20240921/2311.11208v2.json

{
    "title": "LogicNet: A Logical Consistency Embedded Face Attribute Learning Network",
    "abstract": "Ensuring logical consistency in predictions is a crucial yet overlooked aspect in face attribute classification. We explore the potential reasons for this oversight and introduce two pressing challenges to the field: 1) How can we ensure that a model, when trained with data checked for logical consistency, yields predictions that are logically consistent? 2) How can we achieve the same with training data that hasn\u2019t undergone logical consistency checks? Minimizing manual effort is also essential for enhancing automation. To address these challenges, we introduce two datasets, FH41K and CelebA-logic, and propose LogicNet, which combines adversarial learning and label poisoning to learn the logical relationship between attributes without need for post-processing steps.\nAccuracy of LogicNet surpasses that of the next-best approach by 13.36%, 9.96%, and 1.01% on FH37K, FH41K, and CelebA-logic, respectively.\nIn real-world case analysis, our approach can achieve a reduction of more than 50% in the average number of failed cases (logically inconsistent attributes) compared to other methods.\nCode link: https://github.com/HaiyuWu/LogicNet/tree/main.",
    "sections": [
        {
            "section_id": "1",
            "parent_section_id": null,
            "section_name": "Introduction",
            "text": "Where does the logical consistency problem arise in computer vision?\nIn the realm of multi-attribute classification, models are trained to predict the attributes represented in a given image. Examples include facial attributes [31  ###reference_b31###, 23  ###reference_b23###, 46  ###reference_b46###], clothing styles [30  ###reference_b30###, 7  ###reference_b7###], autonomous driving [12  ###reference_b12###], human action recognition [28  ###reference_b28###], and others.\nWhenever multiple attributes are predicted for an image, logical relationships may potentially exist among these attributes.\nFor instance, in a popular scheme for predicting attributes in face images [31  ###reference_b31###], the attributes goatee, no beard, and mustache are predicted independently.\nNote that, in CelebA, mustache is a type of beard based on the ground truth.\nLogically, then, if no beard is predicted as true, then both goatee and mustache should be predicted as false.\nLogical consistency issues may arise in more subtle interactions as well.\nFor example, if wearing hat is predicted as true, then the information required to make a prediction for bald is occluded.\nSimilarly, if wearing sunglasses is predicted as true, then the information to predict narrow eyes or eyes closed is occluded.\nAnalogous logical relationships exist in other datasets.\nIn DeepFashion [30  ###reference_b30###], it would be logically inconsistent to predict both long-sleeve and sleeveless as true for the same garment.\nIn ROAD-R [12  ###reference_b12###], red light and green light are mutually exclusive.\nIssues of logical consistency can arise in various areas of computer vision, particularly in the area of multi-attribute classification.\n###figure_1### Why is logical consistency of predictions important in face attribute classification?\nFace and body attributes have been extensively utilized in various research domains, including face matching/recognition [40  ###reference_b40###, 3  ###reference_b3###, 6  ###reference_b6###, 24  ###reference_b24###, 23  ###reference_b23###, 36  ###reference_b36###], re-identification [35  ###reference_b35###, 37  ###reference_b37###, 38  ###reference_b38###], training GANs [8  ###reference_b8###, 9  ###reference_b9###, 18  ###reference_b18###, 25  ###reference_b25###], bias analysis [46  ###reference_b46###, 32  ###reference_b32###, 42  ###reference_b42###, 4  ###reference_b4###, 48  ###reference_b48###], and others.\nFor a fair accuracy comparison across demographic groups, it is important to balance the distribution of non-demographic attributes across the groups [48  ###reference_b48###].\nFor example, if a group wants to understand how facial hair affects face recognition accuracy across demographic groups, they have to tightly control variation on facial hair. However, if a model predicts {clean-shaven and beard-length-short} or {beard-at-chin-area and full-beard} for the same image, this type of prediction will put same images in two conflicting categories and significantly impact the validity of results.\nTo train a face editing GAN, face attributes are used to guide the model to generate the target images [19  ###reference_b19###, 29  ###reference_b29###, 22  ###reference_b22###].\nHowever, if images exhibit logically inconsistent sets of attribute values, these applications of the attributes become problematic and prone to errors.\nHence,\nlogical consistency of attribute predictions is crucial for essentially all higher-level computer vision tasks.\nWhy has logical consistency not received more attention in face attribute classification?\n1) Attribute design: Unlike traffic signs and objects, the attributes in the existing face attribute datasets are more ambiguous [47  ###reference_b47###], such as high cheekbones, attractive, oval face, which makes it hard to determine the logical relationship between attributes. 2) Accuracy measurement metric: Accuracy is commonly measured by , which considers predictions independently across attributes. In multi-attribute classification, this measurement ignores the logical relationships and hides the imbalanced performance on positive and negative samples. Hence, the logical consistency problem cannot be reflected by accuracy numbers. 3) Ground truth accuracy: Wu et al. [47  ###reference_b47###] and Lingenfelter et al. [27  ###reference_b27###] reported on accuracy problems with CelebA labels. Since the model performance is only measured in the aforementioned way, involving logical relationships might not boost, or could even hurt, the accuracy.\nThese three reasons could give rise to the situation where none of the recent face attribute survey papers [1  ###reference_b1###, 2  ###reference_b2###, 43  ###reference_b43###, 51  ###reference_b51###] even mentions the problem of logical consistency.\nThis paper introduces two challenging tasks for face attribute classification:\n(1) Training a model with labels in the training data that have been checked for logical consistency (FH37K and FH41K), aiming to improve the accuracy and logical consistency of predictions; and (2) Training a model with labels in the training data that have not been checked for logical consistency (CelebA-logic). No post-processing steps should be used in these tasks.\nContributions of this work include:\nA set of logical-relationship-cleaned annotations for CelebA validation and testing sets to support a more challenging task: train a logically consistent model with logical-consistency-unchecked data.\nA larger benchmark dataset, FH41K, which compensates the lack of samples of the minority group in the existing facial hair dataset.\nProposing a new training method, LogicNet, which combining adversarial learning and data poisoning algorithms to achieve higher accuracy and lower logical inconsistency across three face attribute datasets without using any post-processing steps."
