Cutting-off Redundant Repeating Generations for Neural Abstractive Summarization

Introduction

The RNN-based encoder-decoder (EncDec) approach has recently been providing significant progress in various natural language generation (NLG) tasks, i.e., machine translation (MT) Sutskever et al. (2014); Cho et al. (2014) and abstractive summarization (ABS) Rush et al. (2015). Since a scheme in this approach can be interpreted as a conditional language model, it is suitable for NLG tasks. However, one potential weakness is that it sometimes repeatedly generates the same phrase (or word).

This issue has been discussed in the neural MT (NMT) literature as a part of a coverage problem Tu et al. (2016); Mi et al. (2016). Such repeating generation behavior can become more severe in some NLG tasks than in MT. The very short ABS task in DUC-2003 and 2004 Over et al. (2007) is a typical example because it requires the generation of a summary in a pre-defined limited output space, such as ten words or 75 bytes. Thus, the repeated output consumes precious limited output space. Unfortunately, the coverage approach cannot be directly applied to ABS tasks since they require us to optimally find salient ideas from the input in a lossy compression manner, and thus the summary (output) length hardly depends on the input length; an MT task is mainly loss-less generation and nearly one-to-one correspondence between input and output Nallapati et al. (2016a).

From this background, this paper tackles this issue and proposes a method to overcome it in ABS tasks. The basic idea of our method is to jointly estimate the upper-bound frequency of each target vocabulary that can occur in a summary during the encoding process and exploit the estimation to control the output words in each decoding step. We refer to our additional component as a word-frequency estimation (WFE) sub-model. The WFE sub-model explicitly manages how many times each word has been generated so far and might be generated in the future during the decoding process. Thus, we expect to decisively prohibit excessive generation. Finally, we evaluate the effectiveness of our method on well-studied ABS benchmark data provided by Rush et al. Rush et al. (2015), and evaluated in Chopra et al. (2016); Nallapati et al. (2016b); Kikuchi et al. (2016); Takase et al. (2016); Ayana et al. (2016); Gulcehre et al. (2016).

Baseline RNN-based EncDec Model

The baseline of our proposal is an RNN-based EncDec model with an attention mechanism Luong et al. (2015). In fact, this model has already been used as a strong baseline for ABS tasks Chopra et al. (2016); Kikuchi et al. (2016) as well as in the NMT literature. More specifically, as a case study we employ a 2-layer bidirectional LSTM encoder and a 2-layer LSTM decoder with a global attention Bahdanau et al. (2014). We omit a detailed review of the descriptions due to space limitations. The following are the necessary parts for explaining our proposed method.

Let ${\bm{X}}\!=\!({\bm{x}}_{i})^{I}_{i=1}$ and ${\bm{Y}}\!=\!({\bm{y}}_{j})^{J}_{j=1}$ be input and output sequences, respectively, where ${\bm{x}}_{i}$ and ${\bm{y}}_{j}$ are one-hot vectors, which correspond to the $i$-th word in the input and the $j$-th word in the output. Let ${\cal V}^{\rm t}$ denote the vocabulary (set of words) of output. For simplification, this paper uses the following four notation rules:

$({\bm{x}}_{i})^{I}_{i=1}$ is a short notation for representing a list of (column) vectors, i.e., $({\bm{x}}_{1},\dots,{\bm{x}}_{I})=({\bm{x}}_{i})^{I}_{i=1}$.

$\bm{v}(a,D)$ represents a $D$-dimensional (column) vector whose elements are all $a$, i.e., $\bm{v}(1,3)=(1,1,1)^{\top}$.

$\bm{x}[i]$ represents the $i$-th element of $\bm{x}$, i.e., $\bm{x}=(0.1,0.2,0.3)^{\top}$, then $\bm{x}=0.2$.

