the parameters or coefficients, per output only, that are the result of training the Deep Neural Network.
Convolution Layer  A type of layer in the Deep Neural Network that has local connectivity and shared weights, other naming are Locality connected with shared weights.
Fully Connected Layer  All inputs to the layer affect outputs of the layer , in other words connection from every element of input to every element of output.
Activation Layer  A layer that performs operations on every input data and is inspired by the neuron activation function approximated usually using nonLinear functions.
The documentation below uses the abbreviations IFM and OFM, which stand for “Input Feature Maps” and “Output Feature Maps,” respectively. Each feature map is a 2 dimensional image. A CNN input or output tensor will typically have 3 dimensions, where the first two are the width and height of the images, and the third is the number of feature maps. For inputs, the third dimension is the number of IFMs, and for outputs, the third dimension is the number of OFMs.
1.3. Introduction
The Neural Networks extension enables execution and integration of Deep
Neural Networks in OpenVX processing graphs.
The extension is dependent on a vx_tensor
object which is introduced
in OpenVX 1.2.
Therefore this extension is extending OpenVX 1.2 and not previous OpenVX
specifications.
The vx_tensor
object is a multidimensional array with an arbitrary
number of dimensions.
The vx_tensor
object can represent all varieties of data typically
used in a Deep Neural Network.
It can represent 2dimensional images, 3dimensional sequences of images
(usually the input and outputs of a Deep Neural Network) and 4dimensional
weights.
Application can build an OpenVX graph that represents Deep Neural Network
topologies where the layers are represented as OpenVX nodes (vx_node
)
and the vx_tensor
as the data objects connecting the nodes (layers) of
the OpenVX graph (Deep Neural Network).
The application can as well build an OpenVX graph that is a mix of Deep
Neural Network layers and Vision nodes.
All graphs (including Deep Neural Networks) are treated as any OpenVX graph,
and must comply with the graph concepts as specified in section 2.8 of
OpenVX 1.1, especially but not limit to the graph formalisms in section
2.8.6.
Additionally, this extension defines several auxiliary functions to create,
release, and copy vx_tensor
objects.
Moreover, the extension introduces the concept of “view” for
vx_tensor
objects, which is similar to the ROI of a vx_image
.
The use of “view” enables splitting and merging vx_tensor
objects,
which are common operations in Convolutional Networks.
The layers of the Deep Neural Network (represented by vx_node
objects)
perform the computations on the tensor data objects and form a dataflow
graph of computations.
The extension defines the following layer types: convolution, activation,
pooling, fullyconnected, and softmax.
1.4. Weights/Biasses Setting
It is assumed that the Deep Neural Networks are trained in framework
external to OpenVX and imported.
This requires the application to allocate a memory area for the
weights/biasses, read the weight values from a file into this memory area,
and then use the vxCopyTensorPatch
API to copy the weights/biasses from
the memory area into the appropriate OpenVX Tensor object.
The vxCopyTensorPatch
function will convert the application memory to the
implementationspecific format before putting it into the Tensor object.
While effective, this method has the drawback that an intermediate memory
area needs to be allocated and a copy and conversion needs to be done.
A separate “import/export” extension defines a vxImportBinary
function
that can be implemented more efficiently.
Implementations of vxImportBinary
could read a weight file or perhaps an
entire graph description directly without the need for an intermediate copy.
The format of this binary will be implementationdependent.
OpenVX implementations that support both the Neural Network extension and
the binary import/export extension can use this more efficient method to set
the Deep Neural Networks weights/biasses.
The vxImportBinary
function will return a handle to an object that can be
queried to get handles for the individual objects within it via the
vxGetImportReferenceByName
or vxGetImportReferenceByIndex
functions.
Further details and alternate usages of the vxImportBinary
function are
provided in the specification of the “import/export” extension.
OpenVX objects (tensors, scalars, enums) for weights, biases and other
static parameters of CNN layers must have actual data loaded into them
before vxVerifyGraph()
is called, therefore implementation may cache them
prior to execution or use them for other optimizations.
Optionally, implementation may explicitly define support to change weights
after vxVerifyGraph()
was called or between vxProcessGraph()
calls.
For convenience we tag [static] the parameters that must have actual data
loaded into them before vxVerifyGraph()
.
1.5. Kernel names
When using vxGetKernelByName
the following are strings specifying the
Neural Networks extension kernel names:

