trainnet

Train deep learning neural network

Since R2023b

Syntax

netTrained = trainnet(images,net,lossFcn,options)

netTrained = trainnet(images,targets,net,lossFcn,options)

netTrained = trainnet(sequences,net,lossFcn,options)

netTrained = trainnet(sequences,targets,net,lossFcn,options)

netTrained = trainnet(features,net,lossFcn,options)

netTrained = trainnet(features,targets,net,lossFcn,options)

netTrained = trainnet(data,net,lossFcn,options)

[netTrained,info] = trainnet(___)

Description

netTrained = trainnet(images,net,lossFcn,options) trains the neural network specified by net for image tasks using the images and targets specified by images and the training options defined by options.

netTrained = trainnet(images,targets,net,lossFcn,options) trains using the images specified by images and targets specified by targets.

netTrained = trainnet(sequences,net,lossFcn,options) trains a neural network for sequence or time-series tasks (for example, an LSTM or GRU neural network) using the sequences and targets specified by sequences.

netTrained = trainnet(sequences,targets,net,lossFcn,options) trains using the sequences specified by sequences and targets specified by targets.

netTrained = trainnet(features,net,lossFcn,options) trains a neural network for feature tasks (for example, a multilayer perceptron (MLP) neural network) using the feature data and targets specified by features.

netTrained = trainnet(features,targets,net,lossFcn,options) trains using the feature data specified by features and targets specified by targets.

netTrained = trainnet(data,net,lossFcn,options) trains a neural network with other data layouts or combinations of different types of data.

[netTrained,info] = trainnet(___) also returns information on the training using any of the previous syntaxes.

Examples

Train Neural Network with Image Data

If you have a data set of images, then you can train a deep neural network using an image input layer.

Unzip the digit sample data and create an image datastore. The imageDatastore function automatically labels the images based on folder names.

unzip("DigitsData.zip")

imds = imageDatastore("DigitsData", ...
    IncludeSubfolders=true, ...
    LabelSource="foldernames");

Divide the data into training and test data sets, so that each category in the training set contains 750 images, and the test set contains the remaining images from each label. splitEachLabel splits the image datastore into two new datastores for training and test.

numTrainFiles = 750;
[imdsTrain,imdsTest] = splitEachLabel(imds,numTrainFiles,"randomized");

Define the convolutional neural network architecture. Specify the size of the images in the input layer of the network and the number of classes in the final fully connected layer. Each image is 28-by-28-by-1 pixels.

inputSize = [28 28 1];
numClasses = numel(categories(imds.Labels));

layers = [
    imageInputLayer(inputSize)
    convolution2dLayer(5,20)
    batchNormalizationLayer
    reluLayer
    fullyConnectedLayer(numClasses)
    softmaxLayer];

Specify the training options.

• Train using the SGDM solver.

• Train for four epochs.

• Monitor the training progress in a plot and monitor the accuracy metric.

• Disable the verbose output.

options = trainingOptions("sgdm", ...
    MaxEpochs=4, ...
    Verbose=false, ...
    Plots="training-progress", ...
    Metrics="accuracy");

Train the neural network. For classification, use cross-entropy loss.

net = trainnet(imdsTrain,layers,"crossentropy",options);

Test the network using the labeled test set.

Extract the image data and labels from the test datastore.

XTest = readall(imdsTest);
TTest = imdsTest.Labels;
classNames = categories(TTest);

Concatenate the images into a numeric array and convert it to single.

XTest = cat(4,XTest{:});
XTest = single(XTest);

Predict the classification scores using the trained network then convert the predictions to labels using the onehotdecode function.

YTest = predict(net,XTest);
YTest = onehotdecode(YTest,classNames,2);

Visualize the predictions in a confusion chart.

confusionchart(TTest,YTest)

Train Network with Tabular Data

If you have a data set of numeric features (for example tabular data without spatial or time dimensions), then you can train a deep neural network using a feature input layer.

