---
title: "Robust Interpretable Text Classification against Spurious Correlations Using AND-rules with Negation"
authors:
  - "Rohan Kumar Yadav"
  - "Lei Jiao"
  - "Ole-Christoffer Granmo"
  - "Morten Goodwin"
doi: "10.24963/ijcai.2022/616"
url: "https://ijcai.org/proceedings/2022/616"
pdf: "https://ijcai.org/proceedings/2022/0616.pdf"
venue: "Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence"
year: 2022
pages: "4439-4446"
track: "Main Track"
keywords:
  - "Natural Language Processing: Text Classification"
  - "Machine Learning: Robustness"
  - "Natural Language Processing: Interpretability and Analysis of Models for NLP"
  - "Natural Language Processing: Applications"
---

# Robust Interpretable Text Classification against Spurious Correlations Using AND-rules with Negation

Rohan Kumar Yadav, Lei Jiao, Ole-Christoffer Granmo, Morten Goodwin

*Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence*, pages 4439-4446. DOI: [10.24963/ijcai.2022/616](https://doi.org/10.24963/ijcai.2022/616)

## Abstract

The state-of-the-art natural language processing models have raised the bar for excellent performance on a variety of tasks in recent years. However, concerns are rising over their primitive sensitivity to distribution biases that reside in the training and testing data. This issue hugely impacts the performance of the models when exposed to out-of-distribution and counterfactual data. The root cause seems to be that many machine learning models are prone to learn the shortcuts, modelling simple correlations rather than more fundamental and general relationships. As a result, such text classifiers tend to perform poorly when a human makes minor modifications to the data, which raises questions regarding their robustness. In this paper, we employ a rule-based architecture called Tsetlin Machine (TM) that learns both simple and complex correlations by ANDing features and their negations. As such, it generates explainable AND-rules using negated and non-negated reasoning. Here, we explore how non-negated reasoning can be more prone to distribution biases than negated reasoning. We further leverage this finding by adapting the TM architecture to mainly perform negated reasoning using the specificity parameter s. As a result, the AND-rules becomes robust to spurious correlations and can also correctly predict counterfactual data. Our empirical investigation of the model's robustness uses the specificity s to control the degree of negated reasoning. Experiments on publicly available Counterfactually-Augmented Data demonstrate that the negated clauses are robust to spurious correlations and outperform Naive Bayes, SVM, and Bi-LSTM by up to 20 %, and  ELMo by almost 6 % on counterfactual test data.

## Full text

## 1 Introduction

Despite impressive advances of Deep Neural Network (DNN) architectures for Natural Language Processing (NLP), their implementations still suffer from various challenges. One of the challenges is associated with DNN's capability of learning simple correlations and ignoring more complex ones [Sauer and Geiger, 2021]. This behavior of DNN becomes questionable when the simple correlation is spurious and absent from the test data, or occurs in an unfitting context. For instance, in the sentence Nolan's films are always great mostly because of his excellent direction, the influential word for predicting a positive sentiment should be "great" and "excellent" instead of "Nolan's" and "direction". However, due to the majority of samples consist of "Nolan having a great movie", it makes the classifier learn that "Nolan" corresponds to a positive sentiment word [Wang and Culotta, 2020]. Similarly, a toxicity classifier learns that "gay" corresponds to a toxic comments [Wulczyn et al., 2017] and a medical diagnosis classification system learns the disease associated with the patient ID [Kaufman et al., 2012] The issue of spurious patterns also moderately impacts the out-ofdistribution (OOD) generalization of models that are trained on independent identical distribution (IID) data, resulting in performance degradation when the distribution shifts.

Researchers recently have found that the decay in model performance, as well as social bias in NLP, appear out-ofdomain due to sensitivity towards spurious signals. One of the solutions to deal with such vulnerability in NLP models is data augmentation with counterfactual samples [Kaushik et al., 2020], which can help the model with learning real causal correlations between input and labels. For instance, a man-made counterfactual sample of the last example could be Nolan's films are always boring mostly because of his poor direction. Inserting such counterfactual data into the original training sets has shown to be beneficial for learning real causal correlation thereby improving the robustness of the model [Kaushik et al., 2020]. However, augmentation with counterfactual data usually relies on a human-in-the-loop system to generate sentiment-flipped samples. For this process, humans are asked to make minimal and believable edits to generate counterfactual samples. Even though such an addition of data makes the model robust against spurious correlations, completing a human-in-the-loop process is costly and time-consuming.

