SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Lemma 1 If  $X_{-Z}$  and  $Y$  are  $d$ -separated by  $X_Z$ , we then have that all of the direct causal features in  $X$  must be included in  $X_Z$ :
$$
X _ {- Z} \text {a n d} Y \text {a r e} d \text {s e p a r a t e d b y} X _ {Z} \Longrightarrow X _ {R} \subset X _ {Z}. \tag {10}
$$
The proof is in Appendix B.5. And it's very easy to intuitively understand it: a direct cause has a one-hop path to the label. To block this path, this cause must be included in  $X_Z$ .
Assumption 1 The label  $Y$  has no causal effect on any variables in  $X$ .
Assumption 1 is naturally valid in most real world applications due to the temporal sequence between  $X$  and  $Y$ . We also provide some failure cases of this assumption in Appendix B.6. Assumption 1 specifies that there is no arrow pointing from  $Y$  to any nodes in  $X$ .
Lemma 2 If Assumption 1 holds, we have:
$$
X _ {- Z} \text {a n d} Y \text {a r e} d \text {s e p a r a t e d b y} X _ {Z} \Longleftarrow X _ {R} \subset X _ {Z}. \tag {11}
$$
The proof is in Appendix B.7. Combining Lemma 1 and Lemma 2, we then have:
Theorem 1 If Assumption 1 holds, then all the direct causal features to  $Y$  within  $X$  will be included in  $X_Z$  if and only if  $X_{-Z}$  and  $Y$  are  $d$ -separated by  $X_Z$ :
$$
X _ {- Z} \text {a n d} Y \text {a r e} d \text {- s e p a r a t e d b y} X _ {Z} \Longleftrightarrow X _ {R} \subset X _ {Z}. \tag {12}
$$
Remark. In light of Theorem 1, we understand that if we aim to achieve  $Y \perp X_{-Z}|X_Z$ , we will consequently incorporate all direct causes of  $Y$  into  $X_Z$ . It should be noted that the compactness of  $X_Z$  is facilitated through the sparsity constraint expressed in Equation 4.
4.3 The proposed method
Minimum conditional dependence criterion. Although previous research tried to design various auxiliary modules or regularizers to fix the problems of maximum mutual information criterion (Chang et al., 2020; Yue et al., 2023; Liu et al., 2022), we do not follow them to move on this line. Based on Theorem 1, we propose a distinct criterion for identifying the causal rationale, which involves minimizing the dependence between  $Y$  and the unselected input  $X_{-Z}$ , conditioned on  $X_Z$ :
$$
X _ {Z} ^ {*} = \underset {X _ {Z}} {\arg \min } \mathcal {C} (Y, X _ {- Z} | X _ {Z}), \tag {13}
$$
where  $\mathcal{C}$  is a criterion for dependence. For instance,  $\mathcal{C}$  could take the form of partial correlation (applicable only to linear associations), mutual information, divergence, or the Hilbert-Schmidt Independence Criterion (HSIC) (Gretton et al., 2007), among others.
It then leads to the question of how we can apply this criterion in practice. In this study, we only present a straightforward and practical method to validate our assertion with respect to Theorem 1, leaving the exploration of other measurements for future work. We first rewrite  $Y \perp X_{-Z}|X_Z$  as
$$
P (Y \mid X _ {Z}) = P (Y \mid X _ {Z}, X _ {- Z}) = P (Y \mid X). \tag {14}
$$
Obviously,  $P(Y|X_Z) = P(Y|X)$  if and only if the divergence between the two distributions is zero:
$$
Y \perp X _ {- Z} | X _ {Z} \Longleftrightarrow P (Y | X _ {Z}) = P (Y | X) \Longleftrightarrow D _ {K L} \left(P (Y | X) \| P (Y | X _ {Z})\right) = 0. \tag {15}
$$
Figure 3: The architecture of our proposed MCD. The approximators for the two distributions are shared to reduce the model complexity (this trick is not necessary).
