Exploring Practical Gaps in Using Cross Entropy to Implement Maximum Mutual Information Criterion for Rationalization Open Access

With the success of deep learning, there are growing concerns over interpretability (Lipton, 2018). Ideally, the explanation should be both faithful (reflecting the model’s actual behavior) and plausible (aligning with human understanding) (Jacovi and Goldberg, 2020; Chan et al., 2022). Post-hoc explanations, which are trained separately from the prediction process, may not faithfully represent an agent’s decision, despite appearing plausible (Lipton, 2018). In contrast to post-hoc methods, ante-hoc (or self-explaining) techniques typically offer increased transparency (Lipton, 2018) and faithfulness (Yu et al., 2021), as the prediction is made based on the explanation itself. There is a stream of research that has exposed the unreliability of post-hoc explanations and called for self-explanatory methods (Rudin, 2019; Ghassemi et al., 2021; Ren et al., 2024).

In this study, our primary focus is on investigating a general model-agnostic self-explaining framework called Rationalizing Neural Predictions (RNP, also known as rationalization) (Lei et al., 2016). RNP utilizes a cooperative game involving a selector and a predictor. This game is designed with a focus on “data-centric” (i.e., it is to explain the connection between a text and the model-agnostic task label, rather than explaining the output of a specific model) feature importance: The selector first identifies the most informative part of the input, termed the rationale (in practice, rationale selection is achieved through masking unuseful tokens). Subsequently, the rationale is transmitted to the predictor to make predictions, as illustrated in Figure 1. The selector and predictor are trained cooperatively to maximize prediction accuracy. RNP and its variants have been one of the mainstreams to facilitate the interpretability of NLP models (Sha et al., 2021, 2023; Yue et al., 2023; Liu et al., 2023c; Storek et al., 2023; Zhang et al., 2023). And besides its use for interpretability, rationalization can also serve as a method for data cleaning, since the extracted (Z, Y ) samples can act as a new dataset. Some recent studies find that a predictor trained with such a dataset can be more robust (Chen et al., 2022) and generalizable (Wu et al., 2022), since task-irrelevant, harmful information has been removed.

Despite its strength, the cooperative game of rationalization is difficult to train if the selector and the predictor are not well coordinated (Yu et al., 2021). In this paper, we begin by analyzing the objective of cooperative rationalization, decomposing the practical assessment of rationale candidates by the selector (i.e., $Hc(Y,Ŷ∣Z)$⁠) into two parts: the model-agnostic informativeness of the rationale candidates (i.e., H(Y |Z)), and the degree to which the predictor fits the conditional distribution P(Y |Z) (i.e., $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$⁠), as shown in §4.1. Initially, due to random initialization, the selector samples all rationale candidate regions evenly, and all rationale candidates are fairly fitted by the predictor, resulting in similar D_KL. Therefore, the selector tends to choose candidates with relatively lower H(Y |Z). We then empirically observe that once the selector identifies some good (but not necessarily optimal) rationale candidates that have relatively low H(Y |Z), it dramatically increases the probability of selecting these candidates and decreases the probability of selecting others, sampling within a very small area (in fact, even a single point, as shown in Empirical observation 1 of §4.2). This results in the predictor’s perspective being limited to a small local area, only capable of reasonably fitting a narrow range of rationale candidates. Consequently, the optimal rationale, despite having the lowest H(Y |Z), may be overlooked due to a high $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$ (please refer to Empirical observation 2 in §4.2).

To mitigate this issue, ensuring that the predictor equally fits any rationale candidates might be a viable solution. However, we also find the negative result that completely random sampling across all possible areas, to allow the predictor to fit all rationale candidates equally, renders the predictor ineffective due to an excessively low signal-to-noise ratio (see §4.3). As a result, we try to develop a compromise solution.

