dlarray

Deep learning array for custom training loops

Description

A deep learning array stores data with optional data format labels for custom training loops, and enables functions to compute and use derivatives through automatic differentiation.

Tip

For most deep learning tasks, you can use a pretrained network and adapt it to your own data. For an example showing how to use transfer learning to retrain a convolutional neural network to classify a new set of images, see Train Deep Learning Network to Classify New Images. Alternatively, you can create and train networks from scratch using layerGraph objects with the trainNetwork and trainingOptions functions.

If the trainingOptions function does not provide the training options that you need for your task, then you can create a custom training loop using automatic differentiation. To learn more, see Define Deep Learning Network for Custom Training Loops.

Creation

Syntax

dlX = dlarray(X)

dlX = dlarray(X,fmt)

dlX = dlarray(v,dim)

Description

dlX = dlarray(X) returns a dlarray object representing X. If X is a dlarray, dlX is a copy of X.

dlX = dlarray(X,fmt) formats the data in dlX with dimension labels according to the data format in fmt. Dimension labels help in passing deep learning data between functions. For more information on dimension labels, see Usage. If X is a formatted dlarray, then fmt replaces the existing format.

dlX = dlarray(v,dim) accepts a vector v and a single character format dim, and returns a column vector dlarray. The first dimension of dlX has the dimension label dim, and the second (singleton) dimension has the dimension label 'U'.

Input Arguments

X — Data array

numeric array of data type double or single | logical array | gpuArray object | dlarray object

Data array, specified as a numeric array of data type double or single, a logical array, a gpuArray object, or a dlarray object. X must be full, not sparse.

Example: rand(31*23,23)

Data Types: single | double | logical
Complex Number Support: Yes

fmt — Data format

character vector | string scalar

Data format, specified as a character vector or string scalar. Each character in fmt must be one of the following dimension labels:

• S — Spatial

• C — Channel

• B — Batch observations

• T — Time or sequence

• U — Unspecified

You can specify any number of S and U labels. You can specify at most one of each of the C, B, and T labels.

Each element of fmt labels the matching dimension of dlX. If fmt is not in the listed order ('S' followed by 'C' and so on), then dlarray implicitly permutes both fmt and the data to match the order without changing the storage of the data.

fmt must contain at least the same number of dimension labels as the number of dimensions of dlX. If you specify more than that number of dimension labels, dlarray creates empty (singleton) dimensions for the additional labels.

The following table indicates recommended data formats for common types of data.

Data	Example
	Shape	Data Format
2-D images	h-by-w-by-c-by-n numeric array, where h, w, c and n are the height, width, number of channels of the images, and number of observations, respectively.	"SSCB"
3-D images	h-by-w-by-d-by-c-by-n numeric array, where h, w, d, c and n are the height, width, depth, number of channels of the images, and number of image observations, respectively.	"SSSCB"
Vector sequences	c-by-s-by-n matrix, where c is the number of features of the sequence, s is the sequence length, and n is the number of sequence observations.	"CTB"
2-D image sequences	h-by-w-by-c-by-s-by-n array, where h, w, and c correspond to the height, width, and number of channels of the image, respectively, s is the sequence length, and n is the number of image sequence observations.	"SSCTB"
3-D image sequences	h-by-w-by-d-by-c-by-s-by-n array, where h, w, d, and c correspond to the height, width, depth, and number of channels of the image, respectively, s is the sequence length, and n is the number of image sequence observations.	"SSSCTB"
Features	c-by-n array, where c is the number of features, and n is the number of observations.	"CB"

For information on how data formats are used in deep learning functions, see Usage.

Example: "SSB"

Example: 'CBUSS', which dlarray reorders to 'SSCBU'

v — Data vector

numeric vector of data type double or single | logical vector | dlarray vector object

Data vector, specified as a numeric vector of data type double or single, logical vector, or dlarray vector object. Here, "vector" means any array with exactly one nonsingleton dimension.

Example: rand(100,1)

dim — Dimension label

single character

Dimension label, specified as a single character of the type allowed for fmt.

Example: "S"

Example: 'S'

Output Arguments

dlX — Deep learning array

dlarray object

Deep learning array, returned as a dlarray object. dlX enables automatic differentiation using dlgradient and dlfeval. If you supply the fmt argument, dlX has labels.

• If X is a numeric or logical array, dlX contains its data, possibly reordered because of the data format in fmt.

• If X is a gpuArray, the data in dlX is also on the GPU. Subsequent calculations using dlX are performed on the GPU.

Usage

dlarray data formats enable you to execute the functions in the following table with assurance that the data has the appropriate shape.

Function	Operation	Validates Input Dimension	Affects Size of Input Dimension
avgpool	Compute the average of the input data over moving rectangular (or cuboidal) spatial ('S') regions defined by a pool size parameter.	'S'	'S'
batchnorm	Normalize the values contained in each channel ('C') of the input data.	'C'
crossentropy	Compute the cross-entropy between estimates and target values, averaged by the size of the batch ('B') dimension.	'S', 'C', 'B', 'T', 'U' (Estimates and target arrays must have the same sizes.)	'S', 'C', 'B', 'T', 'U' (Output is an unformatted scalar.)
dlconv	Compute the deep learning convolution of the input data using an array of filters, matching the number of spatial ('S') and (a function of the) channel ('C') dimensions of the input, and adding a constant bias.	'S', 'C'	'S', 'C'
dltranspconv	Compute the deep learning transposed convolution of the input data using an array of filters, matching the number of spatial ('S') and (a function of the) channel ('C') dimensions of the input, and adding a constant bias.	'S', 'C'	'S', 'C'
fullyconnect	Compute a weighted sum of the input data and apply a bias for each batch ('B') and time ('T') dimension.	'S', 'C', 'U'	'S', 'C', 'B', 'T', 'U' (Output always has data format 'CB', 'CT', or 'CTB'.)
gru	Apply a gated recurrent unit calculation to the input data.	'S', 'C', 'T'	'C'
lstm	Apply a long short-term memory calculation to the input data.	'S', 'C', 'T'	'C'
maxpool	Compute the maximum of the input data over moving rectangular spatial ('S') regions defined by a pool size parameter.	'S'	'S'
maxunpool	Compute the unpooling operation over the spatial ('S') dimensions.	'S'	'S'
mse	Compute the half mean squared error between estimates and target values, averaged by the size of the batch ('B') dimension.	'S', 'C', 'B', 'T', 'U' (Estimates and target arrays must have the same sizes.)	'S', 'C', 'B', 'T', 'U' (Output is an unformatted scalar.)
softmax	Apply the softmax activation to each channel ('C') of the input data.	'C'

