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- 1. 1東北⼤学 ⼩林颯介 @ NLP-DL
- 2. • • • • • 2東北⼤学 ⼩林颯介 @ NLP-DL
- 3. • • • • • • • 3東北⼤学 ⼩林颯介 @ NLP-DL
- 4. • • • • • 4東北⼤学 ⼩林颯介 @ NLP-DL
- 5. • • • 5 killed a man yesterday . <EOS> John killed a man yesterday . 東北⼤学 ⼩林颯介 @ NLP-DL
- 6. • • • • • • • 6東北⼤学 ⼩林颯介 @ NLP-DL
- 7. 7 • • 東北⼤学 ⼩林颯介 @ NLP-DL
- 8. • • • • • 8東北⼤学 ⼩林颯介 @ NLP-DL
- 9. • • • • • 9 [Jozefowicz+15] 東北⼤学 ⼩林颯介 @ NLP-DL
- 10. • • • • • 10 10 [Jozefowicz+15] 東北⼤学 ⼩林颯介 @ NLP-DL
- 11. • • • • • • • 11 [Jozefowicz+15] 東北⼤学 ⼩林颯介 @ NLP-DL
- 12. • • • • • • 12 [Jozefowicz+15] ) . (18) T recurrence +1) ) C +1) (19) the model) aining RNN- (20) 1)T (21) )T . (22) ormance of wo baseline tion capture mean frame- of compari- RBM is per- ling starting ptimally. d on a simu- er & Hinton, Figure 3. Receptive ﬁelds of 48 hidden units of an RNN- RBM trained on the bouncing balls dataset. Each square shows the input weights of a hidden unit as an image. The human motion capture dataset2 is represented by a sequence of joint angles, translations and rotations of the base of the spine in an exponential-map parame- terization (Hsu et al., 2005; Taylor et al., 2007). Since the data consists of 49 real values per time step, we use the Gaussian RBM variant (Welling et al., 2005) for this task. We use up to 450 hidden units and an initial learning rate of 0.001. The mean squared pre- diction test error is 20.1 for the RTRBM and reduced substantially to 16.2 for the RNN-RBM. 6 Modeling sequences of polyphonic music In this section, we show results with main applica- tion of interest for this paper: probabilistic modeling of sequences of polyphonic music. We report our ex- periments on four datasets of varying complexity con- verted to our input format. Piano-midi.de is a classical piano MIDI archive that was split according to Poliner & Ellis (2007). Nottingham is a collection of 1200 folk tunes3 with chords instantiated from the ABC format. MuseData is an electronic library of orchestral and piano classical music from CCARH4 . JSB chorales refers to the entire corpus of 382 four- part harmonized chorales by J. S. Bach with the split of Allan & Williams (2005). 2 people.csail.mit.edu/ehsu/work/sig05stf 3 ifdo.ca/~seymour/nottingham/nottingham.html 東北⼤学 ⼩林颯介 @ NLP-DL
- 13. • • • • 13 [Jozefowicz+15] for Nottingham, N-dropout stands for Nottingham with nonzero dropout, and P stands for Piano-Midi. Arch. 5M-tst 10M-v 20M-v 20M-tst Tanh 4.811 4.729 4.635 4.582 (97.7) LSTM 4.699 4.511 4.437 4.399 (81.4) LSTM-f 4.785 4.752 4.658 4.606 (100.8) LSTM-i 4.755 4.558 4.480 4.444 (85.1) LSTM-o 4.708 4.496 4.447 4.411 (82.3) LSTM-b 4.698 4.437 4.423 4.380 (79.83) GRU 4.684 4.554 4.559 4.519 (91.7) MUT1 4.699 4.605 4.594 4.550 (94.6) MUT2 4.707 4.539 4.538 4.503 (90.2) MUT3 4.692 4.523 4.530 4.494 (89.47) Table 3. Perplexities on the PTB. The preﬁx (e.g., 5M) denotes the number of parameters in the model. The sufﬁx “v” denotes validation negative log likelihood, the sufﬁx“tst” refers to the test set. The perplexity for select architectures is reported in paren- theses. We used dropout only on models that have 10M or 20M parameters, since the 5M models did not beneﬁt from dropout at all, and most dropout-free models achieved a test perplexity of 108, and never greater than 120. In particular, the perplexity of the best models without dropout is below 110, which outperforms the results of Mikolov et al. (2014). 東北⼤学 ⼩林颯介 @ NLP-DL
- 14. • • • • • • • • 14 [Greff+15] 東北⼤学 ⼩林颯介 @ NLP-DL
- 15. • • • • • • • 15東北⼤学 ⼩林颯介 @ NLP-DL
- 16. • 16 • • 東北⼤学 ⼩林颯介 @ NLP-DL
- 17. • • • • 17 resurgence of new structural designs for recurrent neural networks (RNNs) esigns are derived from popular structures including vanilla RNNs, Long works (LSTMs) [4] and Gated Recurrent Units (GRUs) [5]. Despite of their ost of them share a common computational building block, described by the (Wx + Uz + b), (1) Rm are state vectors coming from different information sources, W 2 Rd⇥n e-to-state transition matrices, and b is a bias vector. This computational a combinator for integrating information ﬂow from the x and z by a sum by a nonlinearity . We refer to it as the additive building block. Additive ly implemented in various state computations in RNNs (e.g. hidden state RNNs, gate/cell computations of LSTMs and GRUs. an alternative design for constructing the computational building block by of information integration. Speciﬁcally, instead of utilizing sum operation e Hadamard product “ ” to fuse Wx and Uz: (Wx Uz + b) (2) ucture Description and Analysis neral Formulation of Multiplicative Integration idea behind Multiplicative Integration is to integrate different information ﬂows Wx adamard product “ ”. A more general formulation of Multiplicative Integration e bias vectors 1 and 2 added to Wx and Uz: ((Wx + 1) (Uz + 2) + b) 1, 2 2 Rd are bias vectors. Notice that such formulation contains the ﬁrst order itive building block, i.e., 1 Uht 1 + 2 Wxt. In order to make the Mult on more ﬂexible, we introduce another bias vector ↵ 2 Rd to gate2 the term W g the following formulation: (↵ Wx Uz + 1 Uz + 2 Wx + b), t the number of parameters of the Multiplicative Integration is about the same as t building block, since the number of new parameters (↵, 1 and 2) are negligible c number of parameters. Also, Multiplicative Integration can be easily extended to Us3 , that adopt vanilla building blocks for computing gates and output states, wher replace them with the Multiplicative Integration. More generally, in any kind of information ﬂows (k 2) are involved (e.g. RNN with multiple skip connect dforward models like residual networks [12]), one can implement pairwise Mult on for integrating all k information sources.東北⼤学 ⼩林颯介 @ NLP-DL
