quadraticLayer

Quadratic layer

Description

A quadratic layer calculates the pair-wise products of the elements of the input (the quadratic monomials).

Creation

Syntax

layer = quadraticLayer

layer = quadraticLayer(Name=name)

Description

layer = quadraticLayer creates a quadratic layer.

layer = quadraticLayer(Name=name) also sets the layer name. For example, Name="quad" sets the layer name to "quad".

Input Arguments

name — Layer name

"quadratic" (default) | character vector | string scalar

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

This argument sets the Name property.

Data Types: char | string

Properties

Name — Layer name

'quadratic' (default) | character vector | string scalar

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

The QuadraticLayer object stores this property as a character vector.

Data Types: char | string

Description — One-line description of the layer

Read-only: 'Quadratic' (default)

This property is read-only.

One-line description of the layer, stored as 'Quadratic'. This description appears when you display a Layer array and when you use the analyzeNetwork function.

Type — Type of the layer

Read-only: 'Quadratic' (default)

This property is read-only.

Type of the layer, stored as 'Quadratic'. The type appears when you display a Layer array and when you use the analyzeNetwork function.

NumInputs — Number of inputs

Read-only: 1 (default)

This property is read-only.

Number of inputs to the layer, stored as 1. This layer accepts a single input only.

Data Types: double

InputNames — Input names

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

This property is read-only.

Input names, stored as {'in'}. This layer accepts a single input only.

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 Quadratic Layer

Create a quadratic layer with the name "quad".

layer = quadraticLayer(Name="quad")

layer = 
  QuadraticLayer with properties:

    Name: 'quad'

   Learnable Parameters
    No properties.

   State Parameters
    No properties.

  Show all properties

Include a quadratic layer in a layer array.

layers = [
    featureInputLayer(3)
    quadraticLayer
    fullyConnectedLayer(1)];

Algorithms

Quadratic Layer

A quadratic layer calculates the pair-wise products of the elements of the input (the quadratic monomials).

The output of the layer is

$$Y=\left[\begin{array}{c}{x}_1{x}_1\\ x_1{x}_2\\ x_2{x}_2\\ x_1{x}_3\\ x_2{x}_3\\ x_3{x}_3\\ ⋮\\ x_{N-1}{x}_N\\ x_N{x}_N\end{array}\right],$$

where

$$x=\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ x_N\end{array}\right]$$

is the layer input.

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 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).

QuadraticLayer objects support data of any format with one or two dimensions only. The layer operates over the first dimension. The layer and does not add or remove any dimensions and outputs data with the same format the input data.

Version History

Introduced in R2019a

R2025a: Moved to Deep Learning Toolbox

This layer now requires Deep Learning Toolbox™ only. In previous releases, this layer also required Reinforcement Learning Toolbox™.

There are some changes to the layer:

• The default value of the Description property is 'Quadratic'. In previous releases, the default value is 'Quadratic layer'.

• Setting the Description using a name-value argument is not recommended. Use the default value instead. Code that sets the Description argument continues to work.

• The default value of the Type property is 'Quadratic'. In previous releases, the default value is "QuadraticLayer".

• quadraticLayer objects have different class names. If you have code that refers to the previous class names of these objects, then replace the references with the new class names. In most cases, your code will continue to run.

  This table shows the change of outputs of the class function for this layers.

  layer	class(layer) (Before R2025a)	class(layer) (Starting in R2025a)
  quadraticLayer object	'rl.layer.QuadraticLayer'	'nnet.cnn.layer.QuadraticLayer

  The isa function returns the same value as for previous releases. For example, in R2025a, both isa(layer,"nnet.cnn.layer.QuadraticLayer") and isa(layer,"rl.layer.QuadraticLayer") return 1 (true) for quadraticLayer objects.

  If you have code that uses the value returned by the class function, then you must update your code to use the new class name. For example, replace instances of

  if class(layer) == "rl.layer.QuadraticLayer"
      ...
  end

  with

  if isa(layer,"nnet.cnn.layer.QuadraticLayer")
      ...
  end