Read the transmission casing data from the CSV file "transmissionCasingData.csv".

filename = "transmissionCasingData.csv";
tbl = readtable(filename,TextType="String");

Convert the labels for prediction to categorical using the convertvars function.

labelName = "GearToothCondition";
tbl = convertvars(tbl,labelName,"categorical");

To train a network using categorical features, you must first convert the categorical features to numeric. First, convert the categorical predictors to categorical using the convertvars function by specifying a string array containing the names of all the categorical input variables. In this data set, there are two categorical features with names "SensorCondition" and "ShaftCondition".

categoricalPredictorNames = ["SensorCondition" "ShaftCondition"];
tbl = convertvars(tbl,categoricalPredictorNames,"categorical");

Loop over the categorical input variables. For each variable, convert the categorical values to one-hot encoded vectors using the onehotencode function.

for i = 1:numel(categoricalPredictorNames)
    name = categoricalPredictorNames(i);
    tbl.(name) = onehotencode(tbl.(name),2);
end

View the first few rows of the table. Notice that the categorical predictors have been split into multiple columns.

head(tbl)

    SigMean     SigMedian    SigRMS    SigVar     SigPeak    SigPeak2Peak    SigSkewness    SigKurtosis    SigCrestFactor    SigMAD     SigRangeCumSum    SigCorrDimension    SigApproxEntropy    SigLyapExponent    PeakFreq    HighFreqPower    EnvPower    PeakSpecKurtosis    SensorCondition    ShaftCondition    GearToothCondition
    ________    _________    ______    _______    _______    ____________    ___________    ___________    ______________    _______    ______________    ________________    ________________    _______________    ________    _____________    ________    ________________    _______________    ______________    __________________

    -0.94876     -0.9722     1.3726    0.98387    0.81571       3.6314        -0.041525       2.2666           2.0514         0.8081        28562              1.1429             0.031581            79.931            0          6.75e-06       3.23e-07         162.13             0    1             1    0          No Tooth Fault  
    -0.97537    -0.98958     1.3937    0.99105    0.81571       3.6314        -0.023777       2.2598           2.0203        0.81017        29418              1.1362             0.037835            70.325            0          5.08e-08       9.16e-08         226.12             0    1             1    0          No Tooth Fault  
      1.0502      1.0267     1.4449    0.98491     2.8157       3.6314         -0.04162       2.2658           1.9487        0.80853        31710              1.1479             0.031565            125.19            0          6.74e-06       2.85e-07         162.13             0    1             0    1          No Tooth Fault  
      1.0227      1.0045     1.4288    0.99553     2.8157       3.6314        -0.016356       2.2483           1.9707        0.81324        30984              1.1472             0.032088             112.5            0          4.99e-06        2.4e-07         162.13             0    1             0    1          No Tooth Fault  
      1.0123      1.0024     1.4202    0.99233     2.8157       3.6314        -0.014701       2.2542           1.9826        0.81156        30661              1.1469              0.03287            108.86            0          3.62e-06       2.28e-07         230.39             0    1             0    1          No Tooth Fault  
      1.0275      1.0102     1.4338     1.0001     2.8157       3.6314         -0.02659       2.2439           1.9638        0.81589        31102              1.0985             0.033427            64.576            0          2.55e-06       1.65e-07         230.39             0    1             0    1          No Tooth Fault  
      1.0464      1.0275     1.4477     1.0011     2.8157       3.6314        -0.042849       2.2455           1.9449        0.81595        31665              1.1417             0.034159            98.838            0          1.73e-06       1.55e-07         230.39             0    1             0    1          No Tooth Fault  
      1.0459      1.0257     1.4402    0.98047     2.8157       3.6314        -0.035405       2.2757            1.955        0.80583        31554              1.1345               0.0353            44.223            0          1.11e-06       1.39e-07         230.39             0    1             0    1          No Tooth Fault  

View the class names of the data set.

classNames = categories(tbl{:,labelName})

classNames = 2x1 cell
    {'No Tooth Fault'}
    {'Tooth Fault'   }

Set aside data for testing. Partition the data into a training set containing 85% of the data and a test set containing the remaining 15% of the data. To partition the data, use the trainingPartitions function, attached to this example as a supporting file. To access this file, open the example as a live script.

numObservations = size(tbl,1);
[idxTrain,idxTest] = trainingPartitions(numObservations,[0.85 0.15]);

tblTrain = tbl(idxTrain,:);
tblTest = tbl(idxTest,:);

Convert the data to a format that the trainnet function supports. Convert the predictors and targets to numeric and categorical arrays, respectively. For feature input, the network expects data with rows that correspond to observations and columns that correspond to the features. If your data has a different layout, then you can preprocess your data to have this layout or you can provide layout information using data formats. For more information, see Deep Learning Data Formats.

predictorNames = ["SigMean" "SigMedian" "SigRMS" "SigVar" "SigPeak" "SigPeak2Peak" ...
    "SigSkewness" "SigKurtosis" "SigCrestFactor" "SigMAD" "SigRangeCumSum" ...
    "SigCorrDimension" "SigApproxEntropy" "SigLyapExponent" "PeakFreq" ...
    "HighFreqPower" "EnvPower" "PeakSpecKurtosis" "SensorCondition" "ShaftCondition"];
XTrain = table2array(tblTrain(:,predictorNames));
TTrain = tblTrain.(labelName);