- 18. • • • 18 Figure 2: Several examples of cells with interpretable activa [Karpathy+15] 東北⼤学 ⼩林颯介 @ NLP-DL
- 19. 19 [Kádár+16] • • • • • • omission(i, S) = 1 cosine(hend(S), hend(Si)) (12) 東北⼤学 ⼩林颯介 @ NLP-DL
- 20. 20 • [Kádár+16] 東北⼤学 ⼩林颯介 @ NLP-DL
- 21. 21 • • • [Kádár+16] 東北⼤学 ⼩林颯介 @ NLP-DL
- 22. • • • • • 22東北⼤学 ⼩林颯介 @ NLP-DL
- 23. • • • • 23東北⼤学 ⼩林颯介 @ NLP-DL
- 24. • • • • • 24東北⼤学 ⼩林颯介 @ NLP-DL
- 25. Pixel Recurrent Neu x1 xi xn xn2 Figure 2. Left: To generate pixel xi one conditions on all the pre- viously generated pixels left and above of xi. Center: Illustration of a Row LSTM with a kernel of size 3. The dependency ﬁeld of the Row LSTM does not reach pixels further away on the sides of the image. Right: Illustration of the two directions of the Di- agonal BiLSTM. The dependency ﬁeld of the Diagonal BiLSTM covers the entire available context in the image. Figure 3. In the Diagonal BiLSTM, to allow for parallelization along the diagonals, the input map is skewed by offseting each row by one position with respect to the previous row. When the spatial layer is computed left to right and column by column, the output map is shifted back into the original size. The convolution uses a kernel of size 2 ⇥ 1. (2015); Uria et al. (2014)). By contrast we model p(x) as a discrete distribution, with every conditional distribution 3 T th tu fo x p d la T in T a c L th tw u T (s re in la T th s h Pixel Recurrent Neural Networks x1 xi xn xn2 Figure 2. Left: To generate pixel xi one conditions on all the pre- viously generated pixels left and above of xi. Center: Illustration of a Row LSTM with a kernel of size 3. The dependency ﬁeld of the Row LSTM does not reach pixels further away on the sides of the image. Right: Illustration of the two directions of the Di- agonal BiLSTM. The dependency ﬁeld of the Diagonal BiLSTM covers the entire available context in the image. 3.1. Row LSTM The Row LSTM is a unidirectiona the image row by row from top to b tures for a whole row at once; the formed with a one-dimensional con xi the layer captures a roughly triang pixel as shown in Figure 2 (center). dimensional convolution has size k larger the value of k the broader the c The weight sharing in the convoluti invariance of the computed features The computation proceeds as follow an input-to-state component and a r component that together determine th LSTM core. To enhance parallelizat • • • 25 as a conference paper at ICLR 2016 2d Grid LSTM blockblock m0 h0 h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Block cks form the standard LSTM and those that form Grid LSTM networks of N = 1, 2 ons. The dashed lines indicate identity transformations. The standard LSTM block a memory vector in the vertical dimension; by contrast, the 2d Grid LSTM block has ector m1 applied along the vertical dimension. er review as a conference paper at ICLR 2016 2d Grid LSTM blockandard LSTM block m0 h0 h0 I ⇤ xi h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Block re 1: Blocks form the standard LSTM and those that form Grid LSTM networks of N = 1, 2 3 dimensions. The dashed lines indicate identity transformations. The standard LSTM block not have a memory vector in the vertical dimension; by contrast, the 2d Grid LSTM block has memory vector m1 applied along the vertical dimension. review as a conference paper at ICLR 2016 2d Grid LSTM blockard LSTM block m0 h0 h0 I ⇤ xi h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Block 1: Blocks form the standard LSTM and those that form Grid LSTM networks of N = 1, 2 dimensions. The dashed lines indicate identity transformations. The standard LSTM block ot have a memory vector in the vertical dimension; by contrast, the 2d Grid LSTM block has mory vector m1 applied along the vertical dimension. conference paper at ICLR 2016 2d Grid LSTM block m0 h0 h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Block orm the standard LSTM and those that form Grid LSTM networks of N = 1, 2 The dashed lines indicate identity transformations. The standard LSTM block mory vector in the vertical dimension; by contrast, the 2d Grid LSTM block has m1 applied along the vertical dimension. onference paper at ICLR 2016 2d Grid LSTM block m0 h0 h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Block rm the standard LSTM and those that form Grid LSTM networks of N = 1, 2 The dashed lines indicate identity transformations. The