MGR: Multi-generator Based Rationalization
Year: 2023

Abstract:
Rationalization is to employ a generator and a predictor to construct a self-explaining NLP model in which the generator selects a subset of human-intelligible pieces of the input text to the following predictor. However, rationalization suffers from two key challenges, i.e., spurious correlation and degeneration, where the predictor overfits the spurious or meaningless pieces solely selected by the not-yet well-trained generator and in turn deteriorates the generator. Although many studies have been proposed to address the two challenges, they are usually designed separately and do not take both of them into account. In this paper, we propose a simple yet effective method named MGR to simultaneously solve the two problems. The key idea of MGR is to employ multiple generators such that the occurrence stability of real pieces is improved and more meaningful pieces are delivered to the predictor. Empirically1, we show that MGR improves the F1 score by up to 20.9% as compared to state-of-the-art methods.

heading: 1 Introduction
text: The widespread use of deep learning in NLP models has led to increased concerns about interpretability. To solve this problem, Lei et al. (2016) proposed rationalization framework RNP in which a generator selects human-intelligible subsets (i.e., rationales) from the input text and feeds them to the subsequent predictor that maximizes the text classification accuracy, as shown in Figure 1. Unlike post-hoc approaches for explaining black-box models, the RNP framework has the built-in selfexplaining ability through a cooperative game between the generator and the predictor. RNP and its variants have become one of the mainstreams
∗Corresponding author † This paper is a collaborative work between the Intelligent and Distributed Computing Laboratory at Huazhong University of Science and Technology, and iWudao Tech.
1https://github.com/jugechengzi/Rationalization-MGR
to facilitate the interpretability of NLP models (Yu et al., 2021; Liu et al., 2022, 2023). Notably, given the versatility of the self-explaining rationalization framework, such methods have significant potential for application in diverse fields such as multiaspect recommender systems (Deng et al., 2023) and computer vision (Yuan et al., 2022).
Despite its strength, rationalization schemes are notoriously hard to train. Two main training obstacles are the spurious correlations (Chang et al., 2020) and the degeneration (Yu et al., 2019). As shown in the example of Table 1(a), the problem of spurious correlations is that the predictor mistakenly makes a correlation between the label on some specific aspect and the spurious pieces on another similar aspect, which commonly exists in multiaspect classification (Chang et al., 2020; Plyler et al., 2021; Yue et al., 2023). Degeneration means that the predictor may overfit to meaningless rationales generated by the not yet well-trained generator (Yu et al., 2019), causing the converged generator tends to select these uninformative rationales, which is illustrated in the example of Table 1(b).
Many prior efforts have separately considered the problem of spurious correlations or degeneration in rationalization. For instance, to solve the problem of spurious correlations, some recent methods leverage the idea of causal inference to build the causal relationship between the rationale and label (Chang et al., 2020; Yue et al., 2023). The common idea to address the degeneration problem is to introduce some auxiliary modules such that the predictor has access to the full texts, and thus
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it cannot overfit the meaningless rationales solely provided by the generator (Yu et al., 2019; Huang et al., 2021; Yu et al., 2021).
Although these approaches may be effective at either solving the problem of spurious correlations or degeneration isolation, they are usually designed separately and do not take both of them into account. In this paper, we seek to simultaneously solve the two problems. Specifically, we identify that both two problems arise from that the predictor has only access to the limited view of pieces provided by the single generator, and thus may learn corruptly when this generator selects spurious or meaningless rationales. Besides, recent studies find that the initialization of the model has a significant impact over the training performance, which implicitly indicates that the rationalization model is hardly to train once the single generator is not well initialized (Jain et al., 2020; Yu et al., 2021).
Considering these limitations of the rationalization with one single generator, as shown in Figure 2, we design a novel architecture where there is a predictor but with multiple generators. These generators are initialized with different parameters. In this way, the view of the predictor is not limited to one single generator and it can have access to more meaningful rationales. We theoretically show that the occurrence stability of real rationales increases such that the predictor has lower risks at learning spurious correlations, and that the diversity of the rationales is improved such that the predictor can hardly deviate to some specific meaningless rationale. Extensive experiments conducted on three widely used rationalization benchmarks, i.e., the correlated BeerAdvocate dataset (McAuley et al., 2012), the decorrelated BeerAdvocate dataset (Lei et al., 2016), and the Hotel Reviews dataset (Wang et al., 2010), show that MGR achieves significant improvements over several state-of-the-art methods in terms of the rationale quality. Our contributions can be summarized as:● To the best of our knowledge, this paper is the first to simultaneously solve the spurious correlations and degeneration problem in rationalization. We propose a simple but effective method, namely, MGR, that facilitates the predictor to have a broader view of the rationales by using multiple generators.●We theoretically prove that using multiple generators can provide real rationales more stably such that the risk of the predictor learning spurious correlations is reduced. Besides, we prove that multiple
generators can produce more diverse rationales and thus the predictor will not overfit to some specific meaningless rationale.●We conduct extensive experiments over various datasets and show that MGR achieves an improvement by up to 20.9% as compared to state-of-theart rationalization methods in terms of F1 score.

