Train shallow neural network

This function trains a shallow neural network. For deep learning with
convolutional or LSTM neural networks, see `trainNetwork`

instead.

`[`

trains a network with additional options specified by one or more name-value pair
arguments.`trainedNet`

,`tr`

] = train(`net`

,`X`

,`T`

,`Xi`

,`Ai`

,`EW`

,`Name,Value`

)

Here input `x`

and targets `t`

define a
simple function that you can plot:

```
x = [0 1 2 3 4 5 6 7 8];
t = [0 0.84 0.91 0.14 -0.77 -0.96 -0.28 0.66 0.99];
plot(x,t,'o')
```

Here `feedforwardnet`

creates a two-layer feed-forward
network. The network has one hidden layer with ten neurons.

net = feedforwardnet(10); net = configure(net,x,t); y1 = net(x) plot(x,t,'o',x,y1,'x')

The network is trained and then resimulated.

net = train(net,x,t); y2 = net(x) plot(x,t,'o',x,y1,'x',x,y2,'*')

This example trains an open-loop nonlinear-autoregressive network with
external input, to model a levitated magnet system defined by a control
current `x`

and the magnet’s vertical position response
`t`

, then simulates the network. The function `preparets`

prepares the data
before training and simulation. It creates the open-loop network’s combined
inputs `xo`

, which contains both the external input
`x`

and previous values of position
`t`

. It also prepares the delay states
`xi`

.

[x,t] = maglev_dataset; net = narxnet(10); [xo,xi,~,to] = preparets(net,x,{},t); net = train(net,xo,to,xi); y = net(xo,xi)

This same system can also be simulated in closed-loop form.

netc = closeloop(net); view(netc) [xc,xi,ai,tc] = preparets(netc,x,{},t); yc = netc(xc,xi,ai);

Parallel Computing Toolbox™ allows Deep Learning Toolbox™ to simulate and train networks faster and on larger datasets than can fit on one PC. Parallel training is currently supported for backpropagation training only, not for self-organizing maps.

Here training and simulation happens across parallel MATLAB workers.

parpool [X,T] = vinyl_dataset; net = feedforwardnet(10); net = train(net,X,T,'useParallel','yes','showResources','yes'); Y = net(X);

Use Composite values to distribute the data manually, and get back the results as a Composite value. If the data is loaded as it is distributed then while each piece of the dataset must fit in RAM, the entire dataset is limited only by the total RAM of all the workers.

[X,T] = vinyl_dataset; Q = size(X,2); Xc = Composite; Tc = Composite; numWorkers = numel(Xc); ind = [0 ceil((1:numWorkers)*(Q/numWorkers))]; for i=1:numWorkers indi = (ind(i)+1):ind(i+1); Xc{i} = X(:,indi); Tc{i} = T(:,indi); end net = feedforwardnet; net = configure(net,X,T); net = train(net,Xc,Tc); Yc = net(Xc);

Note in the example above the function configure was used to set the dimensions and processing settings of the network's inputs. This normally happens automatically when train is called, but when providing composite data this step must be done manually with non-Composite data.

Networks can be trained using the current GPU device, if it is supported by Parallel Computing Toolbox. GPU training is currently supported for backpropagation training only, not for self-organizing maps.

[X,T] = vinyl_dataset; net = feedforwardnet(10); net = train(net,X,T,'useGPU','yes'); y = net(X);

To put the data on a GPU manually:

[X,T] = vinyl_dataset; Xgpu = gpuArray(X); Tgpu = gpuArray(T); net = configure(net,X,T); net = train(net,Xgpu,Tgpu); Ygpu = net(Xgpu); Y = gather(Ygpu);

Note in the example above the function configure was used to set the dimensions and processing settings of the network's inputs. This normally happens automatically when train is called, but when providing gpuArray data this step must be done manually with non-gpuArray data.

To run in parallel, with workers each assigned to a different unique GPU, with extra workers running on CPU:

net = train(net,X,T,'useParallel','yes','useGPU','yes'); y = net(X);

Using only workers with unique GPUs might result in higher speed, as CPU workers might not keep up.

net = train(net,X,T,'useParallel','yes','useGPU','only'); Y = net(X);

Here a network is trained with checkpoints saved at a rate no greater than once every two minutes.

[x,t] = vinyl_dataset; net = fitnet([60 30]); net = train(net,x,t,'CheckpointFile','MyCheckpoint','CheckpointDelay',120);

After a computer failure, the latest network can be recovered and used to
continue training from the point of failure. The checkpoint file includes a
structure variable `checkpoint`

, which includes the
network, training record, filename, time, and number.

[x,t] = vinyl_dataset; load MyCheckpoint net = checkpoint.net; net = train(net,x,t,'CheckpointFile','MyCheckpoint');

Another use for the checkpoint feature is when you stop a parallel
training session (started with the `'UseParallel'`

parameter) even though the Neural Network Training Tool is not available
during parallel training. In this case, set a
`'CheckpointFile'`

, use Ctrl+C to stop training any
time, then load your checkpoint file to get the network and training
record.