Estimating divergence through approximation. The real distributions of  $P(Y|X_Z)$  and  $P(Y|X)$  are not directly accessible. So we need further efforts to approximate them. We try to approximate them by making use of the predictor. We first approximate  $P(Y|X_Z)$  with  $P(\hat{Y}_Z|X_Z)$  by minimizing the cross-entropy  $H_c(Y, \hat{Y}_Z|X_Z)$ , and we also approximate  $P(Y|X)$  with  $P(\hat{Y}_X|X)$  by minimizing  $H_c(Y, \hat{Y}_X|X)$ , where  $\hat{Y}_Z, \hat{Y}_X$  are the predictor's outputs with the inputs being  $Z$  and  $X$ , respectively.
Thus, the training process for our MCD is depicted in Figure 3: the explainer first generates a rationale candidate  $X_Z$  from the input  $X$ . Subsequently,  $X_Z$  and  $X$  are fed into the predictor to obtain two distributions,  $P(\hat{Y}_Z|X_Z)$  and  $P(\hat{Y}_X|X)$ . By replacing  $X_Z$  with  $f_E(X)$  and  $\hat{Y}$  with  $f_P(\cdot)$ , the overall objective of our model becomes (The pytorch implementation is in Appendix A.2):
$$
\begin{array}{l} \min  _ {\theta_ {p}} E _ {(X, Y) \sim \mathcal {D}} \left[ H _ {c} \left(Y, \hat {Y} _ {Z} \mid X _ {Z}\right) + H _ {c} \left(Y, \hat {Y} _ {X} \mid X\right) \right] \\ + \min  _ {\theta_ {e}} E _ {(X, Y) \sim \mathcal {D}} \left[ D _ {K L} \left(P \left(\hat {Y} _ {X} | X\right) \| P \left(\hat {Y} _ {Z} | X _ {Z}\right)\right) + \Omega (M) \right], \tag {16} \\ \end{array}
$$
$$
s. t., X _ {Z} = f _ {E} (X), P (\hat {Y} _ {X} | X) = f _ {P} (X), P (\hat {Y} _ {Z} | X _ {Z}) = f _ {P} (X _ {Z}).
$$
Notably, although the first term  $H_{c}(Y,\hat{Y}_{Z}|X_{Z})$  is similar to the one used in Equation 3, it is detached from the explainer's parameters  $\theta_e$ . It is now only used to help the predictor approximate the real distribution  $P(Y|X_Z)$  rather than to guide the explainer to find a good rationale.
5.1 Datasets and metrics
Datasets 1) BeerAdvocate (McAuley et al., 2012) is a multi-aspect sentiment prediction dataset widely adopted in rationalization studies. Given the high correlation among the rating scores of different aspects within the same review, rationale selection encounters severe feature correlation challenges. Following INVRAT (Chang et al., 2020) and Inter_RAT (Yue et al., 2023), we utilize the original dataset (which we refer to as correlated BeerAdvocate) to verify MCD's effectiveness in handling both feature correlation and mask correlation simultaneously. 2) HotelReviews (Wang et al., 2010) is another multi-aspect sentiment classification dataset containing less feature correlation, which is used by the latest SOTA method FR (Liu et al., 2022) to evaluate the effectiveness of addressing degeneration. We utilize the Service aspect to further demonstrate the competitive edge of our MCD. Among these datasets, each aspect itself can be seen as a dataset and is trained independently.
Metrics. Considering that the annotators assign the label of the target aspect by observing the causal features, the overlap between the tokens selected by the model and those annotated by humans provides a robust metric for rationale causality. The terms  $P, R, F1$  denote precision, recall, and  $F1$  score respectively. 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.  $Acc$  stands for the predictive accuracy.
5.2 Baselines and implementation details
We compare with various recent MMI-based methods that are highly relevant to our study. These include methods like INVRAT (Chang et al., 2020) and Inter_RAT (Yue et al., 2023), which are
Table 2: Results on correlated BeerAdvocate. Each aspect is trained independently. “*”: results obtained from Inter RAT (Yue et al., 2023). The second best F1 scores are underlined.
