FR: Folded Rationalization with a Unified Encoder
Abstract
Conventional works generally employ a two-phase model in which a generator selects the most important pieces, followed by a predictor that makes predictions based on the selected pieces.
However, such a two-phase model may incur the degeneration problem where the predictor overfits to the noise generated by a not yet well-trained generator and in turn, leads the generator to converge to a sub-optimal model that tends to select senseless pieces.
To tackle this challenge, we propose Folded Rationalization (FR) that folds the two phases of the rationale model into one from the perspective of text semantic extraction.
The key idea of FR is to employ a unified encoder between the generator and predictor, based on which FR can facilitate a better predictor by access to valuable information blocked by the generator in the traditional two-phase model and thus bring a better generator.
Empirically, we show that FR improves the F1 score by up to 10 .
3% as compared to state-of-the-art methods.
Our codes are available at https://github.com/jugechengzi/FR.
Introduction
There are growing concerns over the interpretability of NLP models, especially when language models are being rapidly applied on various critical fields (Lipton, 2016; Du et al., 2019; Xiang et al., 2019; Miller, 2019; Sun et al., 2021).
Rationalization, using a cooperative game between a generator and a predictor in which the generator selects distinguishable and human-intelligible pieces of the inputting text (i e., rationale) to the followed predictor that maximizes the predictive accuracy, has become one of the mainstream approaches to improve the interpretability of NLP models.
The standard rationalization method named RNP (Lei et al., 2016) organizes the generator and predictor with a two-phase framework (see Figure 2(a)).
However, as illustrated in Table 1, such a two-phase model suffers from the degeneration problem where the predictor may overfit to meaningless but distinguishable rationales generated by the not yet well-trained generator (Yu et al., 2019), leading the generator to converge to the sub-optimal model that tends to select these uninformative rationales.
Many approaches have been proposed to address the degeneration issue.
The basic idea of these approaches is to regularize the predictor using supplementary modules that make use of the full text such that the predictor does not rely entirely on the rationale provided by the generator.
For example, as shown in the Figure 2, 3PLAYER (Yu et al., 2019) adopts an extra predictor to squeeze informative parts from the unselected text pieces into the rationale; DMR (Huang et al., 2021) additionally aligns with prediction distribution and feature distribution of of the full text; A2R (Yu et al., 2021) combines binary selection with soft selection in which every token in the inputting text is partly contained. [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table]
[Table]
[Table]
[Table]
[Figure] Although these regularized methods can greatly alleviate the degeneration problem, they still maintain the two fragmented phases in which the spoiled predictor can only be partially calibrated by the extra modules. More specifically, we identify that the predictor has notably higher learning speed than the generator under the two-phase framework, indicating that a regularized predictor will not immediately lead to a well-trained generator and has to continuously learn from generated uninformative rationales until convergence.
To show this, we consider the RNP method with different learning rates for the generator and predictor.
We defer the experimental details to Appendix B.2 and present the results of rationale quality (F1 score) in Figure 1.
As can be seen, the results usually get better when the learning rate of the predictor is smaller than the generator.
In particular, the result achieves the best when the learning rate of the predictor is approximately 1 / 5 that of the generator, where the learning speed of the predictor is exceptionally limited.
Although balancing the learning speed between the generator and predictor can effectively improve the performance, tuning the learning rates involves careful coordination between the two phases and requires much human effort, especially when some existing methods are designed with more modules.
To tackle this challenge, we in this work propose a frustratingly simple but effective method, Folded Rationalization (FR), which folds the two phases of the current rationalization method into one using a unified encoding mechanism.
Specifically, FR shares a unified text encoder between the generator and the predictor.
The predictor is enforced with the same learning speed as the generator and has significant chances of learning informative rationales from a well-trained generator.
On the other hand, the generator can also get a higher learning speed with the auxiliary of the predictor.
Additionally, as theoretically analyzed, the encoder of the generator can also be seen as a special regularizer for the predictor, which helps it get a global view of all the possible rationale candidates from the full text and thus prohibits it from overfitting to the uninformative ones.