Given the continuity of textual semantics (“continuity” does not refer to the adjacency of words, but rather to the gradual, smooth change in meaning when a small number of words are altered, rather than a sudden shift), an empirical conjecture is that if the selector identifies suboptimal rationale candidates with relatively low H(Y |Z), then the optimal rationale is likely within its vicinity. Therefore, the predictor only needs to focus on fitting the rationale candidates within this vicinity. Inspired by the philosophy of variational autoencoders (VAE), we construct the vicinity by introducing random perturbations to the selected rationale candidates and use this new vicinity to train the predictor. The architecture of our method is shown in Figure 7, with Figure 8 showing its intuition. Through this approach, we significantly improved the rationale quality extracted by the standard RNP on six datasets from two widely used rationalization benchmarks, surpassing some recently published RNP variants.

Our contributions are summarized as follows: (1) Problem Identification: We formally analyze the objective of rationalization and identify the practical gap between the rationales’ informativeness and the model’s assessment of them, which is the primary contribution of this paper. (2) Empirical Evidence: We provide various empirical evidence to demonstrate how this gap can affect the quality of extracted rationales. (3) Simple Solution: We introduce a simple yet effective method named vicinal evaluation rationalization (VER) to mitigate this gap. Empirical results on several widely used benchmarks demonstrate the effectiveness of the proposed method. Additionally, our method is straightforward and does not require any additional auxiliary modules, preserving its potential to be combined with future methods.

Rationalization is a general framework first proposed by Lei et al. (2016). By extracting rationales before making predictions, this framework can ensure the rationale’s faithfulness to the model prediction, as the predictor is just trained on the selected rationales (Yu et al., 2021; Chang et al., 2020). Rationalization has been one of the mainstreams to facilitate the interpretability of NLP models (Yue et al., 2023; Storek et al., 2023; Zhang et al., 2023; Liu et al., 2023b, 2024a, 2025). Recently, there has also been some work attempting to extend it to the field of graph learning (Luo et al., 2020) and computer vision (Yuan et al., 2022). Apart from improving interpretability, recent work has also discovered that it can serve as a method of data cleaning, as training a predictor with the extracted rationales has been found to increase robustness (Chen et al., 2022) and generalization (Wu et al., 2022; Gui et al., 2023).

The rationalization framework involves a cooperative framework between the selector and the predictor, which requires careful optimization to coordinate and is hard to train. Given this challenge, a number of research efforts focus on refining the optimization process to improve the rationalization. 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 selector and predictor networks using saliency threshold. Chang et al. (2020) tried to learn the invariance in rationalization. Liu et al. (2023c) suggested that the selector and the predictor need to be assigned different learning rates. Yu et al. (2019) found that if not properly coordinated, the selector and the predictor may collude to use trivial patterns to make the correct prediction. To address this issue, 3PLAYER (Yu et al., 2019) tries to make the unselected parts incapable of predicting the label, so that informative parts are squeezed into the selected parts; DMR (Huang et al., 2021) tries to match the distribution between the selected rationales and the raw inputs; FR (Liu et al., 2022) shares the encoder between the selector and the predictor to make them regularize each other; MGR (Liu et al., 2023a) reduces the likelihood of collusion by training multiple selectors; NIR (Storek et al., 2023) constructs a large vocabulary based on the dataset and uses manually defined rules to determine which tokens in the rationale candidates selected by the selector are likely to be irrelevant to the prediction, and randomly replaces them with other meaningful words from the vocabulary. Inter_RAT (Yue et al., 2023) reduces training difficulties by blocking shortcuts. CR (Zhang et al., 2023) selects rationales by additionally calculating the necessity and sufficiency of each token. A2I (Liu et al., 2024b) attempts to reduce the influence of model-added spurious correlations through an attack-based instructor.

Our research can also be categorized as a solution to training difficulties, and the distinct contribution is a detailed analysis of a new potential cause of these training difficulties. Our practical method may seem similar to NIR at first glance, but the underlying concept is completely different. NIR stabilizes the training of the predictor by replacing tokens in the selected rationale candidates that are likely to lack specific semantics with tokens from the vocabulary that have rich semantics (which may not be present in the original input X). However, a fundamental flaw of NIR is that if the predictor scores the replaced rationale candidate highly, the feedback received by the selector would be to increase the probability of selecting the original rationale candidate before replacement (which is not necessarily good because the high score may come from the newly added tokens). We will take NIR as a baseline and also include some of the other latest methods.