The main reason behind the failure of DNNs on counterfactual data during inference is still unclear because of their black-box nature [Rudin, 2018]. What they learn from the data that limits the models' robustness against different distribution samples is currently an open research question. Some researchers argue that the attention mechanism provides an explanation of DNN models, which assigns soft weights to the input representations, and then extracts highly weighted tokens as rationales [Bahdanau et al., 2015]. However, these attention weights do not provide faithful explanations for classification [Serrano and Smith, 2019; Brunner et al., 2020]. In addition, DNNs fail to conduct logical reasoning in various tasks. Logical reasoning is one of the most important prerequisites in NLP that supports various practical applications such as legal assistants, medical decision support, and personalized recommender systems. Due to these issues, DNNs have failed to demonstrate their robustness on counterfactual data. On the other hand, a rulebased knowledge system is a powerful tool that offers logical reasoning because of its explainability. However, most rule-based systems rely on static rules that are hand-crafted. Without learning capability, the performance and generalization is limited. Keeping these two challenges in consideration, we employ a recent architecture called Tsetlin machine (TM), which is an interpretable rule-based model that learns both simple and complex correlations via conjunctive clauses [Granmo, 2018]. Unlike DNNs and simple rule-based architectures, TM learns rules with logical reasoning as a human does and it also offers a transparent and interpretable learning [Yadav et al., 2021a]. Such rule-based logical reasoning is important for processing counterfactual data, and we here study the TM robustness towards counterfactual test data compared with DNNs. In addition, we demonstrate how TM supports reasoning with negation, which is completely different from attention-based DNN models. The main contributions of the paper are as follows:

- We design a TM-based approach that is robust to spurious correlations on counterfactual and out-of-domain data, without any data augmentation.
- Our in-depth analysis of TM specificity parameter s records transparent learning and explainable predictions on counterfactual data.

## 2 RelatedWork

Many recent papers have shown that the DNN-based NLP models do not seem to learn the aspects that humans seem important for a particular classification. The state-of-theart models have been vulnerable to fabricated transformations. Effective fabrications include distractor phrases, adversarial example generation with paraphrasing, and templatebased modifications. As the result, researchers develop counterfactual data augmentation approaches for building robust classifiers [Lu et al., 2020] to eliminate the effect of spurious correlations. In attempt to augment counterfactual data, [Kaushik et al., 2020] develops a human-in-the-loop system using crowd-sourcing methods [Kaushik et al., 2020]. It is shown that such augmented data makes the trained model robust not only to counterfactual data but also to outof-domain datasets. However, due to the fact that crowdsourcing is time-consuming and expensive, an automatic augmentation of counterfactual data with causal identification is proposed [Wang and Culotta, 2020]. Here, causal words are employed to generate counterfactual data using BERT sentence similarity.

Apart from data augmentation, there has been little research on studying the reason for the failure of ML models for counterfactual data. Perception and reasoning are two crucial abilities a model needs for successful problem-solving. Recent ML models such as DNNs have shown extraordinary performance in various perception tasks [Krizhevsky et al., 2012]. However, such models hardly exploit refined domain knowledge in symbolic form in order to support reasoning. Despite the recent DNNs' ability to consider relational and differential knowledge representation, they still lack comprehensive logical reasoning across the dataset [Jia and Liang, 2017]. Hence, there has been an increasing interest in combining ML with logical reasoning especially in the field of NLP. For instance, Fuzzy Logic [Goguen, 1973], Statistical Relational Learning [Getoor and Taskar, 2007], and Probabilistic Logic Programming [Raedt and Kimmig, 2015] have come into the picture to enhance traditional logic-based methods. However, they often require handcrafted symbols as input from humans. There has been little research on alternative ML models that have a learning ability comparable to DNN and also possess human-like logical reasoning.

Since counterfactual inference is all about understanding the logical reasoning behind the training data, we here incorporate a recent ML model, TM [Granmo, 2018], which not only offers a transparent learning mechanism but also facilitates human-level model interpretation [Yadav et al., 2021a]. Unlike DNN attention weights that arguably explain predictions after training, the TM learning process itself is fully transparent and produces logically explainable prediction [Yadav et al., 2021b]. Indeed, TM has been widely accepted for its interpretability and logical reasoning [Lei et al., 2021; Abeyrathna et al., 2021]. Hence, in this paper, we propose and investigate how TM can deal with counterfactual test data as well as out-of-domain distributions. We further show that it produces rules as human-like logical reasoning and is more robust than DNNs. In particular, we explore its interpretability in-depth contrasting the logic-based rules with the attention weights utilized by DNNs. Thereby, we analyse the reasons that explain TM's robustness against spurious correlations. To our knowledge, this is the first time that a rulebased human-level interpretable model is used to tackle spurious correlations.

