Recurrent and Recursive Networks

Transcription

1 Neural Networks with Applications to Vision and Language Recurrent and Recursive Networks Marco Kuhlmann

2 Introduction

3 Applications of sequence modelling Map unsegmented connected handwriting to strings. Map sequences of acoustic signals to sequences of phonemes. Translate sentences from one language into another one. Generate baby names, poems, source code, patent applications.

4 The bag-of-words model The gorgeously elaborate continuation of The Lord of the Rings trilogy is so huge that a column of words cannot adequately describe co-writer/director Peter Jackson s expanded vision of J.R.R. Tolkien s Middle-earth. pos is a sour little movie at its core; an exploration of the emptiness that underlay the relentless gaiety of the 1920 s, as if to stop would hasten the economic and global political turmoil that was to come. neg

5 The bag-of-words model a adequately cannot co-writer column continuation describe director elaborate expanded gorgeously huge is J.R.R. Jackson Lord Middle-earth of of of of Peter Rings so that The The the Tolkien trilogy vision words pos 1920 s a an and as at come core economic emptiness exploration gaiety global hasten if is its little movie of of political relentless sour stop that that the the the the to to turmoil underlay was would neg

6 Part-of-speech tagging jag bad om en kort bit PN VB PP DT JJ NN NN NN SN PN AB VB PL RG NN AB NN

7 Hidden Markov Models (HMMs) P(bad VB) P(kort JJ) P(jag PN) P(om PP) P(en DT) P(bit NN) jag bad om en kort bit PN VB PP DT JJ NN P(PN BOS) P(PP VB) P(JJ DT) P(EOS NN) P(VB PN) P(DT PP) P(NN JJ) transition probabilities, emission probabilities

8 P(VB VB) VB P(w VB) P(VB BOS) P(EOS VB) BOS P(PN VB) P(VB PN) EOS P(PN BOS) P(EOS PN) PN P(w PN) P(PN PN)

9 A weakness of Hidden Markov Models The only information that an HMM has access to at any given point in time is its state. Suppose that the HMM has n states. Then the number of the current state can be written using log n bits. Thus the current state contains at most log n bits of information about the sequence generated so far.

10 Strengths of recurrent neural networks Distributed hidden state In recurrent neural networks, several units can be active at once, which allows them to store a lot of information efficiently. contrast that with one current state in HMMs Non-linear dynamics Different units can interact with each other in non-linear ways. This makes recurrent neural networks Turing-complete. contrast that with linear dynamical systems Attribution: Geoffrey Hinton

11 Recurrent neural networks (RNNs) Recurrent neural networks can be visualised as networks with feedback connections, which form directed cycles between units. These feedback connections are unfolded over time. A crucial property of recurrent neural networks is that they share the same set of parameters across different timesteps.

12 RNN, cyclic representation o f = delay of one timestep h x

13 RNN, unrolled o (1) o (2) o (3) f f f h (1) h (2) h (3) f x (1) x (2) x (3)

14 General observations The parameters of the model are shared across all timesteps. The hidden state can be influenced by the entire input seen so far. Contrast this with the Markov assumption of HMMs. The hidden state can be a lossy summary of the input sequence. Hopefully, this state will encode useful information for the task at hand. The model has the same input size regardless of sequence length. specified in terms of transitions from one state to the other

15 Different types of RNN architectures transducer encoder generator

16 Training recurrent neural networks

17 Computation graph for a standard architecture y (1) y (2) y (3) L (1) L (2) L (3) o (1) o (2) o (3) W h (1) V W V W h (2) h (3) V W U U U x (1) x (2) x (3)

18 Assumptions The hidden states are computed by some nonlinear activation function, such as tanh. The outputs at each time step are normalised log-probabilities representing distributions over a finite set of labels. In the book, this is assumed to happen implicitly when computing the loss.

19 Backpropagation through time Unrolled recurrent neural networks are just feedforward networks, and can therefore be trained using backpropagation. parameter sharing; linear constraints on the parameters This way of training recurrent neural networks is called backpropagation through time. Given that the unrolled computation graphs can be very deep, the vanishing gradient problem is exacerbated in RNNs.

20 t E f y k z k w jk f y j z j w ij y i

21 t E f w jk f w ij y k z k y j z j y i

22 Backpropagation through time y (1) y (2) y (3) L (1) L (2) L (3) o (1) o (2) o (3) W h (1) V W V W h (2) h (3) V W U U U x (1) x (2) x (3)

23 Initial values of the hidden state We could manually specify the initial state in terms of some sensible starting value. We could learn the initial state by starting with a random guess and then updating that guess during backpropagation.

24 Networks with output recurrence y (1) y (2) y (3) L (1) L (2) L (3) W W W o (1) o (2) o (3) V V V W h (1) h (2) h (3) U U U x (1) x (2) x (3)

25 The limitations of recurrent neural networks In principle, recurrent networks are capable of learning longdistance dependencies. In practice, standard gradient-based learning algorithms do not perform very well. Bengio et al. (1994) the vanishing gradient problem Today, there are several methods available for training recurrent neural networks that avoids these problems. LSTMs, optimisation with small gradients, careful weight initialisations,

26 Vanishing and exploding gradients sigmoid tanh relu sigmoid tanh relu 1 1 0,5 0,75 0 0,5-0,5 0, activation functions gradients

27 Recursive neural networks L o y U W U W U W V V V V x (1) x (2) x (3) x (4)

28 Long Short-Term Memory (LSTM)

29 Long Short-Term Memory The Long Short-Term Memory (LSTM) architecture was specifically designed to battle the vanishing gradients problem Metaphor: The dynamic state of the neural network can be considered as a short-term memory. The LSTM architecture tries to make this short-term memory last as long as possible by preventing vanishing gradients. Central idea: gating mechanism

30 Memory cell and gating mechanism The crucial innovation in an LSTM is the design of its memory cell. Information is written into the cell whenever its write gate is on. The information stays in the cell as long as its keep gate is on. Information is read from the cell whenever its read gate is on.

31 Information flow in an LSTM 1.7 write write write keep 1.7 keep 1.7 keep 1.7 keep write write write time 1.7 Attribution: Geoffrey Hinton

32 A look inside an LSTM cell y (i) s (i 1) + tanh s (i) h (i 1) x (i) σ σ tanh σ h (i) Attribution: Chris Olah

33 The keep gate ( forget gate ) h (i 1) x (i) σ Attribution: Chris Olah

34 The write gate ( input gate ) h (i 1) x (i) σ Attribution: Chris Olah

35 Update candidate h (i 1) x (i) tanh Attribution: Chris Olah

36 Updating the internal state s (i 1) + s (i) x (i) Attribution: Chris Olah

37 The write gate ( output gate ) h (i 1) x (i) σ Attribution: Chris Olah

38 Updating the external state y (i) tanh h (i) Attribution: Chris Olah

39 Peephole connections y i s i 1 + tanh s i x i σ σ tanh σ Attribution: Chris Olah

40 Gated Recurrent Unit (GRU) h (i 1) + h (i) 1 σ σ tanh x (i) Attribution: Chris Olah

41 Bidirectional RNNs In speech recognition, the correct interpretation of a given sound may depend on both the previous sounds and the next sounds. Bidirectional RNNs combine one RNN that moves forward through time with another RNN that moves backward. The output can be a representation that depends on both the past and the future, without having to specify a fixed-sized window.

42 A bidirectional RNN y (1) y (2) y (3) h (1) h (2) F B g (2) g (3) x (1) x (2) x (3) Attribution: Chris Olah