DL4S provides a high-level API for many accelerated operations common in neural networks and deep learning. It furthermore has automatic differentiation builtin, which allows you to create and train neural networks without needing to manually implement backpropagation.

Features include implementations for many basic binary and unary operators, broadcasting, matrix operations, convolutional and recurrent neural networks, commonly used optimizers, second derivatives and much more. DL4S provides implementations for common network architectures, such as VGG, AlexNet, ResNet and Transformers.

While its primary purpose is deep learning and optimization, DL4S can be used as a library for vectorized mathematical operations like numpy.

Read the full documentation

Overview

1. Installation
2. Features
   1. Layers
   2. Optimizers
   3. Losses
   4. Tensor Operations
   5. Engines
   6. Architectures
3. Examples

Installation

iOS / tvOS / macOS

1. In Xcode, select “File” > “Swift Packages” > “Add Package Dependency”
2. Enter https://github.com/palle-k/DL4S.git into the Package URL field and click “Next”.
3. Select “Branch”, “master” and click “Next”.
4. Enable the Package Product DL4S, your app in the “Add to Target” column and click “Next”.

Note: Installation via CocoaPods is no longer supported for newer versions.

Swift Package

Add the dependency to your Package.swift file:

.package(url: "https://github.com/palle-k/DL4S.git", .branch("master"))

Then add DL4S as a dependency to your target:

.target(name: "MyPackage", dependencies: ["DL4S"])

MKL / IPP / OpenMP Support

DL4S can be accelerated with Intel’s Math Kernel Library, Integrated Performance Primitives and OpenMP (Installation Instructions).

On Apple devices, DL4S uses vectorized functions provided by the builtin Accelerate framework by default. If no acceleration library is available, a fallback implementation is used.

Compiling with MKL/IPP:

# After adding the APT repository as described in the installation instructions
sudo apt-get install intel-mkl-64bit-2019.5-075 intel-ipp-64bit-2019.5-075 libiomp-dev

export MKLROOT=/opt/intel/mkl
export IPPROOT=/opt/intel/ipp
export LD_LIBRARY_PATH=${MKLROOT}/lib/intel64:${IPPROOT}/lib/intel64:${LD_LIBRARY_PATH}

swift build -c release \
    -Xswiftc -DMKL_ENABLE \
    -Xlinker -L${MKLROOT}/lib/intel64 \
    -Xlinker -L${IPPROOT}/lib/intel64

TensorBoard Support

DL4S-Tensorboard provides a summary writer that can write tensorboard compatible logs.

LLDB Extension

DL4S includes a LLDB python script that provides custom descriptions for Tensors (util/debugger_support/tensor.py).

To use enhanced summaries, execute command script import /path/to/DL4S/util/debugger_support/tensor.py either directly in LLDB or add the command to your ~/.lldbinit file.

Then you can use the print or frame variable commands to print human-readable descriptions of tensors.

Features

Layers

Core:

Convolution
Transposed Convolution
Dense/Linear/Fully Connected
LSTM
Gated Recurrent Unit (GRU)
Vanilla RNN
Embedding

Pooling:

Max Pooling
Average Pooling
Adaptive Max Pooling
Adaptive Average Pooling

Norm:

Batch Norm
Layer Norm

Utility:

Sequential
Bidirectional RNNs
Dropout
Lambda

Activation:

Relu
Tanh
Sigmoid
Softmax
Log Softmax
Gelu
Swish
Mish
LiSHT

Transformer:

Positional Encoding
Scaled Dot Product Attention
Multihead Attention
Pointwise Feed Forward
Transformer Encoder Block
Transformer Decoder Block

Optimizers

SGD
Momentum
Adam
AMSGrad
AdaGrad
AdaDelta
RMSProp

Losses

Binary Cross-Entropy
Categorical Cross-Entropy
Categorical Negative Log Likelihood (NLL Loss)
MSE
L1 & L2 regularization

Tensor Operations

Behavior of broadcast operations is consistent with numpy rules.

broadcast-add
broadcast-sub
broadcast-mul
broadcast-div
matmul
neg
exp
pow
log
sqrt
sin
cos
tan
tanh
sum
max
relu
leaky relu
heaviside
elementwise max
elementwise min
reduce sum
reduce max
mean
variance
scatter
gather
conv2d
transposed conv2d
max pool
avg pool
subscript
subscript range
transpose
axis permute
reverse
im2col
col2im
stack / concat
swish activation
mish activation
lisht activation
band matrix
diagonal matrix generation
diagonal extraction

Engines

CPU (Accelerate framework for Apple Devices)
CPU (Intel Math Kernel Library and Integrated Performance Primitives)
CPU (Generic)
GPU (Metal)

For an experimental, early stage Metal implementation, check out feature/metal.