Generative explanation is a research line that is close but orthogonal to our research. With the great success of LLMs, a new research line for explanation is chain-of-thought. By generating (in contrast to selecting) intermediate reasoning steps before inferring the answer, the reasoning steps can be seen as a kind of explanation. The intriguing technique is called chain-of-thought (CoT) reasoning (Wei et al., 2022). However, LLMs sometimes exhibit unpredictable failure modes (Kıcıman et al., 2023) or hallucination reasoning (Ji et al., 2023), making this kind of generative explanation not trustworthy enough in some high-stakes scenarios. Also, some recent research finds that LLMs are not good at extractive tasks (Qin et al., 2023; Li et al., 2023; Ye et al., 2023).

Compared to traditional “model- centric” XAI methods which solely focus on the model’s learned information, “data-centric” approaches primarily aim to extract model-agnostic patterns inherent in the data. So, apart from improving interpretability, rationalization can serve as a method of data cleaning (Seiler, 2023).

Domain-specific large models often require supervised fine-tuning using domain-specific data. Uncleaned data may contain harmful information such as biases and stereotypes (Sun et al., 2024). Recent research suggests that training predictors with extracted rationales can remove irrelevant harmful information, enhancing robustness (Chen et al., 2022) and generalization (Wu et al., 2022; Gui et al., 2023). Considering that small models are sufficient for simple supervised tasks and are more flexible and cost-effective for training on single datasets (e.g., searching hyperparameters and adding auxiliary regularizers), using small models for rationalization on a single dataset and then using the extracted rationales for supervised fine-tuning might prevent large models from learning harmful information from new data. Additionally, shortening input texts can also reduce the memory required for fine-tuning (Guan et al., 2022). A recent study also finds that training a small model for data selection and producing a small subset is useful for fine-tuning LLMs (Xia et al., 2024).

Then, we introduce the rationalization task. The overall target of the rationalization task is to find the evidence from X that best supports Y (not the model predicted $Ŷ$ in ante-hoc explanation). Based on this target, the intuition is that good rationales can be used to achieve high prediction accuracy. As a result, the practical way to identify rationales is to train a selector and a predictor that cooperatively maximize the prediction accuracy, as specified below.

It then leads to two questions: Why can $Hc(Y,Ŷ∣Z)$ be used to approximate H(Y |Z), and what specific approximations have been assumed? Exploring these two questions will help us gain a more specific and detailed understanding of the effectiveness of Equation (3), going beyond vague intuitions. This can assist us in more accurately identifying potential issues in practice.

Although the effectiveness of Equation (3) in identifying rationales is theoretically supported with the MMI criterion, the previous analysis in §4.1 tells us there is a gap between theory and practice. This section aims to provide empirical evidence to verify the existence of the theoretical gap.

Specifically, the selector gets the feedback about the importance of the selected rationale candidates through the predictor’s output $Hc(Y,Ŷ∣Z)$⁠, which consists of two components: the model-agnostic informativeness of Z, and how well the predictor assesses Z (i.e., $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$⁠), as is shown in Equation (6). Thus, the selector will be guided to choose the rationales that have both low H(Y |Z) and low $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$⁠, while the optimal rationales can only guarantee themselves with low H(Y |Z). In practice, however, the predictor can only learn to assess rationales that have already been selected by the selector. If the selector’s selection set is focused on a small local area, the assessment of the predictor on unsampled regions will be biased. The problem is that although the optimal rationales have the lowest H(Y |Z), they are not guaranteed to have low $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$⁠, resulting in obtaining only suboptimal rationales. In the following, we will show some empirical evidence that the optimal rationales are usually not properly valued and do not have the lowest cross-entropy under the RNP framework.