## 3 Detailed Implementation

## 3.1 TsetlinMachine

TM is a recent ML model that learns correlations between features and labels using propositional logic [Granmo, 2018]. A propositional logic formula in TM, namely a clause, is a conjunction of negated and non-negated forms of the input features. The negated or non-negated forms of the input features are known as literals and are controlled by a set of Tsetlin Automata (TA). In a simple way, each input feature corresponds to two TAs, i.e., TA and TA'. TA controls the original (non-negated) form of the literal whereas TA' controls its negation. Each TA decides either to include or exclude the literal, and has two actions (Include/Exclude) with 2N states. When a TA moves from state 1 to N, action Exclude is performed. When a TA moves from state N + 1

to 2N, it performs the Include action. Each move of TA is triggered by feedback in the form of Reward, Penalty, or Inaction [Granmo, 2018].

The most important component of TM is the clause, which represents a certain sub-pattern among a particular set of patterns. This sub-pattern is in propositional AND-form making it highly interpretable and amendable for logical understanding of the task. To have a clear comprehension of what a clause looks like, let us consider a bag-of-words input X = [x1, · · · , xn], xk ∈ {0, 1}, k ∈ {1, . . . , n} where xk = 1 means the presence of a word in the sentence and n is the size of the vocabulary. Let us assume there are γ classes in total. If each class needs α clauses to learn the pattern, altogether the model is represented by γ×α clauses C κ ι , 1 ≤ κ ≤ γ, 1 ≤ ι ≤ α, as:

<!-- formula-not-decoded -->

where I κ ι and ¯ I κ ι are non-overlapping subsets of the input variable indices, I ικ , ¯ I ικ ⊆ {1, · · · , n}, I ικ ∩ ¯ I ικ = ∅. I κ ι represents the set of indices of the features that the TAs include in original form, while the set ¯ I κ ι contains the indices of the features that the TAs include in negated form.

Here, clauses with odd indexes in each class are allocated positive polarity (+), whereas those with even indexes are assigned negative polarity (-). Positive polarity clauses vote in favor of the target class, while negative polarity clauses vote against it. As demonstrated in Eq. (2), a summation operator aggregates them by subtracting the total number of negative votes from the total number of positive votes.

<!-- formula-not-decoded -->

For γ classes, the final output ˆ y is given by the argmax operator to classify the input based on the highest net sum of votes, as shown in Eq. (3).

<!-- formula-not-decoded -->

## 3.2 Learning Rule-based Clauses for Counterfactual Inference

The step-by-step explanation for the learning process of TM can be found in [Yadav et al., 2021b]. Here we explain briefly the learning of the rule-based clauses in TM for counterfactual inference via an example. Let the sentence "Long, boring, blasphemous. Never have I been so glad to see ending credits roll." be the training sample that has negative sentiment. Each of the input words in the sentence is controlled by two TAs where TA controls non-negated literal such as "Long", and TA' controls the negated form such as "¬Long". The input that represents this particular sample is a sparse Boolean bag-of-words. All the vocabulary words that are present in the given sentence get the truth value 1, while those absent get the truth value 0. By explicitly representing missing words in vector form like [0, 0, 0, 1, 0, · · · , 0, 1, 0, 0, 0, 1], the representation becomes dense. However, logically, such representation not only captures the presence of a particular word, but also equally well represents those words that are not present. This explicit bag-of-words representation is ideal for TMs. This is because the TM can then pick informative negated features in the very first hundred iterations of learning using the selection parameter specificity (s). We detail the role of s next.

Table 1: The Type I Feedback.

| Input           | Clause - Literal   | 1     | 0     | 0 - 1   | 0     |
|-----------------|--------------------|-------|-------|---------|-------|
| Include Literal | P(Reward)          | s-1 s | NA    | 0       | 0     |
| Include Literal | P(Inaction)        | 1s    | NA    | s-1 s   | s-1 s |
| Include Literal | P(Penalty)         | 0     | NA    | 1s      | 1s    |
| Exclude Literal | P(Reward)          | 0     | 1s    | 1s      | 1s    |
| Exclude Literal | P(Inaction)        | 1s    | s-1 s | s-1 s   | s-1 s |
| Exclude Literal | P(Penalty)         | s-1 s | 0     | 0       | 0     |

Table 2: The Type II Feedback.

| Input           | Clause - Literal   |   1 | 1 - 0   |   0 - 1 |   0 |
|-----------------|--------------------|-----|---------|---------|-----|
| Include Literal | P(Reward)          |   0 | NA      |       0 |   0 |
|                 | P(Inaction)        | 1.0 | NA      |     1.0 | 1.0 |
|                 | P(Penalty)         |   0 | NA      |       0 |   0 |
| Exclude Literal | P(Reward)          |   0 | 0       |       0 |   0 |
| Exclude Literal | P(Inaction)        | 1.0 | 0       |     1.0 | 1.0 |
| Exclude Literal | P(Penalty)         |   0 | 1.0     |       0 |   0 |