Encoder: Let $\Omega^{\rm s}(\cdot)$ denote the overall process of our 2-layer bidirectional LSTM encoder. The encoder receives input $\bm{X}$ and returns a list of final hidden states $\bm{H}^{\rm s}=(\bm{h}^{\rm s}_{i})^{I}_{i=1}$:

Decoder: We employ a $K$-best beam-search decoder to find the (approximated) best output $\hat{\bm{Y}}$ given input $\bm{X}$. Figure 1 shows a typical $K$-best beam search algorithm used in the decoder of EncDec approach. We define the (minimal) required information $h$ shown in Figure 1 for the $j$-th decoding process is the following triplet, $h=(s_{j-1},\hat{\bm{Y}}_{j-1},\bm{H}^{\rm t}_{j-1})$, where $s_{j-1}$ is the cumulative log-likelihood from step 0 to $j-1$, $\hat{\bm{Y}}_{j-1}$ is a (candidate of) output word sequence generated so far from step 0 to $j-1$, that is, $\hat{\bm{Y}}_{j-1}=(\bm{y}_{0},\dots,\bm{y}_{j-1})$ and $\bm{H}^{\rm t}_{j-1}$ is the all the hidden states for calculating the $j$-th decoding process. Then, the function calcLL in Line 8 can be written as follows:

where ${\tt Softmax}(\cdot)$ is the softmax function for a given vector and $\Omega^{\rm t}(\cdot)$ represents the overall process of a single decoding step.

Word Frequency Estimation

This section describes our proposed method, which roughly consists of two parts:

a sub-model that estimates the upper-bound frequencies of the target vocabulary words in the output, and

architecture for controlling the output words in the decoder using estimations.

Let $\hat{\bm{a}}$ denote a vector representation of the frequency estimation. $\odot$ denotes element-wise product. $\hat{\bm{a}}$ is calculated by:

where ${\tt Sigmoid}(\cdot)$ and ${\tt ReLu}(\cdot)$ represent the element-wise sigmoid and ReLU Glorot et al. (2011), respectively. Thus, $\hat{\bm{r}}\!\in\![0,+\infty]^{M}$, $\hat{\bm{g}}\!\in\!^{M}$, and $\hat{\bm{a}}\!\in\![0,+\infty]^{M}$.

We incorporate two separated components, $\hat{\bm{r}}$ and $\hat{\bm{g}}$, to improve the frequency fitting. The purpose of $\hat{\bm{g}}$ is to distinguish whether the target words occur or not, regardless of their frequency. Thus, $\hat{\bm{g}}$ can be interpreted as a gate function that resembles estimating the fertility in the coverage Tu et al. (2016) and a switch probability in the copy mechanism Gulcehre et al. (2016). These ideas originated from such gated recurrent networks as LSTM Hochreiter and Schmidhuber (1997) and GRU Chung et al. (2014). Then, $\hat{\bm{r}}$ can much focus on to model frequency equal to or larger than 1. This separation can be expected since $\hat{\bm{r}}[m]$ has no influence if $\hat{\bm{g}}[m]\!=\!0$.

2 Effective usage

3 Calculation

Figure 2 shows the detailed procedure for calculating ${\bm{g}}$ and ${\bm{r}}$ in Eq. 3. For ${\bm{r}}$, we sum up all of the features of the input given by the encoder (Line 2) and estimate the frequency. In contrast, for ${\bm{g}}$, we expect Lines 5 and 6 to work as a kind of voting for both positive and negative directions since ${\bm{g}}$ needs just occurrence information, not frequency. For example, ${\bm{g}}$ may take large positive or negative values if a certain input word (feature) has a strong influence for occurring or not occurring specific target word(s) in the output. This idea is borrowed from the Max-pooling layer Goodfellow et al. (2013).

4 Parameter estimation (Training)

where ${\cal W}$ represents the overall parameters. The form of $\Psi^{\rm wfe}(\cdot)$ is closely related to that used in support vector regression (SVR) Smola and Schölkopf (2004). We allow estimation $\hat{\bm{a}}[m]$ for all $m$ to take a value in the range of $[\bm{a}^{*}[m]-\epsilon,\bm{a}^{*}[m]+\epsilon]$ with no penalty (the loss is zero). In our case, we select $\epsilon=0.25$ since all the elements of $\bm{a}^{*}$ are an integer. The remaining 0.25 for both the positive and negative sides denotes the margin between every integer. We select $b=2$ to penalize larger for more distant error, and $c_{1}\!<\!c_{2}$, i.e., $c_{1}\!=\!0.2,c_{2}\!=\!1$, since we aim to obtain upper-bound estimation and to penalize the under-estimation below the true frequency $\bm{a}^{*}$.