        },
        {
            "section_id": "2",
            "parent_section_id": null,
            "section_name": "Related Work",
            "text": ""
        },
        {
            "section_id": "3",
            "parent_section_id": null,
            "section_name": "Benchmarks",
            "text": "The ambiguity of attribute names and the reasons listed in Section 1  ###reference_### limit the research in evaluating model performance on the dimension of logical consistency. We enlarge the FH37K dataset and clean the test and validation sets of CelebA for future benchmark tests. The rules are listed in the Algo. 1 and 2 of Supplementary Material.\nFH37K [46  ###reference_b46###] is the first dataset checking both logical consistency and accuracy of the annotations. It contains 37,565 images, coming from a subset of CelebA [31  ###reference_b31###] and a subset of WebFace260M [53  ###reference_b53###]. Each image has 22 attributes of facial hair and baldness. However, due to the small number of positive samples of attributes \u201cBald Sides Only\u201d (161 images), \u201cLong\u201d beard (747 images), and \u201cBald Top and Sides\u201d (1,321 images), insufficient train/val/test samples limits the performance measurement on logical consistency.\nTo address this, we augment this dataset by adding more positive samples to minority classes.\n###figure_2### FH41K is our extended version of FH37K.\nWe added 3,712 images from 2,096 identities from WebFace260M to increase the number of positive examples of attributes that had too low of a representation in FH37K. Specifically, we used the best facial hair classification model trained with FH37K111https://github.com/HaiyuWu/LogicalConsistency#testing\nto select the images that have confidence value higher than 0.8 for both \u201dLong\u201d and for \u201dBald Sides Only\u201d. We then engaged a human annotator, with the prior knowledge learnt from the documentation provided by  [46  ###reference_b46###], to manually check the selected images in order to ensure the accuracy and logical consistency of the added images. Major changes are in Table 1  ###reference_###.\nBoth FH37K and FH41K have a set of rigorously defined rules based on the logical relationships including mutually exclusive, dependency, and collectively exhaustive. The annotations are evaluated based on these relationships.\nHowever, previous existing face attribute datasets were created without considering the issue of logical consistency in annotations. For example, in CelebA, there are 1,503 images having \u201cBald=true\u201d and \u201cReceding_Hairline=true\u201d, 235 images having both \u201dMustache=true\u201d and \u201dNo_Beard=true\u201d, and 139 images having \u201cMale=false\u201d and \u201cNo_Beard=false\u201d.\nThis raises an important question.\nIs it possible to train a model to produce logically consistent attribute predictions using a training dataset that does not have logically consistent annotations?\nWe compiled an additional dataset based on CelebA to study this question.\nCelebA-logic is the variation of CelebA, where the logical relationship between attributes is checked for both validation and test sets, as shown in Table 2  ###reference_###. Given the absence of a definitive guide of how these 40 attributes are marked and what the definition is for each attribute, we categorized the attribute relationships into three groups, based on our knowledge, as shown in Figure 2  ###reference_###. To make a fair set of logical rules, only Strong relationships are used to check the logical consistency. Moreover,  [27  ###reference_b27###, 47  ###reference_b47###] reported that CelebA suffers from a substantial rate of inaccurate annotations. Hence, we conducted an annotation cleaning process for those strong relationship attributes upon the MSO-cleaned-annotations [47  ###reference_b47###]. To get the cleaned facial hair and baldness related attributes, we converted the FH37K annotations back to the CelebA version and updated the labels to the corresponding images. Two human annotators then marked \u201cBangs\u201d, \u201cReceding Hairline\u201d and \u201cMale\u201d based on the designed definitions for all the images in the validation and test sets. To ensure the consistency and accuracy of the new annotations, a third human annotator with knowledge of definitions marked 1,000 randomly selected samples. The estimated consistency rate is 88.73%, measured by Eq. 6  ###reference_###. Consequently, 1) all images are cropped and aligned to 224x224 based on the given landmarks,\n2) 975 images are omitted from the original dataset, 3) 63,557 (31.8%) images have at least one different label than the original, and 4) all test and validation annotations obey the Strong logical relationships."