In TM, each TA that controls a literal decides the action "Include" or "Exclude" based on the feedback it receives. There are two types of feedback: Type I Feedback and Type II Feedback, shown in Tables 1 and 2 [Granmo et al., 2019]. Type I Feedback is activated when a given input feature is either correctly assigned to the target label (true positive) or mistakenly ignored (false negative), while Type II Feedback is activated when an input feature is wrongly assigned to the target label (false positive). From Tables 1 and 2 we can see that parameter s, s ≥ 1, plays a very important role in the learning process, as it controls how strongly the model favours the action "Include". It also determines how many "fine-grained" sub-patterns the clauses will acquire. The greater the value of s, the more the TAs are encouraged to include literals in their clauses. Since s decides which literals take part in the clause for classification, it is vital to finetune it for reducing the vulnerability against spurious correlation. For the above-mentioned training example, when s is large, the states for the corresponding TAs in a clause after training are shown in Fig. 1. As seen, the high value of s enforces TA to include many literals in the clause, such as including "ending", "boring", "credits", "¬friendly", "¬good", and "¬like". Among the included literals, spurious correlations that do not carry sentiment information, such as "ending" and "credits", indeed influence the model's prediction on counterfactual data.

When we have a small s, as shown in Fig. 2, the number of included literals is reduced and the majority, if not all, of the included literals are in the negated form. One can see from the figure that the non-negated literals are now not enforced to be included in the clause. The states in TA for "ending", "boring", and "credits" have not reached to action "Include". Nevertheless, TM still learns negated features easily in contrast to non-negated features due to sparse input representation thereby not affecting the states of "¬friendly", "¬good", and "¬like".

Figure 1: States of TAs when s is high for a particular clause.

![Image](https://ijcai.org/proceedings/2022/fulltext/616/image_000000_217059d9e09d152818790f257c6ead38462fe958fac33adf3aaae66559e3d962.png)

Figure 2: States of TAs when s is low for a particular clause.

![Image](https://ijcai.org/proceedings/2022/fulltext/616/image_000001_ed4cfb54d570b5f9111f793e038c5920dcf063f05d3c90864c016fc701aeda26.png)

## 3.3 Robustness against Counterfactual Sample

In this subsection, we will detail the reason why a trained TM model is robust and insusceptible to spurious correlations. Let us consider a model trained with a low value of s = 2 and two sentences with different sentiment labels: S1 with positive and S2 with negative sentiment. From Fig. 3, we can see the behavior of trained clauses for the negative class and the positive class for the original samples. The rulebased logic that is formulated by TM is in propositional form, ANDing several literals. The clause associated with propositional logic becomes 1 if an input satisfies the conjunction.

When context S1 is received by the model, it correctly predicts negative sentiment because it triggers all the five clauses in the negative class, whereas only one clause for the positive class. Similarly, when S2 is given, it predicts positive sentiment because the input triggers all five clauses in the positive class compared to only one clauses in the negative class.

Now consider two human generated counterfactual samples Scf 1 for S1 and Scf 2 for S2 as shown in Fig. 4. For S1, the word "boring" is replaced by "fascinating"; "blasphemous" is replaced by "soulful"; and "glad" is replaced by "sad". Similarly, for S2, the word "friendly" is replaced by "depressing"; "charming" is replaced by "charmless"; and "unpretentious" is replaced by "pretentious". This means that the labels for the corresponding counterfactual samples are now flipped. When Scf 1 is sent to the trained TM model with s = 2, it only triggers two clauses from the negative class and three clauses in the positive class. Similarly, when Scf 2 is given to the model, it triggers four clauses in the negative class but only one clause in the positive class. Even though the probability of being in a class decreases due to the reduction in clause score, it still manages to predict such counterfactual samples correctly.

Since most of the entries in the sparse bag-of-word representation are zeros, the majority of literals presented in the clause will be in the negated form after a few iterations. With a comparatively small number of included literals due to the small s, the majority of clauses most likely becomes monotone in the negated form. Negated literals provide a more general form of the features that are not presented in a particular input sample thereby being less sensitive to spurious correlations as compared with the non-negated literals. We can clearly observe from Fig. 4 that the non-monotone clauses that have non-negated features are the ones that fail to capture counterfactual reasoning. This means monotonous clauses that have only negated features are more insusceptible to such modified data.

## 4 Experiments and Results

In this section, we present experimental results for analyzing the performance of TM on counterfactual data. As we have already discussed the significance of s for inheriting robustness in the model, we experiment with different values of s on the dataset designed by [Kaushik et al., 2020] 1 . This dataset has been developed using IMDB reviews that consist of 50k samples divided equally across train/test splits after removing 20% of reviews. Among them, 2.5k reviews have been split into training, validation, and testing of 1707, 245, and 488 respectively. These reviews are modified using Amazon's Mechanical Turk crowdsourcing so that the labels are flipped to generate counterfactual samples. In addition, to evaluate the out-of-domain performance of the proposed model, we used Amazon reviews [Ni et al., 2019] on data aggregated over six domains, i.e., beauty, fashion, appliances, gift cards, magazines, and software, SemEval Twitter sentiment analysis [Rosenthal et al., 2017], and Yelp challenge dataset.