standard LSTM block mory vector in the vertical dimension; by contrast, the 2d Grid LSTM block has m1 applied along the vertical dimension. review as a conference paper at ICLR 2016 2d Grid LSTM blockdard LSTM block m0 h0 h0 I ⇤ xi h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Block e 1: Blocks form the standard LSTM and those that form Grid LSTM networks of N = 1, 2 dimensions. The dashed lines indicate identity transformations. The standard LSTM block ot have a memory vector in the vertical dimension; by contrast, the 2d Grid LSTM block has emory vector m1 applied along the vertical dimension. Under review as a conference paper at ICLR 2016 2d Grid LSTM blockStandard LSTM block m m0 h0 h h0 I ⇤ xi h1 h2 h0 2 h0 1 m1 m0 1 m0 2m2 1d Grid LSTM Block 3d Grid LSTM Figure 1: Blocks form the standard LSTM and those that form Grid LSTM networks o and 3 dimensions. The dashed lines indicate identity transformations. The standard LS does not have a memory vector in the vertical dimension; by contrast, the 2d Grid LSTM the memory vector m1 applied along the vertical dimension. 東北⼤学 ⼩林颯介 @ NLP-DL
- 26. • • • • 26 Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing, pages 1556–1566, Beijing, China, July 26-31, 2015. c 2015 Association for Computational Linguistics works, a type of recurrent neural net- work with a more complex computational unit, have obtained strong results on a va- riety of sequence modeling tasks. The only underlying LSTM structure that has been explored so far is a linear chain. However, natural language exhibits syn- tactic properties that would naturally com- bine words to phrases. We introduce the Tree-LSTM, a generalization of LSTMs to tree-structured network topologies. Tree- LSTMs outperform all existing systems and strong LSTM baselines on two tasks: predicting the semantic relatedness of two sentences (SemEval 2014, Task 1) and sentiment classiﬁcation (Stanford Senti- ment Treebank). 1 Introduction Most models for distributed representations of phrases and sentences—that is, models where real- valued vectors are used to represent meaning—fall into one of three classes: bag-of-words models, sequence models, and tree-structured models. In bag-of-words models, phrase and sentence repre- sentations are independent of word order; for ex- ample, they can be generated by averaging con- stituent word representations (Landauer and Du- mais, 1997; Foltz et al., 1998). In contrast, se- quence models construct sentence representations as an order-sensitive function of the sequence of tokens (Elman, 1990; Mikolov, 2012). Lastly, tree-structured models compose each phrase and sentence representation from its constituent sub- phrases according to a given syntactic structure over the sentence (Goller and Kuchler, 1996; Socher et al., 2011). x1 x2 x4 x5 x6 y1 y2 y3 y4 y6 Figure 1: Top: A chain-structured LSTM net- work. Bottom: A tree-structured LSTM network with arbitrary branching factor. Order-insensitive models are insufﬁcient to fully capture the semantics of natural language due to their inability to account for differences in meaning as a result of differences in word order or syntactic structure (e.g., “cats climb trees” vs. “trees climb cats”). We therefore turn to order- sensitive sequential or tree-structured models. In particular, tree-structured models are a linguisti- cally attractive option due to their relation to syn- tactic interpretations of sentence structure. A nat- ural question, then, is the following: to what ex- tent (if at all) can we do better with tree-structured models as opposed to sequential models for sen- tence representation? In this paper, we work to- wards addressing this question by directly com- paring a type of sequential model that has recently been used to achieve state-of-the-art results in sev- eral NLP tasks against its tree-structured general- ization. Due to their capability for processing arbitrary- length sequences, recurrent neural networks 1556 w0 w0w1w2 w4 w5 w6 w0 w4 w5 G EN -L GEN-NX-LGEN-NX-L G EN -R GEN-NX-R GEN-NX-R w1w2w3 LD LD Figure 4: Generation of left and right dependents of node w0 In order to jointly take into account, we employ y goes from the furthest lef left dependent (LD is a dent). As shown in Figur representation of all left d this representation is then right dependent of the sam w0 w1w2w3 w4 w5 w6 Generated by four LSTMs with tied We and tied Who w0 w1w2w3 w0w1w2 w4 w5 w6 w0 w4 w5 G EN -L GEN-NX-LGEN-NX-L G EN -R GEN-NX-R GEN-NX-R Figure 3: Generation process of left (w1,w2,w3) and right Who 2 R|V|⇥d the output matrix of our model, where |V| is the vocabulary size, s the word embedding size and d the hidden unit size. We use tied We and tied Who for the four LSTMs to reduce the number of pa- rameters in our model. The four LSTMs also share their hidden states. Let H 2 Rd⇥(n+1) denote the shared hidden states of all time steps and e(wt) the one-hot vector of wt. Then, H[:,t] represents D(wt) at time step t, and the computation2 is: xt = We ·e(wt0 ) (2a) z 0 東北⼤学 ⼩林颯介 @ NLP-DL