heading: 2 Related Work

heading: 2.1 Rationalization
text: The base cooperative framework of rationalization named RNP (Lei et al., 2016) is flexible and offers a unique advantage, i.e., certification of exclusion, which means any unselected input is guaranteed to have no contribution to prediction (Yu et al., 2021). However, such a method is hard to train. To tackle this challenge, many methods have been proposed to improve RNP from different aspects. Rationales sampling. Many works focus on refining the sampling process of the rationales. Bao et al. (2018) used Gumbel-softmax to do the reparameterization for binarized selection. Bastings et al. (2019) replaced the Bernoulli sampling distributions with rectified Kumaraswamy distributions. Jain et al. (2020) disconnected the training regimes of the generator and predictor via a saliency threshold. Paranjape et al. (2020) imposed a discrete bottleneck objective to balance the task performance and the rationale length. Hase et al. (2020) explored better metrics for the explanations. Rajagopal et al. (2021) used phrase-based concepts to conduct a self-explaining model. These methods are orthogonal to our method. Degeneration. Degeneration is one of the major problem in rationalization. To solve this problem, many efforts seek to regularize the predictor using supplementary modules which have access to the information of the full text (Yu et al., 2019; Huang et al., 2021; Yu et al., 2021) such that the generator and the predictor will not collude to uninformative rationales. 3PLAYER (Yu et al., 2019) takes the unselected text Zc into consideration by inputting it to a supplementary predictor Predictorc. DMR (Huang et al., 2021) tries to align the distributions of rationale with the full input text in both the output space and feature space. A2R (Yu et al., 2021) endows the predictor with the information of full text by introducing a soft rationale. Spurious correlations. The predictor in rationalization model may make correlations between spurious rationales and the label. To tackle this chal-
lenge, the typical methods mainly adopt causal inference to exclude the spurious correlations. For instance, Chang et al. (2020) introduced an environment-agnostic predictor to recognize the spurious correlations. Yue et al. (2023) aimed to remove the spurious correlations based on the backdoor adjustment.

heading: 2.2 Model Ensemble Methods
text: Ensemble methods that combine the outputs of several different models to improve the prediction performance and robustness have been studied for a long time (Breiman, 1996; Wolpert, 1992; Schapire, 1999). Ensemble methods train N models with different datasets independently and fuse the outputs of different models during inference. This requires maintaining N models and running each of them at test time, which increases the costs of computational resources and brings obstacles to applications (Singh and Jaggi, 2020). Although our method is similar to ensemble methods to some extent, it has essential differences with ensemble methods. In our method, different generators are not trained entirely independently. In fact, they all play a cooperative game with the same predictor on one same training dataset. With different initializations, different generators can provide diverse
rationales to train a robust and stable predictor at early training stage. But with the same training target and dataset, different generators can converge to get the same output (Ainsworth et al., 2022), thus we only need to keep one generator during inference, which is also empirically supported by the experimental results in Figure 3(b).

heading: 3 Problem Definition
text: Notation. fG(⋅) and fP (⋅) represent the generator and predictor, respectively. θG and θP represent the parameters of the generator and predictor, respectively. D represents the distribution of dataset. We consider the classification problem, where the input is a text sequence X=∥x1, x2,⋯, xl∥ with xi being the i-th token and l being the number of tokens. The label of X is a one-hot vector Y ∈ {0,1}c, where c is the number of categories.
Cooperative rationalization. Rationalization framework consists of a generator and a predictor. The goal of the generator is to find the most informative pieces containing several tokens in the original input text X . For each sample (X,Y ) ∼ D, the generator firstly outputs a sequence of binary mask M = ∥m1,⋯,ml∥ ∈ {0,1}l. Then, it forms the rationale Z by the element-wise product of X
and M :
Z =M ⊙X = ∥m1x1,⋯,mlxl∥. (1) To simplify the notation, we denote Z = fG(X). In cooperative rationalization, the informativeness of the rationale Z provided by the generator is measured by the negative cross entropy −H(Y, Ŷz), where Ŷz is the output of the predictor with the input being Z. Consequently, the generator and the predictor are usually optimized cooperatively:
min θG,θP ∑(X,Y )∼DH(Y, fP (fG(X))). (2) Regularizer of shortness and coherence. To make the selected rationales human-intelligible, the original RNP constrains the rationales by short and coherent regularization terms. In this paper, we use the constraints updated by Chang et al. (2019):
Ω(M) = λ1∣ ∣∣M ∣∣1 l − s∣ + λ2 l∑
t=2 ∣mt −mt−1∣. (3) The first term encourages that the percentage of the tokens being selected as rationales is close to a pre-defined level s. The second term encourages the rationales to be coherent.