Methods	Appearance	Aroma	Palate
S	Acc	P	R	F1	S	Acc	P	R	F1	S	Acc	P	R	F1
RNP*	10.0	-	32.4	18.6	23.6	10.0	-	44.8	32.4	37.6	10.0	-	24.6	23.5	24.0
INVRAT*	10.0	-	42.6	31.5	36.2	10.0	-	41.2	39.1	40.1	10.0	-	34.9	45.6	39.5
Inter-RAT*	11.7	-	66.0	46.5	54.6	11.7	-	55.4	47.5	51.1	12.6	-	34.6	48.2	40.2
FR	11.1	75.8	70.4	42.0	52.6	9.7	87.7	68.1	42.2	52.1	11.7	87.9	43.7	40.9	42.3
MCD(ours)	9.5	81.5	94.2	48.4	63.9	9.9	87.5	84.6	53.9	65.8	9.4	87.3	60.9	47.1	53.1
RNP*	20.0	-	39.4	44.9	42.0	20.0	-	37.5	51.9	43.5	20.0	-	21.6	38.9	27.8
INVRAT*	20.0	-	58.9	67.2	62.8	20.0	-	29.3	52.1	37.5	20.0	-	24.0	55.2	33.5
Inter-RAT*	21.7	-	62.0	76.7	68.6	20.4	-	44.2	65.4	52.8	20.8	-	26.3	59.1	36.4
FR	20.9	84.6	74.9	84.9	79.6	19.5	89.3	58.7	73.3	65.2	20.2	88.2	36.6	59.4	45.3
MCD(ours)	20.0	85.5	79.3	85.5	82.3	19.3	88.4	65.8	81.4	72.8	19.6	87.7	41.3	65.0	50.5
RNP*	30.0	-	24.2	41.2	30.5	30.0	-	27.1	55.7	36.4	30.0	-	15.4	42.2	22.6
INVRAT*	30.0	-	41.5	74.8	53.4	30.0	-	22.8	65.1	33.8	30.0	-	20.9	71.6	32.3
Inter-RAT*	30.5	-	48.1	82.7	60.8	29.4	-	37.9	72.0	49.6	30.4	-	21.8	66.1	32.8
FR	29.6	86.4	50.6	81.4	62.3	30.8	88.1	37.4	75.0	49.9	30.1	87.0	24.5	58.8	34.6
MCD(ours)	29.7	86.7	59.6	95.6	73.4	29.6	90.2	46.1	87.5	60.4	29.4	87.0	30.5	72.4	42.9
focused on addressing feature correlation, as well as methods such as FR (Liu et al., 2022) that aim to mitigate mask correlation (i.e., degeneration). Among these, FR represents the latest SOTA approach in addressing mask correlation, while Inter_RAT stands as the SOTA in handling feature correlation.
Both the explainer and the predictor are composed of an encoder (which can be an RNN or Transformer) and a linear layer. Some of the baseline methods have not provided runnable source codes. To ensure a fair comparison, we keep the major settings consistent with those of the baselines, which are commonly utilized in the field of rationalization (Chang et al., 2020; Yu et al., 2021; Liu et al., 2022; Yue et al., 2023). Specifically, we employ the 100-dimensional GloVe (Pennington et al., 2014) for word embedding and 200-dimensional GRUs (Cho et al., 2014) to obtain text representation. The re-parameterization trick for binarized selection is Gumbel-softmax (Jang et al., 2017). The hyperparameters of the reimplemented baselines are initialized with the values reported in their source codes, and are then manually tuned multiple times to determine the optimal settings. We do not use BERT (Devlin et al., 2019) in the main experiments because some recent research (Chen et al., 2022; Liu et al., 2022; Zhang et al., 2022) has found it to be a challenging task to fine-tune large pretrained models within the rationalization framework (see Appendix A.4 for more discussion). However, as a supplement, we also conduct experiments with two pretrained models, ELECTRA (Clark et al., 2020) and BERT. The optimizer is Adam (Kingma and Ba, 2015). All models are trained on a RTX3090 GPU. More details are in Appendix A.1.