- 27. Figure 2: Attentional Encoder-Decoder model. dj is calculated as the summation vector weighted by ↵j(i): dj = nX i=1 ↵j(i)hi. (6) To incorporate the attention mechanism into the decoding process, the context vector is used for the the j-th word prediction by putting an additional hidden layer ˜sj: ˜s = tanh(W [s ; d ] + b ), (7) Figure 3: Proposed model: Tree-to-sequence tentional NMT model. a sentence inherent in language. We propose novel tree-based encoder in order to explicitly ta the syntactic structure into consideration in t NMT model. We focus on the phrase structure a sentence and construct a sentence vector fro phrase vectors in a bottom-up fashion. The se tence vector in the tree-based encoder is the • • • • • 27東北⼤学 ⼩林颯介 @ NLP-DL
- 28. The hungry cat NP (VP(S REDUCE GENNT(NP)NT(VP) … cat hungry The a<t p(at) ut TtSt gure 5: Neural architecture for deﬁning a distribution over at given representations of the stack (St), output buffer (Tt) and story of actions (a<t). Details of the composition architecture of the NP, the action history LSTM, and the other elements of the ack are not shown. This architecture corresponds to the generator state at line 7 of Figure 4. f the forward and reverse LSTMs are concatenated, assed through an afﬁne transformation and a tanh onlinearity to become the subtree embedding.4 Be- ause each of the child node embeddings (u, v, w in ig. 6) is computed similarly (if it corresponds to an ternal node), this composition function is a kind of cursive neural network. 2 Word Generation 4.4 Discriminative Parsing Model A discriminative parsing model can be obtained by replacing the embedding of Tt at each time step with an embedding of the input buffer Bt. To train this model, the conditional likelihood of each sequence of actions given the input string is maximized.5 5 Inference via Importance Sampling Our generative model p(x, y) deﬁnes a joint dis- • 28 3.5 Comparison to Other Models Our generation algorithm algorithm differs from previous stack-based parsing/generation algorithms in two ways. First, it constructs rooted tree struc- tures top down (rather than bottom up), and sec- ond, the transition operators are capable of directly generating arbitrary tree structures rather than, e.g., assuming binarized trees, as is the case in much prior work that has used transition-based algorithms to produce phrase-structure trees (Sagae and Lavie, 2005; Zhang and Clark, 2011; Zhu et al., 2013). 4 Generative Model RNNGs use the generator transition set just pre- sented to deﬁne a joint distribution on syntax trees (y) and words (x). This distribution is deﬁned as a sequence model over generator transitions that is pa- rameterized using a continuous space embedding of the algorithm state at each time step (ut); i.e., p(x, y) = |a(x,y)| Y t=1 p(at | a<t) = |a(x,y)| Y t=1 exp r> at ut + bat P a02AG(Tt,St,nt) exp r> a0 ut + ba0 , and where action-speciﬁc embeddings ra and bias vector b are parameters in ⇥. The representation of the algorithm state at time t, ut, is computed by combining the representation of the generator’s three data structures: the output dard RNN encoding architecture. The stack (S) is more complicated for two reasons. First, the ele- ments of the stack are more complicated objects than symbols from a discrete alphabet: open nontermi- nals, terminals, and full trees, are all present on the stack. Second, it is manipulated using both push and pop operations. To efﬁciently obtain representations of S under push and pop operations, we use stack LSTMs (Dyer et al., 2015). 4.1 Syntactic Composition Function When a REDUCE operation is executed, the parser pops a sequence of completed subtrees and/or to- kens (together with their vector embeddings) from the stack and makes them children of the most recent open nonterminal on the stack, “completing” the constituent. To compute an embedding of this new subtree, we use a composition function based on bidirectional LSTMs, which is illustrated in Fig. 6. NP u v w NP u v w NP x x Figure 6: Syntactic composition function based on bidirec- tional LSTMs that is executed during a REDUCE operation; the network on the right models the structure on the left. The ﬁrst vector read by the LSTM in both the for- ward and reverse directions is an embedding of the [Dyer+16] Input: The hungry cat meows . Stack Buffer Action 0 The | hungry | cat | meows | . NT(S) 1 (S The | hungry | cat | meows | . NT(NP) 2 (S | (NP The | hungry | cat | meows | . SHIFT 3 (S | (NP | The hungry | cat | meows | . SHIFT 4 (S | (NP | The | hungry cat | meows | . SHIFT 5 (S | (NP | The | hungry | cat meows | . REDUCE 6 (S | (NP The hungry cat) meows | . NT(VP) 7 (S | (NP The hungry cat) | (VP meows | . SHIFT 8 (S | (NP The hungry cat) | (VP meows . REDUCE 9 (S | (NP The hungry cat) | (VP meows) . SHIFT 10 (S | (NP The hungry cat) | (VP meows) | . REDUCE 11 (S (NP The hungry cat) (VP meows) .) Figure 2: Top-down parsing example. tackt Termst Open NTst Action Stackt+1 Termst+1 Open NTst+1 T n NT(X) S | (X T n + 1 T n GEN(x) S | x T | x n | (X | ⌧1 | . . . | ⌧` T n REDUCE S | (X ⌧1 . . . ⌧`) T n 1 ure 3: Generator transitions. Symbols deﬁned as in Fig. 1 with the addition of T representing the history of generated terminals. Stack Terminals Action 0 NT(S) 1 (S NT(NP) 2 (S | (NP GEN(The) 3 (S | (NP | The The GEN(hungry) 4 (S | (NP | The | hungry The | hungry GEN(cat) 5 (S | (NP | The | hungry | cat The | hungry | cat REDUCE 6 (S | (NP The hungry cat) The | hungry | cat NT(VP) 7 (S | (NP The hungry cat) | (VP The | hungry | cat GEN(meows) 8 (S | (NP The hungry cat) | (VP meows The | hungry | cat | meows REDUCE 9 (S | (NP The hungry cat) | (VP meows) The | hungry | cat | meows GEN(.) 