Recurrent Models

Recurrent Cells

In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.

y₁ = f(x₁)
y₂ = f(x₂)
y₃ = f(x₃)
# ...

Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.

h = # ... initial state ...
h, y₁ = f(h, x₁)
h, y₂ = f(h, x₂)
h, y₃ = f(h, x₃)
# ...

Information stored in h is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given x depends on all the inputs previously fed into the model.

(This might be important if, for example, each x represents one word of a sentence; the model's interpretation of the word "bank" should change if the previous input was "river" rather than "investment".)

Flux's RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard Dense layer, and the output is also the hidden state.

Wxh = randn(5, 10)
Whh = randn(5, 5)
b   = randn(5)

function rnn(h, x)
  h = tanh.(Wxh * x .+ Whh * h .+ b)
  return h, h
end

x = rand(10) # dummy data
h = rand(5)  # initial hidden state

h, y = rnn(h, x)

If you run the last line a few times, you'll notice the output y changing slightly even though the input x is the same.

We sometimes refer to functions like rnn above, which explicitly manage state, as recurrent cells. There are various recurrent cells available, which are documented in the layer reference. The hand-written example above can be replaced with:

using Flux

rnn2 = Flux.RNNCell(10, 5)

x = rand(10) # dummy data
h = rand(5)  # initial hidden state

h, y = rnn2(h, x)

Stateful Models

For the most part, we don't want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the Recur wrapper to do this.

x = rand(10)
h = rand(5)

m = Flux.Recur(rnn, h)

y = m(x)

The Recur wrapper stores the state between runs in the m.state field.

If you use the RNN(10, 5) constructor – as opposed to RNNCell – you'll see that it's simply a wrapped cell.

julia> RNN(10, 5)
Recur(RNNCell(10, 5, tanh))

Sequences

Often we want to work with sequences of inputs, rather than individual xs.

seq = [rand(10) for i = 1:10]

With Recur, applying our model to each element of a sequence is trivial:

m.(seq) # returns a list of 5-element vectors

This works even when we've chain recurrent layers into a larger model.

m = Chain(LSTM(10, 15), Dense(15, 5))
m.(seq)

Finally, we can reset the hidden state of the cell back to its initial value using reset!(m).