Comparison with SOTA Methods. Table 2 shows the results on correlated BeerAdvocate with the rationale sparsity being about  $10\%$ ,  $20\%$ , and  $30\%$ . We set the sparsity to be similar to previous methods by adjusting the sparsity regularization term (i.e.,  $s$ ) in Equation 4. Compared to MMI-based methods, we gain significant improvements across all three aspects and three different sparsity. In particular, we improve
the F1 score by more than  $10\%$  as compared to the previous SOTA in three settings: in the Aroma aspect with  $S \approx 10$ , the Palate aspect with  $S \approx 10$ , and the Appearance aspect with  $S \approx 30$ . We show an visualized example of the selected rationales in Figure 4. Since our MCD criterion (Equation 13) is not limited to a specific measurement of dependence, we also conduct experiments by replacing KL-divergence with JS-divergence, and the results are in Appendix A.5. Table 3 shows the results on another dataset also used in FR, where DMR (Huang et al., 2021) and A2R (Yu et al., 2021) are two recent MMI-based methods. For this dataset, we follow FR to set the sparsity similar to that of the human-annonated rationales. On this dataset, we still beat all the MMI-based methods. We also show the time efficiency in Appendix A.6.
Inducing mask correlation with skewed explainer. In order to evaluate scenarios where feature correlation is not severe and our primary concern is mask correlation, we follow FR's approach to conduct experiments in a synthetic setting where the explainer is specifically initialized to induce
Table 3: Results on HotelReview. "": results obtained from FR (Liu et al., 2022).
Methods	S	Acc	P	R	F1
RNP*	11.0	97.5	34.2	32.9	33.5
DMR*	11.6	-	43.0	43.6	43.3
A2R*	11.4	96.5	37.3	37.2	37.2
FR*	11.5	94.5	44.8	44.7	44.8
MCD(ours)	11.8	97.0	47.0	48.6	47.8
Table 4: Results of skewed explainer that induces degeneration (i.e., mask correlation) in the Palate aspect of BeerAdvocate. “*”: results obtained from the paper of FR.
Setting	RNP*	FR*	MCD(ours)
Pre_acc	S	Acc	R	R	F1	Pre_acc	S	Acc	P	R	F1	Pre_acc	S	Acc	P	R	F1
skew65.0	66.6	14.0	83.9	40.3	45.4	42.7	66.3	14.2	81.5	59.5	67.9	63.4	66.3	12.9	84.6	61.6	63.7	62.6
skew70.0	71.3	14.7	84.1	10.0	11.7	10.8	70.8	14.1	88.3	54.7	62.1	58.1	70.2	13.5	81.1	59.0	64.0	61.4
skew75.0	75.5	14.7	87.6	8.1	9.6	8.8	75.6	13.1	84.8	49.7	52.2	51.0	75.3	13.4	84.2	61.3	65.1	63.1
Table 5: Results of methods using pretrained ELECTRA as the encoder.
Methods	Appearance	Aroma	Plate
S	Acc	P	R	F1	S	Acc	P	R	F1	S	Acc	P	R	F1
FR-ELECTRA	16.3	86.5	19.1	17.0	18.0	14.8	85.9	58.6	54.8	56.7	11.2	78.0	12.0	10.7	11.3
MCD-ELECTRA	18.5	90.0	84.8	85.6	85.2	14.5	86.6	86.2	78.7	82.3	12.1	85.0	63.0	60.3	61.6
mask correlation, also referred to as degeneration. The details of the initialization can be found in Appendix A.3. Following FR, we utilize the Palate aspect of decorrelated BeerAdvocate dataset (a subset of the original BeerAdvocate that has been filtered by Lei et al. (2016)). This subset contains less feature correlation compared to the original dataset. The results are presented in Table 4, where skew  $k$  and Pre_acc indicates the degree of mask correlation. In this situation, the vanilla RNP fails to identify the causal rationales, and FR is also significantly impacted when the degree of mask correlation is high. Our MCD is much less affected, demonstrating its robustness in such scenarios.