org.khronos.nn_extension.convolution_layer

org.khronos.nn_extension.fully_connected_layer

org.khronos.nn_extension.pooling_layer

org.khronos.nn_extension.softmax_layer

org.khronos.nn_extension.local_response_normalization_layer

org.khronos.nn_extension.activation_layer

org.khronos.nn_extension.roi_pooling_layer

org.khronos.nn_extension.deconvolution_layer
1.6. 8bit extension and 16bit extension
The Neural Network Extension is actually two different extensions.
Neural Network 16bit extension and Neural Network 8bit extension.
The 8bit extension is required.
The 16bit extension is optional.
For 8bit extension, VX_TYPE_UINT8
and VX_TYPE_INT8
, with
fixed_point_position 0, must be supported for all functions.
For 16bit extension, VX_TYPE_INT16
with fixed_point_position 8, must
be supported for all functions.
The users can query VX_CONTEXT_EXTENSIONS
, the extension strings are
returned to identify two extensions.
Implementations must return the 8bit extension string, and may return the
16bit extension string.
If implementations return the 16bit extension string, the 8bit extension
string must be returned as well.
The 8bit extension string is "KHR_NN_8"
and the 16bit extension string is
"KHR_NN_16"
.
The legal string combinations are "KHR_NN_8"
or "KHR_NN_8 KHR_NN_16"
.
2. Module Documentation
2.1. Extension: Deep Convolutional Networks API
Convolutional Network Nodes
Data Structures
Macros
Enumerations
Functions
2.1.1. Data Structures
vx_nn_convolution_params_t
Input parameters for a convolution operation.
typedef struct _vx_nn_convolution_params_t {
vx_size padding_x;
vx_size padding_y;
vx_enum overflow_policy;
vx_enum rounding_policy;
vx_enum down_scale_size_rounding;
vx_size dilation_x;
vx_size dilation_y;
} vx_nn_convolution_params_t;
Data Field  Definition 

dilation_x 
“inflate” the kernel by inserting zeros between the kernel elements in the x direction. The value is the number of zeros to insert. 
dilation_y 
“inflate” the kernel by inserting zeros between the kernel elements in the y direction. The value is the number of zeros to insert. 
down_scale_size_rounding 
Rounding method for calculating output dimensions. See vx_nn_rounding_type_e. 
overflow_policy 
A VX_TYPE_ENUM of the vx_convert_policy_e enumeration. 
padding_x 
Number of elements added at each side in the x dimension of the input. 
padding_y 
Number of elements added at each side in the y dimension of the input. 
rounding_policy 
A VX_TYPE_ENUM of the vx_round_policy_e enumeration. 
vx_nn_deconvolution_params_t
Input parameters for a deconvolution operation.
typedef struct _vx_nn_deconvolution_params_t {
vx_size padding_x;
vx_size padding_y;
vx_enum overflow_policy;
vx_enum rounding_policy;
vx_size a_x;
vx_size a_y;
} vx_nn_deconvolution_params_t;
Data Field  Definition 

a_x 
userspecified quantity used to distinguish between the upscale_{x} different possible output sizes. 
a_y 
userspecified quantity used to distinguish between the upscale_{y} different possible output sizes. 
overflow_policy 
A VX_TYPE_ENUM of the vx_convert_policy_e enumeration. 
padding_x 
Number of elements subtracted at each side in the x dimension of the output. 
padding_y 
Number of elements subtracted at each side in the y dimension of the output. 
rounding_policy 
A VX_TYPE_ENUM of the vx_round_policy_e enumeration. 
vx_nn_roi_pool_params_t
Input parameters for ROI pooling operation.
typedef struct _vx_nn_roi_pool_params_t {
vx_enum pool_type;
} vx_nn_roi_pool_params_t;
Data Field  Definition 