We used the original 1.7k samples as the training dataset to evaluate the robustness of the model on human-generated counterfactual test data of size 488. We also train the model using counterfactual data of size 1.7k and evaluate it on the original test samples of size 488. The performance of the model for various values of s is shown in Table 3. Other parameters of TM are the same for all the training datasets selected in the paper, with 3000 clauses per class and the threshold (T) value of 80 × 16. These parameters are selected by trial and error. For evaluating the behavior of s, we only validate on the test samples that are not from the same training data, and the complete performance evaluation is detailed later in the paper. Here, we use the features extension technique as the preprocessing as in [Yadav et al., 2021a]. As seen in Table 3, the accuracy of the model trained on original training samples achieves 72.1% on counterfactual test data when s = 2, and it decreases as s increases. Similarly, the accuracy of the model trained on counterfactual training samples achieves 65.20% when s = 2 and decreases as s increases. This indicates that lowering the value of s fine grains the pattern in the clause with negated literals, which confirms the robustness against counterfactual data as discussed earlier.

[1 https://github.com/acmi-lab/counterfactually-augmented-data](https://github.com/acmi-lab/counterfactually-augmented-data)

Figure 3: Clause triggered by original samples S1 and S2 on both classes when s = 2.

![Image](https://ijcai.org/proceedings/2022/fulltext/616/image_000002_70943cb4ee159664ece997723e1ea20da5e8819e8204d671f51af9ee6741366f.png)

Figure 4: Clauses triggered by counterfactual samples Scf 1 and Scf 2 on both classes when s = 2.

![Image](https://ijcai.org/proceedings/2022/fulltext/616/image_000003_9452536ea8e79b342e3587d7cb0976932417350cd146fd54ce23f3e6b93046c0.png)

To compare the performance of our model with the state of the art, extensive experiments have been carried out. Since s = 2 performs the best against counterfactual samples, we utilize this value for performance comparison. In addition to DNN based models, we also include typical interpretable linear models in our comparison. The models are mainly taken from [Kaushik et al., 2020], as: ·Standard Methods: We train linear standard model such as SVM and Naive Bayes (NB) for sentiment classification using "scikit-learn" [Kim et al., 2016]. ·Bi-LSTM: For training Bi-LSTM, Kaushik et al. [Kaushik et al., 2020] restricted vocabulary of 20k, replacing out-of-vocabulary as UNK tokens. The model consists of bidirectional LSTM with hidden dimension 50, recurrent dropout 0.5, and global max pooling following the embedding layer. ·ELMo: Kaushik et al. [Kaushik et al., 2020] computed contextualized word representation (ELMo) using character based word representation and bidirection LSTM [Peters et al., 2018] using weighted sum of representation of 1024 dimensions. ·BERT: Kaushik et al. [Kaushik et al., 2020] used an off-the-shelf uncased BERT Base model to fine tune each task. In order to consider the BERT's sub tokenization, token length is set at 350 and trained for 20 epochs.

As we can see from Table 4, when the original data is used as the training samples, SVM's accuracy on CF test data drops to 51.0% compared with that of the original test data, i.e., 80%. A similar trend is observed for NB, Bi-LSTM, and ELMo. Interestingly, the performance of BERT suffers less perhaps due to the benefit of large pretrained information. However, disregarding the pre-trained language model of BERT, our proposed TM reaches 73.56% and outperforms all of the remaining models including 66.7% of ELMo. In the case of CF data as the training samples, the accuracy on original test samples by previous best model ELMo is 63.8% except BERT. Again, our proposed TM model outperforms all of them except BERT, achieving 65.98%. Although the main aim of the paper is to evaluate TM on different/counterfactual distribution and it is not necessary to augment both original and CF data, we still show the performance using augmented data as well as the remaining IMDB data of size 19k as training samples, and it can be seen that the performance of TM is on par with the other models.

Here, we demonstrate the performance of various models trained using original and counterfactual data on out-ofdomain balanced test data, as shown in Table 5. For a comparison, we again use preprocessing for feature extension from Glove embedding as in [Yadav et al., 2021a]. The results of other models such as SVM, NB, Bi-LSTM, ELMo and BERT have been taken from [Kaushik et al., 2020]. Here when original data is used as the training sample, understandably, BERT outperforms the other models in all the cases because of its access to huge data and better language understanding than traditional models. Disregarding BERT and ELmo as these have huge pretrained information, TM outperforms all the cases of out-of-domain datasets when trained on only original 1.7k samples as intended. However, when the CF data is added to the original training sample, the performance of all the models increases by a big margin but the change for TM is not very significant compared with other models. This results in some lower accuracy compared to SVM and NB in Semeval and Yelp reviews. This is because TM has been initialized with a low value of s = 2 and most of the features in the clauses are generally in the negated form. For this reason, TM is already less sensitive to spurious correlations and the additional CF training data does not impact much. Hence, only with original training sample of 1.7k, TM outperforms all the previous model combating spurious correlations.