`net`

— Input network`network`

objectInput network, specified as a `network`

object. To create a
`network`

object, use for example, `feedforwardnet`

or `narxnet`

.

`X`

— Network inputsmatrix | cell array | composite data | gpuArray

Network inputs, specified as an
`R`

-by-`Q`

matrix or an
`Ni`

-by-`TS`

cell array, where

`R`

is the input size`Q`

is the batch size`Ni = net.numInputs`

`TS`

is the number of time steps

`train`

arguments can have two formats: matrices, for
static problems and networks with single inputs and outputs, and cell arrays
for multiple timesteps and networks with multiple inputs and outputs.

The matrix format can be used if only one time step is to be simulated (

`TS = 1`

). It is convenient for networks with only one input and output, but can be used with networks that have more. When the network has multiple inputs, the matrix size is (sum of`Ri`

)-by-`Q`

.The cell array format is more general, and more convenient for networks with multiple inputs and outputs, allowing sequences of inputs to be presented. Each element

`X{i,ts}`

is an`Ri`

-by-`Q`

matrix, where`Ri = net.inputs{i}.size`

.

If Composite data is used, then `'useParallel'`

is
automatically set to `'yes'`

. The function takes Composite
data and returns Composite results.

If gpuArray data is used, then `'useGPU'`

is
automatically set to `'yes'`

. The function takes gpuArray
data and returns gpuArray results

If a column of X contains at least one `NaN`

,
`train`

does not use that column for training,
testing, or validation. If a target value in `T`

is a
`NaN`

, then `train`

ignores that
row, and uses the other rows for training, testing, or
validation.

`T`

— Network targetszeros (default) | matrix | cell array | composite data | gpuArray

Network targets, specified as a
`U`

-by-`Q`

matrix or an
`No`

-by-`TS`

cell array, where

`U`

is the output size`Q`

is the batch size`No = net.numOutputs`

`TS`

is the number of time steps

`train`

arguments can have two formats: matrices, for
static problems and networks with single inputs and outputs, and cell arrays
for multiple timesteps and networks with multiple inputs and outputs.

The matrix format can be used if only one time step is to be simulated (

`TS = 1`

). It is convenient for networks with only one input and output, but can be used with networks that have more. When the network has multiple inputs, the matrix size is (sum of`Ui`

)-by-`Q`

.The cell array format is more general, and more convenient for networks with multiple inputs and outputs, allowing sequences of inputs to be presented. Each element

`T{i,ts}`

is a`Ui`

-by-`Q`

matrix, where`Ui = net.outputs{i}.size`

.

If Composite data is used, then `'useParallel'`

is
automatically set to `'yes'`

. The function takes Composite
data and returns Composite results.

If gpuArray data is used, then `'useGPU'`

is
automatically set to `'yes'`

. The function takes gpuArray
data and returns gpuArray results

Note that `T`

is optional and need only be used for
networks that require targets.

Any `NaN`

values in the inputs `X`

or the targets `T`

, are treated as missing data. If a
column of `X`

or `T`

contains at least
one `NaN`

, that column is not used for training,
testing, or validation.

`Xi`

— Initial input delay conditionszeros (default) | cell array | matrix

Initial input delay conditions, specified as an
`Ni`

-by-`ID`

cell array or an
`R`

-by-`(ID*Q)`

matrix, where

`ID = net.numInputDelays`

`Ni = net.numInputs`

`R`

is the input size`Q`

is the batch size

For cell array input, the columns of `Xi`

are ordered
from the oldest delay condition to the most recent:
`Xi{i,k}`

is the input `i`

at time
`ts = k - ID`

.

`Xi`

is also optional and need only be used for
networks that have input or layer delays.

`Ai`

— Initial layer delay conditionszeros (default) | cell array | matrix

Initial layer delay conditions, specified as a
`Nl`

-by-`LD`

cell array or a (sum of
`Si`

)-by-(`LD*Q`

) matrix, where

`Nl = net.numLayers`

`LD = net.numLayerDelays`

`Si = net.layers{i}.size`

`Q`

is the batch size

For cell array input, the columns of `Ai`

are ordered
from the oldest delay condition to the most recent:
`Ai{i,k}`

is the layer output `i`

at
time `ts = k - LD`

.

`EW`

— Error weightscell array

Error weights, specified as a
`No`

-by-`TS`

cell array or a (sum of
`Ui`

)-by-`Q`

matrix, where

`No = net.numOutputs`

`TS`

is the number of time steps`Ui = net.outputs{i}.size`

`Q`

is the batch size

For cell array input. each element `EW{i,ts}`

is a
`Ui`

-by-`Q`

matrix, where

`Ui = net.outputs{i}.size`

`Q`

is the batch size

The error weights `EW`

can also have a size of 1 in
place of all or any of `No`

, `TS`

,
`Ui`

or `Q`

. In that case,
`EW`

is automatically dimension extended to match the
targets `T`

. This allows for conveniently weighting the
importance in any dimension (such as per sample) while having equal
importance across another (such as time, with `TS=1`

). If
all dimensions are 1, for instance if `EW = {1}`

, then all
target values are treated with the same importance. That is the default
value of `EW`

.