pool_type 
Of type vx_nn_pooling_type_e. Only VX_NN_POOLING_MAX pooling is supported. 
2.1.2. Macros
VX_LIBRARY_KHR_NN_EXTENSION
The Neural Network Extension Library Set.
#define VX_LIBRARY_KHR_NN_EXTENSION (0x1)
2.1.3. Enumerations
vx_kernel_nn_ext_e
The list of Neural Network Extension Kernels.
enum vx_kernel_nn_ext_e {
VX_KERNEL_CONVOLUTION_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x0,
VX_KERNEL_FULLY_CONNECTED_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x1,
VX_KERNEL_POOLING_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x2,
VX_KERNEL_SOFTMAX_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x3,
VX_KERNEL_NORMALIZATION_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x4,
VX_KERNEL_ACTIVATION_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x5,
VX_KERNEL_ROI_POOLING_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x6,
VX_KERNEL_DECONVOLUTION_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x7,
VX_KERNEL_LOCAL_RESPONSE_NORMALIZATION_LAYER = VX_KERNEL_BASE(VX_ID_KHRONOS, VX_LIBRARY_KHR_NN_EXTENSION) + 0x8,
};
Enumerator

VX_KERNEL_CONVOLUTION_LAYER
 The Neural Network Extension convolution Kernel. 
VX_KERNEL_FULLY_CONNECTED_LAYER
 The Neural Network Extension fully connected Kernel. 
VX_KERNEL_POOLING_LAYER
 The Neural Network Extension pooling Kernel. 
VX_KERNEL_SOFTMAX_LAYER
 The Neural Network Extension softmax Kernel. 
VX_KERNEL_LOCAL_RESPONSE_NORMALIZATION_LAYER
 The Neural Network Extension Local Response Normalization Kernel. 
VX_KERNEL_ACTIVATION_LAYER
 The Neural Network Extension activation Kernel. 
VX_KERNEL_ROI_POOLING_LAYER
 The Neural Network POI Pooling Kernel. 
VX_KERNEL_DECONVOLUTION_LAYER
 The Neural Network Extension Deconvolution Kernel.
vx_nn_activation_function_e
The Neural Network activation functions list.
enum vx_nn_activation_function_e {
VX_NN_ACTIVATION_LOGISTIC = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x0,
VX_NN_ACTIVATION_HYPERBOLIC_TAN = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x1,
VX_NN_ACTIVATION_RELU = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x2,
VX_NN_ACTIVATION_BRELU = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x3,
VX_NN_ACTIVATION_SOFTRELU = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x4,
VX_NN_ACTIVATION_ABS = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x5,
VX_NN_ACTIVATION_SQUARE = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x6,
VX_NN_ACTIVATION_SQRT = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x7,
VX_NN_ACTIVATION_LINEAR = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE) + 0x8,
};
Function Name  Mathematical definition  Parameters  Parameters type 

logistic 
f(x) = 1 / (1+e^{x}) 

hyperbolic tangent 
f(x) = a ⋅ tanh(b ⋅ x) 
a, b 

relu 
f(x) = max(0,x) 

bounded relu 
f(x) = min(a, max(0,x)) 
a 

soft relu 
f(x) = log(1 + e^{x}) 

abs 
f(x) =  x  

square 
f(x) = x^{2} 

square root 
f(x) = sqrt(x) 