Finally, we minimize Eq. 8 with a standard negative log-likelihood objective function to estimate the baseline EncDec model.

Experiments

We investigated the effectiveness of our method on ABS experiments, which were first performed by Rush et al., Rush et al. (2015). The data consist of approximately 3.8 million training, 400,000 validation and 400,000 test data, respectivelyThe data can be created by the data construction scripts in the author’s code: https://github.com/facebook/NAMAS.. Generally, 1951 test data, randomly extracted from the test data section, are used for evaluationAs previously described Chopra et al. (2016) we removed the ill-formed (empty) data for Gigaword.. Additionally, DUC-2004 evaluation data Over et al. (2007)http://duc.nist.gov/duc2004/tasks.html were also evaluated by the identical models trained on the above Gigaword data. We strictly followed the instructions of the evaluation setting used in previous studies for a fair comparison. Table 1 summarizes the model configuration and the parameter estimation setting in our experiments.

Table 2 shows the results of the baseline EncDec and our proposed EncDec+WFE. Note that the DUC-2004 data was evaluated by recall-based ROUGE scores, while the Gigaword data was evaluated by F-score-based ROUGE, respectively. For a validity confirmation of our EncDec baseline, we also performed OpenNMT toolhttp://opennmt.net. The results on Gigaword data with $B=5$ were, 33.65, 16.12, and 31.37 for ROUGE-1(F), ROUGE-2(F) and ROUGE-L(F), respectively, which were almost similar results (but slightly lower) with our implementation. This supports that our baseline worked well as a strong baseline. Clearly, EncDec+WFE significantly outperformed the strong EncDec baseline by a wide margin on the ROUGE scores. Thus, we conclude that the WFE sub-model has a positive impact to gain the ABS performance since performance gains were derived only by the effect of incorporating our WFE sub-model.

2 Comparison to current top systems

Table 3 lists the current top system results. Our method EncDec+WFE successfully achieved the current best scores on most evaluations. This result also supports the effectiveness of incorporating our WFE sub-model.

MRT Ayana et al. (2016) previously provided the best results. Note that its model structure is nearly identical to our baseline. On the contrary, MRT trained a model with a sequence-wise minimum risk estimation, while we trained all the models in our experiments with standard (point-wise) log-likelihood maximization. MRT essentially complements our method. We expect to further improve its performance by applying MRT for its training since recent progress of NMT has suggested leveraging a sequence-wise optimization technique for improving performance Wiseman and Rush (2016); Shen et al. (2016). We leave this as our future work.

3 Generation examples

Figure 3 shows actual generation examples. Based on our motivation, we specifically selected the redundant repeating output that occurred in the baseline EncDec. It is clear that EncDec+WFE successfully reduced them. This observation offers further evidence of the effectiveness of our method in quality.

4 Performance of the WFE sub-model

To evaluate the WFE sub-model alone, Table 4 shows the confusion matrix of the frequency estimation. We quantized $\hat{\bm{a}}$ by $\lfloor\hat{\bm{a}}[m]+0.5\rfloor$ for all $m$, where 0.5 was derived from the margin in $\Psi^{\rm wfe}$. Unfortunately, the result looks not so well. There seems to exist an enough room to improve the estimation. However, we emphasize that it already has an enough power to improve the overall quality as shown in Table 2 and Figure 3. We can expect to further gain the overall performance by improving the performance of the WFE sub-model.

Conclusion

This paper discussed the behavior of redundant repeating generation often observed in neural EncDec approaches. We proposed a method for reducing such redundancy by incorporating a sub-model that directly estimates and manages the frequency of each target vocabulary in the output. Experiments on ABS benchmark data showed the effectiveness of our method, EncDec+WFE, for both improving automatic evaluation performance and reducing the actual redundancy. Our method is suitable for lossy compression tasks such as image caption generation tasks.

References