        },
        {
            "section_id": "4",
            "parent_section_id": null,
            "section_name": "Proposed Method",
            "text": "To provide a solution for the challenges of logical consistency, we propose LogicNet, which exploits an adversarial training strategy and a label poisoning algorithm, Bag of Labels (BoL).\nLogicNet enables the classifier to learn the logical relationships between attributes, thereby enhancing the model\u2019s capacity to generate logically consistent predictions.\n###figure_3###"
        },
        {
            "section_id": "4.1",
            "parent_section_id": "4",
            "section_name": "Adversarial Training",
            "text": "We propose an adversarial training framework, shown in Figure 3  ###reference_###, to compel the classifier  to make logically consistent predictions while improving the accuracy of predictions.\nFormalizing the desired goal,\nwe consider a set of training images as ,\nfrom which we want to train a model,\n, to project  to the ground truth labels , where each  is a set of attribute labels of . The classification loss is the binary cross entropy loss:\nWhere  is the parameter vector of the classifier . For the adversarial learning, a discriminator that can judge the logical consistency of the predictions is needed. Here, we use a multi-headed self-attention network [44  ###reference_b44###] to give a probability, , for the logical consistency of labels, . The loss of the multi-attribute classifier, , becomes:\nWhere  is the parameter frozen discriminator,  is the parameter vector of the discriminator, and  is used for loss trade-off."
        },
        {
            "section_id": "4.2",
            "parent_section_id": "4",
            "section_name": "Bag of Labels",
            "text": "To train a discriminator, the straightforward approach [45  ###reference_b45###] is to directly feed the predictions (ground truth labels) and treat them as negative (positive) samples. Since the training labels of CelebA are not yet cleaned, using them could mislead the discriminator and cause it to learn incorrect patterns.\nHence, we propose a Bag of Labels algorithm, as shown in Algorithm 1  ###reference_thm1###, that can automatically poison the ground truth labels to generate logically inconsistent labels while detecting the logical consistency of the original label. This algorithm consists with two parts: Condition Group Setup and Label Poisoning.\nCondition Group Setup:\nTo give accurate logic labels  to , following the relationships, we separate the corresponding attributes of each rule to two groups:  and , where the attributes in  have strong logical relationships with the attributes in . For both FH37K and FH41K, we follow the rules given by [46  ###reference_b46###]. For CelebA, we follow the relationships in Figure 2  ###reference_### and the propositional logic version is in the Algo. 2 of Supplementary Material.\nLabel Poisoning:\nTo generate logically inconsistent labels, we first categorize the rules in three cases: inter-class impossible poisoning, intra-class impossible poisoning, and intra-class incomplete poisoning. Inter-class impossible poisoning aims to generate labels where the logical inconsistency happens between the attributes in different classes (e.g. Beard Area(clean shaven)=true and Beard Length(short)=true; Bald=true and Receding_Hairline=true). Intra-class impossible and intra-class incomplete poisoning aim to generate labels where there are multiple positive predictions within one class (e.g. Beard Area(clean shaven)=true and Beard Area(chin area)=true) or no positive predictions within a class. These two poisoning strategies apply to FH37K and FH41K; attributes in CelebA do not have this level of detail and so do not have these logical relationships.\nAfter each poisoning, the initialized logic labels, , are updated on-the-fly. Note that, each poisoning method randomly attacks one relationship at one time. Thus, if the positive attributes are not in the target relationship, no poisoning will happen and .\nThe objective function for the discriminator training is:\nWhere\nHere,  is from BoL algorithm,  is from classifier,  is a randomly generated float number between 0 and 1. When using  the target  is from BoL algorithm, otherwise ."
        },
        {
            "section_id": "5",
            "parent_section_id": null,
            "section_name": "Experiments",
            "text": "In this section, we evaluate the proposed approach from two aspects: accuracy and logical consistency. For accuracy, the traditional average accuracy measurement (Eq. 5  ###reference_###, where  = total number of images,  = number of true positive predictions,  = number of true negative predictions) ignores the imbalanced number of positive and negative images for each attribute.\nIgnoring the imbalance of positive and negative attributes results in an unfair measure of model performances since the multi-attribute classification datasets suffer from sparse annotations. For example, in the original CelebA annotations, if all predictions are negative, the overall test accuracy is 76.87%. Hence, we follow the suggestion in [20  ###reference_b20###] and use average value of the positive accuracy, , and negative accuracy, , to consider the imbalance:\nIn addition, to show how logical consistency of predictions affects the accuracy, we measure the performance under two conditions: 1) without considering the logical consistency on predictions, 2) considering logical consistency by counting logically inconsistent predictions as incorrect. For FH37K and FH41K, we also include the label compensation strategy [46  ###reference_b46###] experiments to complete the accuracy comparison. To evaluate the model performance on logical consistency, we performed logical consistency checking on the predictions of 600K images from WebFace260M [53  ###reference_b53###]. We also independently compare the accuracy values on the strong relationship attributes in CelebA-logic.\nTo give a comprehensive study of the impact of logical consistency on model predictions, we choose six training methods for the experiment. Binary Cross Entropy Loss (BCE) is a baseline which only considers the entropy between predictions and ground truth labels. Binary Focal Loss (BF) [26  ###reference_b26###] aims to focus more on hard samples in order to mitigate the effect of imbalanced data. BCE-MOON [33  ###reference_b33###] tries to balance the effect of positive and negative samples by\ncalculating the ratio of positive and negative samples for each attribute as the weights added to loss values before back propagation. Semantic [50  ###reference_b50###] uses the confidence values of predictions and logical relationships to form a regularization term, in order to constrain the classification loss. Constrained [12  ###reference_b12###] uses the fuzzy logic relaxation of the constraints to constrain the classification loss. Logically Consistent Prediction Loss (LCP) [46  ###reference_b46###] utilizes the conditional probability of the binary predictions to force the probability of the mutually exclusive attributes happening at the same time to be 0 and the probability of the dependency attributes happening at the same time to be 1."
