Documentation

Compute the output shape of a linear transformation.

>>> type InputDim = 'Dim ('Name "input") ('Size 5)
>>> type OutputDim = 'Dim ('Name "output") ('Size 10)
>>> type BatchDim = 'Dim ('Name "batch") ('Size 20)
>>> type WeightShape = 'Shape '[OutputDim, InputDim]
>>> type BiasShape = 'Shape '[OutputDim]
>>> type InputShape = 'Shape '[BatchDim, InputDim]
>>> :kind! LinearWithBiasF WeightShape BiasShape InputShape
LinearWithBiasF WeightShape BiasShape InputShape :: Shape
                                                      [Dim (Name Symbol) (Size Natural)]
= 'Shape
    '[ 'Dim ('Name "batch") ('Size 20),
       'Dim ('Name "output") ('Size 10)]

Applies a linear transformation to the incoming data: \[ \mathrm{output} = \mathrm{input} \mathrm{weight}^{\intercal} + \mathrm{bias}. \]

Supported shapes:

• input: \((N, \ldots, \mathrm{inputFeatures})\), where \(N\) is the batch size, \(\ldots\) means any number of additional dimensions and \(\mathrm{inputFeatures}\) are the input features.
• weight: \((\mathrm{outputFeatures}, \mathrm{inputFeatures})\)
• bias: \((\mathrm{outputFeatures})\)
• output: \((N, \ldots, \mathrm{outputFeatures})\)

Examples:

>>> inputDim = SName @"input" :&: SSize @5
>>> outputDim = SName @"output" :&: SSize @10
>>> batchDim = SName @"batch" :&: SSize @20
>>> weightShape = SShape $ outputDim :|: inputDim :|: SNil
>>> biasShape = SShape $ outputDim :|: SNil
>>> inputShape = SShape $ batchDim :|: inputDim :|: SNil
>>> g <- sMkGenerator (SDevice SCPU) 0
>>> sRandn' = sRandn . TensorSpec (SGradient SWithoutGradient) (SLayout SDense) (SDevice SCPU) (SDataType SFloat)
>>> (weight, g') <- sRandn' weightShape g
[W TensorImpl.h:1463] Warning: Named tensors and all their associated APIs are an experimental feature and subject to change. Please do not use them for anything important until they are released as stable. (function operator())
>>> (bias, g'') <- sRandn' biasShape g'
>>> (input, _) <- sRandn' inputShape g''
>>> result = linearWithBias weight bias input
>>> :type result
result
  :: Tensor
       ('Gradient 'WithoutGradient)
       ('Layout 'Dense)
       ('Device 'CPU)
       ('DataType 'Float)
       ('Shape
          '[ 'Dim ('Name "batch") ('Size 20),
             'Dim ('Name "output") ('Size 10)])