First shalt thou take out the Holy Pin, then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out.
💣 Machine learning which might blow up in your face 💣
Grenade is a composable, dependently typed, practical, and fast recurrent neural network library for concise and precise specifications of complex networks in Haskell.
As an example, a network which can achieve ~1.5% error on MNIST can be specified and initialised with random weights in a few lines of code with
type MNIST = Network '[ Convolution 1 10 5 5 1 1, Pooling 2 2 2 2, Relu , Convolution 10 16 5 5 1 1, Pooling 2 2 2 2, FlattenLayer, Relu , FullyConnected 256 80, Logit, FullyConnected 80 10, Logit] '[ 'D2 28 28, 'D3 24 24 10, 'D3 12 12 10, 'D3 12 12 10 , 'D3 8 8 16, 'D3 4 4 16, 'D1 256, 'D1 256 , 'D1 80, 'D1 80, 'D1 10, 'D1 10] randomMnist :: MonadRandom m => m MNIST randomMnist = randomNetwork
And that’s it. Because the types are so rich, there’s no specific term level code required to construct this network; although it is of course possible and easy to construct and deconstruct the networks and layers explicitly oneself.
If recurrent neural networks are more your style, you can try defining something “unreasonably effective” with
type Shakespeare = RecurrentNetwork '[ R (LSTM 40 80), R (LSTM 80 40), F (FullyConnected 40 40), F Logit] '[ 'D1 40, 'D1 80, 'D1 40, 'D1 40, 'D1 40 ]
Networks in Grenade can be thought of as a heterogeneous lists of layers, where their type includes not only the layers of the network, but also the shapes of data that are passed between the layers.
The definition of a network is surprisingly simple:
data Network :: [*] -> [Shape] -> * where NNil :: SingI i => Network ' '[i] (:~>) :: (SingI i, SingI h, Layer x i h) => !x -> !(Network xs (h ': hs)) -> Network (x ': xs) (i ': h ': hs)
Layer x i o constraint ensures that the layer
x can sensibly perform a
transformation between the input and output shapes
The lifted data kind
Shape defines our 1, 2, and 3 dimension types, used to
declare what shape of data is passed between the layers.
In the MNIST example above, the input layer can be seen to be a two dimensional
D2), image with 28 by 28 pixels. When the first Convolution layer runs, it
outputs a three dimensional (
D3) 24x24x10 image. The last item in the list is
one dimensional (
D1) with 10 values, representing the categories of the MNIST
To perform back propagation, one can call the eponymous function
backPropagate :: forall shapes layers. Network layers shapes -> S (Head shapes) -> S (Last shapes) -> Gradients layers
which takes a network, appropriate input and target data, and returns the
back propagated gradients for the network. The shapes of the gradients are
appropriate for each layer, and may be trivial for layers like
have no learnable parameters.
The gradients however can always be applied, yielding a new (hopefully better) layer with
applyUpdate :: LearningParameters -> Network ls ss -> Gradients ls -> Network ls ss
Layers in Grenade are represented as Haskell classes, so creating one’s own is easy in downstream code. If the shapes of a network are not specified correctly and a layer can not sensibly perform the operation between two shapes, then it will result in a compile time error.
Networks and Layers in Grenade are easily composed at the type level. As a
is an instance of
Layer, one can use a trained Network as a small component in a
larger network easily. Furthermore, we provide 2 layers which are designed to run
layers in parallel and merge their output (either by concatenating them across one
dimension or summing by pointwise adding their activations). This allows one to
write any Network which can be expressed as a
series parallel graph.
A residual network layer specification for instance could be written as
type Residual net = Merge Trivial net
If the type
net is an instance of
Residual net will be too. It will
run the network, while retaining its input by passing it through the
and merge the original image with the output.
See the MNIST example, which has been overengineered to contain both residual style learning as well as inception style convolutions.
Generative Adversarial Networks
As Grenade is purely functional, one can compose its training functions in flexible ways. GAN-MNIST example displays an interesting, type safe way of writing a generative adversarial training function in 10 lines of code.
Grenade layers are normal haskell data types which are an instance of
it’s easy to build one’s own downstream code. We do however provide a decent set
of layers, including convolution, deconvolution, pooling, pad, crop, logit, relu,
elu, tanh, and fully connected.
Grenade is most easily built with the mafia
script that is located in the repository. You will also need the
blas libraries and development tools. Once you have all that, Grenade can be
and the tests run using:
Grenade builds with ghc 7.10 and 8.0.
Writing a library like this has been on my mind for a while now, but a big shout out must go to Justin Le, whose dependently typed fully connected network inspired me to get cracking, gave many ideas for the type level tools I needed, and was a great starting point for writing this library.
Grenade is backed by hmatrix, BLAS, and LAPACK, with critical functions optimised in C. Using the im2col trick popularised by Caffe, it should be sufficient for many problems.
Being purely functional, it should also be easy to run batches in parallel, which would be appropriate for larger networks, my current examples however are single threaded.
Training 15 generations over Kaggle’s 41000 sample MNIST training set on a single core took around 12 minutes, achieving 1.5% error rate on a 1000 sample holdout set.
Contributions are welcome.