XTest = table2array(tblTest(:,predictorNames));
TTest = tblTest.(labelName);

Define a network with a feature input layer and specify the number of features. Also, configure the input layer to normalize the data using Z-score normalization.

numFeatures = size(XTrain,2);
numClasses = numel(classNames);
 
layers = [
    featureInputLayer(numFeatures,Normalization="zscore")
    fullyConnectedLayer(16)
    layerNormalizationLayer
    reluLayer
    fullyConnectedLayer(numClasses)
    softmaxLayer];

Specify the training options:

• Train using the L-BFGS solver. This solver suits tasks with small networks and when the data fits in memory.

• Train using the CPU. Because the network and data is small, the CPU is better suited.

• Display the training progress in a plot.

• Suppress the verbose output.

options = trainingOptions("lbfgs", ...
    ExecutionEnvironment="cpu", ...
    Plots="training-progress", ...
    Verbose=false);

Train the network using the trainnet function. For classification, use cross-entropy loss.

net = trainnet(XTrain,TTrain,layers,"crossentropy",options);

Predict the labels of the test data using the trained network. Predict the classification scores using the trained network then convert the predictions to labels using the onehotdecode function.

YTest = predict(net,XTest);
YTest = onehotdecode(YTest,classNames,2);

Visualize the predictions in a confusion chart.

confusionchart(TTest,YTest)

Calculate the classification accuracy, The accuracy is the proportion of the labels that the network predicts correctly.

accuracy = mean(YTest == TTest)

accuracy = 0.9062

Input Arguments

Data

images — Image data

numeric array | dlarray object | datastore

Image data, specified as a numeric array, dlarray object, or a datastore.

Tip

For sequences of images, for example video data, use the sequences input argument.

If you have data that fits in memory that does not require additional processing such as data augmentation, then it is usually easiest to specify the input data as a numeric array. If you want to train with image files stored on disk, or want to apply additional processing such as data augmentation, then it is usually easiest to use datastores. For neural networks with multiple inputs, you must use a TransformedDatastore or CombinedDatastore object.

Tip

Neural networks expect input data with a specific layout. For example image classification networks typically expect an image to be represented as a h-by-w-by-c numeric array, where h, w, and c are the height, width, and number of channels of the images, respectively. Most neural networks have an input layer that specifies the expected layout of the data.

Most datastores and functions output data in the layout that the network expects. If your data is in a different layout to what the network expects, then indicate that your data has a different layout by using the InputDataFormats training option or by specifying input data as a formatted dlarray object. It is usually easiest to adjust the InputDataFormats training option than to preprocess the input data.

For neural networks that do not have input layers, you must use the InputDataFormats training option or use formatted dlarray objects.

For more information, see Deep Learning Data Formats.

Numeric Array or dlarray Object

For data that fits in memory and does not require additional processing like augmentation, you can specify a data set of images as a numeric array or a dlarray object. If you specify images as a numeric array or a dlarray object, then you must also specify the targets argument.

The layout of numeric arrays and unformatted dlarray objects depend on the type of image data and must be consistent with the InputDataFormats training option.

Most networks expect image data in these layouts:

Data	Layout
2-D images	h-by-w-by-c-by-N array, where h, w, and c are the height, width, and number of channels of the images, respectively, and N is the number of images. Data in this layout has the data format "SSCB" (spatial, spatial, channel, batch).
3-D images	h-by-w-by-d-by-c-by-N array, where h, w, d, and c are the height, width, depth, and number of channels of the images, respectively, and N is the number of images. Data in this layout has the data format "SSSCB" (spatial, spatial, spatial, channel, batch).

For data in a different layout, indicate that your data has a different layout by using the InputDataFormats training option or use a formatted dlarray object. For more information, see Deep Learning Data Formats.

Datastore

Datastores read batches of images and targets. Datastores are best suited when you have data that does not fit in memory or when you want to apply augmentations or transformations to the data.