10 (S | (NP The hungry cat) | (VP meows) | . The | hungry | cat | meows | . REDUCE 11 (S (NP The hungry cat) (VP meows) .) The | hungry | cat | meows | . • 東北⼤学 ⼩林颯介 @ NLP-DL
- 29. • • 29 [Bowman+16] bu er down sat stack cat the composition tracking transition down sat the cat composition tracking transition down sat the cat tracking (a) The SPINN model unrolled for two transitions during the processing of the sentence the cat sat down. ‘Tracking’, ‘transition’, and ‘composition’ are neural network layers. Gray arrows indicate connections which are blocked by a gating function. bu er stack t = 0 down sat cat the t = 1 down sat cat the t = 2 down sat cat the t = 3 down sat the cat t = 4 down sat the cat t = 5 down sat the cat t = 6 sat down the cat t = 7 = T (the cat) (sat down) output to model for semantic task (b) The fully unrolled SPINN for the cat sat down, with neural network layers omitted for clarity. bu er down sat stack cat the composition tracking transition down sat the cat composition tracking transition down sat the cat tracking (a) The SPINN model unrolled for two transitions during the processing of the sentence the cat sat down. ‘Tracking’, ‘transition’, and ‘composition’ are neural network layers. Gray arrows indicate connections which are blocked by a gating function. bu er stack t = 0 down sat cat the t = 1 down sat cat the t = 2 down sat cat the t = 3 down sat the cat t = 4 down sat the cat t = 5 down sat the cat t = 6 sat down the cat t = 7 = T (the cat) (sat down) output to model for semantic task (b) The fully unrolled SPINN for the cat sat down, with neural network layers omitted for clarity.東北⼤学 ⼩林颯介 @ NLP-DL
- 30. • • • 30 tor with the structure lkj = (1 j/J) (k/d)(1 2j/J) (assuming 1-based indexing), ng the number of words in the sentence, and d is the dimension of the embedding. This presentation, which we call position encoding (PE), means that the order of the words mi. The same representation is used for questions, memory inputs and memory outputs. Encoding: Many of the QA tasks require some notion of temporal context, i.e. in ample of Section 2, the model needs to understand that Sam is in the bedroom after esented by a one-hot vector of length V (where the vocabulary is of size V = 177, simplistic nature of the QA language). The same representation is used for the d answer a. Two versions of the data are used, one that has 1000 training problems second larger one with 10,000 per task. Details wise stated, all experiments used a K = 3 hops model with the adjacent weight sharing all tasks that output lists (i.e. the answers are multiple words), we take each possible of possible outputs and record them as a separate answer vocabulary word. presentation: In our experiments we explore two different representations for s. The ﬁrst is the bag-of-words (BoW) representation that takes the sentence 2, ..., xin}, embeds each word and sums the resulting vectors: e.g mi = P j Axij and j. The input vector u representing the question is also embedded as a bag of words: . This has the drawback that it cannot capture the order of the words in the sentence, ortant for some tasks. propose a second representation that encodes the position of words within the s takes the form: mi = P j lj · Axij, where · is an element-wise multiplication. lj is a 4 4.2 ATTENTION MECHANISMS Neural models with memories coupled to differentiable addressing mechanism have been success- fully applied to handwriting generation and recognition (Graves, 2012), machine translation (Bah- danau et al., 2015a), and more general computation machines (Graves et al., 2014; Weston et al., 2015). Since we are interested in associative memories we employed a “content” based attention. This has the property that the vector retrieved from our memory would not change if we randomly shufﬂed the memory. This is crucial for proper treatment of the input set X as such. In particular, our process block based on an attention mechanism uses the following: qt = LSTM(q⇤ t 1) (3) ei,t = f(mi, qt) (4) ai,t = exp(ei,t) P j exp(ej,t) (5) rt = X i ai,tmi (6) q⇤ t = [qt rt] (7) Read Process Write Figure 1: The Read-Process-and-Write model. where i indexes through each memory vector mi (typically equal to the cardinality of X), qt is a query vector which allows us to read rt from the memories, f is a function that computes a single scalar from mi and qt (e.g., a dot product), and LSTM is an LSTM which computes a recurrent state but which takes