(the selector samples rationale candidates in a small area). Although the selector’s choice already incorporates some randomness, we find that in practical training, when it identifies some relatively good rationale candidates, it quickly increases the probability of selecting these potentially suboptimal rationale candidates to rapidly improve predictive accuracy. This causes its sampling to concentrate in a very small local area, potentially missing the optimal solution.

Initially, the selector explores a wide region, but after finding some relatively good rationale candidates, it rapidly increases the probability of selecting these candidates. Figure 2(a) shows that after about 100 training epochs, the difference of selected rationale candidates between two iterations is only about 4%. Considering that the rationale sparsity is about 20% and the maximum sequence length is 256, there are only about 4% * 20% * 256 ≈ 2 tokens that are changed between two training iterations (even fewer, as most texts are shorter than 256 tokens, see Table 4), which means that the selector’s sampling is focused on an almost “single point” and the predictor sees very limited data. This causes the predictor’s focus to quickly converge to a certain local area, reducing the likelihood that other regions are reasonably assessed. At this point, the quality of the rationale no longer grows (Figure 2(b)), while the training accuracy continues to rise at a high rate (Figure 2(c)). At this stage, the predictor is merely overfitting to some trivial patterns in this locality, as evidenced by the fact that we observed no increase in accuracy on the validation set (Figure 2(c)).

(the cross-entropy does not assess the unselected optimal rationale properly). In intuition, the gold human-annotated rationales are most informative and have the lowest H(Y |Z). Thus, ideally (e.g., a predictor that works like a human expert such that the KL-divergence in Equation (6) is equal to 0 for all possible Z), using the human-annotated rationales can best predict Y. However, we empirically observe that sometimes the human-annotated rationales get lower prediction accuracy than the model-selected ones when sent to RNP’s trained predictor.

Figure 3(a) shows the accuracy of RNP’s trained predictor with model-selected and human-annotated rationales as input on three rationalization datasets. We observe that sometimes the human-annotated gold rationales get much lower accuracy than the model-selected ones. It’s clear that gold rationales have lower H(Y |Z). So, the reason of this phenomenon is that the predictor does not fit the gold rationale well and leads to high $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$ for it. This observation to some extent supports our hypothesis that the predictor does indeed overfit to the points selected by the selector while underfitting the potentially optimal rationales around them, leading to inaccurate assessment of using $H(Y,Ŷ∣Z)$ to approximate H(Y |Z).

(the predictor is overfitting to trivial patterns). In Empirical observation 1, we mentioned that after the selector confines its sampling to a very small area, the predictor overfits this small region while neglecting others. Now, we further provide another evidence of overfitting. Another indirect indicator of the extent to which the model overfits trivial patterns is the smoothness of the model (Virmaux and Scaman, 2018; Fazlyab et al., 2019). If a predictor learns many trivial patterns instead of genuinely meaningful semantic features, then its function surfaces typically exhibit non-smooth patterns such as steep steps or spikes, resulting in poor Lipschitz continuity (Liu et al., 2023c; Szegedy et al., 2014; Weng et al., 2018). Typically, Lipschitz continuity is approximated by the value of the variation of the output with respect to the input over the entire dataset (i.e., Lipschitz constant, lower is better). We follow the method used in Liu et al. (2023c) to compute the Lipschitz constant, which is given in Appendix A.4.

Figure 4 shows the unsmoothness of the predictor during training. “p = 0” refers to the vanilla RNP, and “p ∈ [0.1,0.5]” refer to our method (which will be introduced in §4.3). Lower y value means a smoother model function. We see that the Lipschitz constant (unsmoothness) of RNP grows for a long time, while our method with p = 0.5 grows very slowly after about 70 epochs. Figure 5 shows the corresponding rationale quality. Figures 4 and 5 are from the same experiments, whose details are in Appendix A.4. Combining Figures 4 and 5, we further observe that the predictor’s overfitting significantly prevents the selector from finding good rationales.