For image data, the trainnet function supports these datastores:

Datastore	Description	Example Usage
ImageDatastore	Datastore of images saved on disk.	Train image classification neural network with images saved on disk, where the images are the same size. When the images are different sizes, use an AugmentedImageDatastore object. ImageDatastore objects support image classification tasks only. To use image datastores for regression neural networks, create a transformed or combined datastore that contains the images and targets using the transform and combine functions, respectively.
AugmentedImageDatastore	Datastore that applies random affine geometric transformations, including resizing, rotation, reflection, shear, and translation.	Train image classification neural network with images saved on disk, where the images are different sizes. Train image classification neural network and generate new data using augmentations.
TransformedDatastore	Datastore that transforms batches of data read from an underlying datastore using a custom transformation function.	Train image regression neural network. Train neural networks with multiple inputs. Transform datastores with outputs not supported by the trainnet. Apply custom transformations to datastore output.
CombinedDatastore	Datastore that reads from two or more underlying datastores.	Train image regression neural network. Train neural networks with multiple inputs. Combine predictors and targets from different data sources.
PixelLabelImageDatastore (Computer Vision Toolbox)	Datastore that applies identical affine geometric transformations to images and corresponding pixel labels.	Train neural network for semantic segmentation.
RandomPatchExtractionDatastore (Image Processing Toolbox)	Datastore that extracts pairs of random patches from images or pixel label images and optionally applies identical random affine geometric transformations to the pairs.	Train neural network for object detection.
DenoisingImageDatastore (Image Processing Toolbox)	Datastore that applies randomly generated Gaussian noise.	Train neural network for image denoising.
Custom mini-batch datastore	Custom datastore that returns mini-batches of data.	Train neural network using data in a layout that other datastores do not support. For details, see Develop Custom Mini-Batch Datastore.

Tip

Use augmentedImageDatastore for efficient preprocessing of images for deep learning, including image resizing. Do not use the ReadFcn option of ImageDatastore objects.

ImageDatastore allows batch reading of JPG or PNG image files using prefetching. If you set the ReadFcn option to a custom function, then ImageDatastore does not prefetch and is usually significantly slower.

You can use other built-in datastores for training deep learning neural networks by using the transform and combine functions. These functions can convert the data read from datastores to the layout required by the trainnet function. The required layout of the datastore output depends on the neural network architecture. For more information, see Datastore Customization.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

sequences — Sequence or time series data

cell array of numeric arrays | cell array of dlarray objects | numeric array | dlarray object | datastore

Sequence or time series data, specified a numeric array, a cell array of numeric arrays, a dlarray object, a cell array of dlarray objects, or a datastore.

If you have sequences of the same length that fits in memory that does not require additional processing, then it is usually easiest to specify the input data as a numeric array. If you have sequences of different lengths that fit in memory that does not require additional processing, then it is usually easiest to specify the input data as a cell array of numeric arrays. If you want to train with sequences stored on disk, or want to apply additional processing such as custom transformations, then it is usually easiest to use datastores. For neural networks with multiple inputs, you must use a TransformedDatastore or CombinedDatastore object.

Tip

Neural networks expect input data with a specific layout. For example vector-sequence classification networks typically expect a sequence to be represented as a t-by-c numeric array, where t and c are the number of time steps and channels of sequences, respectively. Neural networks typically have an input layer that specifies the expected layout of the data.

Most datastores and functions output data in the layout that the network expects. If your data is in a different layout to what the network expects, then indicate that your data has a different layout by using the InputDataFormats training option or by specifying input data as a formatted dlarray object. It is usually easiest to adjust the InputDataFormats training option than to preprocess the input data.

For neural networks that do not have input layers, you must use the InputDataFormats training option or use formatted dlarray objects.

For more information, see Deep Learning Data Formats.

Numeric or Cell Array

For data that fits in memory and does not require additional processing like custom transformations, you can specify a single sequence as a numeric array or a data set of sequences as a cell array of numeric arrays. If you specify sequences as a cell or numeric array, then you must also specify the targets argument.

For cell array input, the cell array must be an N-by-1 cell array of numeric arrays, where N is the number of observations. The size and shape of the numeric array representing a sequence depends on the type of sequence data and must be consistent with the InputDataFormats training option.

This table describes the expected layout of data for a neural network with a sequence input layer.

Data	Layout
Vector sequences	s-by-c matrices, where s and c are the numbers of channels (features) and time steps of the sequences, respectively.
1-D image sequences	h-by-c-by-s arrays, where h and c correspond to the height and number of channels of the images, respectively, and s is the sequence length.
2-D image sequences	h-by-w-by-c-by-s arrays, where h, w, and c correspond to the height, width, and number of channels of the images, respectively, and s is the sequence length.
3-D image sequences	h-by-w-by-d-by-c-by-s, where h, w, d, and c correspond to the height, width, depth, and number of channels of the 3-D images, respectively, and s is the sequence length.

For data in a different layout, indicate that your data has a different layout by using the InputDataFormats training option or use a formatted dlarray object. For more information, see Deep Learning Data Formats.

Datastore

Datastores read batches of sequences and targets. Datastores are best suited when you have data that does not fit in memory or when you want to apply transformations to the data.