        },
        {
            "section_id": "5.1",
            "parent_section_id": "5",
            "section_name": "Implementation",
            "text": "We train all the classifiers starting with the pretrained ResNet50 [17  ###reference_b17###] from Pytorch222https://pytorch.org/hub/pytorch_vision_resnet/. The FH37K results in Table 3  ###reference_### are adopted from [46  ###reference_b46###] except the values of . We resize images to 224x224 for all three datasets. The batch size and learning rate are {256, 0.0001} for FH37K and FH41K, and {64, 0.001} for CelebA-logic. We use random horizontal flip for both FH37K and FH41K. We use random horizontal flip, color jitter, and random rotation for CelebA-logic. AFFACT [13  ###reference_b13###] and ALM [34  ###reference_b34###] are the two SOTA models that are available online, which we used for performance comparison on CelebA-logic. The  values for FH37K, FH41K, and CelebA are . The discriminator consists of 8 multi-headed self-attention blocks.\nIt is necessary to know that the ALM algorithm resizes the original (178x218) CelebA images to 128x128 for testing; the other methods use the cropped images mentioned in Section 3  ###reference_### for testing."
        },
        {
            "section_id": "5.2",
            "parent_section_id": "5",
            "section_name": "Accuracy",
            "text": "###table_1### Table 3  ###reference_### and Table 4  ###reference_### show the accuracy values, tested on FH37K, FH41K, and CelebA-logic, under two measurement conditions. In the traditional case of not considering logical consistency of predictions, every method reaches  average accuracy,\nHowever, when logically inconsistent predictions are counted as incorrect,\naccuracy decreases across all training methods.\nFor FH37K and FH41K, the average decreases in accuracy of logical-inconsistency-ignored methods (i.e., BCE, BCE-MOON, and BF) are 39.14% and 42.65%, and the average decreases of logical-consistency-aware methods (i.e. Semantic, Constrained, and LCP) are 28.59% and 23.06%. The proposed method has {12.1%, 11.16%} decrease in accuracy and the overall accuracy is {13.36%, 9.96%} higher than the second-highest accuracy, and {35.35%, 52.12%} higher than the lowest accuracy. The results show that, although incorporating logical relationship in the objective function improves the model\u2019s ability to make logically consistent predictions, logical consistency of predictions is still a serious problem. The proposed method reduces the disparity better than the existing methods.\n[46  ###reference_b46###] proposed a post-processing step, termed label compensation strategy, to resolve incomplete predictions. By using this strategy, the methods other than BCE-MOON have a significant increase in accuracy, {26.70% and 24.91%} on average. This results in two conclusions: 1) Methods that aim to mitigate the imbalanced data effect might give an illusion of high accuracy driven by positive predictions; 2) Other methods can somewhat catch the logical patterns, but need to involve post-processing steps. However, the label compensation strategy is only for solving the collectively exhaustive case (i.e., the model must give one positive prediction in an attribute group). For example, in FH37K and FH41K, the attributes, {clean-shaven, chin-area, side-to-side, beard-area-information-not-visible}, in the Beard Area group can cover any case that is related to beard area. Implementing this type of strategy necessitates extensive manual analysis to determine the most judicious decision-making process, underscoring the imperative for continued research in this domain.\nFor CelebA-logic, when considering logical consistency of predictions, the patterns echo the previous observations. For both AFFACT and ALM, we use the original model weights provided by the authors. The top half of Table 4  ###reference_### shows that either using the original or the cleaned test annotations, there is a 2.49% accuracy decrease after considering logical consistency. Note that the overall increase in accuracy since CelebA was published is 5.98%, so requiring logical consistency erases about half of the improvement seen on CelebA since it was introduced.\n\nThe average accuracy decrease of the models tested on the cleaned annotations is 4.04%, where the BF has the smallest accuracy difference and BCE-MOON has the largest accuracy difference. Our speculation is that BF over-focuses on negative attributes but the logical relationship mostly happens between positive side, so BF has lower probability to violate logical relationships. Conversely, BCE-MOON over-focuses on positive side, so it has higher probability to disobey logical relationships.\nResults in Table 4  ###reference_### and Table 5  ###reference_### show that the proposed method has the best performances on average accuracy of all attributes and strong relationship attributes, where it is {1.01%, 1.71%} higher than the second-highest accuracy. Therefore, the proposed method has the best ability to obtain the logical relationships.\nThe results could be summarized in the following points: 1) Without any post-processing steps, our method performs the best, on average, than either general objective functions (i.e., BCE, MOON, BF) or logical relationship embedded objective functions (i.e., Semantic, Constrained, LCP) across three datasets. 2) Adversarial training implemented in our method does not bring large computing overhead. 3) 1.01% improvement on CelebA-logic dataset is not trivial, as there are 40 attributes and the overall improvement on the original CelebA dataset since it was published is around 5%. In addition, the evaluation of logical consistency on predictions in real-world application and comparison with GPT4-V are in the Supplementary Material."
