# MPSCNNBinaryConvolution A convolution kernel with binary weights and an input image using binary approximations. ``` class MPSCNNBinaryConvolution ``` ## Overview The [`MPSCNNBinaryConvolution`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution) optionally first binarizes the input image and then convolves the result with a set of binary-valued filters, each producing one feature map in the output image (which is a normal image). The output is computed as follows: ![out[i, x, y, c] = ( sum_{dx,dy,f} in[i,x+dx, y+dy, f] x B[c,dx,dy,f] ) * scale[c] * beta[i,x,y] + bias[c]](images/com.apple.metalperformanceshaders/media-2903520@2x.png) where the *sum over* *dx,dy* is over the spatial filter kernel window defined by [`kernelWidth`](/documentation/MetalPerformanceShaders/MPSCNNConvolutionDescriptor/kernelWidth) and [`kernelHeight`](/documentation/MetalPerformanceShaders/MPSCNNConvolutionDescriptor/kernelHeight), *sum over* *f* is over the input feature channel indices within group, *B* contains the binary weights, interpreted as `{-1, 1}` or `{0, 1}` and *scale[c]* is the `outputScaleTerms` array and bias is the `outputBiasTerms` array. Above *i* is the image index in batch the sum over input channels *f* runs through the group indices. The convolution operator ⊗ is defined by [`MPSCNNBinaryConvolutionType`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionType) passed in at initialization time of the filter: - [`MPSCNNBinaryConvolutionType.binaryWeights`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionType/binaryWeights): The input image is not binarized at all and the convolution is computed interpreting the weights as `[0, 1] -> {-1, 1}` with the given scaling terms. - [`MPSCNNBinaryConvolutionType.XNOR`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionType/XNOR): The convolution is computed by first binarizing the input image using the sign function `bin(x) = x < 0 ? -1 : 1` and the convolution multiplication is done with the XNOR-operator: `!(x ^ y) = delta_xy = { (x == y) ? 1 : 0 }` and scaled according to the optional scaling operations. Note that we output the values of the bitwise convolutions to interval `{-1, 1}`, which means that the output of the XNOR-operator is scaled implicitly as follows: `r = 2 * ( !(x ^ y) ) - 1 = { -1, 1 }` This means that for a dot-product of two 32-bit words the result is: `r = 2 * popcount(!(x ^ y) ) - 32 = 32 - 2 * popcount( x ^ y ) = { -32, -30, ..., 30, 32 }` - [`MPSCNNBinaryConvolutionType.AND`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionType/AND): The convolution is computed by first binarizing the input image using the sign function `bin(x) = x < 0 ? -1 : 1` and the convolution multiplication is done with the AND-operator: `(x & y) = delta_xy * delta_x1 = { (x == y == 1) ? 1 : 0 }` and scaled according to the optional scaling operations. Note that we output the values of the AND-operation is assumed to lie in `{0, 1}` interval and hence no more implicit scaling takes place. This means that for a dot-product of two 32-bit words the result is: `r = popcount(x & y) = { 0, ..., 31, 32 }` The input data can be pre-offset and scaled by providing the `inputBiasTerms` and `inputScaleTerms` parameters for the initialization functions and this can be used for example to accomplish batch normalization of the data. The scaling of input values happens before possible beta-image computation. The parameter `beta` above is an optional image which is used to compute scaling factors for each spatial position and image index. For the XNOR-Net based networks this is computed as follows: ![beta[i,x,y] = sum_{dx,dy} A[i, x+dx, y+dy] / (kx * ky)](images/com.apple.metalperformanceshaders/media-2903518@2x.png) where *(dx,dy)* are summed over the convolution filter window. ![[ -kx/2, (kx-1)/2], [ -ky/2, (ky-1)/2 ] and A[i,x,y] = sum_{c} abs( in[i,x,y,c] ) / Nc](images/com.apple.metalperformanceshaders/media-2903519@2x.png) where *in* is the original input image (in full precision) and *Nc* is the number of input channels in the input image. Parameter `beta` is not passed as input and to enable beta-scaling the user can provide [`MPSCNNBinaryConvolutionFlags.useBetaScaling`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionFlags/useBetaScaling) in the flags parameter in the initialization functions. Finally the normal activation neuron is applied and the result is written to the output image. > Note: > ``doc://com.apple.metalperformanceshaders/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution`` does not currently support ``doc://com.apple.metalperformanceshaders/documentation/MetalPerformanceShaders/MPSCNNConvolutionDescriptor/groups`` greater than 1. ## Topics ### Initializers [`init(coder:device:)`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution/init(coder:device:)) [`init(device:convolutionData:outputBiasTerms:outputScaleTerms:inputBiasTerms:inputScaleTerms:type:flags:)`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution/init(device:convolutionData:outputBiasTerms:outputScaleTerms:inputBiasTerms:inputScaleTerms:type:flags:)) Initializes a binary convolution kernel. [`init(device:convolutionData:scaleValue:type:flags:)`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution/init(device:convolutionData:scaleValue:type:flags:)) Initializes a binary convolution kernel. [`MPSCNNConvolutionDataSource`](/documentation/MetalPerformanceShaders/MPSCNNConvolutionDataSource) The protocol that provides convolution filter weights and bias terms. [`MPSCNNBinaryConvolutionType`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionType) Options that defines what operations are used to perform binary convolution. [`MPSCNNBinaryConvolutionFlags`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolutionFlags) Options used to control binary convolution kernels. ### Instance Properties [`inputFeatureChannels`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution/inputFeatureChannels) [`outputFeatureChannels`](/documentation/MetalPerformanceShaders/MPSCNNBinaryConvolution/outputFeatureChannels) --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)