heading: 4 Multi-generator based Rationalization

heading: 4.1 Methodology
text: Based on the framework of RNP, MGR uses multiple generators with different initialized parameters to help the predictor learn from diverse rationale candidates, as shown in Figure 2. For the convenience of comparing with previous methods in experiments, we adopt the bidirectional gated recurrent units (GRUs) (Cho et al., 2014) as the encoder which has been adopted by most previous works (Chang et al., 2020; Huang et al., 2021; Yu et al., 2021).
Training of MGR. MGR is to leverage each generator fGi(⋅) to process the input text X in isolation, and then send the obtained rationales Zi to the predictor fP (⋅) to obtain the prediction Ŷi. Based on Equation 2, MGR computes its loss by calculating the average of the cross entropy between Y and Ŷi in each generator:
min θG1 ,...,θGn ,θP ∑(X,Y )∼DH(Y, Ŷ ) = ∑(X,Y )∼D 1 n n∑ i=1H(Y, fP (fGi(X))).
(4)
Inference of MGR. During inference, MGR only uses one generator, e.g., the first generator Z1 and Ŷ1, to provide the rationale. It’s worth noting that our idea is similar to but not the same as ensemble models. We keep a set of generators during training to help train a good predictor which in turn will promise the cooperative generator to be good. Nevertheless, we only keep the first generator during inference (see experimental results in Figure 3(b)), which is efficient in terms of both time and resource consumption.

heading: 4.2 Dealing with spurious correlations
text: In this section, we seek to show that the proposed method can solve the problem of spurious correlations. Specifically, we specify the principles of our method on the case with simplified settings. Settings. Similar to Yu et al. (2021), we consider the input text X consists of two subsets of the features X1 and X2, where X1 is the causal rationale belonging to the target aspect label, while X2 is the comments about other aspects that correlates with the target aspect. We denote the parameters of the predictor by θ1P when it fits X1, and by θ 0 P when it fits X2. We also assume a payoff table as shown in Table 2, where we denote the negative loss as the payoff. The higher payoff indicates that the rationalization achieves better convergence results. Considering that rationalization is a cooperative game, the payoff of the generator is the same as that of the predictor. Here, a can be seen as the negative loss when the predictor fits the generator’s selection and b is the negative loss when the predictor fits the unselected part. Since the loss is usually smaller when fP (⋅) fits what fGi(⋅) selects, we consider a > b. We denote that there are k generators that select the causal rationale X1 and the other n − k generators select X2. Without losing generality, we consider that the predictor
is randomly initialized by interpolation between θ0P , θ 1 P with θ α P , where α is a random variable in [0,1]. Similar to Yu et al. (2021)2, we consider α to be the probability (or degree) that the predictor tends to fit X1. If α = 1, the predictor always fits X1, and if α = 0, the predictor always fits X2. This is where the third column in Table 2 comes from. Theoretical analysis. For the situation that k generators select X1 and the predictor is θαP , the expected payoff of the predictor is
RP (α) =k ⋅ α ⋅ a + k(1 − α) ⋅ b+ (n − k)(1 − α)a + (n − k) ⋅ α ⋅ b. (5) With the generator’s random initialization, k follows a binomial distribution B(n,Pc), where Pc depends on the dataset (subscript c stands for causality). We assume that Pc > 0.5 because the causality appears more often than the spurious correlation when the target aspect’s label appears (Please refer to Appendix B.4 and Table 11 for more detailed discussion). Apparently, we have
lim n→∞p(k < n − k) = 0, (6)
of which the detailed derivation is in Appendix B.1.
Lemma 1 If the number of generators that select X1 is more than those that select X2 (i.e., k > n−k), the predictor will be optimized to increase α to get a higher payoff (i.e., ∂RP (α)∂α > 0). The proof is in Appendix B.2. Lemma 1 indicates that if k > n − k, by increasing RP (α) (for lower loss), the cooperative game will guide the predictor to move towards θ1P (by increasing α) and fit the right causal rationale X1. In turn, such a good predictor will guide the generator to select the desired causal rationales.
We denote the probability of the predictor overfits to the spurious correlation as pMGR(spu). Ac-
2Our α is similar to π in (Yu et al., 2021). In (Yu et al., 2021), π is the degree that the generator tends to select X1.
cording to Lemma 1, we have
pMGR(spu) =p(∂RP (α) ∂α
< 0) =p(k < n − k) (7) = (n−1)/2∑
k=0 (( n k ) ⋅ P kc ⋅ (1 − Pc)n−k),
where (nk) is the combinatorial number. Combining Lemma 1 with Equation 6, we have the following theorem: Theorem 1 For any tolerable upper bound probability Ps of the predictor overfitting to spurious correlation, if Pc > 0.5, there always exists a constant N such that ∀n > N, pMGR(spu) < Ps. (8) The proof is deferred to Appendix B.3. Theorem 1 indicates that we can reduce the risk of spurious correlations to arbitrarily low levels by increasing the number of the generator. When n = 1, MGR becomes the vanilla RNP and we have pRNP (spu) = 1 − Pc. (9) It is obvious that
∀n > 1, pMGR(spu) < pRNP (spu). (10)