Furthermore, we evaluate our approach on two widely used rationalization benchmarks, i.e., the Beer Reviews dataset (McAuley et al., 2012) and the Hotel Reviews dataset (Wang et al., 2010), of which the empirical results show that FR outperforms all state-of-the-art methods in terms of the rationale quality.
Our contributions are:
• To the best of our knowledge, this paper is the first to solve the degeneration problem in rationalization from the perspective of re-organizing the two-phase framework.
We propose a simple but
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Encoder p min)* $ $ % (d) A2R • The degeneration problem is mainly because the predictor can make correct predictions using uninformative rationales, leading to a sub-optimal generator.
In this paper, we theoretically prove that the predictor of FR will not make correct predictions using these uninformative ones and thus mitigate the degeneration problem.
• We conduct extensive experiments over various datasets.
The performance superiority of FR is demonstrated as compared to traditional rationalization methods.
In particular, the F1 score of FR can be up to 10 .
3% higher than the state-of-the-art method.
Related work
Optimization for neural rationales.
Most current rationalization methods adopt a cooperative framework between generator and predictor (Lei et al., 2016), which requires careful optimization to coordinate and is hard to train.
Considering this challenge, a series of research efforts focus on refining the optimization process to improve the rationalization.
For instance, Bao et al.
(2018) used
Gumbel softmax to do the reparameterization.
Bastings et al.
(2019) replaced the Bernoulli sampling distributions with rectified Kumaraswamy distributions.
Chang et al.
(2019) introduced a adversarial game and produces both positive and negative rationales.
Jain et al.
(2020) disconnected the training regimes of the generator and predictor networks using saliency threshold.
Chang et al.
(2020) tried to learn the invariance in rationalization.
Jiang et al.
(2021) used a post-hoc local approach to generate rationales for well-trained models.
These methods are orthogonal to our proposed method FR that shares an encoder between the generator and predictor.
Regularization for neural rationales.
Another series of efforts seek to regularize the predictor using supplementary modules which have access to the information of the full text (Yu et al., 2019;
Sha et al., 2021; Huang et al., 2021; Yu et al., 2021).
Figure 2 shows a comparison of some representative methods, where X, Z, Y represent the input text, the generated rationale, and the predictive output, respectively.
Yu et al.
(2019) took the unselected text Z c into consideration by employing a supplementary predictor Predictor c , as shown in Figure 2(b).
The generator and the supplementary predictor play an adversarial game.
Predictor c tries to maximize the predictive accuracy while the Generator seeks to minimize the predictive accuracy of Predictor c such that all the informative pieces is squeezed into Z from Z c .
Huang et al.
(2021) tried to align the distributions of rationale with the full input text in both the output space and feature space, as shown in Figure 2(c).
To make alignment in the output space, they introduce a teacher predictor Predictor t pre-trained with the full text and minimize the cross-entropy between the distributions of Y and Y t ( OutPenalty ).
In feature space, they minimize the central moment discrepancy ( FeaPenalty ) (Zellinger et al., 2017) between the representation of X and Z .
Yu et al.
(2021) endowed the predictor with the information of full text by introducing a soft rationale, which is shown in Figure 2(d).
Specifically, the supplementary predictor takes the masked text by soft attention Z soft as the input.
To convey the formation of full text to the predictor, the model minimizes the JS-divergence between the output Y of the original predictor and Y s of the supplementary predictor.
These methods are mostly related to our work.
However, different from these methods, we in this paper solve the degeneration problem from a new perspective.
We fold the two phases of the rationalization framework into one such that the predictor gets direct access to the original full text.
Problem definition
Notation In the following sections, we use P ( · ) and p ( · ) to represent distribution and probability, respectively. gen ( · ) and pred ( · ) represent the generator and predictor, respectively.
θ g
and θ p 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
=
[ x 1 , x 2 , · · · , x l ] with x i 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 Cooperative 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 =
[ m 1 , · · · , m l ] ∈ { 0 , 1 } l .