no inputs. q⇤ t is the state which this LSTM evolves, and is formed by concatenating the query qt with the resulting attention readout rt. t is the index which indicates how many “processing steps” are being carried to compute the state to be fed to the decoder. Note that permuting mi and mi0 has no effect on the read vector rt. 4.3 READ, PROCESS, WRITE Our model, which naturally handles input sets, has three components (the exact equations and im- plementation will be released in an appendix prior to publication): • A reading block, which simply embeds each element xi 2 X using a small neural network onto a memory vector mi (the same neural network is used for all i). • A process block, which is an LSTM without inputs or outputs performing T steps of com- putation over the memories mi. This LSTM keeps updating its state by reading mi repeat- edly using the attention mechanism described in the previous section. At the end of this block, its hidden state q⇤ T is an embedding which is permutation invariant to the inputs. See eqs. (3)-(7) for more details. 4 fully applied to handwriting generation a danau et al., 2015a), and more general c 2015). Since we are interested in associa This has the property that the vector retri shufﬂed the memory. This is crucial for our process block based on an attention m qt = LSTM(q⇤ t 1) (3) ei,t = f(mi, qt) (4) ai,t = exp(ei,t) P j exp(ej,t) (5) rt = X i ai,tmi (6) q⇤ t = [qt rt] (7) where i indexes through each memory v a query vector which allows us to read single scalar from mi and qt (e.g., a do recurrent state but which takes no inputs by concatenating the query qt with the re how many “processing steps” are being c that permuting mi and mi0 has no effect o 4.3 READ, PROCESS, WRITE Our model, which naturally handles inpu plementation will be released in an appen • A reading block, which simply e onto a memory vector mi (the sa • A process block, which is an LS putation over the memories mi. edly using the attention mechan block, its hidden state q⇤ T is an em eqs. (3)-(7) for more details. 東北⼤学 ⼩林颯介 @ NLP-DL
- 31. • • • • • • 31東北⼤学 ⼩林颯介 @ NLP-DL
- 32. • • • • • 32東北⼤学 ⼩林颯介 @ NLP-DL
- 33. • • • • • • • 33 , d(ht−1)] + bh), (4) function from Equation 2. d-forward fully connected is a signiﬁcant difference: ks every fully-connected only once, while it is not nt layer: each training ex- mposed of a number of in- ropout this results in hid- on every step. This obser- tion of how to sample the re two options: sample it sequence (per-sequence) mask on every step (per- wo strategies for sampling etail in Section 3.4. ht = ot ∗ f(ct), where it, ft, ot are input, output and forget gate step t; gt is the vector of cell updates and ct is updated cell vector used to update the hidden s ht; σ is the sigmoid function and ∗ is the elem wise multiplication. Our approach is to apply dropout to the cell date vector ct as follows: ct = ft ∗ ct−1 + it ∗ d(gt) In contrast, Moon et al. (2015) propose to ply dropout directly to the cell values and use sequence sampling: ct = d(ft ∗ ct−1 + it ∗ gt) We will discuss the limitations of the appro of Moon et al. (2015) in Section 3.4 and sup Figure 1: Illustration of the three types circles represent connections, hidden state we apply dropout. gt = f(Wg xt, rt ∗ ht−1 + bg) ht = (1 − zt) ∗ ht−1 + zt ∗ gt Similarly to the LSTMs, we propoose dropout to the hidden state updates vector ht = (1 − zt) ∗ ht−1 + zt ∗ d(gt) To the best of our knowledge, this work is to study the effect of recurrent dropout networks. 3.4 Dropout and memory Before going further with the explanatio 東北⼤学 ⼩林颯介 @ NLP-DL
- 34. • • • • • 34 hidden-to-hidden transformations. We introduce the batch-normalizing transform BN( · ; , ) the LSTM as follows: 0 B B @ ˜ft ˜it ˜ot ˜gt 1 C C A = BN(Whht 1; h, h) + BN(Wxxt; x, x) + b (6) ct = (˜ft) ct 1 + (˜it) tanh( ˜gt) (7) ht = (˜ot) tanh(BN(ct; c, c)) (8) network by discarding the absolute scale of activations. We want to a preserve the information in the network, by normalizing the activations in a training example relative to the statistics of the entire training data. 3 Normalization via Mini-Batch Statistics Since the full whitening of each layer’s inputs is costly and not everywhere differentiable, we make two neces- sary simpliﬁcations. The ﬁrst is that instead of whitening the features in layer inputs and outputs jointly, we will normalize each scalar feature independently, by making it have the mean of zero and the variance of 1. For a layer with d-dimensional input x = (x(1) . . . x(d) ), we will nor- malize each dimension x(k) = x(k) − E[x(k) ] Var[x(k)] where the expectation and variance are computed over the training data set. As shown in (LeCun et al., 1998b), such normalization speeds up convergence, even when the fea- tures are not decorrelated. Note that simply normalizing each input of a layer may change what the layer can represent. For instance, nor- B = {x1...m} Let the normalized values be x1...m formations be y1...m. We refer to t BNγ,β : x1...m → as the Batch Normalizing Transfor Transform in Algorithm 1. In the a added to the mini-batch variance f Input: Values of x over a mini-ba Parameters to be learned: Output: {yi = BNγ,β(xi)} µB ← 1 m m i=1 xi σ2 B ← 1 m m i=1 (xi − µB)2 xi ← xi − µB σ2 B + ϵ yi ← γxi + β ≡ BNγ,β(xi) Algorithm 1: Batch Normalizing 東北⼤学 ⼩林颯介 @ NLP-DL