heading: 4.3 Dealing with Degeneration
text: In this section, we consider X,Y,Z as random variables rather than deterministic ones. The principle behind Equation 2 is to maximize the mutual information between Y and Z (Chang et al., 2020; Yu et al., 2021):
max Z I(Y ;Z) =max Z (H(Y ) −H(Y ∣Z)). (11)
Since H(Y ) is irrelevant to Z, the equation is equal to minimizing H(Y ∣Z). Degeneration happens because the diversity of the rationales is not taken into account. Hence, the generator of RNP may get rationale candidates with low diversity (i.e., low H(Z)). Under this case, the predictor may overfit to some specific patterns that are contained in the limited rationale candidates and has a high risk of occurring degeneration when the rationales are merely noises.
Next, we show that MGR with multiple generators improves the diversity of the selected rationale candidates. Specifically, by viewing the rationales of different generators as different variables, we can compute the rationale diversity of MGR as
H(ZMGR) =H(Z1, Z2,⋯, Zn). (12)
Theorem 2 For ∀i ∈ ∥1, n∥, we have H(Zi) ≤H(Z1, Z2,⋯, Zn) ≤ n∑
k=1H(Zk), (13) where the right equality holds if and only if∀i, j, Zi á Zj , and the left equality holds if and only if ∀i, j, Zi = Zj . The proof is in Appendix B.5. Theorem 2 indicates that the diversity of MGR with multiple generators is equivalent to the case with one single generator when all generators are the same. More specifically, since RNP consists of only one generator, we have
H(ZRNP ) =H(Zi) ≤max i H(Zi), (14) where i ∈ ∥1, n∥. We always have H(ZMGR) ≥ H(ZRNP ) no matter how different generators are coupled together, thus alleviating degeneration.
Besides, Theorem 2 also indicates that the diversity of MGR achieves the maxima when all the generators are completely independent. Accordingly, we seek to decrease the correlation between different generators to make that H(ZMGR) gets closer to ∑nk=1H(Zk) during training which is specified in the next section.

heading: 4.4 Diverse Training with Separate Learning Rates
text: To facilitate the improvement of the diversity of rationales while guaranteeing the convergence of rationalization models, we consider that training MGR has to satisfy two conditions. First, to deal with degeneration, generators should be different from each other to guarantee that the predictor continuously learns from diverse rationales before it learns adequate information. Second, different generators should be able to achieve the same convergence result, i.e., selecting the same rationales for any given text, after the predictor has learned enough information and converged. Only in this way can we keep one single generator during inference to guarantee that MGR is efficient in terms of latency and resource consumption.
To satisfy the two properties, we propose separately setting the learning rates of different generators. Intuitively, separate learning rates provide different generators with different learning states in any training moment, thus keeping them diverse during the learning process. On the other side, learning rates do not modify the loss landscape of generators and thus these generators can eventually achieve the same convergence result although
maybe at different speeds (Ainsworth et al., 2022). The argument is also empirically supported by the results in Figure 3(b).
Formally, we denote the learning rate of the i-th generator as ηi and the loss as L. generatori and generatorj are updated during training as:
θGi ′ = θGi − ηi ⋅ ∇θGiL, θGj ′ = θGj − ηj ⋅∇θGjL, (15)
Practically, we first find a learning rate η and set the i-th generator’s learning rate simply to be i ⋅ η. And to alleviate the problem that the loss function of the predictor is too large due to the superposition of multiple loss functions, we set the learning rate of the predictor to be ηn .
To support our claims, we conduct two practical experiments on decorrelated BeerAdvocate dataset, where the main problem is degeneration. First, we compare the performance of MGR using one learning rate to MGR using separate learning rates. The results are shown in Figure 3(a). Although using separate learning rates does not help much in the relatively easy aspects including Appearance and Aroma, it makes a significant improvement in the hard Palate aspect. Second, we compare the performance of keeping only one generator for inference to averaging the results of multiple generators, as shown in Figure 3(b). The results show that keeping only one generator hardly influences the performance, which indicates that different generators can finally converge to get the same outputs and only one generator is required in inference time. We also show the differences in the rationales generated by different generators in Figure 7 of Appendix A.5.