        },
        {
            "section_id": "5.3",
            "parent_section_id": "5",
            "section_name": "Discussion",
            "text": "Simply using adversarial learning does not achieve the best performance because the classifier eventually learns good patterns. Always regarding predictions as logically inconsistent can lead to model collapse. Purely using the poisoned labels from the BoL algorithm to train the discriminator makes the discriminator work as a reward model. It helps the classifier learn logical relationships but can easily reach the local minimum. LogicNet combines these two, which surpass the performance of implementing each individually, as shown in Table 6  ###reference_###. Table 7  ###reference_### shows that LogicNet brings the least computational complexity compared to other methods. Hence, it is more efficient and effective than other methods.\nAlthough LogicNet does not perform the best after involving post-processing steps, the complexity of pre-training design for each method is different. For any of the \u201clogic-involved methods\u201d, they need to list 19 circumstances for FH37K and FH41K training and 20 circumstances for CelebA training, whereas LogicNet only needs 4 conditions for the label poisoning of each dataset training. Note that as the number of attributes increases, the complexity increases rapidly. Therefore, LogicNet can significantly reduce the complexity of pre-training design.\nFirst, FH37K is the only dataset checking the logical consistency of the ground truth labels, so it fits our task well. Second, there are larger datasets, e.g., MAAD and CelebV-HQ, but they use the same set of CelebA attributes and the logical consistency of labels is not checked. To provide a dataset for the second of the aforementioned challenge, the validation and testing sets need to be cleaned. To this end, CelebA is a proper dataset with sufficient images and relatively easy to manually correct the validation and testing data.\nThere is significant number of works trying to improve the performance on CelebA dataset [10  ###reference_b10###, 5  ###reference_b5###, 14  ###reference_b14###, 39  ###reference_b39###, 45  ###reference_b45###, 49  ###reference_b49###]. However, unlike these works doing the regular test on CelebA, which does not need the weights from other works, the logical test in this paper needs to retrain the model and test them on the cleaned test sets. Unfortunately, none of them provide official implementation/weights for their methods. Under this situation, we tried our best to ask for weights and re-implement methods, so AFFACT [13  ###reference_b13###], ALM [34  ###reference_b34###], MOON [33  ###reference_b33###], Semantic loss [50  ###reference_b50###] and Constrained loss [12  ###reference_b12###] can be compared in this paper. It is impossible for us to re-implement all other methods.\nLogicNet provides a general solution to cause model predictions to be more logically consistent than previous methods, but the accuracy difference before and after considering logical consistency of predictions is still large and the failed ratio is not negligible for both challenges. Moreover, LogicNet needs more epochs to be well-trained than other methods. Specifically, the validation accuracy of other methods mostly saturates around 10 epochs, but LogicNet needs around 18 epochs to get the best validation accuracy."
        },
        {
            "section_id": "6",
            "parent_section_id": null,
            "section_name": "Conclusions and Limitations",
            "text": "We provide two new datasets for two logical consistency challenges: 1) Train a classifier with logical-consistency-checked data to learn a classifier that makes logically consistent predictions, and 2) Train a classifier with training data that contains logically inconsistent labels and still achieves logically consistent predictions.\nTo our best knowledge, this is the first work that comprehensively discusses the problem of logical consistency of predictions in face attribute classification.\nWe propose the LogicNet, which does not involve any post-processing steps and significantly improves performance, {13.36% (FH37K), 9.96% (FH41K), 1.01% (CelebA-logic), 1.71% (CelebA-logic 9 attributes)} compared to the second best, under logical-consistency-checked condition for all three datasets. For the real-world case analysis, the proposed method can substantially reduce the fraction of failed (logically inconsistent) predictions."
        }
    ],
    "appendix": [],
    "tables": {
        "1": {
            "table_html": "<figure class=\"ltx_table ltx_figure_panel ltx_align_center\" id=\"S3.T1\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S3.T1.2.1.1\" style=\"font-size:90%;\">Table 1</span>: </span><span class=\"ltx_text\" id=\"S3.T1.3.2\" style=\"font-size:90%;\">The number of positive samples of under-represented attributes between FH37K and FH41K.</span></figcaption>\n</figure>",
            "capture": "Table 1: The number of positive samples of under-represented attributes between FH37K and FH41K."
        },
        "2": {
            "table_html": "<figure class=\"ltx_table ltx_figure_panel ltx_align_center\" id=\"S3.T2\">\n<figcaption class=\"ltx_caption\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S3.T2.2.1.1\" style=\"font-size:90%;\">Table 2</span>: </span><span class=\"ltx_text\" id=\"S3.T2.3.2\" style=\"font-size:90%;\">Changes between CelebA and CelebA-logic. \u201c-\u201d means logical consistency is not manually checked.</span></figcaption>\n</figure>",
            "capture": "Table 2: Changes between CelebA and CelebA-logic. \u201c-\u201d means logical consistency is not manually checked."