Then, it forms the rationale Z by the element-wise product of X and M :
[Equation]
In cooperative rationalization, the informativeness of the rationale Z provided by the generator is measured by the negative cross entropy − H
( Y, Y z ) , where Y z is the output of the predictor with the input being Z .
Consequently, the generator and the predictor are usually optimized cooperatively:
[Equation]
Regularizer of shortness and coherence Instead of using more complicated regularizers in the other models trying to mitigate degeneration (Yu et al., 2019; Huang et al., 2021), our model only needs a basic regularizer (Chang et al., 2019) as follows, which is similar to RNP (Lei et al., 2016), to effectively control the sparsity and coherence of the selected rationales:
[Equation]
where l denotes the number of tokens in the input text.
The first term encourages that the percentage of the tokens being selected as rationales is close to a pre-defined level α .
The second term encourages the rationales to be coherent.
Folded rationalization using unified encoder
In this section, we specify FR and analyze why it works both intuitively and formally.
4.1 Architecture of folded rationalization
Based on the framework of RNP, the architecture of FR is to share the encoder between the generator and the predictor, as shown in Figure 3.
It is worthwhile to note that we have no constraints on the types of the encoder and it can be any models such as RNN and Transformer (Vaswani et al., 2017).
For the convenience of comparing with current methods in experiments, in this paper, we adopt the bidirectional gated recurrent units (GRU) (Cho et al., 2014) as the encoder which has been adopted by most previous works (Huang et al., 2021; Yu et al., 2021).
In FR, the full text X is first sent to the unified Encoder in the generator and it outputs a representation for each token in X .
Then, the representation of each token is independently sent to Linear g which is a linear layer acting as the generator head.
Linear g outputs a value of probability following the Bernoulli distribution from which the mask of each token is independently sampled using gumbel-softmax (Jang et al., 2016).
After that, the generator outputs Z using equation 1 and further sends it to the unified encoder Encoder in the predictor.
By pre-processing the output of Encoder with max-pooling, the predictor uses the linear layer Linear p to make the prediction.
We adopt the similar objective function as RNP, i.e., equation 2 and 3, to optimize the generator and predictor cooperatively. (cid:2180) Encoder
Linear g (cid:2182) (cid:2182)
Encoder Linear p (cid:2181) Generator Predictor
Shared
Param.
Intuition for guaranteed predictive accuracy By taking the classification problem as example, we here discuss why FR will not reduce the predictive accuracy of the predictor.
In principle, the generator and the predictor seek to extract the same semantic information from the similar input text.
Specifically, to select the most informative pieces from the original text, the generator has to extract the semantic information of the text which is usually specific and distinguishable from other texts.
On the other hand, to make the correct prediction, the predictor needs to transform the selected pieces mostly relative to the input text into the semantic features which are distinguishable and separable.
Therefore, a unified encoder will not degrade the performance of the predictor, but will encourage them to benefit from each other.
Mutually reinforcing generator and predictor The main problem in RNP is that both the generator and the predictor only have access to partial information of the original data pairs, which requires careful coordination to obtain the missed information from each other.
FR with a unified encoder provides inherent benefits for the coordination and promotes the information sharing.
To be more specific, the generator has access to the input text but no true labels, while the predictor is on the contrary.
To achieve good results, they have to carefully make a coordination such that receive valuable information from one another.
However, there are 2 l candidate rationales for each X with length l , which is exceptionally difficult for a not well trained generator to select informative ones from such a large space.
As a consequence, the predictor of RNP has high risks in overfitting the uninformative noise provided by the generator.
There is a similar case for the generator as obtaining backward information from the predictor.
FR addresses this issue by allowing the generator and predictor to directly access to the full information of the original data.
Specifically, the predictor with the unified encoder has a global view of all the rationale candidates by direct access to X , which prevents itself from overfitting to uninformative ones.
In turn, with the encoder of the predictor, the generator’s ability of summarizing and extracting information from the original text is greatly enhanced.