heading: 5 Experiments

heading: 5.1 Experimental Setup
text: Datasets 1) BeerAdvocate (McAuley et al., 2012) is a multi-aspect sentiment prediction dataset widely used in rationalization. There is a high correlation among the rating scores of different aspects in the same review, making the rationale selecting faces a severe spurious correlation. We use the original dataset to verify the effectiveness of MGR in dealing with spurious correlation and degeneration at the same time. In addition, following the previous work (Lei et al., 2016; Huang et al., 2021; Yu et al., 2021), we use the subsets containing less spurious correlation (Lei et al., 2016) to see the effectiveness in dealing with solitary degeneration. 2) Hotel Reviews (Wang et al., 2010) is another multiaspect sentiment classification dataset also widely used in rationalization. Each aspect itself can be seen as a dataset and is trained independently. Baselines and implementation details. In parcitce, we set n = 3 (the number of generators) as for our MGR as a performance-time trade-off. We compare MGR to the vanilla RNP (Lei et al., 2016) and several latest published methods that achieve state-of-the-art results: INVRAT (Chang et al., 2020), DMR (Huang et al., 2021), A2R (Yu et al., 2021), Inter-RAT (Yue et al., 2023), all of which have been specified in Section 2. Following the commonly used rationalization settings (Chang et al., 2019; Yu et al., 2019; Chang et al., 2020;
Huang et al., 2021; Yu et al., 2021; Yue et al., 2023), we use the 100-dimension Glove (Pennington et al., 2014) as the word embedding and 200-dimension GRUs to get the text representation. We do not use BERT (Devlin et al., 2019) because it is still a challenging task to finetune large pretrained models on the RNP cooperative framework (see Table 4 in Chen et al. (2022) and Appendix A.2). We use Adam (Kingma and Ba, 2015) as the optimizer. All the baselines are tuned multiple times manually to find the best hyperparameters. The complexity of different models are shown in Table 4 All of the models are trained on a RTX3090 GPU. More details are in Appendix A.1. Metrics. All the methods get similar predictive accuracy. Following (Chang et al., 2020; Huang et al., 2021; Yu et al., 2021; Yue et al., 2023), we mainly focus on the quality of rationales, which is measured by the overlap between the model-selected tokens and human-annotated tokens. P,R,F1 indicate the precision, recall, and F1 score, respectively. S indicates the average sparsity of the selected rationales, i.e., the percentage of selected tokens to the whole texts. Acc indicates the predictive accuracy of the test set.