These functions require each dimension to have a label. You can specify the dimension label format by providing the first input as a formatted dlarray, or by using the 'DataFormat' name-value argument of the function.

dlarray enforces the dimension label ordering of 'SCBTU'. This enforcement eliminates ambiguous semantics in operations which implicitly match labels between inputs. dlarray also enforces that the dimension labels 'C', 'B', and 'T' can each appear at most once. The functions that use these dimension labels accept at most one dimension for each label.

dlarray provides functions for obtaining the data format associated with a dlarray (dims), removing the data format (stripdims), and obtaining the dimensions associated with specific dimension labels (finddim).

For more information on how a dlarray behaves with formats, see Notable dlarray Behaviors.

Object Functions

avgpool	Pool data to average values over spatial dimensions
batchnorm	Normalize data across all observations for each channel independently
crossentropy	Cross-entropy loss for classification tasks
dims	Dimension labels of dlarray
dlconv	Deep learning convolution
dlgradient	Compute gradients for custom training loops using automatic differentiation
dltranspconv	Deep learning transposed convolution
extractdata	Extract data from dlarray
finddim	Find dimensions with specified label
fullyconnect	Sum all weighted input data and apply a bias
gru	Gated recurrent unit
leakyrelu	Apply leaky rectified linear unit activation
lstm	Long short-term memory
maxpool	Pool data to maximum value
maxunpool	Unpool the output of a maximum pooling operation
mse	Half mean squared error
relu	Apply rectified linear unit activation
sigmoid	Apply sigmoid activation
softmax	Apply softmax activation to channel dimension
stripdims	Remove dlarray data format

A dlarray also allows functions for numeric, matrix, and other operations. See the full list in List of Functions with dlarray Support.

Examples

Create Unformatted dlarray

Create an unformatted dlarray from a matrix.

X = randn(3,5);
dlX = dlarray(X)

dlX = 
  3x5 dlarray

    0.5377    0.8622   -0.4336    2.7694    0.7254
    1.8339    0.3188    0.3426   -1.3499   -0.0631
   -2.2588   -1.3077    3.5784    3.0349    0.7147

Create Formatted dlarray

Create a dlarray that has a data format containing the dimension labels 'S' and 'C'.

X = randn(3,5);
dlX = dlarray(X,'SC')

dlX = 
  3(S) x 5(C) dlarray

    0.5377    0.8622   -0.4336    2.7694    0.7254
    1.8339    0.3188    0.3426   -1.3499   -0.0631
   -2.2588   -1.3077    3.5784    3.0349    0.7147

If you specify the dimension labels in the opposite order, dlarray implicitly reorders the underlying data.

dlX = dlarray(X,'CS')

dlX = 
  5(S) x 3(C) dlarray

    0.5377    1.8339   -2.2588
    0.8622    0.3188   -1.3077
   -0.4336    0.3426    3.5784
    2.7694   -1.3499    3.0349
    0.7254   -0.0631    0.7147

Create Formatted dlarray Vector

Create a dlarray vector with the first dimension label 'T'. The second dimension label, which dlarray creates automatically, is 'U'.

X = randn(6,1);
dlX = dlarray(X,'T')

dlX = 
  6(T) x 1(U) dlarray

    0.5377
    1.8339
   -2.2588
    0.8622
    0.3188
   -1.3077

If you specify a row vector for X, dlarray implicitly reorders the result to be a column vector.

X = X';
dlX = dlarray(X,'T')

dlX = 
  6(T) x 1(U) dlarray

    0.5377
    1.8339
   -2.2588
    0.8622
    0.3188
   -1.3077

Tips

• A dlgradient call must be inside a function. To obtain a numeric value of a gradient, you must evaluate the function using dlfeval, and the argument to the function must be a dlarray. See Use Automatic Differentiation In Deep Learning Toolbox.

• To enable the correct evaluation of gradients, dlfeval must call functions that use only supported functions for dlarray. See List of Functions with dlarray Support.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

For usage recommendations and list of functions with dlarray code generation support, see Code Generation for dlarray (MATLAB Coder). For an example showing how to use dlnetwork and dlarray objects to generate MEX for a trained variational autoencoder (VAE) network, see Generate Digit Images Using Variational Autoencoder on Intel CPUs (MATLAB Coder).

For dlarray code generation limitations, see dlarray Limitations for Code Generation (MATLAB Coder).

GPU Code Generation

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

Usage notes and limitations:

For usage recommendations and list of functions with dlarray code generation support, see Code Generation for dlarray (GPU Coder). For an example showing how to use dlnetwork and dlarray objects to generate CUDA^® MEX for a trained variational autoencoder (VAE) network, see Generate Digit Images on NVIDIA GPU Using Variational Autoencoder (GPU Coder).

For dlarray code generation limitations, see dlarray Limitations for Code Generation (GPU Coder).

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).