Table 3: Accuracy of TM on Counterfactual (CF) test data using Original (Orig) training samples and vice-versa for various values of s.

| Training Data   | s = 2 - Orig   | s = 2 - CF   | s = 3 - Orig   | s = 3 - CF   | s = 5 - Orig   | s = 5 - CF   | s = 10 - Orig   | s = 10 - CF   | s = 15 - Orig   | s = 15 - CF   | s = 20 - Orig   | s = 20 - CF   | s = 30 - Orig   | s = 30 - CF   | s = 50 - Orig   | s = 50 - CF   |
|-----------------|----------------|--------------|----------------|--------------|----------------|--------------|-----------------|---------------|-----------------|---------------|-----------------|---------------|-----------------|---------------|-----------------|---------------|
| Orig (1.7k)     | -              | 72.1         | -              | 71.1         | -              | 68.87        | -               | 65.53         | -               | 64.73         | -               | 60.64         | -               | 58.63         | -               | 54.31         |
| CF (1.7k)       | 65.20          | -            | 63.92          | -            | 62.45          | -            | 62.92           | -             | 61.01           | -             | 59.01           | -             | 57.70           | -             | 54.27           | -             |

Table 4: Experiment results of various models trained using Original and Counterfactual training dataset on their respective opposite test data. The upper results show the best reproducible accuracy and lower ones represent the mean and standard deviation of the last 50 epochs when running the model for five times.

| Training Data    |   SVM - Orig |   SVM - CF |   NB - Orig |   NB - CF |   ELMo - Orig |   ELMo - CF |   Bi-LSTM - Orig |   Bi-LSTM - CF |   BERT - Orig |   BERT - CF | TM - Orig            | TM - CF              |
|------------------|--------------|------------|-------------|-----------|---------------|-------------|------------------|----------------|---------------|-------------|----------------------|----------------------|
| Orig (1.7k)      |         80.0 |       51.0 |        74.9 |      47.3 |          81.9 |        66.7 |             79.3 |           55.7 |          87.4 |        82.2 | 85.65 (84.30 ± 0.78) | 73.56 (72.1 ± 0.40)  |
| CF (1.7k)        |         58.3 |       91.2 |        50.9 |      88.7 |          63.8 |        82.0 |             62.5 |           89.1 |          80.4 |        90.8 | 65.98 (65.20 ± 0.80) | 92.20 (91.09 ± 0.55) |
| Orig (19k)       |         87.8 |       60.9 |        84.3 |      42.8 |          86.5 |        64.3 |             86.3 |           68.0 |          93.2 |        88.3 | 88.14 (87.94 ± 0.16) | 73.77 (72.46 ± 0.70) |
| Orig + CF (3.4k) |         83.7 |       87.3 |        86.1 |      91.2 |          85.0 |        92.0 |             81.5 |           92.0 |          88.5 |        95.1 | 84.22 (83.45 ± 0.42) | 91.2 (89.95 ± 0.75)  |

Table 5: Results on out-of-domain balanced test data.

| Training Data                      | SVM                                | NB                                 | ELMo                               | Bi-LSTM                            | BERT                               | TM                                 |
|------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------|
| Accuracy on Amazon Reviews         | Accuracy on Amazon Reviews         | Accuracy on Amazon Reviews         | Accuracy on Amazon Reviews         | Accuracy on Amazon Reviews         | Accuracy on Amazon Reviews         | Accuracy on Amazon Reviews         |
| Orig (1.7k)                        | 74.7                               | 66.9                               | 79.1                               | 65.9                               | 80.0                               | 76.2                               |
| Orig + CF (3.4k)                   | 77.1                               | 82.6                               | 78.4                               | 82.7                               | 85.1                               | 78.5                               |
| Accuracy on Semeval 2017 (Twitter) | Accuracy on Semeval 2017 (Twitter) | Accuracy on Semeval 2017 (Twitter) | Accuracy on Semeval 2017 (Twitter) | Accuracy on Semeval 2017 (Twitter) | Accuracy on Semeval 2017 (Twitter) | Accuracy on Semeval 2017 (Twitter) |
| Orig (1.7k)                        | 61.2                               | 64.6                               | 69.5                               | 55.3                               | 79.3                               | 65.2                               |
| Orig + CF (3.4k)                   | 66.5                               | 73.9                               | 70.0                               | 68.7                               | 82.9                               | 66.2                               |
| Accuracy on Yelp Reviews           | Accuracy on Yelp Reviews           | Accuracy on Yelp Reviews           | Accuracy on Yelp Reviews           | Accuracy on Yelp Reviews           | Accuracy on Yelp Reviews           | Accuracy on Yelp Reviews           |
| Orig (1.7k)                        | 81.8                               | 77.5                               | 82.0                               | 78.0                               | 85.3                               | 82.5                               |
| Orig + CF (3.4k)                   | 87.6                               | 89.6                               | 87.2                               | 86.2                               | 89.4                               | 85.7                               |