heading: 5.2 Results
text: We first conduct an experiment on the correlated BeerAdvocate dataset, where the problems of degeneration and spurious correlation both may damage the rationale quality. Methods that achieve the state-of-the-art results on this dataset are INVRAT (Chang et al., 2020) and Inter-RAT (Yue et al., 2023). We tune s in Equation 3 to get similar rationale sparsity as previous methods do. The results are shown in Table 3. We improve the F1 score by up to 20.9% (Palate aspect with 20% sparsity) over
the latest SOTA. Besides, except the Palate aspect with 30% sparsity, we get over 10% improvements under all the other settings.
We then conduct an experiment on the decorrelated BeerAdvocate dataset, where the main problem is degeneration. Methods that achieve the stateof-the-art results on this dataset are DMR (Huang et al., 2021) and A2R (Yu et al., 2021). Since the rationales of BeerAdvocate on a sentence level, A2R in its original paper does sentence level selection (i.e., selecting one sentence as the rationale) on this dataset. We also reimplement A2R according to its source codes to do the token-level selection. The results are shown in Table 4(a). The sparsity is set to be close to that of the human-annotated rationales. We beat all the methods in terms of F1 score. We do not get as significant improvements as those in Table 3 because the spurious correlation is removed manually in this dataset. But we still get up to 10.8% (Appearance aspect) improvements as compared to the SOTA.
To show the generalizability of our method, we further conduct an experiment on HotelReviews. Methods that achieve the state-of-the-art results on this dataset are DMR (Huang et al., 2021) and
CAR (Chang et al., 2019). We also beat all the baselines and get up to 6.8% (Cleanliness aspect) improvements on this dataset.
Results of MGR with different numbers of generators. Although we set n = 3 in our previous experiments, we also show the results of our MGR with different values of n in Table 7. When n grows, the results are somewhat better than those of n = 3. However, n = 3 yields the most improvements per additional generator and proved to be a good performance-cost trade-off. And note that, having too many generators may not always result in better outcomes, because the learning rate for the i-th generator, which is i × η, may become too large for stable training.
Beer-Skewed. To show that our MGR does not suffer from the degeneration problem, we conduct the same synthetic experiment that deliberately induces degeneration as Yu et al. (2021) did. The details of the experimental setup are in Appendix A.3. We use the relatively harder Palate aspect (Yu et al., 2021). The results are shown in Table 4(b). The results of RNP and A2R are obtained from (Yu et al., 2021). For all the settings, we outperform both RNP and A2R. Especially, for skew20, RNP and A2R can not work at all while our MGR is only slightly influenced as compared to the corresponding result in Table 4(a). Sharing encoders between generators. The major limitation of MGR is the increased computational costs. One plausible trade-off method may be sharing some parameters between the generators. We conduct an experiment where we share the generators’ GRUs but keep their own linear heads. Figure 4 shows the results on correlated BeerAdvocate with sparsity around 20%. More results are in Appendix A.4. Although simply sharing the generators’ encoders sometimes cause damage to the performance of MGR, it still outperforms the state-of-the-art method Inter_RAT. We leave how to better decrease the computational costs without hurting the model performance as future work.

heading: 6 Conclusion and future work
text: In this paper, we design a new framework MGR to simultaneously tackle the two major challenges including the spurious correlation and degeneration in the self-explaining rationalization schemes. Specifically, we propose leveraging multiple generators to select rationales such that the predictor can have access to more meaningful rationales stably. We theoretically show that the proposed method can solve the two problems. Finally, empirical results conducted on various datasets demonstrate the great effectiveness of our proposed method.

heading: Limitations
text: More generators bring significant benefits to the model performance to our MGR, but the training cost is also increased with the number of generators growing. Although we have verified that we only need to keep one generator during test, there is no denying that the training cost is still an important problem. In the future, we will explore some methods like multi-task learning and model fusion, to reduce the model complexity.

heading: Acknowledgements
text: This work is supported by National Natural Science Foundation of China under grants U1836204, U1936108, 62206102, and Science and Technology Support Program of Hubei Province under grant 2022BAA046. We thank the anonymous reviewers for their valuable comments on improving the quality of this paper.

heading: A More Results

heading: A.1 More implementation details
text: To the best of our knowledge, both datasets are sufficiently anonymized to make identification of individuals impossible without significant effort. Both datasets are in English. For correlated BeerAdvocate, we preprocess the data in the same way as Yue et al. (2023). For decorrelated BeerAdvocate and Hotel Reviews, we preprocess them in the same way as Huang et al. (2021). The maximum text length is set to 256. More statistics of the datasets are in Table 8.
Some previous methods needs very careful hyper-parameter tuning. To make fair comparisons, most results of the baselines are copied from previous papers. But some settings are not unified, so we also reimplement them according to their source codes.
For DMR, we adopt its source code and adjust its sparsity constraint to get a sparsity similar to the annotated rationales. For A2R, we re-implement it to do token-level selection as other methods do.
The hyper-parameters of reimplemented models are manually tuned multiple times to get the best results. For our MGR, the early stopping technique is conducted according to the predictive accuracy of the development set. For our reimplemented DMR and A2R, although we have tried our best to tune the hyper-parameters, chances are that the hyper-parameters are not the best. To compensate for this potential issue, we do the test after every training epoch and choose their best results when they get the best F1 score on the test set.
The random seed is kept the same across all the experiments rather than manually selected. We think the experiments with one same random seed on multiple different settings and different datasets are enough to show the stability of our method. We also provide the standard deviations with running the experiments in Table 3 with five different ran-
dom seeds. The standard deviations are shown in Table 9.