Architectures

Default implementations are provided for the following architectures:

ResNet18
VGG (11, 13, 16, 19)
AlexNet
Transformer

Examples

Some high level examples have been implemented in other repositories:

• Neural Machine Translation based on seq2seq with Attention
• Generative Adversarial Networks - Wasserstein GAN with Gradient Penalty (WGAN-GP)
• Reinforcement Learning - Trains an agent to find the exit in a 2D grid world.

Arithmetic & Differentiation

DL4S provides a high-level interface to many vectorized operations on tensors.

let a = Tensor<Float, CPU>([[1,2],[3,4],[5,6]], requiresGradient: true)
let prod = a.transposed().matrixMultipled(with: a)
let s = prod.reduceSum()
let l = log(s)
print(l) // 5.1873856

When a tensor is marked to require a gradient, a compute graph will be captured. The graph stores all operations, which use that tensor directly or indirectly as an operand.

It is then possible to backpropagate through that graph using the gradients(of:) function:

// Backpropagate
let dl_da = l.gradients(of: [a])[0]

print(dl_da)
/*
[[0.034, 0.034]
 [0.078, 0.078]
 [0.123, 0.123]]
*/

Second derivatives

The operations used during backpropagation are themselves differentiable. Therefore, second derivatives can be computed by computing the gradient of the gradient.

When higher order derivatives are required, the compute graph of the backwards pass has to be explicitly retained.

let t = Tensor<Float, CPU>([1,2,3,4], requiresGradient: true)

let result = t * t * t
print(result) // [1, 8, 27, 64]

let grad = result.gradients(of: [t], retainBackwardsGraph: true)[0]
print(grad) // [3, 12, 27, 48]

let secondGrad = grad.gradients(of: [t], retainBackwardsGraph: true)[0]
print(secondGrad) // [6, 12, 18, 24]

let thirdGrad = secondGrad.gradients(of: [t])[0]
print(thirdGrad) // [6, 6, 6, 6]

Convolutional Networks

Example for MNIST classification

// Input must be batchSizex1x28x28
var model = Sequential {
   Convolution2D<Float, CPU>(inputChannels: 1, outputChannels: 6, kernelSize: (5, 5))
   Relu<Float, CPU>()
   MaxPool2D<Float, CPU>(windowSize: 2, stride: 2)

   Convolution2D<Float, CPU>(inputChannels: 6, outputChannels: 16, kernelSize: (5, 5))
   Relu<Float, CPU>()
   MaxPool2D<Float, CPU>(windowSize: 2, stride: 2)

   Flatten<Float, CPU>()

   Dense<Float, CPU>(inputSize: 256, outputSize: 120)
   Relu<Float, CPU>()

   Dense<Float, CPU>(inputSize: 120, outputSize: 10)
   LogSoftmax<Float, CPU>()
}

var optimizer = Adam(model: model, learningRate: 0.001)

// Single iteration of minibatch gradient descent
let batch: Tensor<Float, CPU> = ... // shape: [batchSize, 1, 28, 28]
let y_true: Tensor<Int32, CPU> = ... // shape: [batchSize]

// use optimizer.model, not model
let pred = optimizer.model(batch)
let loss = categoricalNegativeLogLikelihood(expected: y_true, actual: pred)

let gradients = loss.gradients(of: optimizer.model.parameters)
optimizer.update(along: gradients)

Recurrent Networks

Example for MNIST classification

The Gated Reccurent Unit scans the image from top to bottom and uses the final hidden state for classification.

let model = Sequential {
    GRU<Float, CPU>(inputSize: 28, hiddenSize: 128, direction: .forward)
    Lambda<GRU<Float, CPU>.Outputs, Tensor<Float, CPU>, Float, CPU> { inputs in
        inputs.0
    }
    Dense<Float, CPU>(inputSize: 128, outputSize: 10)
    LogSoftmax<Float, CPU>()
}

var optimizer = Adam(model: model, learningRate: 0.001)

let batch: Tensor<Float, CPU> = ... // shape: [batchSize, 28, 28]
let y_true: Tensor<Int32, CPU> = ... // shape: [batchSize]

let x = batch.permuted(to: 1, 0, 2) // Swap first and second axis
let pred = optimizer.model(x)
let loss = categoricalNegativeLogLikelihood(expected: y_true, actual: pred)

let gradients = loss.gradients(of: optimizer.model.parameters)
optimizer.update(along: gradients)