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epresents probability distribution P (wt|wt−4, wt−3, wt−2, wt−1). I have proposed an alternative feedforward architecture of the neural network language model in [48]. The problem of learning n-gram NNLM is decomposed into two steps: learning a bigram NNLM (with only the previous word from the history encoded in the input layer), and then training an n-gram NNLM that projects words from the n-gram history into the lower dimensional space by using the already trained bigram NNLM. Both models are simple feedforward neural networks with one hidden layer, thus this solution is simpler for implementation and for understanding than the original Bengio’s model. It provides almost identical results as the original model, as will be shown in the following chapter. 3.2 Recurrent Neural Network Based <strong>Language</strong> Model I have described a recurrent neural network language model (RNNLM) in [49] and exten- sions in [50]. The main difference between the feedforward and the recurrent architecture is in representation of the history - while for feedforward NNLM, the history is still just previous several words, for the recurrent model, an effective representation of history is learned from the data during training. The hidden layer of RNN represents all previous history and not just n − 1 previous words, thus the model can theoretically represent long context patterns. Another important advantage of the recurrent architecture over the feedforward one is the possibility to represent more advanced patterns in the sequential data. For example, patterns that rely on words that could have occurred at variable position in the history can be encoded much more efficiently with the recurrent architecture - the model can simply remember some specific word in the state of the hidden layer, while the feedforward architecture would need to use parameters for each specific position of the word in the history; this not only increases the total amount of parameters in the model, but also the number of training examples that have to be seen to learn the given pattern. The architecture of RNNLM is shown in Figure 3.1. The input layer consists of a vector w(t) that represents the current word wt encoded as 1 of V (thus size of w(t) is equal to the size of the vocabulary), and of vector s(t−1) that represents output values in the hidden layer from the previous time step. After the network is trained, the output layer y(t) represents P (wt+1|wt, s(t−1)). 28
w(t) s(t-1) s(t) U V W y(t) Figure 3.1: Simple recurrent neural network. The network is trained by stochastic gradient descent using either usual backpropagation (BP) algorithm, or backpropagation through time (BPTT) [65]. The network is represented by input, hidden and output layers and corresponding weight matrices - matrices U and W between the input and the hidden layer, and matrix V between the hidden and the output layer. Output values in the layers are computed as follows: sj(t) = f wi(t)uji + sl(t−1)wjl i l (3.1) ⎛ yk(t) = g ⎝ ⎞ sj(t)vkj ⎠ (3.2) where f(z) and g(z) are sigmoid and softmax activation functions (the softmax function in the output layer is used to ensure that the outputs form a valid probability distribution, i.e. all outputs are greater than 0 and their sum is 1): f(z) = j 1 1 + e−z , g(zm) = ezm k ezk (3.3) Note that biases are not used in the neural network, as no significant improvement of performance was observed - following the Occam’s razor, the solution is as simple as it needs to be. Alternatively, the equations 3.1 and 3.2 can be rewritten as a matrix-vector multiplication: s(t) = f (Uw(t) + Ws(t−1)) (3.4) 29
Page 1 and 2: VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ
Page 3 and 4: Abstrakt Statistické jazykové mod
Page 5 and 6: Contents 1 Introduction 4 1.1 Motiv
Page 7 and 8: 6.2.3 Reduction of Vocabulary Size
Page 9 and 10: Maybe the most popular vision of fu
Page 11 and 12: Chapter 6 presents further extensio
Page 13 and 14: Chapter 2 Overview of Stati
Page 15 and 16: 2.1 Evaluation 2.1.1 Perplexity Eva
Page 17 and 18: ALP can be used to obtain prior pro
Page 19 and 20: • Good theoretical motivation •
Page 21 and 22: abilities of n-grams are stored in
Page 23 and 24: main (static) n-gram model. As the
Page 25 and 26: There are many popular examples sho
Page 27 and 28: y Chen et al., who proposed a so-ca
Page 29 and 30: confusion among researchers, and ma
Page 31: language model took almost a week u
Page 35 and 36: ate is halved at start of every new
Page 37 and 38: or using matrix-vector notation as
Page 39 and 40: information for more than 5 time st
Page 41 and 42: A simple solution to the exploding
Page 43 and 44: output layer changes to computation
Page 45 and 46: While RNN models can overcome this
Page 47 and 48: complex or random architectures (su
Page 49 and 50: While for any of the previous point
Page 51 and 52: where λ is the interpolation weigh
Page 53 and 54: model with default SRILM cutoffs pr
Page 55 and 56: experiments, we have used the one i
Page 57 and 58: Perplexity (Penn corpus) 145 140 13
Page 59 and 60: with syntactical NNLMs would be pre
Page 61 and 62: Table 4.3: Combination of individua
Page 63 and 64: Table 4.6: Results on Penn Treebank
Page 65 and 66: 4.6 Conclusion of the Model Combina
Page 67 and 68: were: 400 classes, hidden layer siz
Page 69 and 70: Entropy per word on the WSJ test da
Page 71 and 72: Table 5.3: Results on the WSJ setup
Page 73 and 74: Table 5.5: Results for models <stro
Page 75 and 76: trained together with a maximum ent
Page 77 and 78: wt-3 wt-2 wt-1 D D D P(wt|context)
Page 79 and 80: n-gram probabilities. However, it w
Page 81 and 82: Table 6.1: Training corpora for NIS
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Perplexity 360 340 320 300 280 260
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Entropy per word 9 8.5 8 7.5 7 6.5
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1 a a a 1 2 3 P(w(t)|*) ONE TWO THR
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Table 6.4: Perplexity on the evalua
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Entropy reduction per word over KN4
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Table 6.6: Perplexity with the new
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Entropy reduction over KN5 -0.04 -0
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as a baseline, and 12.3% after resc
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Table 7.1: BLEU on IWSLT 2005 Machi
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Table 7.3: Size of compressed text
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Table 7.4: Accuracy of different la
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Table 7.6: Entropy on PTB with n-gr
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8.1 Machine Learning One possible d
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that almost every non-trivial compu
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supervision such as one digit at a
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Chapter 9 Conclusion and Future Wor
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from the expensive part of the mode
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Bibliography [1] A. Alexandrescu, K
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[23] D. Filimonov, M. Harper. A joi
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[50] T. Mikolov, S. Kombrink, L. Bu
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[77] W. Wang, M. Harper. The SuperA
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Test Phase After the model is train
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• compute sentence-level scores g
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Appendix B: Data generated from mod
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Appendix C: Example of decoded utte
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AND SAYS THIS SWING IS WITHIN A REA
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