multiplicationLayer

Multiplication layer

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

This property is read-only after object creation. To set this property, use the corresponding positional input argument when you create the MultiplicationLayer object.

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

Layer name, specified as a character vector. For Layer array input, the trainnet and dlnetwork functions automatically assign names to unnamed layers.

Data Types: char

InputNames — Input Names

Read-only: {'in1','in2',…,'inN'} (default)

This property is read-only.

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

Data Types: cell

NumOutputs — Number of outputs

Read-only: 1 (default)

This property is read-only.

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

Data Types: double

OutputNames — Output names

Read-only: {'out'} (default)

This property is read-only.

Output names, stored 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.

  Show 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

Most 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 format consists 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

• 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 to 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 of the formats that the layer supports. The layer might support additional formats, such as formats with additional "S" (spatial) or "U" (unspecified) dimensions.

Multiplication layers support inputs of any format. The layer uses implicit expansion to combine inputs. The layer introduces singleton dimensions (dimensions of size 1) into the inputs, as necessary, to make the dimensionality consistent for element-wise multiplication. For formatted inputs, the layer inserts singleton dimensions at the end of each block of dimensions with the same label. The sizes of the dimensions must be consistent for element-wise multiplication using implicit expansion. The output format is a combination of the input formats. (since R2026a)

Before R2026a: Each input must have data of the same format.

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.

Perform multiplication using implicit expansion

MultiplicationLayer objects support implicit expansion to combine inputs. The layer introduces singleton dimensions (dimensions of size 1) into the inputs, as necessary, to make the dimensionality consistent for element-wise multiplication.