4.2 Theoretical analysis
In the cooperative rationalization, the generator uses the predictor to evaluate the informativeness of rationales.
If the predictor can always classify uninformative rationales into true labels, then the generator may be fooled and converge to be sub-optimal.
Here we will show that the predictor in FR is regularized by the generator through the unified encoder and can not stably classify uninformative rationales into true labels any more.
In this way, only informative rationales can promise high predictive accuracy.
To this end, once the equation 2 is optimized to maximize the final predictive accuracy, the selected rationales is guaranteed to be informative ones.
To quantify the uninformativeness, we first give a definition of uninformative tokens:
Definition 1 For X ∼ D , X s is a subset of X , for a given token t , we say it is uninformative for X if the following equation holds:
[Equation]
It means that token t is independent of Y given X s .
This definition comes from how the Shapley value is calculated for no contribution, i.e., all marginal contributions are zero.
In this situation, we can say t is uninformative to Y for X naturally.
When equation 2 gets the optimal solution, we have pred ( gen ( X ))
=
p ( Y | X ) and pred ( gen ([ X, t ]))
=
p ( Y | X, t ) , where “[ X, t ]” denotes the result of adding token t to any position of X .
Then, we derive the following lemma.
Lemma 1 When an uninformative token t is added to the original text X , the predictive results will hardly change:
[Equation]
where ϵ is an error depending on the learning error of the neural network.
When equation 2 gets the optimal solution, the absolute value of ϵ is 0 .
Without losing generality, we consider the case when equation 2 achieves the optimal solution for simplicity.
For ease of exposition, we here denote gen ( X ) and gen ([ X, t ]) as Z ( X ) and [ Z 1 ( X ) , Z 2 ( t )] respectively, where Z 1 ( X ) represents the binary masks of tokens in X and Z 2 ( t ) represents the mask of the new token t .
Using equation 5 and ϵ = 0 , we have pred ( Z ( X ))
=
pred ([ Z 1 ( X ) , Z 2 ( t )]) .
To promise the same prediction, we get Z ( X ) =
Z 1 ( X ) , which indicates
[Equation]
where gen ([ X, t ]) denotes the first item of generator’s output, e.g., Z 1 ( X ) .
For convenience of analyzing the functionality of the unified encoder, we decompose the generator and the predictor as
[Equation]
where “ ◦ ” stands for functional composition, i.e., ( f ◦ h )( X ) =
f ( h ( X )) .
h and f represent the encoder and linear layer, respectively.
Obviously, we have h g = h p for FR.
We rewrite equation 6 as f g ◦ h g
( X ) =
f g ◦ h g
([ X, t ]) .
Since f g is a linear function, and the mask is selected independently for each token in practice, we get h g ( X )
=
h g ([ X, t ]) .
Now, we have the following lemma.
Lemma
If equation 2 gets the optimal solution, adding an uninformative token t to the text X does not change the representation of the original tokens in X output by the encoder of the generator, i.e.,
[Equation]
where h g ( X ) x i represents the token x i ’s representation with X being the input of the encoder h g .
In the following, we consider h g as a general one-way RNN network.
Note that bidirectional RNN is almost the same.
Besides, our analysis also holds for Transformer encoder which we leave its proof in the Appendix A.2.
For the i -th token in X , the representation can be expressed as:
[Equation]
where e i , s i are the word embedding and hidden state of the i -th token.
φ g , ψ g are two functions corresponding to the type of RNN units.
When an uninformative token t is added between x i and x i − 1 , we have
[Equation]
where s ′ i is the hidden state of the original x i in this new text and we denote it by h g ([ X, t ]) x ′ i = φ g ( s ′ i ) .
From Lemma 2, we have h g ( X ) x i =
h g ([ X, t ]) x ′ i .
Using the first term of of the first equation 9, we get
[Equation]
Then we easily get s i
=
s ′
i .
Using the second term of equation 10, we have
[Equation]
Then we have s t =
s i − 1 very smoothly, which is specified in the following lemma.
