Advanced Model Building and Customisation

Here we will try and describe usage of some more advanced features that Flux provides to give more control over model building.

Custom Model Example

Here is a basic example of a custom model. It simply adds the input to the result from the neural network.

struct CustomModel

function (m::CustomModel)(x)
  # Arbitrary code can go here, but note that everything will be differentiated.
  # Zygote does not allow some operations, like mutating arrays.

  return m.chain(x) + x

# Call @functor to allow for training. Described below in more detail.
Flux.@functor CustomModel

You can then use the model like:

chain = Chain(Dense(10, 10))
model = CustomModel(chain)

For an intro to Flux and automatic differentiation, see this tutorial.

Customising Parameter Collection for a Model

Taking reference from our example Affine layer from the basics.

By default all the fields in the Affine type are collected as its parameters, however, in some cases it may be desired to hold other metadata in our "layers" that may not be needed for training, and are hence supposed to be ignored while the parameters are collected. With Flux, it is possible to mark the fields of our layers that are trainable in two ways.

The first way of achieving this is through overloading the trainable function.

julia> @functor Affine

julia> a = Affine(rand(3,3), rand(3))
Affine{Array{Float64,2},Array{Float64,1}}([0.66722 0.774872 0.249809; 0.843321 0.403843 0.429232; 0.683525 0.662455 0.065297], [0.42394, 0.0170927, 0.544955])

julia> Flux.params(a) # default behavior
Params([[0.66722 0.774872 0.249809; 0.843321 0.403843 0.429232; 0.683525 0.662455 0.065297], [0.42394, 0.0170927, 0.544955]])

julia> Flux.trainable(a::Affine) = (a.W,)

julia> Flux.params(a)
Params([[0.66722 0.774872 0.249809; 0.843321 0.403843 0.429232; 0.683525 0.662455 0.065297]])

Only the fields returned by trainable will be collected as trainable parameters of the layer when calling Flux.params.

Another way of achieving this is through the @functor macro directly. Here, we can mark the fields we are interested in by grouping them in the second argument:

Flux.@functor Affine (W,)

However, doing this requires the struct to have a corresponding constructor that accepts those parameters.

Freezing Layer Parameters

When it is desired to not include all the model parameters (for e.g. transfer learning), we can simply not pass in those layers into our call to params.

Consider a simple multi-layer perceptron model where we want to avoid optimising the first two Dense layers. We can obtain this using the slicing features Chain provides:

m = Chain(
      Dense(784 => 64, relu),
      Dense(64 => 64, relu),
      Dense(32 => 10)

ps = Flux.params(m[3:end])

The Zygote.Params object ps now holds a reference to only the parameters of the layers passed to it.

During training, the gradients will only be computed for (and applied to) the last Dense layer, therefore only that would have its parameters changed.

Flux.params also takes multiple inputs to make it easy to collect parameters from heterogenous models with a single call. A simple demonstration would be if we wanted to omit optimising the second Dense layer in the previous example. It would look something like this:

Flux.params(m[1], m[3:end])

Sometimes, a more fine-tuned control is needed. We can freeze a specific parameter of a specific layer which already entered a Params object ps, by simply deleting it from ps:

ps = Flux.params(m)
delete!(ps, m[2].bias) 

Custom multiple input or output layer

Sometimes a model needs to receive several separate inputs at once or produce several separate outputs at once. In other words, there multiple paths within this high-level layer, each processing a different input or producing a different output. A simple example of this in machine learning literature is the inception module.

Naively, we could have a struct that stores the weights of along each path and implement the joining/splitting in the forward pass function. But that would mean a new struct any time the operations along each path changes. Instead, this guide will show you how to construct a high-level layer (like Chain) that is made of multiple sub-layers for each path.

Multiple inputs: a custom Join layer

Our custom Join layer will accept multiple inputs at once, pass each input through a separate path, then combine the results together. Note that this layer can already be constructed using Parallel, but we will first walk through how do this manually.

We start by defining a new struct, Join, that stores the different paths and a combine operation as its fields.

using Flux
using CUDA

# custom join layer
struct Join{T, F}

# allow Join(op, m1, m2, ...) as a constructor
Join(combine, paths...) = Join(combine, paths)

Notice that we parameterized the type of the paths field. This is necessary for fast Julia code; in general, T might be a Tuple or Vector, but we don't need to pay attention to what it specifically is. The same goes for the combine field.

The next step is to use Functors.@functor to make our struct behave like a Flux layer. This is important so that calling params on a Join returns the underlying weight arrays on each path.

Flux.@functor Join

Finally, we define the forward pass. For Join, this means applying each path in paths to each input array, then using combine to merge the results.

(m::Join)(xs::Tuple) = m.combine(map((f, x) -> f(x), m.paths, xs)...)
(m::Join)(xs...) = m(xs)

Lastly, we can test our new layer. Thanks to the proper abstractions in Julia, our layer works on GPU arrays out of the box!

model = Chain(
                   Chain(Dense(1 => 5, relu), Dense(5 => 1)), # branch 1
                   Dense(1 => 2),                             # branch 2
                   Dense(1 => 1)                              # branch 3
              Dense(4 => 1)
             ) |> gpu

xs = map(gpu, (rand(1), rand(1), rand(1)))

# returns a single float vector with one value

Using Parallel

Flux already provides Parallel that can offer the same functionality. In this case, Join is going to just be syntactic sugar for Parallel.

Join(combine, paths) = Parallel(combine, paths)
Join(combine, paths...) = Join(combine, paths)

# use vararg/tuple version of Parallel forward pass
model = Chain(
                   Chain(Dense(1 => 5, relu), Dense(5 => 1)),
                   Dense(1 => 2),
                   Dense(1 => 1)
              Dense(4 => 1)
             ) |> gpu

xs = map(gpu, (rand(1), rand(1), rand(1)))

# returns a single float vector with one value

Multiple outputs: a custom Split layer

Our custom Split layer will accept a single input, then pass the input through a separate path to produce multiple outputs.

We start by following the same steps as the Join layer: define a struct, use Functors.@functor, and define the forward pass.

using Flux
using CUDA

# custom split layer
struct Split{T}

Split(paths...) = Split(paths)

Flux.@functor Split

(m::Split)(x::AbstractArray) = map(f -> f(x), m.paths)

Now we can test to see that our Split does indeed produce multiple outputs.

model = Chain(
              Dense(10 => 5),
              Split(Dense(5 => 1, tanh), Dense(5 => 3, tanh), Dense(5 => 2))
             ) |> gpu

# returns a tuple with three float vectors

A custom loss function for the multiple outputs may look like this:

using Statistics

# assuming model returns the output of a Split
# x is a single input
# ys is a tuple of outputs
function loss(x, ys, model)
  # rms over all the mse
  ŷs = model(x)
  return sqrt(mean(Flux.mse(y, ŷ) for (y, ŷ) in zip(ys, ŷs)))