Experiments with pretrained language models. In the field of rationalization, researchers generally focus on frameworks of the models and the methodology rather than engineering SOTA. The methods most related to our work do not use BERT or other pre-trained encoders (Chang et al., 2020; Yu et al., 2021; Liu et al., 2022; Yue et al., 2023). Experiments in some recent work (Chen et al., 2022; Liu et al., 2022) suggest that there are some unforeseen obstacles making it hard to finetune large pretrained models within the rationalization framework. For example,
Table 6: The F1 scores of models trained with different encoders. “*”: results obtained from (Chen et al., 2022). “**”: results obtained from FR. The dataset is decorrelated Beer-Appearance.
Method	GRU	ELECTRA	BERT
VIB*	-	-	20.5
SPECTRA*	-	-	28.6
RND**	72.3	13.7	14.7
FR**	82.8	14.6	29.8
MCD(ours)	80.1	85.2	87.1
Table 6 shows that two improved rationalization methods (VIB (Paranjape et al., 2020) and SPECTRA (Guerreiro and Martins, 2021)) and the latest published FR all fail to find the informative rationales when replacing GRUs with pretrained BERT. To eliminate potential factors that could lead to an unfair comparison, we adopt the most widely used GRUs as the encoders in our main experiments, which can help us focus more on substantiating our claims themselves, rather than unknown tricks. But to show the competitiveness of our MCD, we also provide some experiments with pretrained language models as the supplement. Due to limited GPU resources, we adopt the relatively small ELECTRA-small in all three aspects of BeerAdvocate and the relatively large BERT-base in the Appearance aspect. We compare our MCD with the latest SOTA FR (Liu et al., 2022). We follow FR to set the sparsity similar to human-annotated rationales. More details are in Appendix A.4.
The results with BERT are shown in Table 6 and results with ELECTRA are shown in Table 5. We see that our method can greatly benefit from pretrained models. In fact, recent research has found that finetuning large pretrained models can be easily affected by overfitting (Zhang et al., 2021), and spurious correlations can exacerbate this overfitting, particularly in larger models (Zhou et al., 2022; Lin et al., 2022a), which somewhat explains the great progress achieved by our MCD.
6 Conclusion, future work, and limitations
In this study, we first illustrate the two primary issues of feature correlation and degeneration in MMI-based rationalization under a unified causal perspective. Subsequently, we uncover the conditional independence relationship between the target label and non-causal and causal features. Based on this observation, we propose a criterion of minimizing conditional dependence to concurrently address the two aforementioned problems.
Given the versatility of the self-explaining rationalization framework, our proposed methods show significant potential for application across diverse fields such as computer vision and graph learning. Additionally, with the recent remarkable success of large language models (LLMs), exploring how our MCD can aid in training trustworthy LLMs is another avenue worth pursuing.
Label (aroma aspect): Positive.
Prediction: Positive.
Input: got this one on tap at kelly 's olympian in portland . lighting made the colour difficult to ascertain , but i would be surprised if it were n't a very dark brown . came with a good head which stuck around , adding to the feel of the pint . i 'm useless on the sniff test in these smoky bars , so all i could distinguish was a malty cherry whiff . felt very smooth and went down very easily . was sweeter and more syrupy than i would expect an english brown ale to be . the smell did prove indicative of the initial taste , although where i expected it to give way to a somewhat hoppy finish , a thankfully subtle coffee flavour kicked in instead . i detest coffee , but this was subtle enough to be tolerable .
(a) RNP
Input: got this one on tap at kelly 's olympian in portland. lighting made the colour difficult to ascertain, but i would be surprised if it were n't a very dark brown . came with a good head which stuck around , adding to the feel of the pint . i'm useless on the sniff test in these smoky bars, so all i could distinguish was a malty cherry whiff , felt very smooth and went down very easily . was sweeter and more syrupy than i would expect an english brown ale to be . the smell did prove indicative of the initial taste , although where i expected it to give way to a somewhat hoppy finish , a thankfully subtle coffee flavour kicked in instead . i detest coffee , but this was subtle enough to be tolerable .