For sequence and time-series data, the trainnet function supports these datastores:

Datastore	Description	Example Usage
TransformedDatastore	Datastore that transforms batches of data read from an underlying datastore using a custom transformation function.	Transform datastores with outputs not supported by the trainnet function. Apply custom transformations to datastore output.
CombinedDatastore	Datastore that reads from two or more underlying datastores.	Combine predictors and targets from different data sources.
Custom mini-batch datastore	Custom datastore that returns mini-batches of data.	Train neural network using data in a layout that other datastores do not support. For details, see Develop Custom Mini-Batch Datastore.

You can use other built-in datastores for training deep learning neural networks by using the transform and combine functions. These functions can convert the data read from datastores to the layout required by the trainnet function. For example, you can transform and combine data read from in-memory arrays and CSV files using ArrayDatastore and TabularTextDatastore objects, respectively. The required layout of the datastore output depends on the neural network architecture. For more information, see Datastore Customization.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | cell
Complex Number Support: Yes

features — Feature or tabular data

datastore | numeric array

Feature or tabular data, specified as a numeric array or a datastore.

If you have data that fits in memory that does not require additional processing, then it is usually easiest to specify the input data as a numeric array. If you want to train with feature or tabular data stored on disk, or want to apply additional processing such as custom transformations, then it is usually easiest to use datastores. For neural networks with multiple inputs, you must use a TransformedDatastore or CombinedDatastore object.

Tip

Neural networks expect input data with a specific layout. For example feature classification networks typically expect feature and tabular data to be represented as a 1-by-c vector, where c is the number features of the data. Neural networks typically have an input layer that specifies the expected layout of the data.

Most datastores and functions output data in the layout that the network expects. If your data is in a different layout to what the network expects, then indicate that your data has a different layout by using the InputDataFormats training option or by specifying input data as a formatted dlarray object. It is usually easiest to adjust the InputDataFormats training option than to preprocess the input data.

For neural networks that do not have input layers, you must use the InputDataFormats training option or use formatted dlarray objects.

For more information, see Deep Learning Data Formats.

Numeric Array

For feature data that fits in memory and does not require additional processing like custom transformations, you can specify feature data as a numeric array. If you specify feature data as a numeric array, then you must also specify the targets argument.

For a neural network with a feature input layer, the expected layout of input data is an N-by-numFeatures numeric array, where N is the number of observations and numFeatures is the number of features of the input data.

Datastore

Datastores read batches of feature data and targets. Datastores are best suited when you have data that does not fit in memory or when you want to apply transformations to the data.

For feature and tabular data, the trainnet function supports these datastores:

Data Type	Description	Example Usage
TransformedDatastore	Datastore that transforms batches of data read from an underlying datastore using a custom transformation function.	Train neural networks with multiple inputs. Transform datastores with outputs not supported by the trainnet function. Apply custom transformations to datastore output.
CombinedDatastore	Datastore that reads from two or more underlying datastores.	Train neural networks with multiple inputs. Combine predictors and targets from different data sources.
Custom mini-batch datastore	Custom datastore that returns mini-batches of data.	Train neural network using data in a layout that other datastores do not support. For details, see Develop Custom Mini-Batch Datastore.

You can use other built-in datastores for training deep learning neural networks by using the transform and combine functions. These functions can convert the data read from datastores to the table or cell array format required by trainnet. For more information, see Datastore Customization.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

data — Generic data or combinations of data types

numeric array | dlarray object | datastore

Generic data or combinations of data types, specified as a numeric array, dlarray object, or a datastore.

If you have data that fits in memory that does not require additional processing, then it is usually easiest to specify the input data as a numeric array. If you want to train with data stored on disk, or want to apply additional processing, then it is usually easiest to use datastores. For neural networks with multiple inputs, you must use a TransformedDatastore or CombinedDatastore object.

Tip

Neural networks expect input data with a specific layout. For example vector-sequence classification networks typically expect a sequence to be represented as a t-by-c numeric array, where t and c are the number of time steps and channels of sequences, respectively. Neural networks typically have an input layer that specifies the expected layout of the data.

Most datastores and functions output data in the layout that the network expects. If your data is in a different layout to what the network expects, then indicate that your data has a different layout by using the InputDataFormats training option or by specifying input data as a formatted dlarray object. It is usually easiest to adjust the InputDataFormats training option than to preprocess the input data.

For neural networks that do not have input layers, you must use the InputDataFormats training option or use formatted dlarray objects.

For more information, see Deep Learning Data Formats.

