multiplicationLayer

Multiplication layer

Since R2020b

Description

A multiplication layer multiplies inputs from multiple neural network layers element-wise.

Specify the number of inputs to the layer when you create it. The inputs to the layer have the names 'in1','in2',...,'inN', where N is the number of inputs. Use the input names when connecting or disconnecting the layer by using connectLayers or disconnectLayers, respectively. The size of the inputs to the multiplication layer must be either same across all dimensions or same across at least one dimension with other dimensions as singleton dimensions.

Creation

Syntax

layer = multiplicationLayer(numInputs)

layer = multiplicationLayer(numInputs,'Name',name)

Description

layer = multiplicationLayer(numInputs) creates a multiplication layer that multiplies numInputs inputs element-wise. This function also sets the NumInputs property.

layer = multiplicationLayer(numInputs,'Name',name) also sets the Name property.

Properties

NumInputs — Number of inputs

positive integer

Number of inputs to the layer, specified as a positive integer greater than or equal to 2.

The inputs have the names 'in1','in2',...,'inN', where N is NumInputs. For example, if NumInputs is 3, then the inputs have the names 'in1','in2', and 'in3'. Use the input names when connecting or disconnecting the layer using the connectLayers or disconnectLayers functions.

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to layers with the name "".

The MultiplicationLayer object stores this property as a character vector.

Data Types: char | string

InputNames — Input Names

{'in1','in2',…,'inN'} (default)

Input names, specified as {'in1','in2',...,'inN'}, where N is the number of inputs of the layer.

Data Types: cell

NumOutputs — Number of outputs

1 (default)

This property is read-only.

Number of outputs from the layer, returned as 1. This layer has a single output only.

Data Types: double

OutputNames — Output names

{'out'} (default)

This property is read-only.

Output names, returned as {'out'}. This layer has a single output only.

Data Types: cell

Examples

Create and Connect Multiplication Layer

Create a multiplication layer with two inputs and the name 'mul_1'.

mul = multiplicationLayer(2,'Name','mul_1')

mul = 
  MultiplicationLayer with properties:

          Name: 'mul_1'
     NumInputs: 2
    InputNames: {'in1'  'in2'}

   Learnable Parameters
    No properties.

   State Parameters
    No properties.

Use properties method to see a list of all properties.

Create two ReLU layers.

relu_1 = reluLayer('Name','relu_1');
relu_2 = reluLayer('Name','relu_2');

Create a dlnetwork object.

net = dlnetwork;

Add them to the network and connect them to the multiplication layer. The multiplication layer multiplies the outputs from the ReLU layers.

net = addLayers(net,relu_1);
net = addLayers(net,relu_2);
net = addLayers(net,mul);

net = connectLayers(net,'relu_1','mul_1/in1');
net = connectLayers(net,'relu_2','mul_1/in2');

plot(net);

Algorithms

Layer Input and Output Formats

Layers in a layer array or layer graph pass data to subsequent layers as formatted dlarray objects. The format of a dlarray object is a string of characters in which each character describes the corresponding dimension of the data. The formats consist of one or more of these characters:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, you can describe 2-D image data that is represented as a 4-D array, where the first two dimensions correspond to the spatial dimensions of the images, the third dimension corresponds to the channels of the images, and the fourth dimension corresponds to the batch dimension, as having the format "SSCB" (spatial, spatial, channel, batch).

You can interact with these dlarray objects in automatic differentiation workflows, such as those for developing a custom layer, using a functionLayer object, or using the forward and predict functions with dlnetwork objects.

This table shows the supported input formats of MultiplicationLayer objects and the corresponding output format. If the software passes the output of the layer to a custom layer that does not inherit from the nnet.layer.Formattable class, or a FunctionLayer object with the Formattable property set to 0 (false), then the layer receives an unformatted dlarray object with dimensions ordered according to the formats in this table. The formats listed here are only a subset. The layer may support additional formats such as formats with additional "S" (spatial) or "U" (unspecified) dimensions.

Each input must have data of the same format.

Input Format	Output Format
"CB" (channel, batch)	"CB" (channel, batch)
"SCB" (spatial, channel, batch)	"SCB" (spatial, channel, batch)
"SSCB" (spatial, spatial, channel, batch)	"SSCB" (spatial, spatial, channel, batch)
"SSSCB" (spatial, spatial, spatial, channel, batch)	"SSSCB" (spatial, spatial, spatial, channel, batch)
"CBT" (channel, batch, time)	"CBT" (channel, batch, time)
"SCBT" (spatial, channel, batch, time)	"SCBT" (spatial, channel, batch, time)
"SSCBT" (spatial, spatial, channel, batch, time)	"SSCBT" (spatial, spatial, channel, batch, time)
"SSSCBT" (spatial, spatial, spatial, channel, batch, time)	"SSSCBT" (spatial, spatial, spatial, channel, batch, time)
"CU" (channel, unspecified)	"CU" (channel, unspecified)
"SC" (spatial, channel)	"SC" (spatial, channel)
"SSC" (spatial, spatial, channel)	"SSC" (spatial, spatial, channel)
"SSSC" (spatial, spatial, spatial, channel)	"SSSC" (spatial, spatial, spatial, channel)
"BU" (batch, unspecified)	"BU" (batch, unspecified)

In dlnetwork objects, MultiplicationLayer objects also support these input and output format combinations.

Input Format	Output Format
"CT" (channel, time)	"CT" (channel, time)
"SCT" (spatial, channel, time)	"SCT" (spatial, channel, time)
"SSCT" (spatial, spatial, channel, time)	"SSCT" (spatial, spatial, channel, time)
"SSSCT" (spatial, spatial, spatial, channel, time)	"SSSCT" (spatial, spatial, spatial, channel, time)

Complex Numbers

MultiplicationLayer objects support complex-valued input and outputs. (since R2024a) The layer applies the same underlying operation to complex-valued input as it does to real-valued input and outputs complex-valued data where applicable.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced in R2020b

R2024a: Support for complex-valued inputs and outputs

MultiplicationLayer objects support complex-valued input and outputs. The layer applies the same underlying operation to complex-valued input as it does to real-valued input and outputs complex-valued data where applicable.