        },
        "3": {
            "table_html": "<figure class=\"ltx_table\" id=\"S5.T3\">\n<table class=\"ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle\" id=\"S5.T3.20\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S5.T3.20.21.1\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr ltx_border_t\" id=\"S5.T3.20.21.1.1\" rowspan=\"2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.21.1.1.1\">Methods</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" colspan=\"3\" id=\"S5.T3.20.21.1.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">FH37K</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" colspan=\"3\" id=\"S5.T3.20.21.1.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">FH41K</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.6.6\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.1.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.2.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T3.3.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.4.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.5.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T3.6.6.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.22.2\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_tt\" colspan=\"7\" id=\"S5.T3.20.22.2.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Logical consistency is not taken into account.</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.23.3\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr ltx_border_t\" id=\"S5.T3.20.23.3.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.20.23.3.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.23</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.20.23.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.72</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T3.20.23.3.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">63.73</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.20.23.3.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">83.88</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.20.23.3.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.20.23.3.6.1\">95.50</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T3.20.23.3.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">72.27</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.24.4\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.20.24.4.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE-MOON\u00a0<cite class=\"ltx_cite ltx_citemacro_cite\">[<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2311.11208v2#bib.bib33\" title=\"\">33</a>]</cite>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.24.4.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.24.4.2.1\" style=\"color:#1A09F3;\">86.21</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.24.4.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">90.67</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.20.24.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.24.4.4.1\" style=\"color:#1A09F3;\">81.75</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.24.4.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.24.4.5.1\" style=\"color:#1A09F3;\">88.02</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.24.4.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">91.29</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.20.24.4.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.24.4.7.1\" style=\"color:#1A09F3;\">84.75</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.25.5\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.20.25.5.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BF\u00a0<cite class=\"ltx_cite ltx_citemacro_cite\">[<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2311.11208v2#bib.bib26\" title=\"\">26</a>]</cite>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.25.5.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">76.92</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.25.5.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.20.25.5.3.1\">95.43</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.20.25.5.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.25.5.4.1\" style=\"color:#E92341;\">58.41</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.25.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">75.81</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.25.5.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.25.5.6.1\" style=\"color:#1A09F3;\">97.78</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.20.25.5.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.25.5.7.1\" style=\"color:#E92341;\">52.85</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.26.6\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.20.26.6.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.1.1\" style=\"background-color:#DFDFDF;\">Semantic\u00a0<cite class=\"ltx_cite ltx_citemacro_cite\">[<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2311.11208v2#bib.bib50\" title=\"\">50</a>]</cite></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.26.6.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.2.1\" style=\"background-color:#DFDFDF;\">80.30</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.26.6.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.3.1\" style=\"background-color:#DFDFDF;\">94.26</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.20.26.6.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.4.1\" style=\"background-color:#DFDFDF;\">66.33</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.26.6.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.5.1\" style=\"background-color:#DFDFDF;\">83.73</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.26.6.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.6.1\" style=\"background-color:#DFDFDF;\">95.52</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.20.26.6.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.26.6.7.1\" style=\"background-color:#DFDFDF;\">71.95</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.27.7\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.20.27.7.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.1.1\" style=\"background-color:#DFDFDF;\">Constrained\u00a0<cite class=\"ltx_cite ltx_citemacro_cite\">[<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2311.11208v2#bib.bib12\" title=\"\">12</a>]</cite></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.27.7.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.2.1\" style=\"background-color:#DFDFDF;\">80.45</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.27.7.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.3.1\" style=\"background-color:#DFDFDF;\">94.20</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.20.27.7.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.4.1\" style=\"background-color:#DFDFDF;\">66.69</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.27.7.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.5.1\" style=\"background-color:#DFDFDF;\">83.78</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.27.7.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.6.1\" style=\"background-color:#DFDFDF;\">95.43</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.20.27.7.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.27.7.7.1\" style=\"background-color:#DFDFDF;\">72.13</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.28.8\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.20.28.8.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.28.8.1.1\" style=\"background-color:#DFDFDF;\">LCP\u00a0<cite class=\"ltx_cite ltx_citemacro_cite\">[<a class=\"ltx_ref\" href=\"https://arxiv.org/html/2311.11208v2#bib.bib46\" title=\"\">46</a>]</cite></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.28.8.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.28.8.2.1\" style=\"background-color:#DFDFDF;\">79.64</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.28.8.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.28.8.3.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">95.98</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.20.28.8.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.28.8.4.1\" style=\"background-color:#DFDFDF;\">63.30</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.28.8.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.28.8.5.1\" style=\"background-color:#DFDFDF;\">84.93</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.28.8.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.28.8.6.1\" style=\"background-color:#DFDFDF;\">95.09</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.20.28.8.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.28.8.7.1\" style=\"background-color:#DFDFDF;\">74.77</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.29.9\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.20.29.9.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.29.9.1.1\" style=\"background-color:#DFDFDF;\">Ours</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.29.9.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.20.29.9.2.1\" style=\"background-color:#DFDFDF;\">83.65</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.29.9.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.29.9.3.1\" style=\"background-color:#DFDFDF;\">93.46</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.20.29.9.