Numeric or dlarray Objects

For data that fits in memory and does not require additional processing like custom transformations, you can specify feature data as a numeric array. If you specify feature data as a numeric array, then you must also specify the targets argument.

For a neural network with an inputLayer object, the expected layout of input data is a given by the InputFormat property of the layer.

For data in a different layout, indicate that your data has a different layout by using the InputDataFormats training option or use a formatted dlarray object. For more information, see Deep Learning Data Formats.

Datastores

Datastores read batches of data and targets. Datastores are best suited when you have data that does not fit in memory or when you want to apply transformations to the data.

Generic data or combinations of data types, the trainnet function supports these datastores:

Data Type	Description	Example Usage
TransformedDatastore	Datastore that transforms batches of data read from an underlying datastore using a custom transformation function.	Train neural networks with multiple inputs. Transform outputs of datastores not supported by trainnet to the have the required format. Apply custom transformations to datastore output.
CombinedDatastore	Datastore that reads from two or more underlying datastores.	Train neural networks with multiple inputs. Combine predictors and targets from different data sources.
Custom mini-batch datastore	Custom datastore that returns mini-batches of data.	Train neural network using data in a format that other datastores do not support. For details, see Develop Custom Mini-Batch Datastore.

You can use other built-in datastores for training deep learning neural networks by using the transform and combine functions. These functions can convert the data read from datastores to the table or cell array format required by trainnet. For more information, see Datastore Customization.

targets — Training targets

categorical array | numeric array | cell array of sequences

Training targets, specified as a categorical array, numeric array, or a cell array of sequences.

Tip

Loss functions expect data with a specific layout. For example for sequence-to-vector regression networks, the loss function typically expects a target vectors to be represented as a 1-by-R vector, where R is the number of responses.

Most datastores and functions output data in the layout that the loss function expects. If your target data is in a different layout to what the loss function expects, then indicate that your targets have a different layout by using the TargetDataFormats training option or by specifying the target data as a formatted dlarray object. It is usually easiest to adjust the TargetDataFormats training option than to preprocess the target data.

For more information, see Deep Learning Data Formats.

The expected layout of the targets depends on the loss function and the type of task. The targets listed here are only a subset. The loss functions may support additional targets with different layouts such as targets with additional dimensions. For custom loss functions, the software uses the format information of the network output data to determine the type of target data and applies the corresponding layout in this table.

Loss Function	Target	Target Layout
"crossentropy"	Categorical labels	N-by-1 categorical vector of labels, where N is the number of observations.
	Sequences of categorical labels	t-by-N categorical array, where t and N are the numbers of time steps and observations, respectively. N-by-1 cell array of sequences, where N is the number of observations. The sequences are t-by-1 categorical vectors. The sequences can have different lengths.
"binary-crossentropy"	Binary labels (single label)	N-by-1 vector, where N is the number of observations.
	Binary labels (mutlilabel)	N-by-c vector, where N and c are the numbers of observations and classes, respectively.
"mse" "mean-squared-error" "l2loss" "mae" "mean-absolute-error" "l1loss" "huber"	Numeric scalars	N-by-1 vector, where N is the number of observations.
	Numeric vectors	N-by-R matrix, where N is the number of observations and R is the number of responses.
	2-D images	h-by-w-by-c-by-N numeric array, where h, w, and c are the height, width, and number of channels of the images, respectively, and N is the number of images.
	3-D images	h-by-w-by-d-by-c-by-N numeric array, where h, w, d, and c are the height, width, depth, and number of channels of the images, respectively, and N is the number of images.
	Numeric sequences of scalars	t-by-1-by-N array, where t and N are the numbers of time steps and sequences, respectively. N-by-1 cell array of sequences, where N is the number of sequences. The sequences are t-by-1 vectors, where t is the number of time steps. The sequences can have different lengths.
	Numeric sequences of vectors	t-by-c-by-N array, where t, c, and N are the numbers of time steps, channels, and sequences, respectively. N-by-1 cell array of sequences, where N is the number of sequences. The sequences are t-by-c matrices, where t and c are the numbers of time steps and channels of the sequences, respectively. The sequences can have different lengths.
	Sequences of 1-D images	h-by-c-by-N-by-t array, where h, c, and t are the height, number of channels, and number of numbers of time steps of the sequences, respectively, and N is the number of sequences. N-by-1 cell array of sequences, where N is the number of sequences. The sequences are h-by-c-by-t arrays, where h, t, and c are the height, number of time steps, and number of channels of the sequences, respectively. The sequences can have different lengths.
	Sequences of 2-D images	h-by-w-by-c-by-N-by-t array, where h, w, c, and t are the height, width, number of channels, and number of numbers of time steps of the sequences, respectively, and N is the number of sequences. N-by-1 cell array of sequences, where N is the number of sequences. The sequences are h-by-w-by-c-by-t arrays, where h, w, t, and c are the height, width, number of time steps, and number of channels of the sequences, respectively. The sequences can have different lengths.
	Sequences of 2-D images	h-by-w-by-d-by-cby-N-t array, where h, w, d, c, and t are the height, width, depth, number of channels, and number of numbers of time steps of the sequences, respectively, and N is the number of sequences. N-by-1 cell array of sequences, where N is the number of sequences. The sequences are h-by-w-by-d-by-c-by-t arrays, where h, w, d, t, and c are the height, width, depth, number of time steps, and number of channels of the sequences, respectively. The sequences can have different lengths.

