Convolution¶

General¶

Convolution operation performs the convolution between src tensor and weight tensor, which is defined as by the following formulas. Variable names follow the standard Naming Conventions.

Let \(\src\), \(\weights\) and \(\dst\) tensors have shape \(N \times IC \times IH \times IW\), \(OC \times IC \times KH \times KW\), and \(N \times OC \times OH \times OW\) respectively.

Furthermore, let the remaining convolution parameters be:

Parameter	Depth	Height	Width	Comment
Paddings: Front, top, and left	\(PD_L\)	\(PH_L\)	\(PW_L\)	In the attributes we use `pads_begin` to indicate the corresponding vector of paddings
Padding: Back, bottom, and right	\(PD_R\)	\(PH_R\)	\(PW_R\)	In the attributes we use `pads_end` to indicate the corresponding vector of paddings
Stride	\(SD\)	\(SH\)	\(SW\)	In the attributes we use `strides` to indicate the corresponding vector of strides
Dilation	\(DD\)	\(DH\)	\(DW\)	In the attributes we use `dilations` to indicate the corresponding vector of dilations

To further simplify the formulas, we assume that the attribute data_format and weights_format are set to NCX and OIX respectively. NCX means the fist axis represents batch dimension, the second axis represents channel dimension and the rest represents spatial dimensions. OIX means the first axis represents output channel dimension, the second axis represents input channel dimension and the rest represents weights spatial dimensions.

Regular Convolution¶

This is the same as the formula in Convolution primitive.

\[\begin{split}\dst(n, oc, oh, ow) = \bias(oc) \\ + \sum_{ic=0}^{IC-1}\sum_{kh=0}^{KH-1}\sum_{kw=0}^{KW-1} \src(n, ic, oh \cdot SH + kh - PH_L, ow \cdot SW + kw - PW_L) \cdot \weights(oc, ic, kh, kw).\end{split}\]

Here:

\(OH = \left\lfloor{\frac{IH - KH + PH_L + PH_R}{SH}} \right\rfloor + 1,\)
\(OW = \left\lfloor{\frac{IW - KW + PW_L + PW_R}{SW}} \right\rfloor + 1.\)

Convolution with Groups¶

The attribute groups is set to \(>1\).

\[\begin{split}\dst(n, g \cdot OC_G + oc_g, oh, ow) = \bias(g \cdot OC_G + oc_g) \\ + \sum_{ic_g=0}^{IC_G-1}\sum_{kh=0}^{KH-1}\sum_{kw=0}^{KW-1} \src(n, g \cdot IC_G + ic_g, oh \cdot SH + kh - PH_L, ow \cdot SW + kw - PW_L) \cdot \weights(g, oc_g, ic_g, kh, kw),\end{split}\]

where

\(IC_G = \frac{IC}{G}\),
\(OC_G = \frac{OC}{G}\), and
\(oc_g \in [0, OC_G).\)

Convolution with Dilation¶

The attribute dilation contains the element which is \(>1\).

\[\begin{split}\dst(n, oc, oh, ow) = \bias(oc) \\ + \sum_{ic=0}^{IC-1}\sum_{kh=0}^{KH-1}\sum_{kw=0}^{KW-1} \src(n, ic, oh \cdot SH + kh \cdot DH - PH_L, ow \cdot SW + kw \cdot DW - PW_L) \cdot \weights(oc, ic, kh, kw).\end{split}\]

Here:

\(OH = \left\lfloor{\frac{IH - DKH + PH_L + PH_R}{SH}} \right\rfloor + 1,\) where \(DKH = 1 + (KH - 1) \cdot DH\), and
\(OW = \left\lfloor{\frac{IW - DKW + PW_L + PW_R}{SW}} \right\rfloor + 1,\) where \(DKW = 1 + (KW - 1) \cdot DW\).

Operation attributes¶

Attribute Name	Description	Value Type	Supported Values	Required or Optional
strides	Controls the strides the weights tensor is moved when computing convolution	s64	A s64 list containing positive values	Required
pads_begin	Controls number of zeros to be add to the front/top/left of spatial dimensions	s64	A s64 list containing non-negative values	Required
pads_end	Controls number of zeros to be add to the back/bottom/right of spatial dimensions	s64	A s64 list containing non-negative values	Required
dilations	Controls the amount of stretching the kernel before convolution ( visualization link )	s64	A s64 list containing positive values (>1 means dilated convolution)	Required
auto_pad	Controls how the padding is calculated	string	`none` (default), `same_upper` , `same_lower` , `valid`	Optional
groups	Controls how input channels and output channels are divided into	s64	A positive s64 value, `1` by default	Optional
data_format	Controls how to interpret the shape of `src` and `dst` .	string	`NCX` , `NXC` (default)	Optional
weights_format	Controls how to interpret the shape of `weights`	string	`OIX` , `XIO` (default)	Optional

Execution arguments¶

The inputs and outputs must be provided according to below index order when constructing an operation.

Inputs¶

Index	Argument Name	Required or Optional
0	`src`	Required
1	`weights`	Required
2	`bias`	Optional

Note

The shape of \(\weights\) is \((out\_channels, in\_channels / groups, spatial\_shape)\) for OIX format or \((spatial\_shape, in\_channels / groups, out\_channels)\) for XIO format. Both \(in\_channels\) and \(out\_channels\) must be divisible by groups attribute.

Outputs¶

Index	Argument Name	Required or Optional
0	`dst`	Required

Supported data types¶

Convolution operation supports the following data type combinations.

Src	Weights	Bias	Dst
f32	f32	f32	f32
bf16	bf16	bf16	bf16
f16	f16	f16	f16

Concat ConvolutionBackwardData