(negative results of equally assessing all possible rationale candidates). An intuitive way to address the issue is to decouple the training data of the predictor from the selector. If the predictor’s training data (⁠$Dz$ as mentioned in §3) is sampled randomly rather than conditioned on the selector, then the rationale candidates in every regions will be able to be equally fitted, mitigating the impact of unbalanced evaluation on Eq. (6). In practice, however, random sampling may lead to a very low signal-to-noise ratio, preventing the predictor from effectively learning the semantics. For example, in a widely used rationalization dataset called Beer-Appearance, the average percentage of the ground-truth rationale is about 18.4%. This means that about 81.6% of the tokens in an input text act as noise, making this method intractable in practice. Figure 6 shows the results of such a method. In the first 300 epochs, we randomly sample a set of rationale candidates (with the sparsity constraint only) to form a $Dz$ for each epoch to train the predictor. And in the latter 300 epochs, the predictor is fixed and we train the selector in the same way as RNP (please refer to Appendix A.6 for more details). Under this training approach, the predictor is expected to be capable of evaluating rationale candidates effectively in any regions. But Figure 6 does not show the results as we expect. In fact, the model does not work at all, due to the low signal-to-noise ratio received by the predictor.

Based on the issues mentioned above, we try to develop a compromise solution. Considering the continuity of textual semantics, an empirical conjecture is that if the selector identifies suboptimal rationale candidates with low H(Y |Z), then the optimal rationales should be within their vicinity (note that continuity here does not refer to the adjacent positioning of words, but rather to the number of words that need to be changed). This conjecture is based on two considerations. First, in a random state (where the predictor has no bias toward any Z offset), all rationale candidates have similar $DKL(P(Y∣Z)∣∣P(Ŷ∣Z))$ values, but the optimal rationales have lower H(Y |Z). Combining this with Equation (6), theoretically, the optimal rationales are more likely to be favored by the predictor at the beginning of training. Second, empirically, the vanilla RNP can select relatively good rationales in most cases.

Based on this assumption, the predictor only needs to evaluate the vicinity of the selector’s selected region. Then, borrowing from the philosophy of VAE, we randomly perturb the selector’s output to sample a vicinity. Specifically, we start by randomly flipping the elements in the selector’s output m for which m_i = 1 with a probability of p (p is a hyperparameter), and then we count the number of flips. Subsequently, we select the same number of elements for which m_j = 0 and flip them to 1.

Figure 7 shows the comparison between the standard rationalization framework RNP and our method. Our approach is very simple and does not involve any adjustments to the model structure, making it scalable to those complex methods that rely on structural modifications. Figure 8 provides a toy example to show the intuition of our method. On the left is the original raw input X. The black dots represent rationale candidates, among which the red one is the optimal rationale. The blue region is the area that the selector has a high probability to sample. The region is quite small because the selector quickly becomes overconfident about certain suboptimal rationale candidates, leading to a concentration of sampling in a very narrow local area (see Empirical observation 1 in §4.2).

Although the process of rationale extraction is unsupervised, the rationalization task requires comparing the rationale quality extracted by different models. This necessitates that the test set includes ground-truth rationales, which imposes special requirements on the datasets. Following the conventional setup in the field of rationalization, we employ six text classification datasets from two widely used benchmarks.

The datasets are Beer-Appearance, Beer- Aroma, and Beer-Palate (collected from the BeerAdvocate [McAuley et al., 2012] benchmark); and Hotel-Location, Hotel-Service, and Hotel-Cleanliness (collected from the HotelReviews [Wang et al., 2010] benchmark). Among them, the beer-related datasets are most important and used by nearly all previous research in the field of rationalization. All of these datasets contain human-annotated ground-truth rationales on the test set (but not on the training set), making it convenient to compare different methods’ performance fairly. Among them, the three beer-related datasets are most important and used by nearly all of previous research in the field of rationalization. The statistics of the datasets are in Appendix A.1.