(b) Inter_RAT
Prediction: Positive
Input: got this one on tap at kelly 's olympian in portland . lighting made the colour difficult to ascertain , but i would be surprised if it were n't a very dark brown . came with a good head which stuck around , adding to the feel of the pint . i'm useless on the sniff test in these smoky bars , so all i could distinguish was a malty cherry whiff , felt very smooth and went down very easily . was sweeter and more syrupy than i would expect an english brown ale to be . the smell did prove indicative of the initial taste , although where i expected it to give way to a somewhat hoppy finish , a thankfully subtle coffee flavour kicked in instead . i detest coffee , but this was subtle enough to be tolerable .
(d) MCD
Figure 4: An example of selected rationales in the Aroma aspect of BeerAdvocate. The sparsity is set to be about  $10\%$ . The underlined texts are human-annotated rationales. (a): RNP selects palate only. (b): Inter_RAT selects aroma but also palate ("felt very smooth"). (c): FR is similar to Inter_RAT. (d): MCD selects aroma only.
A potential limitation is that, similar to IRM-based methods, our primary focus is on identifying rationales with causal effects, rather than quantitatively computing the precise values of these causal effects. Although quantifying causality often relies on strong assumptions, this quantification may be a desideratum for certain applications. We aim to explore this direction in future work to accommodate a wider range of applications. Another limitation is that we focus on the text classification task. Different tasks may have very different causal structures. Thus, how to extend this method to other tasks is also a challenge that needs to be explored. The third limitation is that the obstacles in utilizing powerful pretrained language models under the rationalization framework remain mysterious. Although we have made some progress in this direction, we have to say that the empirical results with pretrained models are very sensitive to hyperparameter tuning. A recent paper has also shown that very small changes in hyperparameters can lead to significant differences in results (see Remark 6.1 and Appendix G.2 in (Zhang et al., 2023)). To avoid being distracted by irrelevant factors, until this issue is resolved, we call for research papers to use small models to better verify their claims.
This work is supported by National Natural Science Foundation of China under grants 62376103, 62302184, 62206102, and Science and Technology Support Program of Hubei Province under grant 2022BAA046. We are also grateful for the valuable suggestions provided by the anonymous reviewers, which greatly helped to improve the quality of this paper.
Mo Yu, Yang Zhang, Shiyu Chang, and Tommi S. Jaakkola. 2021. Understanding interlocking dynamics of cooperative rationalization. In Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pages 12822-12835.
Hao Yuan, Lei Cai, Xia Hu, Jie Wang, and Shuiwang Ji. 2022. Interpreting image classifiers by generating discrete masks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(4):2019-2030.
Linan Yue, Qi Liu, Li Wang, Yanqing An, Yichao Du, and Zhenya Huang. 2023. Interventional rationalization.
Tianyi Zhang, Felix Wu, Arzoo Katiyar, Kilian Q. Weinberger, and Yoav Artzi. 2021. Revisiting few-sample BERT fine-tuning. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net.
Wenbo Zhang, TONG WU, Yunlong Wang, Yong Cai, and Hengrui Cai. 2022. On causal rationalization. In NeurIPS 2022 Workshop on Causality for Real-world Impact.
Wenbo Zhang, Tong Wu, Yunlong Wang, Yong Cai, and Hengrui Cai. 2023. Towards trustworthy explanation: On causal rationalization. In International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pages 41715-41736. PMLR.
Yiming Zheng, Serena Booth, Julie Shah, and Yilun Zhou. 2022. The irrationality of neural rationale models. In Proceedings of the 2nd Workshop on Trustworthy Natural Language Processing (TrustNLP 2022), pages 64-73, Seattle, U.S.A. Association for Computational Linguistics.
Xiao Zhou, Yong Lin, Weizhong Zhang, and Tong Zhang. 2022. Sparse invariant risk minimization. In International Conference on Machine Learning, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pages 27222-27244. PMLR.