linear 
f(x) = a x + b 
a, b 
Enumerator
vx_nn_enum_e
NN extension type enums.
enum vx_nn_enum_e {
VX_ENUM_NN_ROUNDING_TYPE = 0x1A,
VX_ENUM_NN_POOLING_TYPE = 0x1B,
VX_ENUM_NN_NORMALIZATION_TYPE = 0x1C,
VX_ENUM_NN_ACTIVATION_FUNCTION_TYPE = 0x1D,
};
Enumerator
vx_nn_norm_type_e
The Neural Network normalization type list.
enum vx_nn_norm_type_e {
VX_NN_NORMALIZATION_SAME_MAP = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_NORMALIZATION_TYPE) + 0x0,
VX_NN_NORMALIZATION_ACROSS_MAPS = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_NORMALIZATION_TYPE) + 0x1,
};
Enumerator
vx_nn_pooling_type_e
The Neural Network pooling type list.
enum vx_nn_pooling_type_e {
VX_NN_POOLING_MAX = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_POOLING_TYPE) + 0x0,
VX_NN_POOLING_AVG = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_POOLING_TYPE) + 0x1,
};
kind of pooling done in pooling function
Enumerator
vx_nn_rounding_type_e
down scale rounding.
enum vx_nn_rounding_type_e {
VX_NN_DS_SIZE_ROUNDING_FLOOR = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ROUNDING_TYPE) + 0x0,
VX_NN_DS_SIZE_ROUNDING_CEILING = VX_ENUM_BASE(VX_ID_KHRONOS, VX_ENUM_NN_ROUNDING_TYPE) + 0x1,
};
Due to different scheme of downscale size calculation in the various training frameworks. Implementation must support 2 rounding methods for down scale calculation. The floor and the ceiling. In convolution and pooling functions. Relevant when input size is even.
Enumerator
vx_nn_type_e
The type enumeration lists all NN extension types.
enum vx_nn_type_e {
VX_TYPE_NN_CONVOLUTION_PARAMS = 0x025,
VX_TYPE_NN_DECONVOLUTION_PARAMS = 0x026,
VX_TYPE_NN_ROI_POOL_PARAMS = 0x027,
};
Enumerator

VX_TYPE_NN_CONVOLUTION_PARAMS
 Avx_nn_convolution_params_t
. 
VX_TYPE_NN_DECONVOLUTION_PARAMS
 Avx_nn_deconvolution_params_t
. 
VX_TYPE_NN_ROI_POOL_PARAMS
 Avx_nn_roi_pool_params_t
.
2.1.4. Functions
vxActivationLayer
[Graph] Creates a Convolutional Network Activation Layer Node.
The function operate a specific function (Specified in
vx_nn_activation_function_e
), On the input data.
the equation for the layer is:

outputs(i,j,k,l) = function(inputs(i,j,k,l), a, b)
for all i,j,k,l.
vx_node vxActivationLayer(
vx_graph graph,
vx_tensor inputs,
vx_enum function,
vx_float32 a,
vx_float32 b,
vx_tensor outputs);
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor data. Implementations must support input tensor data types indicated by the extension strings"KHR_NN_8"
or"KHR_NN_8 KHR_NN_16"
. 
[in]
function  [static] Nonlinear function (seevx_nn_activation_function_e
). Implementations must supportVX_NN_ACTIVATION_LOGISTIC
,VX_NN_ACTIVATION_HYPERBOLIC_TAN
andVX_NN_ACTIVATION_RELU