As noted above, the error weights `EW`

can be of the
same dimensions as the targets `T`

, or have some
dimensions set to 1. For instance if `EW`

is
1-by-`Q`

, then target samples will have different
importances, but each element in a sample will have the same importance. If
`EW`

is (sum of
`Ui`

)-by-`Q`

, then each output element
has a different importance, with all samples treated with the same
importance.

Specify optional
comma-separated pairs of `Name,Value`

arguments. `Name`

is
the argument name and `Value`

is the corresponding value.
`Name`

must appear inside quotes. You can specify several name and value
pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

`'useParallel','yes'`

`'useParallel'`

— Option to specify parallel calculations`'no'`

(default) | `'yes'`

Option to specify parallel calculations, specified as
`'yes'`

or `'no'`

.

`'no'`

– Calculations occur on normal MATLAB thread. This is the default`'useParallel'`

setting.`'yes'`

– Calculations occur on parallel workers if a parallel pool is open. Otherwise calculations occur on the normal MATLAB^{®}thread.

`'useGPU'`

— Option to specify GPU calculations`'no'`

(default) | `'yes'`

| `'only'`

Option to specify GPU calculations, specified as
`'yes'`

, `'no'`

, or
`'only'`

.

`'no'`

– Calculations occur on the CPU. This is the default`'useGPU'`

setting.`'yes'`

– Calculations occur on the current`gpuDevice`

if it is a supported GPU (See Parallel Computing Toolbox for GPU requirements.) If the current`gpuDevice`

is not supported, calculations remain on the CPU. If`'useParallel'`

is also`'yes'`

and a parallel pool is open, then each worker with a unique GPU uses that GPU, other workers run calculations on their respective CPU cores.`'only'`

– If no parallel pool is open, then this setting is the same as`'yes'`

. If a parallel pool is open then only workers with unique GPUs are used. However, if a parallel pool is open, but no supported GPUs are available, then calculations revert to performing on all worker CPUs.

`'showResources'`

— Option to show resources`'no'`

(default) | `'yes'`

Option to show resources, specified as `'yes'`

or
`'no'`

.

`'no'`

– Do not display computing resources used at the command line. This is the default setting.`'yes'`

– Show at the command line a summary of the computing resources actually used. The actual resources may differ from the requested resources, if parallel or GPU computing is requested but a parallel pool is not open or a supported GPU is not available. When parallel workers are used, each worker’s computation mode is described, including workers in the pool that are not used.

`'reduction'`

— Memory reduction1 (default) | positive integer

Memory reduction, specified as a positive integer.

For most neural networks, the default CPU training computation mode is
a compiled MEX algorithm. However, for large networks the calculations
might occur with a MATLAB calculation mode. This can be confirmed using
`'showResources'`

. If MATLAB is being used and memory is an issue, setting the
reduction option to a value N greater than 1, reduces much of the
temporary storage required to train by a factor of N, in exchange for
longer training times.

`'CheckpointFile'`

— Checkpoint file`''`

(default) | character vectorCheckpoint file, specified as a character vector.

The value for `'CheckpointFile'`

can be set to a
filename to save in the current working folder, to a file path in
another folder, or to an empty string to disable checkpoint saves (the
default value).

`'CheckpointDelay'`

— Checkpoint delay60 (default) | nonnegative integer

Checkpoint delay, specified as a nonnegative integer.

The optional parameter `'CheckpointDelay'`

limits how
often saves happen. Limiting the frequency of checkpoints can improve
efficiency by keeping the amount of time saving checkpoints low compared
to the time spent in calculations. It has a default value of 60, which
means that checkpoint saves do not happen more than once per minute. Set
the value of `'CheckpointDelay'`

to 0 if you want
checkpoint saves to occur only once every epoch.

`trainedNet`

— Trained network`network`

objectTrained network, returned as a `network`

object.

`tr`

— Training recordstructure

Training record (`epoch`

and `perf`

),
returned as a structure whose fields depend on the network training function
(`net.NET.trainFcn`

). It can include fields such
as:

Training, data division, and performance functions and parameters

Data division indices for training, validation and test sets

Data division masks for training validation and test sets

Number of epochs (

`num_epochs`

) and the best epoch (`best_epoch`

).A list of training state names (

`states`

).Fields for each state name recording its value throughout training

Performances of the best network (

`best_perf`

,`best_vperf`

,`best_tperf`

)

`train`

calls the function indicated by
`net.trainFcn`

, using the training parameter values indicated by
`net.trainParam`

.

Typically one epoch of training is defined as a single presentation of all input vectors to the network. The network is then updated according to the results of all those presentations.

Training occurs until a maximum number of epochs occurs, the performance goal is met,
or any other stopping condition of the function `net.trainFcn`

occurs.

Some training functions depart from this norm by presenting only one input vector (or
sequence) each epoch. An input vector (or sequence) is chosen randomly for each epoch
from concurrent input vectors (or sequences). `competlayer`

returns networks that use `trainru`

, a training function that does this.

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