## 5 Global Interpretation of TMon Spurious Correlation

The fundamental of TM is the clauses in propositional logic that learn the sub-pattern for a particular task. Hence, TM can be accessed to have multiple forms of interpretation. Generally, two forms of interpretation are highly accepted, namely Global Interpretation and Local Interpretation.

- Global Interpretation: From Eq. (2), we can obtain the clause score for each feature of a trained model. This

Figure 5: Visualization of words' weightages of attention based model vs TM on a counterfactual sample.

| Model                                                 | Word's Weightage in the Sentence                                                                                                                                                                                                                                                                                               | Sentiment Label                        |
|-------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------|
| Bi-LSTM with Attention Visualization                  | Really good movie. Maybe the best I've ever seen. Alien invasion, a la The Blob, with crazy good acting. Meteorite turns beautiful woman into a host body for nasty tongue. Engaging plot, great tongue. Absurd comedy worth watching. Maybe don't wash your hair or take out the trash but take time out to watch this movie. | Original: Positive Predicted: Negative |
| Word's weightage based on clause score (TM with s=20) | Really good movie. Maybe the best I've ever seen. Alien invasion, a la The Blob, with crazy good acting. Meteorite turns beautiful woman into a host body for nasty tongue. Engaging plot, great tongue. Absurd comedy worth watching. Maybe don't wash your hair or take out the trash but take time out to watch this movie. | Original: Positive Predicted: Negative |
| Word's weightage based on clause score (TM with s =2) | Really good movie. Maybe the best I've ever seen. Alien invasion, a la The Blob, with crazy good acting. Meteorite turns beautiful woman into a host body for nasty tongue. Engaging plot, great tongue. Absurd comedy worth watching. Maybe don't wash your hair or take out the trash but take time out to watch this movie. | Original: Positive Predicted: Positive |

clause score provides the weightage of each input on the model. It has been employed in many applications such as word scoring mechanism [Bhattarai et al., 2022] and novelty detection [Bhattarai et al., 2020].

- Local Interpretation: Local interpretation is achieved by analyzing the form of propositional logic. It can be observed by visualizing each clause that votes for the particular input. This interpretation is an important feature of TM since it offers rule-based logic to explain the prediction, such as for sentiment analysis [Yadav et al., 2021b]. This is explained in detail in Section 3.

Since we have already shown the local interpretation previously in Figs. 3 and 4 when learning is introduced, here we demonstrate the benefit of our approach against the spurious correlation using the global interpretation of the model. We examine how the weightage of each feature changes as a function of s. In more detail, we calculate the clause score of each word in the selected vocabulary via Eq. (2). Since the vocabulary is huge, for ease of illustration, we select the highest weighted 20 words for illustration. When we train the model using s = 20, words such as bad, worst, horror, 1, and 2 are the most important features that represent the negative class as shown in Table 6. However, there are certain words such as minutes, money, instead, reason, and plot that do not necessarily carry the sentiment of the context but are still highly correlated to negative sentiment. Similarly, words such as family, young, performances, especially, lives, life, and gives that do not carry positive sentiment are present as highest weighted words in positive class. On the other hand, when the model is trained using s = 2, we can see that such words are removed from the given list as shown in Table 7. Table 8 shows the detail of genuine and spurious correlation for two different values of s for the top 50 words. It clearly shows that the number of spurious correlations reduces significantly, making the model robust.

Table 6: Clause scores (weightages) of top 20 words for each sentiment class when the model is trained using s = 20.

