regressionLayer

R2026b

(Not recommended) Regression output layer

regressionLayer is not recommended. Use the trainnet function and set the loss function to "mse" instead. For more information, see Version History.

To learn more about how to transition trainNetwork, SeriesNetwork, and DAGNetwork code to dlnetwork workflows, see Transition trainNetwork, SeriesNetwork, and DAGNetwork Code to dlnetwork Workflows.

Syntax

layer = regressionLayer

layer = regressionLayer(Name,Value)

Description

A regression layer computes the half-mean-squared-error loss for regression tasks.

layer = regressionLayer returns a regression output layer for a neural network as a RegressionOutputLayer object.

layer = regressionLayer(Name,Value) sets the optional Name and ResponseNames properties using name-value pairs. For example, regressionLayer('Name','output') creates a regression layer with the name 'output'. Enclose each property name in single quotes.

Examples

Create Regression Output Layer

Create a regression output layer.

Create a regression output layer with the name 'routput'.

layer = regressionLayer('Name','routput')

layer = 
  RegressionOutputLayer with properties:

             Name: 'routput'
    ResponseNames: {}

   Hyperparameters
     LossFunction: 'mean-squared-error'

The default loss function for regression is mean-squared-error.

Include a regression output layer in a Layer array.

layers = [ ...
    imageInputLayer([28 28 1])
    convolution2dLayer(12,25)
    reluLayer
    fullyConnectedLayer(1)
    regressionLayer]

layers = 
  5x1 Layer array with layers:

     1   ''   Image Input         28x28x1 images with 'zerocenter' normalization
     2   ''   2-D Convolution     25 12x12 convolutions with stride [1  1] and padding [0  0  0  0]
     3   ''   ReLU                ReLU
     4   ''   Fully Connected     1 fully connected layer
     5   ''   Regression Output   mean-squared-error

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: regressionLayer('Name','output') creates a regression layer with the name 'output'

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainNetwork function automatically assigns names to layers with the name "".

The RegressionOutputLayer object stores this property as a character vector.

Data Types: char | string

ResponseNames — Names of responses

{} (default) | cell array of character vectors | string array

Names of the responses, specified a cell array of character vectors or a string array. At training time, the software automatically sets the response names according to the training data. The default is {}.

Data Types: cell

Output Arguments

layer — Regression output layer

RegressionOutputLayer object

Regression output layer, returned as a RegressionOutputLayer object.

More About

Regression Output Layer

A regression layer computes the half-mean-squared-error loss for regression tasks. For typical regression problems, a regression layer must follow the final fully connected layer.

For a single observation, the mean-squared-error is given by:

$$\text{MSE}={\displaystyle \sum }_{i=1}^R\frac{{(t_i-y_i)}^2}{R},$$

where R is the number of responses, t_i is the target output, and y_i is the network’s prediction for response i.

For image and sequence-to-one regression networks, the loss function of the regression layer is the half-mean-squared-error of the predicted responses, not normalized by R:

$$\text{loss}=\frac{1}{2}{\displaystyle \sum }_{i=1}^R{(t_i-y_i)}^2.$$

For image-to-image regression networks, the loss function of the regression layer is the half-mean-squared-error of the predicted responses for each pixel, not normalized by R:

$$\text{loss}=\frac{1}{2}{\displaystyle \sum }_{p=1}^{HWC}{(t_p-y_p)}^2,$$

where H, W, and C denote the height, width, and number of channels of the output respectively, and p indexes into each element (pixel) of t and y linearly.

For sequence-to-sequence regression networks, the loss function of the regression layer is the half-mean-squared-error of the predicted responses for each time step, not normalized by R:

$$\text{loss}=\frac{1}{2S}{\displaystyle \sum }_{i=1}^S{\displaystyle \sum }_{j=1}^R{(t_{ij}-y_{ij})}^2,$$

where S is the sequence length.

When training, the software calculates the mean loss over the observations in the mini-batch.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The code generator represents characters in an 8-bit ASCII codeset that the locale setting determines. Therefore, the use of non-ASCII characters in class names, layer names, layer description, or network names might result in errors. For more information, see Encoding of Characters in Code Generation (MATLAB Coder).

GPU Code Generation

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

Usage notes and limitations:

• To generate CUDA^® or C++ code by using GPU Coder™, you must first construct and train a deep neural network. Once the network is trained and evaluated, you can configure the code generator to generate code and deploy the convolutional neural network on platforms that use NVIDIA^® or ARM^® GPU processors. For more information, see Deep Learning with GPU Coder (GPU Coder).

• For this layer, you can generate code that takes advantage of the NVIDIA CUDA deep neural network library (cuDNN), NVIDIA TensorRT™ high performance inference library, or the ARM Compute Library for Mali GPU.

• The code generator represents characters in an 8-bit ASCII codeset that the locale setting determines. Therefore, the use of non-ASCII characters in class names, layer names, layer description, or network names might result in errors. For more information, see Encoding of Characters in Code Generation (MATLAB Coder).

Version History

Introduced in R2017a

R2024a: Not recommended

Starting in R2024a, RegressionOutputLayer objects are not recommended, use the trainnet and set the loss function to "mse" instead.

There are no plans to remove support for RegressionOutputLayer objects. However, the trainnet function has these advantages and is recommended instead:

• trainnet supports dlnetwork objects, which support a wider range of network architectures that you can create or import from external platforms.

• trainnet enables you to easily specify loss functions. You can select from built-in loss functions or specify a custom loss function.

• trainnet outputs a dlnetwork object, which is a unified data type that supports network building, prediction, built-in training, visualization, compression, verification, and custom training loops.

• trainnet is typically faster than trainNetwork.

This table shows some typical usages of the trainNetwork function with RegressionOutputLayer objects and how to update your code to use the trainnet function instead.

Not Recommended	Recommended
net = trainNetwork(X,T,layers,options), where layers contains a RegressionOutputLayer object.	net = trainnet(X,T,layers,"mse",options); In this example, layers specifies same network without a RegressionOutputLayer object.
net = trainNetwork(data,layers,options), where layers contains a RegressionOutputLayer object.	net = trainnet(data,layers,"mse",options); In this example, layers specifies same network without a RegressionOutputLayer object.

To learn more about how to transition trainNetwork, SeriesNetwork, and DAGNetwork code to dlnetwork workflows, see Transition trainNetwork, SeriesNetwork, and DAGNetwork Code to dlnetwork Workflows.