For targets in a different layout, indicate that your targets has a different layout by using the TargetDataFormats training option or use a formatted dlarray object. For more information, see Deep Learning Data Formats.

Tip

Normalizing the targets often helps to stabilize and speed up training of neural networks for regression. For more information, see Train Convolutional Neural Network for Regression.

Training Details

net — Neural network architecture

dlnetwork object | layer array

Neural network architecture, specified as a dlnetwork object or a layer array.

For a list of supported layers, see List of Deep Learning Layers.

lossFcn — Loss function

"crossentropy" | "binary-crossentropy" | "mse" | "mean-squared-error" | "l2loss" | "mae" | "mean-absolute-error" | "l1loss" | "huber" | function handle

Loss function to use for training, specified as one of these values:

• "crossentropy" — Cross-entropy loss for classification tasks.

• "binary-crossentropy" — Binary cross-entropy loss for binary and multilabel classification tasks.

• "mse" / "mean-squared-error" / "l2loss" — Mean squared error for regression tasks.

• "mae" / "mean-absolute-error" / "l1loss" — Mean absolute error for regression tasks.

• "huber" — Huber loss for regression tasks

• Function handle with the syntax loss = f(Y1,...,Yn,T1,...,Tm), where Y1,...,Yn are dlarray objects that correspond to the n network predictions and T1,...,Tm are dlarray objects that correspond to the m targets.

Tip

For weighted cross-entropy, use the function handle @(Y,T) crossentropy(Y,T,weights).

options — Training options

TrainingOptionsSGDM | TrainingOptionsRMSProp | TrainingOptionsADAM | TrainingOptionsLBFGS

Training options, specified as a TrainingOptionsSGDM, TrainingOptionsRMSProp, TrainingOptionsADAM, or TrainingOptionsLBFGS object returned by the trainingOptions function.

Output Arguments

netTrained — Trained network

dlnetwork object

Trained network, returned as a dlnetwork object.

info — Training information

TrainingInfo object

Training information, returned as a TrainingInfo object with these properties:

• TrainingHistory — Information about training iterations

• ValidationHistory — Information about validation iterations

• OutputNetworkIteration — Iteration that corresponds to trained network

• StopReason — Reason why training stopped

You can also use info to open and close the training progress plot using the show and close functions.

Tips

• For regression tasks, normalizing the targets often helps to stabilize and speed up training. For more information, see Train Convolutional Neural Network for Regression.

• In most cases, if the predictor or targets contain NaN values, then they are propagated through the network and the training fails to converge.

• To input complex-valued data into a neural network, the SplitComplexInputs option of the input layer must be 1.

• To convert a numeric array to a datastore, use ArrayDatastore.

• When you combine layers in a neural network with mixed types of data, you may need to reformat the data before passing it to a combination layer (such as a concatenation or an addition layer). To reformat the data, you can use a flatten layer to flatten the spatial dimensions into the channel dimension, or create a FunctionLayer object or custom layer that reformats and reshapes the data.

Algorithms

Datastore Customization

Most datastores output data in the layout that neural networks expect. If you create your own datastore, or apply custom transformations to datastores, then you must ensure that the datastore outputs data in the supported layout.

There are two main aspects:

• The structure of the batch of data. The datastore must output a table or cell array with rows that correspond to observations, and columns that correspond to the inputs and targets.

• The layout of the predictors and targets. For example, the predictors and targets must be in a layout that is supported by the network and loss function.

Structure of Batches

When you use a datastore for training a neural network, the structure of the datastore output depends on the neural network architecture.