[in]
a  [static] Function parameters a. must be positive. 
[in]
b  [static] Function parameters b. must be positive. 
[out]
outputs  The output tensor data. Output will have the same number of dimensions as input.
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxConvolutionLayer
[Graph] Creates a Convolutional Network Convolution Layer Node.
vx_node vxConvolutionLayer(
vx_graph graph,
vx_tensor inputs,
vx_tensor weights,
vx_tensor biases,
const vx_nn_convolution_params_t* convolution_params,
vx_size size_of_convolution_params,
vx_tensor outputs);
This function implement Convolutional Network Convolution layer. For fixedpoint data types, a fixed point calculation is performed with round and saturate according to the number of accumulator bits. The number of the accumulator bits are implementation defined, and should be at least 16.
round: rounding according the vx_round_policy_e
enumeration.
saturate: A saturation according the vx_convert_policy_e
enumeration.
The following equation is implemented:
\(outputs[j,k,i] = saturate(round(\sum_{l} (\sum_{m,n} inputs[j+m,k+n,l] \times weights[m,n,l,i]) + biasses[j,k,i]))\)
Where (m, n) are indexes on the convolution matrices.
l is an index on all the convolutions per input.
i is an index per output.
(j, k) are the inputs/outputs spatial indexes.
Convolution is done on the width and height dimensions of the vx_tensor
.
Therefore, we use here the term x for index along the width dimension and y
for index along the height dimension.
Before the Convolution is done, a padding with zeros of the width and height input dimensions is performed. Then down scale is done by picking the results according to a skip jump. The skip in the x and y is determined by the output size dimensions. The relation between input to output is as follows:
\(width_{output} = round(\frac{(width_{input} + 2 * padding_x  kernel_x  (kernel_x  1) * dilation_x)}{skip_x} + 1)\)
and
\(height_{output} = round(\frac{(height + 2 * padding_y  kernel_y  (kernel_y  1) * dilation_y)}{skip_y} + 1)\)
where width is the size of the input width dimension.
height is the size of the input height dimension.
width_{output} is the size of the output width dimension.
height_{output} is the size of the output height dimension.
kernel_{x} and kernel_{y} are the convolution sizes in width and
height dimensions.
skip is calculated by the relation between input and output.
In case of ambiguity in the inverse calculation of the skip.
The minimum solution is chosen.
Skip must be a positive non zero integer.
rounding is done according to vx_nn_rounding_type_e
.
Notice that this node creation function has more parameters than the
corresponding kernel.
Numbering of kernel parameters (required if you create this node using the
generic interface) is explicitly specified here.
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor data. 3 lower dimensions represent a single input, all following dimensions represent number of batches, possibly nested. The dimension order is [width, height, #IFM, #batches]Implementations must support input tensor data types indicated by the extension strings
"KHR_NN_8"
or"KHR_NN_8 KHR_NN_16"
. (Kernel parameter #0) 
[in]
weights  [static] Weights are 4d tensor with dimensions [kernel_x, kernel_y, #IFM, #OFM]. seevxCreateTensor
andvxCreateVirtualTensor
Weights data type must match the data type of the inputs. (Kernel parameter #1)

[in]
biases  [static] Optional, ignored if NULL. The biases, which may be shared (one per ofm) or unshared (one per ofm * output location). The possible layouts are either [#OFM] or [width, height, #OFM]. Biases data type must match the data type of the inputs. (Kernel parameter #2) 
[in]
convolution_params  [static] Pointer to parameters of typevx_nn_convolution_params_t
. (Kernel parameter #3) 
[in]
size_of_convolution_params  [static] Size in bytes of convolution_params. Note that this parameter is not counted as one of the kernel parameters. 
[out]
outputs  The output tensor data. Output will have the same number and structure of dimensions as input. Output tensor data type must be same as the inputs. (Kernel parameter #4)
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxDeconvolutionLayer
[Graph] Creates a Convolutional Network Deconvolution Layer Node.
vx_node vxDeconvolutionLayer(
vx_graph graph,
vx_tensor inputs,
vx_tensor weights,
vx_tensor biases,
const vx_nn_deconvolution_params_t* deconvolution_params,
vx_size size_of_deconv_params,
vx_tensor outputs);
Deconvolution denote a sort of reverse convolution, which importantly and confusingly is not actually a proper mathematical deconvolution. Convolutional Network Deconvolution is upsampling of an image by learned Deconvolution coefficients. The operation is similar to convolution but can be implemented by upsampling the inputs with zeros insertions between the inputs, and convolving the Deconvolution kernels on the upsampled result. For fixedpoint data types, a fixed point calculation is performed with round and saturate according to the number of accumulator bits. The number of the accumulator bits are implementation defined, and should be at least 16.
round: rounding according the vx_round_policy_e
enumeration.
saturate: A saturation according the vx_convert_policy_e
enumeration.
The following equation is implemented:
\(outputs[j,k,i] = saturate(round(\sum_{l} \sum_{m,n}(inputs_{upscaled}[j+m,k+n,l] \times weights[m,n,l,i]) + biasses[j,k,i]))\)
Where (m, n) are indexes on the convolution matrices.
l is an index on all the convolutions per input.
i is an index per output.
(j, k) are the inputs/outputs spatial indexes.
Deconvolution is done on the width and height dimensions of the vx_tensor
.
Therefore, we use here the term x for the width dimension and y for the
height dimension.
before the Deconvolution is done, upscaling the width and height dimensions with zeros is performed. The relation between input to output is as follows:

width_{output} = (width_{input}  1) * upscale_{x}  2 * padding_{x} + kernel_{x} + a_{x}
and

height_{output} = (height_{input}  1) * upscale_{y}  2 * padding_{y} + kernel_{y} + a_{y}
where width_{input} is the size of the input width dimension. height_{input} is the size of the input height dimension. width_{output} is the size of the output width dimension. height_{output} is the size of the output height dimension. kernel_{x} and kernel_{y} are the convolution sizes in width and height. a_{x} and a_{y} are userspecified quantity used to distinguish between the upscale_{x} and upscale_{y} different possible output sizes. upscale_{x} and upscale_{y} are calculated by the relation between input and output. a_{x} and a_{y} must be positive and smaller then upscale_{x} and upscale_{y} respectively. Since the padding parameter is on the output, the effective input padding is:
\(padding_{input_x} = kernel_x padding_x 1\)
\(padding_{input_y} = kernel_y padding_y 1\)
Therfore the following constraints apply: kernel_{x} ≥ padding_{x} 
1 and kernel_{y} ≥ padding_{y}  1.
Rounding is done according to vx_nn_rounding_type_e
.
Notice that this node creation function has more parameters than the
corresponding kernel.
Numbering of kernel parameters (required if you create this node using the
generic interface) is explicitly specified here.
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor. 3 lower dimensions represent a single input, and an optional 4th dimension for batch of inputs. Dimension layout is [width, height, #IFM, #batches]. SeevxCreateTensor
andvxCreateVirtualTensor
. Implementations must support input tensor data types indicated by the extension strings"KHR_NN_8"
or"KHR_NN_8 KHR_NN_16"
. (Kernel parameter #0) 
[in]
weights  [static] The 4d weights with dimensions [width, height, #IFM, #OFM]. SeevxCreateTensor
andvxCreateVirtualTensor
. (Kernel parameter #1) 
[in]
biases  [static] Optional, ignored if NULL. The biases have one dimension [#OFM]. Implementations must support input tensor data type same as the inputs. (Kernel parameter #2) 
[in]
deconvolution_params  [static] Pointer to parameters of typevx_nn_deconvolution_params_t
(Kernel parameter #3) 
[in]
size_of_deconv_params  [static] Size in bytes of deconvolution_params. Note that this parameter is not counted as one of the kernel parameters. 
[out]
outputs  The output tensor. The output has the same number of dimensions as the input. (Kernel parameter #4)
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxFullyConnectedLayer
[Graph] Creates a Fully connected Convolutional Network Layer Node.
vx_node vxFullyConnectedLayer(
vx_graph graph,
vx_tensor inputs,
vx_tensor weights,
vx_tensor biases,
vx_enum overflow_policy,
vx_enum rounding_policy,
vx_tensor outputs);
This function implement Fully connected Convolutional Network layers. For fixedpoint data types, a fixed point calculation is performed with round and saturate according to the number of accumulator bits. The number of the accumulator bits are implementation defined, and should be at least 16.
round: rounding according the vx_round_policy_e
enumeration.
saturate: A saturation according the vx_convert_policy_e
enumeration.
The equation for Fully connected layer:
\(outputs[i] = saturate(round(\sum_{j} (inputs[j] \times weights[j,i]) + biasses[i]))\)
Where j is a index on the input feature and i is a index on the output.
There two possible input tensor layouts:

[#IFM, #batches]. See
vxCreateTensor
andvxCreateVirtualTensor
. 
[width, height, #IFM, #batches]. See
vxCreateTensor
andvxCreateVirtualTensor
In both cases number of batches are optional and may be multidimensional.
The second option is a special case to deal with convolution layer followed
by fully connected.
The dimension order is [#IFM, #batches].
See vxCreateTensor
and vxCreateVirtualTensor
.
Note that batch may be multidimensional.
Implementations must support input tensor data types indicated by the
extension strings "KHR_NN_8"
or "KHR_NN_8 KHR_NN_16"
.
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor data. 
[in]
weights  [static] Number of dimensions is 2. Dimensions are [#IFM, #OFM]. SeevxCreateTensor
andvxCreateVirtualTensor
. Implementations must support input tensor data type same as the inputs. 
[in]
biases  [static] Optional, ignored if NULL. The biases have one dimension [#OFM]. Implementations must support input tensor data type same as the inputs. 
[in]
overflow_policy  [static] AVX_TYPE_ENUM
of thevx_convert_policy_e
enumeration. 
[in]
rounding_policy  [static] AVX_TYPE_ENUM
of thevx_round_policy_e
enumeration. 
[out]
outputs  The output tensor data. Output dimension layout is [#OFM,#batches]. SeevxCreateTensor
andvxCreateVirtualTensor
, where #batches may be multidimensional. Output tensor data type must be same as the inputs.
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxLocalResponseNormalizationLayer
[Graph] Creates a Convolutional Network Local Response Normalization Layer Node.
This function is optional for 8bit extension with the extension string
"KHR_NN_8"
.
vx_node vxLocalResponseNormalizationLayer(
vx_graph graph,
vx_tensor inputs,
vx_enum type,
vx_size normalization_size,
vx_float32 alpha,
vx_float32 beta,
vx_float32 bias,
vx_tensor outputs);
Local Response Normalizing over local input regions. Each input value is divided by
\((bias + \frac{\alpha}{n} \sum_i x^2_i)^\beta\)
where n is the number of elements to normalize across. and the sum is taken over a rectangle region centred at that value (zero padding is added where necessary).
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor data. 3 lower dimensions represent a single input, 4th dimension for batch of inputs is optional.Dimension layout is [width, height, IFM, #batches]. SeevxCreateTensor
andvxCreateVirtualTensor
. Implementations must support input tensor data types indicated by the extension strings"KHR_NN_8 KHR_NN_16"
. Since this function is optional for"KHR_NN_8"
, so implementations only must supportVX_TYPE_INT16
with fixed_point_position 8. 
[in]
type  [static] Either same map or across maps (seevx_nn_norm_type_e
). 
[in]
normalization_size  [static] Number of elements to normalize across. Must be a positive odd number with maximum size of 7 and minimum of 3. 
[in]
alpha  [static] Alpha parameter in the local response normalization equation. must be positive. 
[in]
beta  [static] Beta parameter in the local response normalization equation. must be positive. 
[in]
bias  [static] Bias parameter in the local response normalization equation. must be positive. 
[out]
outputs  The output tensor data. Output will have the same number of dimensions as input.
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxPoolingLayer
[Graph] Creates a Convolutional Network Pooling Layer Node.
vx_node vxPoolingLayer(
vx_graph graph,
vx_tensor inputs,
vx_enum pooling_type,
vx_size pooling_size_x,
vx_size pooling_size_y,
vx_size pooling_padding_x,
vx_size pooling_padding_y,
vx_enum rounding,
vx_tensor outputs);
Pooling is done on the width and height dimensions of the vx_tensor
.
Therefore, we use here the term x for the width dimension and y for the
height dimension.
Pooling operation is a function operation over a rectangle size and then a nearest neighbour down scale. Here we use pooling_size_x and pooling_size_y to specify the rectangle size on which the operation is performed.
before the operation is done (average or maximum value). the data is padded with zeros in width and height dimensions . The down scale is done by picking the results according to a skip jump. The skip in the x and y dimension is determined by the output size dimensions. The first pixel of the down scale output is the first pixel in the input.
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor data. 3 lower dimensions represent a single input, 4th dimension for batch of inputs is optional.Dimension layout is [width, height, #IFM, #batches]. SeevxCreateTensor
andvxCreateVirtualTensor
Implementations must support input tensor data types indicated by the extension strings"KHR_NN_8"
or"KHR_NN_8 KHR_NN_16"
. 
[in]
pooling_type  [static] Either max pooling or average pooling (seevx_nn_pooling_type_e
). 
[in]
pooling_size_x  [static] Size of the pooling region in the x dimension 
[in]
pooling_size_y  [static] Size of the pooling region in the y dimension. 
[in]
pooling_padding_x  [static] Padding size in the x dimension. 
[in]
pooling_padding_y  [static] Padding size in the y dimension. 
[in]
rounding  [static] Rounding method for calculating output dimensions. Seevx_nn_rounding_type_e

