l2loss
Syntax
Description
The L2 loss operation computes the
L2 loss (based on the squared L2 norm) given
network predictions and target values. When the Reduction
option is
"sum"
and the NormalizationFactor
option is
"batch-size"
, the computed value is known as the mean squared error
(MSE).
The l2loss
function calculates the L2 loss
using dlarray
data.
Using dlarray
objects makes working with high
dimensional data easier by allowing you to label the dimensions. For example, you can label
which dimensions correspond to spatial, time, channel, and batch dimensions using the
"S"
, "T"
, "C"
, and
"B"
labels, respectively. For unspecified and other dimensions, use the
"U"
label. For dlarray
object functions that operate
over particular dimensions, you can specify the dimension labels by formatting the
dlarray
object directly, or by using the DataFormat
option.
specifies additional options using one or more name-value arguments. For example,
loss
= l2loss(___,Name=Value
)l2loss(Y,targets,Reduction="none")
computes the
L2 loss without reducing the output to a scalar.
Examples
Mean Squared Error Loss
Create an array of predictions for 12 observations over 10 responses.
numResponses = 10;
numObservations = 12;
Y = rand(numResponses,numObservations);
dlY = dlarray(Y,'CB');
View the size and format of the predictions.
size(dlY)
ans = 1×2
10 12
dims(dlY)
ans = 'CB'
Create an array of random targets.
targets = rand(numResponses,numObservations);
View the size of the targets.
size(targets)
ans = 1×2
10 12
Compute the mean squared error (MSE) loss between the predictions and the targets using the l2loss
function.
loss = l2loss(dlY,targets)
loss = 1x1 dlarray 1.4748
Masked Mean Squared Error for Padded Sequences
Create arrays of predictions and targets for 12 sequences of varying lengths over 10 responses.
numResponses = 10; numObservations = 12; maxSequenceLength = 15; sequenceLengths = randi(maxSequenceLength,[1 numObservations]); Y = cell(numObservations,1); targets = cell(numObservations,1); for i = 1:numObservations Y{i} = rand(numResponses,sequenceLengths(i)); targets{i} = rand(numResponses,sequenceLengths(i)); end
View the cell arrays of predictions and targets.
Y
Y=12×1 cell array
{10x13 double}
{10x14 double}
{10x2 double}
{10x14 double}
{10x10 double}
{10x2 double}
{10x5 double}
{10x9 double}
{10x15 double}
{10x15 double}
{10x3 double}
{10x15 double}
targets
targets=12×1 cell array
{10x13 double}
{10x14 double}
{10x2 double}
{10x14 double}
{10x10 double}
{10x2 double}
{10x5 double}
{10x9 double}
{10x15 double}
{10x15 double}
{10x3 double}
{10x15 double}
Pad the prediction and target sequences in the second dimension using the padsequences
function and also return the corresponding mask.
[Y,mask] = padsequences(Y,2); targets = padsequences(targets,2);
Convert the padded sequences to dlarray
with the format "CTB"
(channel, time, batch). Because formatted dlarray
objects automatically permute the dimensions of the underlying data, keep the order consistent by also converting the targets and mask to formatted dlarray
objects with the format "CTB"
(channel, batch, time).
dlY = dlarray(Y,"CTB"); targets = dlarray(targets,"CTB"); mask = dlarray(mask,"CTB");
View the sizes of the prediction scores, targets, and mask.
size(dlY)
ans = 1×3
10 12 15
size(targets)
ans = 1×3
10 12 15
size(mask)
ans = 1×3
10 12 15
Compute the mean squared error (MSE) between the predictions and the targets. To prevent the loss values calculated from padding from contributing to the loss, set the Mask
option to the mask returned by the padsequences
function.
loss = l2loss(dlY,targets,Mask=mask)
loss = 1x1 dlarray 16.3668
Input Arguments
Y
— Predictions
dlarray
object | numeric array
Predictions, specified as a formatted or unformatted dlarray
object,
or a numeric array. When Y
is not a formatted
dlarray
, you must specify the dimension format using the
DataFormat
argument.
If Y
is a numeric array, targets
must be a
dlarray
object.
targets
— Target responses
dlarray
| numeric array
Target responses, specified as a formatted or unformatted dlarray
or a
numeric array.
The size of each dimension of targets
must match the size of the
corresponding dimension of Y
.
If targets
is a formatted dlarray
, then its format must
be the same as the format of Y
, or the same as
DataFormat
if Y
is
unformatted.
If targets
is an unformatted dlarray
or a numeric array,
then the function applies the format of Y
or the value of
DataFormat
to targets
.
Tip
Formatted dlarray
objects automatically permute the dimensions of the
underlying data to have the order "S"
(spatial), "C"
(channel), "B"
(batch), "T"
(time), then
"U"
(unspecified). To ensure that the dimensions of
Y
and targets
are consistent, when
Y
is a formatted dlarray
, also specify
targets
as a formatted dlarray
.
weights
— Weights
dlarray
| numeric array
Weights, specified as a formatted or unformatted dlarray
or a numeric array.
If weights
is a vector and Y
has two or more
nonsingleton dimensions, then weights
must be a formatted
dlarray
, where the dimension label of the nonsingleton dimension is
either "C"
(channel) or "B"
(batch) and has a size
that matches the size of the corresponding dimension in Y
.
If weights
is a formatted dlarray
with two or more
nonsingleton dimensions, then its format must match the format of
Y
.
If weights
is not a formatted dlarray
and has two or
more nonsingleton dimensions, then its size must match the size of
Y
and the function uses the same format as
Y
. Alternatively, to specify the weights format, use the
WeightsFormat
option.
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.
