Model Building Basics

Functions

Flux's core feature is the @net macro, which adds some superpowers to regular ol' Julia functions. Consider this simple function with the @net annotation applied:

@net f(x) = x .* x
f([1,2,3]) == [1,4,9]

This behaves as expected, but we have some extra features. For example, we can convert the function to run on TensorFlow or MXNet :

f_mxnet = mxnet(f)
f_mxnet([1,2,3]) == [1.0, 4.0, 9.0]

Simples! Flux took care of a lot of boilerplate for us and just ran the multiplication on MXNet. MXNet can optimise this code for us, taking advantage of parallelism or running the code on a GPU.

Using MXNet, we can get the gradient of the function, too:

back!(f_mxnet, [1,1,1], [1,2,3]) == ([2.0, 4.0, 6.0])

At first glance, this may seem broadly similar to building a graph in TensorFlow. The difference is that the Julia code still behaves like Julia code. Error messages continue to give you helpful stacktraces that pinpoint mistakes. You can step through the code in the debugger. The code only runs once when it's called, as usual, rather than once to build the graph and once to execute it.

The Model

... Initialising Photon Beams ...

The core concept in Flux is the model . A model (or "layer") is simply a function with parameters. For example, in plain Julia code, we could define the following function to represent a logistic regression (or simple neural network):

W = randn(3,5)
b = randn(3)
affine(x) = W * x + b

x1 = rand(5) # [0.581466,0.606507,0.981732,0.488618,0.415414]
y1 = softmax(affine(x1)) # [0.32676,0.0974173,0.575823]

affine is simply a function which takes some vector x1 and outputs a new one y1 . For example, x1 could be data from an image and y1 could be predictions about the content of that image. However, affine isn't static. It has parameters W and b , and if we tweak those parameters we'll tweak the result – hopefully to make the predictions more accurate.

Layers

This is all well and good, but we usually want to have more than one affine layer in our network; writing out the above definition to create new sets of parameters every time would quickly become tedious. For that reason, we want to use a template which creates these functions for us:

affine1 = Affine(5, 5)
affine2 = Affine(5, 5)

softmax(affine1(x1)) # [0.167952, 0.186325, 0.176683, 0.238571, 0.23047]
softmax(affine2(x1)) # [0.125361, 0.246448, 0.21966, 0.124596, 0.283935]

We just created two separate Affine layers, and each contains its own (randomly initialised) version of W and b , leading to a different result when called with our data. It's easy to define templates like Affine ourselves (see templates ), but Flux provides Affine out of the box, so we'll use that for now.

Combining Layers

... Inflating Graviton Zeppelins ...

A more complex model usually involves many basic layers like affine , where we use the output of one layer as the input to the next:

mymodel1(x) = softmax(affine2(σ(affine1(x))))
mymodel1(x1) # [0.187935, 0.232237, 0.169824, 0.230589, 0.179414]

This syntax is again a little unwieldy for larger networks, so Flux provides another template of sorts to create the function for us:

mymodel2 = Chain(affine1, σ, affine2, softmax)
mymodel2(x2) # [0.187935, 0.232237, 0.169824, 0.230589, 0.179414]

mymodel2 is exactly equivalent to mymodel1 because it simply calls the provided functions in sequence. We don't have to predefine the affine layers and can also write this as:

mymodel3 = Chain(
  Affine(5, 5), σ,
  Affine(5, 5), softmax)

You now know enough to take a look at the logistic regression example, if you haven't already.

A Function in Model's Clothing

... Booting Dark Matter Transmogrifiers ...

We noted above that a "model" is a function with some number of trainable parameters. This goes both ways; a normal Julia function like exp is effectively a model with 0 parameters. Flux doesn't care, and anywhere that you use one, you can use the other. For example, Chain will happily work with regular functions:

foo = Chain(exp, sum, log)
foo([1,2,3]) == 3.408 == log(sum(exp([1,2,3])))