PairwiseFusion

			PairwiseFusion(connection, layers...)

Arguments

• connection: A function taking 2 inputs and combining them into a single output

• layers: The layers whose outputs are combined

Inputs

This layer behaves differently based on input type:

1. If input x is a tuple of length N (or the input is xs with N x's), matching the number of layers, then each layer receives a new input x[i] combined with the previous output y[i-1] using connection. Thus (y1, y2, y3) = PairwiseFusion(connection, layer1, layer2, layer3)((x1, x2, x3)) may be drawn as:

			x1 → layer1 → y1 ↘
                  connection → layer2 → y2 ↘
              x2 ↗                          connection → layer3 → y3
                                        x3 ↗

... or written as:

			
			
			
			y1
			 
			=
			 
			
			layer1
			(
			x1
			)
			

			
			y2
			 
			=
			 
			
			layer2
			(
			
			connection
			(
			x2
			,
			 
			y1
			)
			)
			

			
			y3
			 
			=
			 
			
			layer3
			(
			
			connection
			(
			x3
			,
			 
			y2
			)
			)

1. With just one input, each layer receives the same x combined with the previous output. Thus y = PairwiseFusion(connection, layers...)(x) obeys:

			
			
			
			
			y
			[
			1
			]
			 
			==
			 
			
			
			layers
			[
			1
			]
			(
			x
			)
			

			
			for
			
			 
			i
			 
			in
			
			 
			2
			:
			
			length
			(
			layers
			)
			
			
    
			
			
			y
			[
			i
			]
			 
			==
			 
			
			connection
			(
			x
			,
			 
			
			
			layers
			[
			i
			]
			(
			
			y
			[
			
			i
			-
			1
			]
			)
			)
			

			end

Returns

A tuple of length N with the output of each fusion (( y1, y2, ..., yN) in the example above).