heading: A.2 Discussion on BERT encoder
text: In the field of rationalization, researchers generally focus on frameworks of the models and the methodology. Methods most related to our work do not use Bert or other pre-trained encoders (Chang et al., 2019, 2020; Huang et al., 2021; Yu et al., 2019, 2021; Yue et al., 2023). We use GRUs and GloVe to ensure the same experimental setup as our baselines for a fair comparison.
More importantly, how to finetune large models on the rationalization framework is still a significant challenge. Some recent studies (Chen et al., 2022) show that the methods with BERT encoders perform much worse than those with simple GRUs on BeerAdvocate and HotelReviews, which is shown in Table 10. VIB and SPECTRA are two RNP-based model. When using BERT, these two methods perform much worse than the vanilla RNP with GRUs (as compared to the results in Table 4(a)).

heading: A.3 The details of Beer-Skewed
text: The experiment was first designed by Yu et al. (2021). It deliberately induces degeneration to show the robustness of A2R compared to RNP. The predictor is first pre-trained using the first sentence of each text for a few epochs. In Beer Reviews, the first sentence is usually about appearance. So, the predictor will overfit to the aspect of Appearance, which is uninformative for Aroma and Palate. In fact, as compared to degeneration, we think it’s more like spurious correlation, which may explain why A2R also fails in this situation.

heading: A.4 More Results about Sharing the GRUs
text: Figure 4 in the main paper has shown the results of sharing the generators’ encoders with the rationale sparsity being around 20%, and we further show the results with the sparsity being around 10% and 30% in Figure 5 and 6, respectively. Simply sharing the encoders may not be the best way to reduce the computational costs due to the damage on the model performance, but it still outperform Inter_RAT in most cases. For Appearance with 10% sparsity, the reason for the poor performance may come from two aspects. First, as compared to the percentage of human-annotated rationales (18.4%), 10% is too small. It is hard to find the true rationales under such sparsity constraint. Second, the shared encoder limits the explore power of MGR, making the above problem more severe. We will look for better method to reduce the computational costs in the future.
A.5 The rationale-overlap between different generators
Corresponding to Figure 3(b), we plot the rationaleoverlap between different generators in Figure 7. The metric is ∣∣Mi−Mj ∣∣1∣∣Mi∣∣1+∣∣Mj ∣∣1 , which represents the percentage of different tokens in rationales from different generators. Mi represents the binary rationale mask from the i-th generator. The figures show that the variance is high initially and gradually converges to a small value. So, the generators are diverse initially and finally converge to be the same.

heading: B Proofs of Theorems

heading: B.1 Derivation of Equation 6
text: To make the presentation succinct, we first discuss the case where n is an odd number.
lim n→∞p(k < n − k) = lim n→∞p(k < n2 ) = lim n→∞ (n−1)/2∑ k=0 (Ckn ⋅ P kc ⋅ (1 − Pc)n−k)
(16)
Since Pc > 0.5, we then have lim n→∞ (n−1)/2∑ k=0 (Ckn ⋅ P kc ⋅ (1 − Pc)n−k) = 0. (17)
There is nothing different expect that the upper limit of the summation should be replaced by n/2− 1 when n is an even number.

heading: B.2 Proof of Lemma 1
text: According to Equation 5, we have
∂RP (α) ∂α
=a ⋅ k − (n − k)a − k ⋅ b + (n − k)b =a ⋅ (k − (n − k)) − b ⋅ (k − (n − k))=(a − b)(k − (n − k)).
(18) Since we have a > b and k > n−k, we get ∂RP (α)∂α > 0. It means that to get a higher payoff, the predictor needs to increase α, i.e., it needs to move towards θ1P . The proof of Lemma 1 is completed.
Correlated∗2+Decorrelated . We only count samples with
negative labels because because the original dataset is unbalanced and we do sampling balance according to the number of negative samples during training.

heading: B.3 Proof of Theorem 1
text: The proof is obvious. It’s equal to that limn→∞ pMGR(spu) = 0. The left derivation is the same as Appendix B.1. B.4 Discussion about Pc > 0.5 For a dataset, there are some samples that contain both the causality and the spurious correlation (i.e., X1 and X2, corresponding to the number of Correlated in Table 11), and the other samples contain only the causality (i.e., X1, corresponding to the number of Decorrelated in Table 11 ). So we always have the number of X1 is larger than that of X2. And for random selection, the probability of selecting X1 is higher than selecting X2, which means that Pc > 0.5. In Table 11, we approximate Pc by
Pc = Number(X1)Number(X1) +Number(X2) = Decorrelated +Correlated Decorrelated + 2 ∗Correlated > 0.5 =1 − Correlated
Correlated ∗ 2 +Decorrelated > 0.5. (19)