- 35. • • • • • • 35 Overﬁtting in machine learning is addressed by restricting the space o considered. This can be accomplished by reducing the number of par with an inductive bias for simpler models, such as early stopping. can be achieved by incorporating more sophisticated prior knowledg activations on a reasonable path can be difﬁcult, especially across lo in mind, we devise a regularizer for the state representation learned RNNs, that aims to encourage stability of the path taken through repr we propose the following additional cost term for Recurrent Neural N 1 T TX t=1 (khtk2 kht 1k2)2 Where ht is the vector of hidden activations at time-step t, and is a h amounts of regularization. We call this penalty the norm-stabilizer, as norms of the hiddens to be stable (i.e. approximately constant acros coherence” penalty of Jonschkowski & Brock (2015), our penalty representation to remain constant, only its norm. In the absence of inputs and nonlinearities, a constant norm would imp to-hidden transition matrix for simple RNNs (SRNNs). However, in t sition matrix, inputs and nonlinearities can still change the norm of instability. This makes targeting the hidden activations directly a mo ing norm stability. Stability becomes especially important when we sequences at test time than those seen during training (the “training h arXiv:1511.08400v 東北⼤学 ⼩林颯介 @ NLP-DL
- 36. • • • nce paper at ICLR 2016 English (unsupervised) German (translation) Tags (parsing)English y Setting – one encoder, multiple decoders. This scheme is useful for either as in Dong et al. (2015) or between different tasks. Here, English and Ger- of words in the respective languages. The α values give the proportions of are allocated for the different tasks. Published as a conference paper at ICLR 2016 English (unsupervised) German (translation) Tags (parsing)English Figure 2: One-to-many Setting – one encoder, multiple decoders. This scheme is useful for either multi-target translation as in Dong et al. (2015) or between different tasks. Here, English and Ger- man imply sequences of words in the respective languages. The α values give the proportions of parameter updates that are allocated for the different tasks. for constituency parsing as used in (Vinyals et al., 2015a), (b) a sequence of German words for ma- chine translation (Luong et al., 2015a), and (c) the same sequence of English words for autoencoders or a related sequence of English words for the skip-thought objective (Kiros et al., 2015). 3.2 MANY-TO-ONE SETTING This scheme is the opposite of the one-to-many setting. As illustrated in Figure 3, it consists of mul- tiple encoders and one decoder. This is useful for tasks in which only the decoder can be shared, for example, when our tasks include machine translation and image caption generation (Vinyals et al., 2015b). In addition, from a machine translation perspective, this setting can beneﬁt from a large amount of monolingual data on the target side, which is a standard practice in machine translation system and has also been explored for neural MT by Gulcehre et al. (2015). English (unsupervised) Image (captioning) English German (translation) Figure 3: Many-to-one setting – multiple encoders, one decoder. This scheme is handy for tasks in which only the decoders can be shared. 3.3 MANY-TO-MANY SETTING Lastly, as the name describes, this category is the most general one, consisting of multiple encoders Published as a conference paper at ICLR 2016 German (translation) English (unsupervised) German (unsupervised) English Figure 4: Many-to-many setting – multiple encoders, multiple decoders. We consider t in a limited context of machine translation to utilize the large monolingual corpora i source and the target languages. Here, we consider a single translation task and two un autoencoder tasks. consist of ordered sentences, e.g., paragraphs. Unfortunately, in many applications th machine translation, we only have sentence-level data where the sentences are unordered. that, we split each sentence into two halves; we then use one half to predict the other hal 36東北⼤学 ⼩林颯介 @ NLP-DL
- 37. • • • • • • 37東北⼤学 ⼩林颯介 @ NLP-DL
- 38. • • • • • 38東北⼤学 ⼩林颯介 @ NLP-DL
- 39. • • • • • • • • • 39東北⼤学 ⼩林颯介 @ NLP-DL
- 40. • • • 40 hello , my name is Tony Jebara . Attentive Read hi , Tony Jebara <eos> hi , Tony h1 h2 h3 h4 h5 s1 s2 s3 s4 h6 h7 h8 “Tony” DNN Embedding for “Tony” Selective Read for “Tony” (a) Attention-based Encoder-Decoder (RNNSearch) (c) State Update s4 SourceVocabulary Softmax Prob(“Jebara”)=Prob(“Jebara”, g) +Prob(“Jebara”, c) … ... (b) Generate-Mode & Copy-Mode ! M M 東北⼤学 ⼩林颯介 @ NLP-DL