Lemma
If the i -th token in X is uninformative, the hidden state of it through the encoder of generator is equal to that of the token preceding it:
[Equation]
Then, let us consider two different uninformative rationales, i.e., Z uninf and Z ′ uninf , which contain only uninformative tokens and come from two different data pairs ( X, Y ) , ( X ′ , Y ′ ) .
Lemma
If equation 13 holds, any two different uninformative rationales have the same representation through the encoder of generator for each token, i.e., h g ( Z uninf )
z i =
h g ( Z ′ uninf )
z j , where h g ( Z uninf ) z i denotes the representation for the i -th token in Z uninf .
The proof can be seen in Appendix A.1.
Now, we immediately get the following theorem.
Theorem 1 If FR gets the optimal solution of equation 2, i.e., P ( Y | X ) =
P ( pred ( gen ( X ))) , and
Z uninf , Z ′ uninf are two different rationales that contain only uninformative tokens and are selected from two different data pairs ( X, Y ) , ( X ′ , Y ′ ) , we have
[Equation]
Theorem 1 indicates that the predictor in FR will give the same output for any uninformative rationales.
Hence, when we optimize the generator and the predictor by maximizing the final predictive accuracy using equation 2, the predictor only recognizes the informative rationales and ignores the uninformative ones.
In this way, our FR greatly mitigates the degeneration problem.
[Table]
Experiments 5.1 Experimental setup
Datasets and Models Following (Huang et al., 2021), we consider two widely used rationalization datasets.
To the best of our knowledge, none of dataset contains personally identifiable information or offensive content.
The details of the two dataset can be found in Appendix B.1.
1) Beer Reviews (McAuley et al., 2012) is a multi-aspect sentiment prediction dataset widely used in rationalization (Lei et al., 2016;
Yu et al., 2019; Chang et al., 2019; Huang et al., 2021; Yu et al., 2021).
There is a high correlation among the rating scores of different aspects in the same review, making it difficult to directly learn a rationalization model from the original data.
Following the previous work (Lei et al., 2016; Huang et al., 2021; Yu et al., 2021), we use the subsets decorrelated by Lei et al.
and binarize the labels as Bao et al.
(2018) did.
2) Hotel Reviews (Wang et al., 2010) is another multi-aspect sentiment classification dataset.
The dataset contains reviews of hotels from three aspects including location, cleanliness, and service.
Each review has a rating on a scale of 0-5 stars.
We binarize the labels as Bao et al.
(2018) did.
On both two dataset, we adopt the GRU (Cho et al., 2014) as the encoder which has been adopted by most previous works (Huang et al., 2021; Yu et al., 2021).
Baselines and implementation details We compare FR to the cooperative rationalization framework
RNP (Lei et al., 2016) and two latest published models that achieve state-of-the-art results: DMR (Huang et al., 2021) and A2R (Yu et al., 2021), both of which have been specified in section 1.
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 models do.
Since DMR and A2R have been validated to outperform 3PLAYER (Huang et al., 2021; Yu et al., 2021), we in this paper ignore its results for clarity of presentation.
Following DMR and A2R, we use the 100-dimension Glove (Pennington et al., 2014) as the word embedding and set the hidden dimension of GRU to be 200.
We use Adam (Kingma and Ba, 2014) as the optimizer.
All the baselines are tuned a lot of times to find the best hyperparameters.
All of the models are implemented with PyTorch and trained on a RTX3090 GPU.
Metrics All the methods get similar predictive accuracy.
Following (Huang et al., 2021; Yu et al., 2021), 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, F 1 indicate the precision, recall, and F 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 on the test set.
5.2 Results
Comparison with baselines on two datasets Table 2(a) and 2(b) show the results of selected rationales on two datasets.
All the methods choose similar percentage of tokens that is close to the human-annotated sparsity by adjusting the sparsity regularization term in equation 3.
Obviously, we gain significant improvements in all six aspects.
In particular, the F1 score of our method FR is 82 .
