.rst .pdf

Contents

Naming Conventions

oneDNN documentation relies on a set of standard naming conventions for variables. This section describes these conventions.

Variable (Tensor) Names

Neural network models consist of operations of the following form:

\[\dst = f(\src, \weights),\]

where \(\dst\) and \(\src\) are activation tensors, and \(\weights\) are learnable tensors.

The backward propagation consists then in computing the gradients with respect to the \(\src\) and \(\weights\) respectively:

\[\diffsrc = df_{\src}(\diffdst, \src, \weights, \dst),\]

and

\[\diffweights = df_{\weights}(\diffdst, \src, \weights, \dst).\]

While oneDNN uses src, dst, and weights as generic names for the activations and learnable tensors, for a specific operation there might be commonly used and widely known specific names for these tensors. For instance, the convolution operation has a learnable tensor called bias. For usability reasons, oneDNN primitives use such names in initialization or other functions to simplify the coding.

To summarize, oneDNN uses the following commonly used notations for tensors:

Name	Me
src	Source tensor
dst	Destination tensor
weights	Weights tensor
bias	Bias tensor (used in Convolution , Inner Product and other primitives)
scale_shift	Scale and shift tensors (used in Batch Normalization and Layer Normalization )
workspace	Workspace tensor that carries additional information from the forward propagation to the backward propagation
scratchpad	Temporary tensor that is required to store the intermediate results
diff_src	Gradient tensor with respect to the source
diff_dst	Gradient tensor with respect to the destination
diff_weights	Gradient tensor with respect to the weights
diff_bias	Gradient tensor with respect to the bias
diff_scale_shift	Gradient tensor with respect to the scale and shift
*_layer	RNN layer data or weights tensors
*_iter	RNN recurrent data or weights tensors

Formulas and Verbose Output

oneDNN uses the following notations in the documentation formulas and verbose output. Here, lower-case letters are used to denote indices in a particular spatial dimension, the sizes of which are denoted by corresponding upper-case letters.

Name	Semantics
n (or mb )	batch
g	groups
oc , od , oh , ow	output channels, depth, height, and width
ic , id , ih , iw	input channels, depth, height, and width
kd , kh , kw	kernel (filter) depth, height, and width
sd , sh , sw	stride by depth, height, and width
dd , dh , dw	dilation by depth, height, and width
pd , ph , pw	padding by depth, height, and width

RNN-Specific Notation

The following notations are used when describing RNN primitives.

Name	Semantics
\(\cdot\)	matrix multiply operator
\(*\)	element-wise multiplication operator
W	input weights
U	recurrent weights
\(^T\)	transposition
B	bias
h	hidden state
a	intermediate value
x	input
\(_t {}_{}\)	timestamp
\(l\)	layer index
activation	tanh, relu, logistic
c	cell state
\(\tilde{c}\)	candidate state
i	input gate
f	forget gate
o	output gate
u	update gate
r	reset gate

Memory Formats Tags

When describing tensor memory formats, which is the oneDNN term for the way that the data is laid out in memory, documentation uses letters of the English alphabet to describe an order of dimensions and their semantics.

The canonical sequence of letters is a, b, c, …, z. In this notation, the ab tag denotes a two-dimensional tensor with a denoting the outermost dimension and b denoting the innermost dimension, where the latter is dense in memory. Further, the ba tag denotes a two-dimensional tensor but with last two dimensions transposed: instead of the naturally dense b dimension, now a is the dense dimension. If we suppose that the two-dimensional tensor is a matrix and the a and b dimensions represent the number of columns and rows, then ab would denote the row-major (C) format and ba would denote the column-major (Fortran) format.

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Upper-case letters are used to indicate that the data is laid out in blocks for a particular dimension. In such cases, the format name contains both upper- and lower-case letters for that dimension with a lower-case letter preceded by the block size. For example, the Ab16a tag denotes a format similar to row-major but with columns split into contiguous blocks of 16 elements each. Moreover, the implicit assumption is that if the number of columns is not divisible by 16, the last block in the in-memory representation will contain padding.

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Since there are many widely used names for specific deep learning domains like convolutional neural networks (CNNs), oneDNN also supports memory format tags in which dimensions have specifically assigned meaning like ‘image width’, ‘image height’, etc. The following table summarizes notations used in such memory format tags.

Letter	Dimension
n	batch
g	groups
c	channels
o	output channels
i	input channels
h	height
w	width
d	depth
t	timestamp
l	layer
d	direction
g	gate
s	state

The canonical sequence of dimensions for four-dimensional data tensors in CNNs is (batch, channels, spatial dimensions). Spatial dimensions are ordered for tensors with three spatial dimensions as (depth, height, width), for tensors with two spatial dimensions as (height, width), and as just (width) for tensors with only one spatial dimension.

In this notation, nchw is a memory format tag for a four-dimensional tensor, with the first dimension corresponding to batch, the second to channel, and the remaining two to spatial dimensions. Due to the canonical order of dimensions for CNNs, this tag is the same as abcd. As another example, nhwc is the same as acdb.