- 41. forms and their meanings is non-trivial (de Saus- sure, 1916). While some compositional relation- ships exist, e.g., morphological processes such as adding -ing or -ly to a stem have relatively reg- ular effects, many words with lexical similarities convey different meanings, such as, the word pairs lesson () lessen and coarse () course. 3 C2W Model Our compositional character to word (C2W) model is based on bidirectional LSTMs (Graves and Schmidhuber, 2005), which are able to learn complex non-local dependencies in sequence models. An illustration is shown in Figure 1. The input of the C2W model (illustrated on bottom) is a single word type w, and we wish to obtain is a d-dimensional vector used to represent w. This model shares the same input and output of a word lookup table (illustrated on top), allowing it to eas- ily replace then in any network. As input, we deﬁne an alphabet of characters C. For English, this vocabulary would contain an entry for each uppercase and lowercase letter as well as numbers and punctuation. The input word w is decomposed into a sequence of characters c1, . . . , cm, where m is the length of w. Each ci cats cat cats job .... .... ........ cats c a t s a c t .... .... s Character Lookup Table Word Lookup Table Bi-LSTM embeddings for word "cats" embeddings for word "cats" • • • • • 41東北⼤学 ⼩林颯介 @ NLP-DL
- 42. Figure 1: Illustration of the Scheduled Sampling approach, • • • 42東北⼤学 ⼩林颯介 @ NLP-DL
- 43. • • • 43 In order to apply the REINFORCE algorithm (Williams, 1992; Zaremba & Sutskever, 2015) to the problem of sequence generation we cast our problem in the reinforcement learning (RL) frame- work (Sutton & Barto, 1988). Our generative model (the RNN) can be viewed as an agent, which interacts with the external environment (the words and the context vector it sees as input at every time step). The parameters of this agent deﬁnes a policy, whose execution results in the agent pick- ing an action. In the sequence generation setting, an action refers to predicting the next word in the sequence at each time step. After taking an action the agent updates its internal state (the hid- den units of RNN). Once the agent has reached the end of a sequence, it observes a reward. We can choose any reward function. Here, we use BLEU (Papineni et al., 2002) and ROUGE-2 (Lin & Hovy, 2003) since these are the metrics we use at test time. BLEU is essentially a geometric mean over n-gram precision scores as well as a brevity penalty (Liang et al., 2006); in this work, we consider up to 4-grams. ROUGE-2 is instead recall over bi-grams. Like in imitation learning, we have a training set of optimal sequences of actions. During training we choose actions according to the current policy and only observe a reward at the end of the sequence (or after maximum sequence length), by comparing the sequence of actions from the current policy against the optimal action sequence. The goal of training is to ﬁnd the parameters of the agent that maximize the expected reward. We deﬁne our loss as the negative expected reward: L✓ = X wg 1 ,...,wg T p✓(wg 1, . . . , wg T )r(wg 1, . . . , wg T ) = E[wg 1 ,...wg T ]⇠p✓ r(wg 1, . . . , wg T ), (9) where wg n is the word chosen by our model at the n-th time step, and r is the reward associated with the generated sequence. In practice, we approximate this expectation with a single sample from the distribution of actions implemented by the RNN (right hand side of the equation above and Figure 9 of Supplementary Material). We refer the reader to prior work (Zaremba & Sutskever, 2015; Williams, 1992) for the full derivation of the gradients. Here, we directly report the partial derivatives and their interpretation. The derivatives w.r.t. parameters are: @L✓ @✓ = X t @L✓ @ot @ot @✓ (10) 6 Published as a conference paper at ICLR 2016 h2 = ✓( , h1) p✓(w| , h1) XENT h1 w2 w3XENT top-k w0 1,...,k p✓(w|w0 1,...,k, h2) w00 1,...,k h3 = ✓(w0 1,...,k, h2) top-k Figure 3: Illustration of the End-to-End BackProp method. The ﬁrst steps of the unrolled sequence (here just the ﬁrst step) are exactly the same as in a regular RNN trained with cross-entropy. How- ever, in the remaining steps the input to each module is a sparse vector whose non-zero entries are the k largest probabilities of the distribution predicted at the previous time step. Errors are back- propagated through these inputs as well. While this algorithm is a simple way to expose the model to its own predictions, the loss function optimized is still XENT at each time step. There is no explicit supervision at the sequence level while training the model. 3.2 SEQUENCE LEVEL TRAINING We now introduce a novel algorithm for sequence level training, which we call Mixed Incremental Cross-Entropy Reinforce (MIXER). The proposed method avoids the exposure bias problem, and oss L using a two-step pro- ass, we compute candidate n violations (sequences with backward pass, we back- ugh the seq2seq RNNs. Un- ining, the ﬁrst-step requires Time Step a red dog smells home today the dog dog barks quickly Friday red blue cat barks straight now runs today a red dog runs quickly today 東北⼤学 ⼩林颯介 @ NLP-DL
- 44. • • • • • 44東北⼤学 ⼩林颯介 @ NLP-DL

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