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.20.29.9.4.1\" style=\"background-color:#DFDFDF;\">73.83</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.29.9.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.20.29.9.5.1\" style=\"background-color:#DFDFDF;\">85.66</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.20.29.9.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.20.29.9.6.1\" style=\"background-color:#DFDFDF;\">94.23</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.20.29.9.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.20.29.9.7.1\" style=\"background-color:#DFDFDF;\">77.10</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.30.10\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_tt\" colspan=\"7\" id=\"S5.T3.20.30.10.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">With label compensation.</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.7.7\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr ltx_border_t\" id=\"S5.T3.7.7.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE<sup class=\"ltx_sup\" id=\"S5.T3.7.7.1.1\">\u2020</sup>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.7.7.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.7.7.2.1\">80.14</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.7.7.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.7.7.3.1\">91.49</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T3.7.7.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">68.78</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.7.7.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.12</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.7.7.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">87.43</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T3.7.7.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">70.81</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.8.8\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.8.8.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE-MOON<sup class=\"ltx_sup\" id=\"S5.T3.8.8.1.1\">\u2020</sup>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.8.8.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.8.8.2.1\" style=\"color:#E92341;\">42.59</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.8.8.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.8.8.3.1\" style=\"color:#E92341;\">50.55</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.8.8.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.8.8.4.1\" style=\"color:#E92341;\">34.62</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.8.8.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.8.8.5.1\" style=\"color:#E92341;\">42.79</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.8.8.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.8.8.6.1\" style=\"color:#E92341;\">47.96</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.8.8.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.8.8.7.1\" style=\"color:#E92341;\">37.61</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.9.9\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.9.9.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BF<sup class=\"ltx_sup\" id=\"S5.T3.9.9.1.1\">\u2020</sup>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.9.9.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">78.48</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.9.9.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">90.91</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.9.9.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">66.05</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.9.9.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.9.9.5.1\" style=\"color:#1A09F3;\">82.85</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.9.9.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.9.9.6.1\" style=\"color:#1A09F3;\">93.53</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.9.9.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.9.9.7.1\">73.17</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.10.10\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.10.10.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.1.1\" style=\"background-color:#DFDFDF;\">Semantic<sup class=\"ltx_sup\" id=\"S5.T3.10.10.1.1.1\"><span class=\"ltx_text\" id=\"S5.T3.10.10.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.10.10.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.2.1\" style=\"background-color:#DFDFDF;\">76.43</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.10.10.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.3.1\" style=\"background-color:#DFDFDF;\">87.50</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.10.10.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.4.1\" style=\"background-color:#DFDFDF;\">65.35</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.10.10.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.5.1\" style=\"background-color:#DFDFDF;\">79.57</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.10.10.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.6.1\" style=\"background-color:#DFDFDF;\">88.07</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.10.10.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.10.10.7.1\" style=\"background-color:#DFDFDF;\">71.06</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.11.11\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.11.11.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.1.1\" style=\"background-color:#DFDFDF;\">Constrained<sup class=\"ltx_sup\" id=\"S5.T3.11.11.1.1.1\"><span class=\"ltx_text\" id=\"S5.T3.11.11.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.11.11.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.2.1\" style=\"background-color:#DFDFDF;\">76.28</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.11.11.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.3.1\" style=\"background-color:#DFDFDF;\">87.23</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.11.11.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.4.1\" style=\"background-color:#DFDFDF;\">65.33</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.11.11.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.5.1\" style=\"background-color:#DFDFDF;\">79.17</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.11.11.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.6.1\" style=\"background-color:#DFDFDF;\">87.67</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.11.11.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.11.11.7.1\" style=\"background-color:#DFDFDF;\">70.68</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.12.12\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.12.12.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.12.12.1.1\" style=\"background-color:#DFDFDF;\">LCP<sup class=\"ltx_sup\" id=\"S5.T3.12.12.1.1.1\"><span class=\"ltx_text\" id=\"S5.T3.12.12.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.12.12.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.12.12.2.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">81.44</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.12.12.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.12.12.3.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">92.65</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.12.12.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.12.12.4.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">70.23</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.12.12.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.12.12.5.1\" style=\"background-color:#DFDFDF;\">79.31</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.12.12.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.12.12.6.1\" style=\"background-color:#DFDFDF;\">87.31</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.12.12.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.12.12.7.1\" style=\"background-color:#DFDFDF;\">71.31</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.13.13\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.13.13.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.13.13.1.1\" style=\"background-color:#DFDFDF;\">Ours<sup class=\"ltx_sup\" id=\"S5.T3.13.13.1.1.1\"><span class=\"ltx_text ltx_font_medium\" id=\"S5.T3.13.13.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.13.13.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.13.13.2.1\" style=\"background-color:#DFDFDF;\">78.28</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.13.13.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.13.13.3.1\" style=\"background-color:#DFDFDF;\">87.23</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.13.13.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.13.13.4.1\" style=\"background-color:#DFDFDF;\">69.32</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.13.13.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.13.13.5.1\" style=\"background-color:#DFDFDF;\">81.53</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.13.13.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.13.13.6.1\" style=\"background-color:#DFDFDF;\">89.10</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.13.13.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.13.13.7.