heading: B.5 Proof of Theorem 2
text: We first proof the left inequality of Theorem 2. For any two random variable Zi, Zj , we have
H(Zi∣Zj) =H(Zi, Zj) −H(Zj) H(Zi∣Zj) ≥ 0
H(Zj) ≥ 0. (20)
So, we have
H(Zi, Zj) ≥H(Zj), (21) where the equality holds if and only if H(Zi∣Zj) = 0, i.e., Zi = Zj . There is nothing different for H(Zi, Zj) ≥ H(Zi). Then we easily get the left inequality of Theorem 2 through Mathematical Induction.
Then we proof the right inequality of Theorem 2. We first have
I(Zi, Zj) =H(Zi) +H(Zj) −H(Zi, Zj) I(Zi, Zj) ≥ 0, (22) where I(Zi, Zj) is the mutual information. I(Zi, Zj) = 0 if and only if Zi á Zj . So, we have H(Zi, Zj) ≤H(Zi) +H(Zj), (23) with the equality holds if and only if Zi á Zj . Then we easily get the right inequality of Theorem 2 through Mathematical Induction.
The proof of Theorem 2 is completed.
ACL 2023 Responsible NLP Checklist

heading: A For every submission:
text: 3 A1. Did you describe the limitations of your work?
Section 7
A2. Did you discuss any potential risks of your work? Not applicable. No potential risks.
3 A3. Do the abstract and introduction summarize the paper’s main claims? Section 1.
7 A4. Have you used AI writing assistants when working on this paper? Left blank.
B 3 Did you use or create scientific artifacts? Section 5.
3 B1. Did you cite the creators of artifacts you used? Section 5.
3 B2. Did you discuss the license or terms for use and / or distribution of any artifacts? Section 5.
3 B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided that it was specified? For the artifacts you create, do you specify intended use and whether that is compatible with the original access conditions (in particular, derivatives of data accessed for research purposes should not be used outside of research contexts)? Appendix B.1.
3 B4. Did you discuss the steps taken to check whether the data that was collected / used contains any information that names or uniquely identifies individual people or offensive content, and the steps taken to protect / anonymize it? Appendix B.1.
3 B5. Did you provide documentation of the artifacts, e.g., coverage of domains, languages, and linguistic phenomena, demographic groups represented, etc.? Appendix B.1.
3 B6. Did you report relevant statistics like the number of examples, details of train / test / dev splits, etc. for the data that you used / created? Even for commonly-used benchmark datasets, include the number of examples in train / validation / test splits, as these provide necessary context for a reader to understand experimental results. For example, small differences in accuracy on large test sets may be significant, while on small test sets they may not be. Appendix B.1.
C 3 Did you run computational experiments? Section 5.
3 C1. Did you report the number of parameters in the models used, the total computational budget (e.g., GPU hours), and computing infrastructure used? Section 5.1.
The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.
3 C2. Did you discuss the experimental setup, including hyperparameter search and best-found hyperparameter values? Appendix B.1.
3 C3. Did you report descriptive statistics about your results (e.g., error bars around results, summary statistics from sets of experiments), and is it transparent whether you are reporting the max, mean, etc. or just a single run? Appendix B.1.
C4. If you used existing packages (e.g., for preprocessing, for normalization, or for evaluation), did you report the implementation, model, and parameter settings used (e.g., NLTK, Spacy, ROUGE, etc.)? Not applicable. Left blank.
D 7 Did you use human annotators (e.g., crowdworkers) or research with human participants? Left blank.
D1. Did you report the full text of instructions given to participants, including e.g., screenshots, disclaimers of any risks to participants or annotators, etc.? No response.
D2. Did you report information about how you recruited (e.g., crowdsourcing platform, students) and paid participants, and discuss if such payment is adequate given the participants’ demographic (e.g., country of residence)? No response.
D3. Did you discuss whether and how consent was obtained from people whose data you’re using/curating? For example, if you collected data via crowdsourcing, did your instructions to crowdworkers explain how the data would be used? No response.
D4. Was the data collection protocol approved (or determined exempt) by an ethics review board? No response.
D5. Did you report the basic demographic and geographic characteristics of the annotator population that is the source of the data? No response.

heading: Future Work
text: We will look for better method to reduce the computational costs in the future. A. 5 The rationale-overlap between different generators
Corresponding to Figure 3(b), we plot the rationaleoverlap between different generators in Figure 7. The metric is ∣∣Mi−Mj ∣∣1∣∣Mi∣∣1+∣∣Mj ∣∣1 , which represents the percentage of different tokens in rationales from different generators. Mi represents the binary rationale mask from the i-th generator. The figures show that the variance is high initially and gradually converges to a small value. So, the generators are diverse initially and finally converge to be the same