8% in the Beer-Appearance dataset, which improves the state-of-the-art result by up to 10 .
[Table] i.e., 72 . 5 of A2R. Table 3 shows some visualized examples of rationales from RNP and FR.
More rationale examples of DMR and A2R are in Appendix B.
[Table]
Comparison with baselines in low sparsity To show the robustness of our FR, we also conduct an experiment where the sparsity of selected rationales is very low, which is the same as CAR (Chang et al., 2019) and DMR.
The results are shown in Table 4.
The results of RNP and CAR are obtained from (Chang et al., 2019), and the results of DMR are obtained from (Huang et al., 2021).
For the aspects of Aroma and Palate , we still achieve great improvement over other methods.
For Appearance , our performance is a little bit worse than DMR.
The reason may be that when the sparsity is far from the ground truth, many informative tokens are lost and the predictor can not make the right prediction.
While DMR uses an adversarial framework same as CAR in practice and the label is used as an additional input to the generator, so it may work better when the sparsity is extremely low.
Skewed predictor To show that our FR 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 can be found in Appendix B.3.
The results are shown in Table 5.
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 Palate-skew 20 , RNP and A2R can not work at all while our FR is still effective.
It can be concluded that FR is much more robust than the other two methods in this situation.
[Table]
[Table]
Skewed generator : To further show that our method is not susceptible to degeneration, we design a new synthetic experiment with special initialization that induces degeneration from the perspective of skewed generator.
We first pretrain the generator separately using the text classification label as the mask label of the first token.
As a result, the predictor will be able to know the category of a rationale merely through whether the first token is selected as part of the rationale or not and may overfit to this positional bias. So before we cooperatively train the generator and predictor together, the generator is initialized with the intentionally misleading pretrained parameters and the predictor is initialized randomly.
We compare the performance of RNP and our FR in the dataset Beer-Palate, because Palate is relatively hard to learn as compared to other aspects (Yu et al., 2021).
Besides, the performance of RNP and FR is similar in this aspect when the generator is not deliberately skewed.
All the hyperparameters we use here are the same as that of the best results in Table 2(a).
The results are shown in Table 6.
The k in “ skew k ” denotes the threshold of the skew: we pretrain the generator as a special classifier of the first token for a few epochs until its predictive accuracy is higher than k .
Since the accuracy increases rapidly in the first a few epochs, obtaining a model that precisely achieves the pre-defined accuracy is almost impossible.
Therefore, we use “ Pre _ acc ” to denote the actual predictive accuracy of the generator-classifier when the pre-training process stops.
Higher “ Pre _ acc ” means easier to degenerate.
We find, in this case, both methods get high predictive accuracy while RNP fails to find the human-annotated rationales.
Failure examples Table 7 shows some failure cases of our method.
Typically, the failures can be summarized as follows.
First, the model fails to grasp high-level language phenomena and world background knowledge.
For example, in the case of Beer-Palate, the model fails to understand the analogy statement of “ almost feels like drinking champagne ” and makes the prediction as negative. Second, the model fails to make logical reasoning. The ground truth of hotel cleanliness should be inferred from the word “ comfortable ” . However, our model makes judgments by selecting the rationales such as “ breakfast, staff was friendly..., stay ” , which have little relevance to the cleanliness but are positive.
A similar failure also occurs in the case of Beer-Aroma, where the model selects texts with a strong sentiment but uncorrelated with the predefined ground truth.
Conclusion, limitations, and future work
In this paper, we analyze the relationship between generator and predictor in terms of working mechanism and propose a simple but effective framework to solve the degeneration problem in the two-phase rationalization.
The experimental results show that our proposed methods significantly outperform state-of-the-arts in terms of the rationale quality.
One limitation may be that our theoretical analysis mainly focuses on the idealized models which have perfectly fitted the distribution of the dataset.
Besides, although sharing the encoder between the generator and predictor is simple, it is limited to the basic RNP which has no extra modules.
Existing [Table] [Table] works have proposed many extra modules to solve the degeneration problem, which demonstrate great effectiveness.