To verify the generalizability of our VER, we also perform supplementary experiments on two different tasks. We use the MultiRC dataset for the reading comprehension task, and use the FEVER dataset for the fact extraction and verification task. These two datasets are taken from the ERASER benchmark (DeYoung et al., 2020).

We compare with RNP (Lei et al., 2016), DMR (Huang et al., 2021), Inter_RAT (Yue et al., 2023), NIR (Storek et al., 2023), CR (Zhang et al., 2023), and A2I (Liu et al., 2024b). Among them, RNP represents the direct counterpart of our VER, and other methods stand for the latest literature. All of them have been discussed in §2. Aside from these rationalizations methods, we also compare with two popular post-hoc methods: LIME (Ribeiro et al., 2016) and Attention.³

Each of the selector and predictor pairs contains an encoder (e.g., RNN/Transformer) followed by a linear layer. We use two types of encoders: GRUs (with 100-dimensional GloVe as the word embedding, following Inter_RAT, Table 1) and “bert-base-uncased” (following CR, Table 2). In comparison with the baselines, we keep the perturbation rate of our VER as p = 0.3 for all the datasets. Then, we further show the influence of hyperparameter p separately (Figure 9). For DMR, NIR, A2I, and our VER, considering they are all variants of the standard RNP, we first manually tune the hyperparameters for RNP, and then apply the hyperparameters to other methods. For Inter_RAT, since it has originally been implemented on the beer-related datasets, we apply its original hyperparameters but only adjust the sparsity regularizer in Equation (4). More details are in Appendix A.2.

Since predictive accuracy is influenced by many other unknown factors besides the quality of the extracted rationale, it is not a good metric. So, following the previous literature of rationalization, we mainly focus on rationale quality, which is measured by the overlap between the human-annotated rationales and the model-selected tokens. (We note that this may not be a perfect metric as evaluating explanation quality is a complex problem [Pruthi et al., 2022]. Nevertheless, this metric has been widely adopted in previous research in this field and has been empirically validated to make sense.) The terms P, R, F1 denote precision, recall, and F1 score, respectively. Among them, P indicates how much useless information is removed from the raw text (the cleanliness of the extracted rationale), and R indicates how much useful information is extracted (comprehensiveness of the extracted rationale). These metrics are the most frequently used in rationalization. The term S represents the average sparsity of the selected rationales, that is, the percentage of selected tokens in relation to the full text. Since the sparsity of ground-truth rationales on beer- and hotel-related datasets is around 10% ∼ 20%, we adjust α in Equation (4) to make S be about 15% (since Equation (4) is only a soft constraint, it cannot strictly limit S to be exactly 15%). Acc stands for the predictive accuracy. For FEVER and MultiRC datasets, we follow NIR to set S to be about 20%. For the results with BERT encoder, we follow CR to make S be about 10%.

Table 1 shows the comparisons of recent methods and our VER with perturbation p = 0.3. In terms of the rationale quality (F1 score), we outperform all of the baselines by a large margin. Specifically, the improvements are up to 6.6% (Beer-Palate dataset). We also improve the prediction accuracy to some extent on the three beer-related datasets. But the improvements on the hotel-related datasets are not significant. The possible reason is that the prediction accuracy of RNP on these datasets is already very high. We also follow CR to conduct a supplement experiment with BERT encoder on the most widely used Beer-Appearance dataset and compare with some other baselines that have been implemented with BERT, and the results are shown in Table 2. We still beat all the baselines.

We show the results for p values of [0,0.1,0.2,0.3,0.4,0.5] in Figure 9 to demonstrate the robustness of our proposed method. In most cases, our method can improve the results of the standard RNP. On the one hand, a higher perturbation rate can bring the predictor a better evaluation of a larger region; on the other hand, an overhigh perturbation rate can also bring a very low signal-to-noise ratio, as mentioned at the beginning of §4.3. We also observe that, for the Appearance and Aroma datasets, p = 0.5 is best, while for other datasets, a lower p = 0.3 is best. This is because in the former two datasets, the gold rationales occupy a larger proportion of the raw input (see the dataset statistics in Table 4 of Appendix A.1), thus have a higher signal-to-noise ratio and are able to tolerate larger perturbations. This phenomenon is consistent with our findings at the beginning of §4.3 that too a high perturbation rate can fail due to the high signal-to-noise ratio (i.e., Empirical observation 4).