Neural Network Architecture	Datastore Output	Example Output
Single input layer	Table or cell array with two columns. The first and second columns specify the predictors and targets, respectively. Table elements must be scalars, row vectors, or 1-by-1 cell arrays containing a numeric array. Custom mini-batch datastores must output tables.	Table for neural network with one input and one output: data = read(ds) data = 4×2 table Predictors Response __________________ ________ {224×224×3 double} 2 {224×224×3 double} 7 {224×224×3 double} 9 {224×224×3 double} 9
		Cell array for neural network with one input and one output: data = read(ds) data = 4×2 cell array {224×224×3 double} {[2]} {224×224×3 double} {[7]} {224×224×3 double} {[9]} {224×224×3 double} {[9]}
Multiple input layers	Cell array with (numInputs + 1) columns, where numInputs is the number of neural network inputs. The first numInputs columns specify the predictors for each input and the last column specifies the targets. The order of inputs is given by the InputNames property of the layer graph layers.	Cell array for neural network with two inputs and one output. data = read(ds) data = 4×3 cell array {224×224×3 double} {128×128×3 double} {[2]} {224×224×3 double} {128×128×3 double} {[2]} {224×224×3 double} {128×128×3 double} {[9]} {224×224×3 double} {128×128×3 double} {[9]}

The datastore must return data in a table or cell array. Custom mini-batch datastores must output tables.

Layout of Predictors and Targets

Neural networks and loss functions expect input data with a specific layout. For example vector-sequence classification networks typically expect a sequence to be represented as a t-by-c numeric array, where t and c are the number of time steps and channels of sequences, respectively. Neural networks typically have an input layer that specifies the expected layout of the data.

Most datastores and functions output data in the layout that the networks and loss functions expect. If your data is in a different layout to what the network or loss function expects, then indicate that your data has a different layout by using the InputDataFormats and TargetDataFormats training options or by specifying the data as a formatted dlarray objects. It is usually easiest to adjust the InputDataFormats and TargetDataFormats training options than to preprocess the input data.

For neural networks that do not have input layers, you must use the InputDataFormats training option or use formatted dlarray objects.

For more information, see Deep Learning Data Formats.

Most networks expect these data layouts of predictors:

Image Input

Data	Predictor Layout
2-D images	h-by-w-by-c numeric array, where h, w, and c are the height, width, and number of channels of the images, respectively.
3-D images	h-by-w-by-d-by-c numeric array, where h, w, d, and c are the height, width, depth, and number of channels of the images, respectively.

Sequence Input

Data	Predictor Layout
Vector sequence	c-by-s matrix, where c is the number of features of the sequence and s is the sequence length.
1-D image sequence	h-by-c-by-s array, where h and c correspond to the height and number of channels of the image, respectively, and s is the sequence length. Each sequence in the batch must have the same sequence length.
2-D image sequence	h-by-w-by-c-by-s array, where h, w, and c correspond to the height, width, and number of channels of the image, respectively, and s is the sequence length. Each sequence in the batch must have the same sequence length.
3-D image sequence	h-by-w-by-d-by-c-by-s array, where h, w, d, and c correspond to the height, width, depth, and number of channels of the image, respectively, and s is the sequence length. Each sequence in the batch must have the same sequence length.

Feature Input

Data	Predictor Layout
Features	c-by-1 column vectors, where c is the number of features.

Most loss functions expect these data layouts for targets:

Target	Target Layout
Categorical labels	Categorical scalar.
Sequences of categorical labels	t-by-1 categorical vector, where t is the number of time steps.
Binary labels (single label)	Numeric scalar
Binary labels (mutlilabel)	1-by-c vector, where c is the numbers of classes, respectively.
Numeric scalars	Numeric scalar
Numeric vectors	1-by-R vector, where R is the number of responses.
2-D images	h-by-w-by-c numeric array, where h, w, and c are the height, width, and number of channels of the images, respectively.
3-D images	h-by-w-by-d-by-c numeric array, where h, w, d, and c are the height, width, depth, and number of channels of the images, respectively.
Numeric sequences of scalars	t-by-1 vector, where t is the numbers of time steps.
Numeric sequences of vectors	t-by-c array, where t, and c are the numbers of time steps and channels, respectively.
Sequences of 1-D images	h-by-c-by-t array, where h, c, and t are the height, number of channels, and number of numbers of time steps of the sequences, respectively.
Sequences of 2-D images	h-by-w-by-c-by-t array, where h, w, c, and t are the height, width, number of channels, and number of numbers of time steps of the sequences, respectively.
Sequences of 2-D images	h-by-w-by-d-by-c-by-t array, where h, w, d, c, and t are the height, width, depth, number of channels, and number of numbers of time steps of the sequences, respectively.

For more information, see Deep Learning Data Formats.

Version History

Introduced in R2023b