Leveraging these extra modules can predictably achieve performance improvement.
However, the relationship among multiple modules will become much more sophisticated, simply sharing the generator and predictor may not be the optimal.
How to effectively incorporate existing optimized techniques is a challenge for FR.
Besides [Table] the sharing encoder of FR is similar to multi-task learning when training the generator and predictor are viewed as two cooperative tasks.
However, existing multi-task learning methods are usually designed for the case where there are multiple output objectives but only one single input sample.
How to bridge FR and multi-task learning both intuitively and theoretically [Table] and then improve the rationalization with techniques in multi-task learning, is still unknown.
We leave them as future work.
Acknowledgements
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.
Checklist
For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
[Yes] (b) Did you describe the limitations of your work?
[Yes] See Section 6.
(c) Did you discuss any potential negative societal impacts of your work?
[Yes] See Section 6. (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?
[Yes] 2.
If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?
[Yes] See Section 4.2.
(b) Did you include complete proofs of all theoretical results?
[Yes] See Section 4.2 and Appendix A. 3.
If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)?
[Yes] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?
[Yes] See Section 5.1.
(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)?
[No] The experiments of most methods for rationalization do not have this item (Lei et al., 2016; Yu et al., 2019; Chang et al., 2019; Huang et al., 2021) because experiments with multiple aspects of multiple datasets under the same random seed are sufficient to verify the stability of the models.
All of our experiments and re-implemented baselines with different settings and datasets are under one same random seed to make a fair comparison.
We have also tried five different random seeds for Beer-Appearance and Beer-Aroma in Table 2(a), and the standard deviations are 1.198 and 0.657 respectively.
(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?
[Yes] See Section 5.1.
If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?
[Yes] (b) Did you mention the license of the assets?
[Yes] See Appendix B.1.
(c) Did you include any new assets either in the supplemental material or as a URL?
[N/A]
(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating?
[Yes] See Appendix B.1.
(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content?
[Yes] See Section 5.1.
If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?
[N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?
[N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
[N/A]
A Theorem proofs A.1 The proof of Lemma 4 and Theorem
Using equation 13, we get that the hidden state of an uninformative token is equal to that of the token precedes it.
Considering two specific uninformative rationales Z = { “ mask ” , “ t 1 ” , “ t 2 ” } and
Z ′ =
{ “ mask ” , “ t 3 ” , “ t 4 ” } where all tokens in them are uninformative, we have:
[Equation]
So the proof of Lemma 4 is completed.
Then, we have maxpool ( h g ( Z ))
=
maxpool ( h g ( Z ′ )) .
Theorem 1 is also proved.
Note that “ mask ” is a special token and its word embedding is a zero vector.
If the hidden state before the first token is initialized as a zero vector, it can be aligned with a “ mask ” token.
If a token is masked out in the input text, we can implement the operation by replacing it with a “ mask ” token as well.
A.2 The proof of Theorem 1 when the encoder is based on Transformer
In fact, we only need to prove Lemma 4 because Theorem 1 can be easily derived from it.
We express h g as :
[Equation]
[Equation]
If x j is an uninformative token, it has no influence on h g ( X ) x
i for any x i according to Lemma 2.
So, we have || φ g ( e j ) ||
=0 for any uninformative x j .
For any Z uninf that contains only uninformative tokens and z i , z j in Z uninf , we have
[Equation]
The proof of Lemma 4 is completed.
B Details of experimental setup B.1 Datasets
Beer Reviews Following (Chang et al., 2019; Huang et al., 2021; Yu et al., 2021), we consider a classification setting by treating reviews with ratings ≤ 0.4 as negative and ≥ 0.6 as positive.
Then we randomly select examples from the original training set to construct a balanced set.
Hotel Reviews Similar to Beer Reviews, we treat reviews with ratings < 3 as negative and > 3 as positive.
More details are in Table 8.
Pos and Neg denote the number of positive and negative examples in each set.