| Negative Class - Words   |   Negative Class - Clause Score | Positive Class - Words   |   Positive Class - Clause Score |
|--------------------------|---------------------------------|--------------------------|---------------------------------|
| bad                      |                            1218 | great                    |                            2483 |
| worst                    |                             560 | wonderful                |                            2052 |
| horror                   |                             344 | romantic                 |                            2038 |
| terrible                 |                             229 | excellent                |                            1951 |
| boring                   |                             233 | perfect                  |                            1913 |
| awful                    |                             281 | love                     |                            1910 |
| waste                    |                             310 | family                   |                            1883 |
| poor                     |                             494 | young                    |                            1863 |
| worse                    |                             609 | best                     |                            1834 |
| stupid                   |                             644 | beautiful                |                            1801 |
| horrible                 |                             660 | especially               |                            1788 |
| 1                        |                             705 | enjoyed                  |                            1768 |
| minutes                  |                             769 | loved                    |                            1748 |
| money                    |                             769 | lives                    |                            1736 |
| instead                  |                             821 | life                     |                            1734 |
| reason                   |                             831 | performances             |                            1710 |
| poorly                   |                             844 | highly                   |                            1710 |
| plot                     |                             864 | performance              |                            1708 |
| dull                     |                             876 | amazing                  |                            1705 |
| 2                        |                             881 | gives                    |                            1697 |

## 6 ACase Study of TMvs Bi-LSTM

In this section, we will compare the weightage of each word in the sentence responsible for a particular prediction. We here visualize the attention weight to explain the model's prediction. For TM, we use the clause score for each word in the sentence and visualize it in a similar way to the attention model. To have a clear interpretation of how s impacts the counterfactual data, we represent two scenarios where the model is trained with s = 2 and s = 20. From Fig. 5, we can see that a particular sample has been predicted incorrectly by the Bi-LSTM model. The scoring of the word shows that Bi-LSTM assigns the highest weightage to spurious correlations such as ever, seen, Alien, Blob, with, and wash. Although it gives attention to some genuine correlations such as crazy, worth, and beautiful, the weightage is low compared with spurious correlations thereby making a wrong prediction. For TM with s = 20, it has high clause scores on spurious correlations such as really, movie, acting, plot, and woman. Although the TM assigns weightage to words such as beautiful, good, and engaging, the weightage for negative sentiment words such as don't, absurd, and nasty are much higher thereby predicting it incorrectly to negative sentiment. On the other hand, for TM with s = 2, it assigns high scores to genuine correlations such as beautiful, engaging, best, good, comedy and great as compared with spurious correlations such as movie, woman, Blob, time, and watch thereby correctly predicting a positive sentiment.

Table 7: Clause scores (weightages) of top 20 words for each sentiment class when the model is trained using s = 2.

| Negative Class - Words   |   Negative Class - Clause Score | Positive Class - Words   |   Positive Class - Clause Score |
|--------------------------|---------------------------------|--------------------------|---------------------------------|
| worst                    |                            2057 | romantic                 |                            1875 |
| horror                   |                            2027 | perfect                  |                            1418 |
| terrible                 |                            1518 | wonderful                |                            1335 |
| waste                    |                            1515 | excellent                |                            1057 |
| awful                    |                            1443 | enjoyed                  |                             948 |
| bad                      |                            1254 | romance                  |                             874 |
| boring                   |                            1254 | great                    |                             871 |
| worse                    |                            1131 | loved                    |                             856 |
| poor                     |                            1077 | favorite                 |                             743 |
| poorly                   |                             834 | heart                    |                             683 |
| horrible                 |                             802 | 8                        |                             671 |
| 1                        |                             796 | lives                    |                             660 |
| stupid                   |                             791 | beautiful                |                             657 |
| pointless                |                             685 | recommended              |                             657 |
| pathetic                 |                             580 | wonderfully              |                             645 |
| effort                   |                             566 | highly                   |                             642 |
| dull                     |                             562 | feelings                 |                             641 |
| badly                    |                             522 | drama                    |                             617 |
| lacks                    |                             515 | amazing                  |                             611 |
| money                    |                             487 | performances             |                             586 |

Table 8: Statistics of genuine and spurious correlation into 50 words for different s values for each sentiment label.

| Sentiment Label   |   s=20 - Genuine Correlation |   s=20 - Spurious Correlation |   s=2 - Genuine Correlation |   s=2 - Spurious Correlation |
|-------------------|------------------------------|-------------------------------|-----------------------------|------------------------------|
| Negative          |                           30 |                            20 |                          39 |                           11 |
| Positive          |                           22 |                            18 |                          41 |                            9 |

## 7 Conclusion

In this paper, we employ TM to design a robust text classification against spurious correlations. TM learns the pattern using a set of clauses that are in the form of propositional logic. Such propositional logic is a combination of features in either non-negated or negated form. Since the propositional logic is human interpretable, it is easy to extract rule-based reasoning from TM. Our methods demonstrate that such a rule can be controlled or fine-tuned by modifying the parameter specificity s. We show that by keeping the value of s small, we can filter the clause from non-monotone to monotone where a majority of features are in the negated form thereby removing spurious correlations and forcing the model to rely on genuine correlations. Experiments results have shown that the proposed s-controlled TM outperforms various existing models on counterfactual test data. In addition, unlike DNNs, the human-level interpretation obtained from the rule-based reasoning of TM gives a complete understanding of how the model achieves its robustness.

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