Ideally, the human-annotated (i.e., optimal) rationale is most informative and should achieve high prediction accuracy when input to a good predictor. But as illustrated in §4.2, this is not always the case in practice, because the predictor could inaccurately assess the gold rationales. To further demonstrate that our VER can enhance the predictor’s ability to assess rationales, we conducted additional experiments comparing the assessment of human-annotated gold annotated rationales by the RNP’s predictor and the VER’s predictor.

Figure 10(a) and 10(b) shows the predictor’s accuracy/cross-entropy with the inputs being human-annotated rationales (the details of the experimental settings are in Appendix A.5). We observe that our method can make the predictor assess the gold rationales more accurately, which allows the selector to receive more accurate feedback about the gold rationales, thereby correctly increasing the probability of selecting them.

To verify the effectiveness of our method on tasks other than classification, we also perform experiments on the reading comprehension task (using the MultiRC dataset) and the fact extraction and verification task (using the FEVER dataset). The datasets for the above two tasks are taken from the ERASER benchmark (DeYoung et al., 2020).

We mainly compare with the baselines that have already performed experiments on these datasets to avoid unfair comparisons resulted from hyperparameter choices. We follow the settings of NIR to use “bert-base-uncased” as the encoder of both the selector and the predictor (see Appendix A.2) and get the results of the baselines from its original paper. The results are shown in Table 3. We see that our VER is still effective on these two tasks.

In this paper, we first theoretically analyze the common approximation of the mutual information maximization criterion, specifically the minimization of cross-entropy, and its shortcomings when applied to the cooperative self-explanatory framework. We provide extensive empirical evidence to verify the existence and negative impact of this issue in practice. Subsequently, we propose a very simple method to mitigate this problem, achieving considerable improvements compared to existing methods. A potential limitation of our approach is that we only consider correlation, not causation, so a future direction may be to integrate our work with causal research studies.

This work is supported by the National Key Research and Development Program of China under grant 2024YFC3307900; the National Natural Science Foundation of China under grants 62376103, 62302184, 62436003 and 62206102; Major Science and Technology Project of Hubei Province under grant 2024BAA008; Hubei Science and Technology Talent Service Project under grant 2024DJC078; and Ant Group through CCF-Ant Research Fund. The computation is completed in the HPC Platform of Huazhong University of Science and Technology.

We sincerely thank the reviewers and the editor for their valuable feedback and efforts during the review process. They have helped considerably in improving the quality of this paper. We thank Yuankai Zhang for his help in providing more baseline results during the revision.

(McAuley et al., 2012) is a benchmark that consists of comments about beer. It contains three widely used text classification datasets: Beer-Appearance, Beer-Aroma, Beer-Palate. In this datasets, each piece of text is a comment about the beer. For the Beer-Appearance dataset, the classification label is the quality (bad/good, [0,1]) of the beer’s appearance. For Beer-Aroma and Beer-Palate, the classification label is about the aroma and palate, respectively.

(Wang et al., 2010) is a benchmark consists of hotel reviews. It contains three widely used datasets: Hotel-Location, Hotel-Service, Hotel-Cleanliness. In this datasets, each piece of text is a review about a hotel. For the Hotel-Location dataset, the classification label is the quality (bad/good, [0,1]) of the hotel’s Location. For Hotel-Service and Hotel-Cleanliness, the classification label is about the service and cleanliness, respectively.

The statistics of the datasets are in Table 4. Pos and Neg denote the number of positive and negative examples in each set. S denotes the average percentage of tokens in human-annotated rationales to the whole texts. avg_len denotes the average length of a text sequence.