[out]
outputs  The output tensor data. Output will have the same number of dimensions as input. Output tensor data type must be same as the inputs.
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxROIPoolingLayer
[Graph] Creates a Convolutional Network ROI pooling node
vx_node vxROIPoolingLayer(
vx_graph graph,
vx_tensor input_data,
vx_tensor input_rois,
const vx_nn_roi_pool_params_t* roi_pool_params,
vx_size size_of_roi_params,
vx_tensor output_arr);
Pooling is done on the width and height dimensions of the vx_tensor
.
The ROI Pooling get an array of roi rectangles, and an input tensor.
The kernel crop the width and height dimensions of the input tensor with the
ROI rectangles and down scale the result to the size of the output tensor.
The output tensor width and height are the pooled width and pooled height.
The down scale method is determined by the pool_type.
Notice that this node creation function has more parameters than the
corresponding kernel.
Numbering of kernel parameters (required if you create this node using the
generic interface) is explicitly specified here.
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor data. 3 lower dimensions represent a single input, 4th dimension for batch of inputs is optional. Dimension layout is [width, height, #IFM, #batches]. SeevxCreateTensor
andvxCreateVirtualTensor
. Implementations must support input tensor data types indicated by the extension strings"KHR_NN_8"
or"KHR_NN_8 KHR_NN_16"
. (Kernel parameter #0) 
[in]
inputs_rois  The roi array tensor. ROI array with dimensions [4, roi_count, #batches] where the first dimension represents 4 coordinates of the top left and bottom right corners of the roi rectangles, based on the input tensor width and height. #batches is optional and must be the same as in inputs. roi_count is the number of ROI rectangles. (Kernel parameter #1) 
[in]
pool_type  [static] Of typevx_nn_pooling_type_e
. OnlyVX_NN_POOLING_MAX
pooling is supported. (Kernel parameter #2) 
[in]
size_of_roi_params  [static] Size in bytes of roi_pool_params. Note that this parameter is not counted as one of the kernel parameters. 
[out]
output_arr  The output tensor. Output will have [output_width, output_height, #IFM, roi_count, #batches] dimensions. #batches is optional and must be the same as in inputs. (Kernel parameter #3)
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.
vxSoftmaxLayer
[Graph] Creates a Convolutional Network Softmax Layer Node.
vx_node vxSoftmaxLayer(
vx_graph graph,
vx_tensor inputs,
vx_tensor outputs);
The softmax function, is a generalization of the logistic function that “squashes” a Kdimensional vector z of arbitrary real values to a Kdimensional vector σ(z) of real values in the range (0, 1) that add up to 1. The function is given by: \(\sigma(z) = \frac{\exp^z}{\sum_i \exp^{z_i}}\)
Parameters

[in]
graph  The handle to the graph. 
[in]
inputs  The input tensor, with the number of dimensions according to the following scheme. In case IFM dimension is 1. Softmax is be calculated on that dimension. In case IFM dimension is 2. Softmax is be calculated on the first dimension. The second dimension is batching. In case IFM dimension is 3. Dimensions are [Width, Height, Classes]. And Softmax is calculated on the third dimension. In case IFM dimension is 4. Dimensions are [Width, Height, Classes, batching]. Softmax is calculated on the third dimension. Regarding the layout specification, seevxCreateTensor
andvxCreateVirtualTensor
. In all cases Implementations must support input tensor data types indicated by the extension strings"KHR_NN_8"
or"KHR_NN_8 KHR_NN_16"
. 
[out]
outputs  The output tensor. Output will have the same number of dimensions as input. Output tensor data type must be same as the inputs.
Returns: A node reference vx_node
.
Any possible errors preventing a successful creation should be checked using
vxGetStatus
.