compressNetworkUsingProjection

Compress neural network using projection

Since R2022b

Syntax

netProjected = compressNetworkUsingProjection(net,mbq)

netProjected = compressNetworkUsingProjection(net,X1,...,XN)

netProjected = compressNetworkUsingProjection(net,npca)

[netProjected, info] = compressNetworkUsingProjection(___)

[netProjected, info] = compressNetworkUsingProjection(___,Name=Value)

Description

The compressNetworkUsingProjection function reduces the number of learnable parameters of layers by performing principal component analysis (PCA) of the neuron activations using a data set representative of the training data and then projects the learnable parameters into the subspace that maintains the highest variance in neuron activations.

Forward passes of a projected deep neural network are typically faster when you deploy the network to embedded hardware using library-free C or C++ code generation.

If you prune or quantize your network, then use compression using projection after pruning and before quantization. Network compression using projection supports projecting LSTM layers only.

netProjected = compressNetworkUsingProjection(net,mbq) compresses the dlnetwork object net by replacing layers with projected layers. The function compresses layers by performing principal component analysis (PCA) of the neuron activations using the data in the minibatchqueue object mbq and projects learnable parameters into the subspace that maintains the highest variance in neuron activations. This function requires the Deep Learning Toolbox™ Model Quantization Library support package. This support package is a free add-on that you can download using the Add-On Explorer. Alternatively, see Deep Learning Toolbox Model Quantization Library.

netProjected = compressNetworkUsingProjection(net,X1,...,XN) compresses the network using the data in the dlarray objects X1,...,XN, where N is the number of network inputs.

netProjected = compressNetworkUsingProjection(net,npca) compresses the network using the neuronPCA object npca. The PCA step can be computationally intensive. If you expect to compress the same network multiple times (for example, when exploring different levels of compression), then you can perform the PCA step up front using a neuronPCA object.

[netProjected, info] = compressNetworkUsingProjection(___) also returns the structure info that contains information about the reduction of learnable parameters and the explained variance achieved during compression.

[netProjected, info] = compressNetworkUsingProjection(___,Name=Value) specifies additional options using one or more name-value arguments.

Examples

Compress Network Using Projection

Load the pretrained network in dlnetJapaneseVowels and the training data.

load dlnetJapaneseVowels
XTrain = japaneseVowelsTrainData;

Create a mini-batch queue containing the training data. To create a mini-batch queue from in-memory data, convert the sequences to an array datastore.

adsXTrain = arrayDatastore(XTrain,OutputType="same");

Create the minibatchqueue object.

• Specify a mini-batch size of 16.

• Preprocess the mini-batches using the preprocessMiniBatchPredictors function, listed in the Mini-Batch Predictors Preprocessing Function section of the example.

• Specify that the output data has format "CTB" (channel, time, batch).

miniBatchSize = 16;

mbq = minibatchqueue(adsXTrain, ...
    MiniBatchSize=miniBatchSize, ...
    MiniBatchFcn=@preprocessMiniBatchPredictors, ...
    MiniBatchFormat="CTB");

Compress the network.

netProjected = compressNetworkUsingProjection(net,mbq);

Compressed network has 82.4% fewer learnable parameters.
Projected layers explain on average 96.6% of layer activation variance.

Mini-Batch Predictors Preprocessing Function

The preprocessMiniBatchPredictors function preprocesses a mini-batch of predictors by extracting the sequence data from the input cell array and truncating them along the second dimension so that they have the same length.

Note: Do not pad sequence data when doing the PCA step for projection as this can negatively impact the analysis. Instead, truncate mini-batches of data to have the same length or use mini-batches of size 1.

function X = preprocessMiniBatchPredictors(dataX)

X = padsequences(dataX,2,Length="shortest");

end

Determine Maximum Possible Compression

To determine the maximum possible compression, set the LearnablesReductionGoal option to 1 or the ExplainedVarianceGoal option to 0.

Load the pretrained network in dlnetJapaneseVowels and the training data.

load dlnetJapaneseVowels
XTrain = japaneseVowelsTrainData;

Create a mini-batch queue containing the training data. To create a mini-batch queue from in-memory data, convert the sequences to an array datastore.

adsXTrain = arrayDatastore(XTrain,OutputType="same");

Create the minibatchqueue object.

• Specify a mini-batch size of 16.

• Preprocess the mini-batches using the preprocessMiniBatchPredictors function, listed in the Mini-Batch Predictors Preprocessing Function section of the example.

• Specify that the output data has format "CTB" (channel, time, batch).

miniBatchSize = 16;

mbq = minibatchqueue(adsXTrain, ...
    MiniBatchSize=miniBatchSize, ...
    MiniBatchFcn=@preprocessMiniBatchPredictors, ...
    MiniBatchFormat="CTB");

Compress the network. To determine the maximum possible compression, set the LearnablesReductionGoal option to 1.

