# BinaryConvolution¶

Versioned name : BinaryConvolution-1

Category : Convolution

Short description : Computes 2D convolution of binary input and binary kernel tensors.

Detailed description : The operation behaves as regular Convolution but uses specialized algorithm for computations on binary data. More thorough explanation can be found in Understanding Binary Neural Networks and Bitwise Neural Networks.

Computation algorithm for mode xnor-popcount :

• X = XNOR(input_patch, filter), where XNOR is bitwise operation on two bit streams

• P = popcount(X), where popcount is the number of 1 bits in the X bit stream

• Output = 2 * P - B, where B is the total number of bits in the P bit stream

Attributes :

• strides

• Description : strides is a distance (in pixels) to slide the filter on the feature map over the (y, x) axes for 2D convolutions. For example, strides equal 2,1 means sliding the filter 2 pixel at a time over height dimension and 1 over width dimension.

• Range of values : integer values starting from 0

• Type : int[]

• Default value : None

• Required : yes

• Description : pads_begin is a number of pixels to add to the beginning along each axis. For example, pads_begin equal 1,2 means adding 1 pixel to the top of the input and 2 to the left of the input.

• Range of values : integer values starting from 0

• Type : int[]

• Default value : None

• Required : yes

• Note : the attribute is ignored when auto_pad attribute is specified.

• Description : pads_end is a number of pixels to add to the ending along each axis. For example, pads_end equal 1,2 means adding 1 pixel to the bottom of the input and 2 to the right of the input.

• Range of values : integer values starting from 0

• Type : int[]

• Default value : None

• Required : yes

• Note : the attribute is ignored when auto_pad attribute is specified.

• dilations

• Description : dilations denotes the distance in width and height between elements (weights) in the filter. For example, dilation equal 1,1 means that all the elements in the filter are neighbors, so it is the same as for the usual convolution. dilation equal 2,2 means that all the elements in the filter are matched not to adjacent elements in the input matrix, but to those that are adjacent with distance 1.

• Range of values : integer value starting from 0

• Type : int[]

• Default value : None

• Required : yes

• mode

• Description : mode defines how input tensor 0/1 values and weights 0/1 are interpreted as real numbers and how the result is computed.

• Range of values :

• xnor-popcount

• Type : string

• Default value : None

• Required : yes

• Note : value 0 in inputs is interpreted as -1, value 1 as 1

• Description : pad_value is a floating-point value used to fill pad area.

• Range of values : a floating-point number

• Type : float

• Default value : None

• Required : yes

• same_upper - the input is padded to match the output size. In case of odd padding value an extra padding is added at the end.

• same_lower - the input is padded to match the output size. In case of odd padding value an extra padding is added at the beginning.

• valid - do not use padding.

• Type : string

• Default value : explicit

• Required : no

Inputs :

• 1 : Input tensor of type T1 and rank 4. Layout is [N, C_IN, Y, X] (number of batches, number of channels, spatial axes Y, X). Required.

• 2 : Kernel tensor of type T2 and rank 4. Layout is [C_OUT, C_IN, Y, X] (number of output channels, number of input channels, spatial axes Y, X). Required.

• Note : Interpretation of tensor values is defined by mode attribute.

Outputs :

• 1 : Output tensor of type T3 and rank 4. Layout is [N, C_OUT, Y, X] (number of batches, number of kernel output channels, spatial axes Y, X).

Types :

• T1 : any numeric type with values 0 or 1.

• T2 : u1 type with binary values 0 or 1.

• T3 : T1 type with full range of values.

Example :

2D Convolution

<layer type="BinaryConvolution" ...>
<input>
<port id="0">
<dim>1</dim>
<dim>3</dim>
<dim>224</dim>
<dim>224</dim>
</port>
<port id="1">
<dim>64</dim>
<dim>3</dim>
<dim>5</dim>
<dim>5</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>64</dim>
<dim>224</dim>
<dim>224</dim>
</port>
</output>
</layer>