Example: loss = l2loss(Y,targets,Reduction="none")
specifies to
compute the L2 loss without reducing the output to a
scalar
Mask
— Mask indicating which elements to include for loss computation
dlarray
| logical array | numeric array
Mask indicating which elements to include for loss computation, specified as a
dlarray
object, a logical array, or a numeric array with the same
size as Y
.
The function includes and excludes elements of the input data for loss computation when the corresponding value in the mask is 1 and 0, respectively.
If Mask
is a formatted dlarray
object, then its
format must match that of Y
. If Mask
is not a
formatted dlarray
object, then the function uses the same format as
Y
.
If you specify the DataFormat
argument, then the function also
uses the specified format for the mask.
The size of each dimension of Mask
must match the size of the
corresponding dimension in Y
. The default value is a logical array
of ones.
Tip
Formatted dlarray
objects automatically permute the dimensions of the
underlying data to have this order: "S"
(spatial), "C"
(channel), "B"
(batch), "T"
(time), and
"U"
(unspecified). For example, dlarray
objects
automatically permute the dimensions of data with format "TSCSBS"
to have
format "SSSCBT"
.
To ensure that the dimensions of Y
and the mask are consistent, when
Y
is a formatted dlarray
, also specify the mask as
a formatted dlarray
.
Reduction
— Loss value array reduction mode
"sum"
(default) | "none"
Loss value array reduction mode, specified as "sum"
or
"none"
.
If the Reduction
argument is "sum"
, then the function
sums all elements in the array of loss values. In this case, the output
loss
is a scalar.
If the Reduction
argument is "none"
, then the
function does not reduce the array of loss values. In this case, the output
loss
is an unformatted dlarray
object
of the same size as Y
.
NormalizationFactor
— Divisor for normalizing reduced loss
"batch-size"
(default) | "all-elements"
| "mask-included"
| "none"
Divisor for normalizing the reduced loss when Reduction
is
"sum"
, specified as one of the following:
"batch-size"
— Normalize the loss by dividing it by the number of observations inY
."all-elements"
— Normalize the loss by dividing it by the number of elements ofY
."mask-included"
— Normalize the loss by dividing the loss values by the product of the number of observations and the number of included elements specified by the mask for each observation independently. To use this option, you must specify a mask using theMask
option."none"
— Do not normalize the loss.
DataFormat
— Description of data dimensions
character vector | string scalar
Description of the data dimensions, specified as a character vector or string scalar.
A data format is a string of characters, where each character describes the type of the corresponding data dimension.
The characters are:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format "CBT"
(channel, batch,
time).
You can specify multiple dimensions labeled "S"
or "U"
.
You can use the labels "C"
, "B"
, and
"T"
once each, at most. The software ignores singleton trailing
"U"
dimensions after the second dimension.
If the input data is not a formatted dlarray
object, then you must
specify the DataFormat
option.
For more information, see Deep Learning Data Formats.
Data Types: char
| string
WeightsFormat
— Description of dimensions of weights
character vector | string scalar
Description of the dimensions of the weights, specified as a character vector or string scalar.
A data format is a string of characters, where each character describes the type of the corresponding data dimension.
The characters are:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format "CBT"
(channel, batch,
time).
You can specify multiple dimensions labeled "S"
or "U"
.
You can use the labels "C"
, "B"
, and
"T"
once each, at most. The software ignores singleton trailing
"U"
dimensions after the second dimension.
If weights
is a numeric vector and
Y
has two or more nonsingleton
dimensions, then you must specify the
WeightsFormat
option.
If weights
is not a vector, or
weights
and
Y
are both vectors, then the
default value of WeightsFormat
is the same
as the format of Y
.
For more information, see Deep Learning Data Formats.
Data Types: char
| string
Output Arguments
loss
— L2 loss
dlarray
L2 loss, returned as an unformatted
dlarray
. The output loss
is an unformatted
dlarray
with the same underlying data type as the input
Y
.
The size of loss
depends on the Reduction
option.
Algorithms
L2 Loss
The L2 loss operation computes the
L2 loss (based on the squared L2 norm) given
network predictions and target values. When the Reduction
option is
"sum"
and the NormalizationFactor
option is
"batch-size"
, the computed value is known as the mean squared error
(MSE).
For each element Yj of the input, the
l2loss
function computes the corresponding element-wise loss values using
where Yj is a predicted value and Tj is the corresponding target value.
To reduce the loss values to a scalar, the function then reduces the element-wise loss using the formula
where N is the normalization factor, mj is the mask value for element j, and wj is the weight value for element j.
If you do not opt to reduce the loss, then the function applies the mask and the weights to the loss values directly:
Deep Learning Array Formats
Most deep learning networks and functions operate on different dimensions of the input data in different ways.
For example, an LSTM operation iterates over the time dimension of the input data, and a batch normalization operation normalizes over the batch dimension of the input data.
To provide input data with labeled dimensions or input data with additional layout information, you can use data formats.
A data format is a string of characters, where each character describes the type of the corresponding data dimension.
The characters are:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, consider an array containing a batch of sequences where the first, second,
and third dimensions correspond to channels, observations, and time steps, respectively. You
can specify that this array has the format "CBT"
(channel, batch,
time).
To create formatted input data, create a dlarray
object and specify the format using the second argument.
To provide additional layout information with unformatted data, specify the formats using the DataFormat
and WeightsFormat
arguments.
For more information, see Deep Learning Data Formats.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The l2loss
function
supports GPU array input with these usage notes and limitations:
When at least one of the following input arguments is a
gpuArray
or adlarray
with underlying data of typegpuArray
, this function runs on the GPU:Y
targets
weights
Mask
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2021b
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