[netProjected,info] = compressNetworkUsingProjection(net,mbq,LearnablesReductionGoal=1);

Compressed network has 95.2% fewer learnable parameters.
Projected layers explain on average 33.8% of layer activation variance.

View the proportion of total number of network learnables removed by inspecting the LearnablesReduction property of the information structure.

info.LearnablesReduction

ans = 0.9518

Mini-Batch Predictors Preprocessing Function

The preprocessMiniBatchPredictors function preprocesses a mini-batch of predictors by extracting the sequence data from the input cell array and truncating them along the second dimension so that they have the same length.

Note: Do not pad sequence data when doing the PCA step for projection as this can negatively impact the analysis. Instead, truncate mini-batches of data to have the same length or use mini-batches of size 1.

function X = preprocessMiniBatchPredictors(dataX)

X = padsequences(dataX,2,Length="shortest");

end

Input Arguments

net — Neural network

initialized dlnetwork object

Neural network, specified as an initialized dlnetwork object.

mbq — Mini-batch queue

minibatchqueue object

Mini-batch queue that outputs data for each input of the network, specified as a minibatchqueue object.

The PCA step typically works best when using the full training set. However, any dataset that is representative of the training data distribution suffices. The input data must contain two or more observations and sequences must contain two or more time steps.

Note

Do not pad sequence as this can negatively impact the analysis. Instead, truncate mini-batches of data to have the same length or use mini-batches of size 1.

X1,...,XN — Input data

formatted dlarray

Input data, specified as a formatted dlarray.

For more information about dlarray formats, see the fmt input argument of dlarray.

The PCA step typically works best when using the full training set. However, any dataset that is representative of the training data distribution suffices. The input data must contain two or more observations and sequences must contain two or more time steps.

Note

Do not pad sequence as this can negatively impact the analysis. Instead, truncate mini-batches of data to have the same length or use mini-batches of size 1.

npca — Neuron principal component analysis

neuronPCA object

Neuron principal component analysis, specified as a neuronPCA object.

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: netProjected = compressNetworkUsingProjection(net,mbq,VerbosityLevel="off") compresses the network using projection and disables the command line display.

LayerNames — Names of layers to compress

string array | cell array of character vectors | character vector

Names of layers to compress, specified as a string array, cell array of character vectors, or a character vector containing a single layer name.

The software, by default, compress all the layers in the network that support projection. Network compression using projection supports projecting LSTM layers only.

Data Types: string | cell

ExplainedVarianceGoal — Target proportion of neuron activation variance explained by principal components

0.95 (default) | nonnegative scalar less than or equal to 1

Target proportion of neuron activation variance explained by the remaining principal components of each projected layer, specified as a value between 0 (maximum compression) and 1 (project layers with minimal compression).

If you specify the ExplainedVarianceGoal option, then you must not specify the LearnablesReductionGoal option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

LearnablesReductionGoal — Target proportion of total number of network learnables to remove

nonnegative scalar less than or equal to 1

Target proportion of total number of network learnables to remove, specified as a nonnegative scalar less than or equal to 1.

If you specify the LearnablesReductionGoal option, then you must not specify the ExplainedVarianceGoal option. If you do not specify the LearnablesReductionGoal option, then the function compresses the network using the ExplainedVarianceGoal option.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

VerbosityLevel — Verbosity level

"summary" (default) | "steps" | "iterations" | "off"

Verbosity level, specified as one of these values:

• "summary" — Display a summary of the compression algorithm.

• "steps" — Display information about the steps of the compression algorithm.

• "iterations" — Display information about the iterations of the compression algorithm.

• "off" — Do not display information.

Output Arguments

netProjected — Projected network

dlnetwork object

Projected network, returned as a dlnetwork object.

After you compress the network using projection, you can fine-tune the network to help regain predictive accuracy lost by the compression process. For an example, see Compress Neural Network Using Projection.

info — Projection information

structure

Projection information, returned as a structure with these fields:

• LearnablesReduction — proportion of total number of network learnables removed

• ExplainedVariance — proportion of neuron activation variance explained by principal components

Extended Capabilities

GPU Arrays

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

Usage notes and limitations:

• This function runs on the GPU if any of these conditions are met:

  • Any of the values of the network learnable parameters inside net.Learnables.Value are dlarray objects with underlying data of type gpuArray

  • The input argument mbq outputs dlarray objects with underlying data of type gpuArray

  • The input arguments X1,...,XN are dlarray objects with underlying data of type gpuArray

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2022b