The other two datasets MultiRC and FEVER are taken from the ERASER benchmark (DeYoung et al., 2020). Readers can refer to this benchmark for details.

The code and detailed running instructions is aviable at https://github.com/jugechengzi/Rationalization-VER.

The maximum sequence length is set to 256. We use the Adam optimizer (Kingma and Ba, 2015) with its default parameters, except for the learning rate. The temperature for gumbel-softmax is the default value 1. We implement the code with PyTorch on a RTX4090 GPU. We report the average results of five random seeds, and the seeds are [1,2,3,4,5].

For NIR and our VER, considering they are both variants of the standard RNP, we first manually tune the hyperparameters for RNP, and then apply the hyperparameters to both NIR and VER. For all datasets, we use a learning rate of 0.0001. The batchsize is 128 for the beer-related datasets and 256 for the hotel-related datasets. These hyperparameters are found by manually tuning the standard RNP and are applied to both NIR and our VER.

The core idea of NIR is to inject noise into the selected rationales. We use RNP as its backbone. A unique hyperparameter of NIR is the proportion of noise. Following the method in the original text, we searched within [0.1,0.2,0.3] and found that 0.1 yielded the best results on most datasets, hence we adopted 0.1 for this.

For our VER, the perturbation rate p is searched within [0.1,0.2,0.3,0.4,0.5]. We find that 0.5 is the best for beer-related datasets but 0.3 is best for hotel-related datasets. For fair comparisons with baselines, we uniformly adopt 0.3 for all datasets.

We found that the training of Inter_RAT is very unstable. To avoid potential unfair factors, our main settings are determined with reference to it. Except for the part about sparsity, we used its original hyperparameters for it.

For CR, we just keep the major settings (“bert-base-uncased”, the Beer-Appearance dataset, and the sparsity of 10%) the same as it and copy its results from its original paper.

For the experiments on the MultiRC and FEVER datasets, we follow the settings of NIR and get the results of the baselines from its original paper. Specifically, we use “bert-base-uncased” as the encoder and the rationale sparsity is set to be about 20%.

We first train RNP in the usual manner. After training is completed, we fix both the selector and the predictor. For “model-selected rationale”: The selector receives the raw text of the test set as input and extracts the corresponding rationale Z, which is then input into the predictor to obtain the prediction accuracy/cross-entropy. For “gold rationale”: The human-annotated rationale is directly input into the predictor to obtain the accuracy/cross-entropy.

The range of cross-entropy is from 0 to $∞$⁠. If we take the mean, similar to accuracy, it might be affected by extreme values and fail to reflect the overall situation of the dataset. Therefore, we use the median instead.

Discussing Lipschitz continuity is beyond the scope of this paper and we just follow the computational method for Lipschitz constant as proposed by Liu et al. (2023c), which is described as follows (Appendix A.4 of Liu et al. (2023c)): For each full text in the whole training set, we first generate one rationale Z with the selector and then calculate ∇f_p(Z). Note that here $∇f(Z)∈Rb×d$ is a matrix, where b is the length of the rationale Z which may varies across different rationales and d is the dimension of the word vector. We then take the average along the length of Z and get the unified $∇fp(Z)∈Rd$⁠. Then we calculate ||∇f_p(Z)||₂ and take the maximum value over the entire training set as the approximate L_c.

We first train RNP and VER separately. Then, we extract and fix their predictors. The human-annotated rationales are input into their predictors for testing, yielding the results shown in Figure 10.

This is the experimental setup of Figure 6. The dataset is the most widely used Beer-Appearance. For training iteration, we randomly select α% (here α = 12.5) tokens from each input text X. And the predictor is trained with the randomly selected $Dz$ for 300 epochs. Note that we resample at each iteration. Then, the predictor is fixed and we train the selector just in the same way as the standard RNP. We choose α = 12.5 because we find that when α = 12.5, the final sparsity on the test set is about 15%, which matches the sparsity of our formal experiments in Table 1.