Sparsity denotes the average percentage of tokens in human-annotated rationales to the whole texts.
We get the license of Beer Reviews by sending an email to Julian McAuley.
The Hotel Reviews is a public dataset and we get it from https://github.com/kochsnow/distribution-matching-rationality.
B.2 The setup of the experiment
in Figure[-
-]
We use the dataset of Beer-Aroma, whose details are shown in Table 8.
We use a fixed batch size of 256 and initialize the learning rates of the two modules to different values as shown in Figure 1.
The values in the cells are F1 scores that indicate the overlaps between the selected tokens and human-annotated rationales.
For different settings, they use the same hyperparameters except the learning rates.
[Table]
B.3 The details of skewed predictor
The experiment was first designed by Yu et al.
It deliberately induces degeneration to show the robustness of A2R compared to RNP.
We first pretrain the predictor separately using only the first sentence of input text, and further cooperatively train the predictor initialized with the pretrained parameters and the generator randomly initialized using normal input text.
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 .
“ skew k ” denotes the predictor is pre-trained for k epochs.
To make a fair comparison, we keep the pre-training process the same as that of A2R: we use a batch size of 500 and a learning rate of 0.001.
B.4 More visualized results
We also provide the visualized rationales from DMR and A2R corresponding to the examples in
Table 3.
The results are shown in Table 9.
B.5 Visualized results of Lemma
[Figure] examples of Lemma To verify Lemma 3, we visualized the representations of the tokens in two special designed sentences “good . , smell” (a,b,c) and “good , .
smell ” (d,e,f) through different encoders in Figure 4.
We choose these two sentences because “ ,” and “ .” are uninformative in most cases, which is consistent with the setting of Lemma 3.
Both our FR and RNP are trained on Beer-Aroma, where the predictive accuracy
[Table]
of the two models are similar while RNP selects bad rationales.
Note that in FR, the encoder of the predictor is just the generator’s encoder.
According to Lemma [Table] the hidden states of “ , ” and “ . ” should be the same as that of the word “ good” after they are passed through the generator’s encoder, thus resulting in the same representation.
We take the first 40 dimensions for better observation.
From Figure 4, we can see for both RNP and FR, the uninformative tokens “ , ” and “ . ” are closer to “ good ” by the encoder of the generator than by the encoder of the predictor.
These results directly verify the conclusion of Lemma
[Table]
C Boarder impact
The interpretability of neural networks aims to improve trust in the models.
However, the problem of degeneration in the traditional two-phase rationalization models makes them untrustworthy for humans.
Although the regularization terms on the predictor introduced by some follow-up work can alleviate this problem, adjusting the regularization terms requires significant manual effort to see whether the model has degenerated or not according to the human-annotated rationales, which are very costly and only present in small numbers in the test set.
Our FR does not suffer from degeneration as long as the predictive accuracy is high, which can be tuned based on the validation set.
So, our model saves a lot of labor cost.
In addition, our model reduces the number of parameters by roughly half compared to traditional RNP and can be used by more applications with limited computational resources.
D Experiments with specialized layers
To make a fair comparison with the baseline models, we use the same setting and focus on the encoder with only one layer of GRUs for the experiments in the main body of our paper.
To better understand the behavior when the encoders are partly [-shared, we further constructed theencoders with 3,4,5 layers of GRUs. The results can be seen in table 10 and 
-]shared
[Table]
we further constructed the encoders with multiple layers of GRUs as shown in Table 10 and Table 11.
[Table]
[Table]
It can be seen from the above tables that the case with the encoder fully shared between the generator and predictor always outperforms the cases where the encoders are partly shared in terms of rationale quality (F1 Scores).
Besides, the above tables showed that the rationale quality gets better as the number of shared layers increases in overall.
We argue that, in order to obtain a good rationale, both the generator and predictor have to capture and encode the same informative sections from an input.
Therefore, sharing the entire encoder can help performance.
We also showed in the theoretical analysis of the paper, the encoder should be fully shared to make the predictor and the generator regularized by each other to get more stable models.