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">73.96</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.31.11\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_tt\" colspan=\"7\" id=\"S5.T3.20.31.11.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Without label compensation. (<span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.31.11.1.1\" style=\"color:#FF4081;\">A general solution</span>)</th>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.14.14\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr ltx_border_t\" id=\"S5.T3.14.14.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE<sup class=\"ltx_sup\" id=\"S5.T3.14.14.1.1\">\u2020</sup>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.14.14.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.14.14.2.1\" style=\"color:#E92341;\">48.50</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.14.14.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.14.14.3.1\" style=\"color:#E92341;\">54.59</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T3.14.14.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.14.14.4.1\" style=\"color:#E92341;\">42.40</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.14.14.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.14.14.5.1\" style=\"color:#E92341;\">56.71</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T3.14.14.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">62.14</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T3.14.14.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.14.14.7.1\" style=\"color:#E92341;\">51.27</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.15.15\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.15.15.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE-MOON<sup class=\"ltx_sup\" id=\"S5.T3.15.15.1.1\">\u2020</sup>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.15.15.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.15.15.2.1\" style=\"color:#E92341;\">40.25</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.15.15.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.15.15.3.1\" style=\"color:#E92341;\">47.54</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.15.15.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.15.15.4.1\" style=\"color:#E92341;\">32.95</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.15.15.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.15.15.5.1\" style=\"color:#E92341;\">40.68</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.15.15.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.15.15.6.1\" style=\"color:#E92341;\">45.39</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.15.15.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.15.15.7.1\" style=\"color:#E92341;\">35.98</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.16.16\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.16.16.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BF<sup class=\"ltx_sup\" id=\"S5.T3.16.16.1.1\">\u2020</sup>\n</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.16.16.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.16.16.2.1\" style=\"color:#E92341;\">36.20</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.16.16.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.16.16.3.1\" style=\"color:#E92341;\">40.95</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.16.16.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.16.16.4.1\" style=\"color:#E92341;\">31.45</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.16.16.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.16.16.5.1\" style=\"color:#E92341;\">22.38</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.16.16.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.16.16.6.1\" style=\"color:#E92341;\">23.84</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.16.16.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.16.16.7.1\" style=\"color:#E92341;\">20.92</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.17.17\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.17.17.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.1.1\" style=\"background-color:#DFDFDF;\">Semantic<sup class=\"ltx_sup\" id=\"S5.T3.17.17.1.1.1\"><span class=\"ltx_text\" id=\"S5.T3.17.17.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.17.17.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.2.1\" style=\"color:#E92341;background-color:#DFDFDF;\">57.74</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.17.17.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.3.1\" style=\"background-color:#DFDFDF;\">65.87</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.17.17.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.4.1\" style=\"color:#E92341;background-color:#DFDFDF;\">49.62</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.17.17.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.5.1\" style=\"color:#E92341;background-color:#DFDFDF;\">56.73</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.17.17.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.6.1\" style=\"background-color:#DFDFDF;\">62.36</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.17.17.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.17.17.7.1\" style=\"color:#E92341;background-color:#DFDFDF;\">51.10</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.18.18\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.18.18.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.1.1\" style=\"background-color:#DFDFDF;\">Constrained<sup class=\"ltx_sup\" id=\"S5.T3.18.18.1.1.1\"><span class=\"ltx_text\" id=\"S5.T3.18.18.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.18.18.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.2.1\" style=\"color:#E92341;background-color:#DFDFDF;\">58.19</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.18.18.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.3.1\" style=\"background-color:#DFDFDF;\">66.14</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.18.18.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.4.1\" style=\"color:#E92341;background-color:#DFDFDF;\">50.25</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.18.18.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.5.1\" style=\"color:#E92341;background-color:#DFDFDF;\">57.25</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.18.18.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.6.1\" style=\"background-color:#DFDFDF;\">62.94</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.18.18.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.18.18.7.1\" style=\"color:#E92341;background-color:#DFDFDF;\">51.56</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.19.19\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_rr\" id=\"S5.T3.19.19.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.19.19.1.1\" style=\"background-color:#DFDFDF;\">LCP<sup class=\"ltx_sup\" id=\"S5.T3.19.19.1.1.1\"><span class=\"ltx_text\" id=\"S5.T3.19.19.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.19.19.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.19.19.2.1\" style=\"color:#E92341;background-color:#DFDFDF;\">38.69</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.19.19.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.19.19.3.1\" style=\"color:#E92341;background-color:#DFDFDF;\">43.70</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T3.19.19.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.19.19.4.1\" style=\"color:#E92341;background-color:#DFDFDF;\">33.67</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.19.19.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.19.19.5.1\" style=\"background-color:#DFDFDF;\">64.54</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T3.19.19.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.19.19.6.1\" style=\"background-color:#DFDFDF;\">70.40</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T3.19.19.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T3.19.19.7.1\" style=\"color:#E92341;background-color:#DFDFDF;\">58.67</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T3.20.20\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_rr\" id=\"S5.T3.20.20.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.1.1\" style=\"background-color:#DFDFDF;\">Ours<sup class=\"ltx_sup\" id=\"S5.T3.20.20.1.1.1\"><span class=\"ltx_text ltx_font_medium\" id=\"S5.T3.20.20.1.1.1.1\" style=\"background-color:#DFDFDF;\">\u2020</span></sup></span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T3.20.20.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.2.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">71.55</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T3.20.20.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.3.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">79.37</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_rr\" id=\"S5.T3.20.20.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.4.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">63.73</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T3.20.20.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.5.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">74.50</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T3.20.20.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.6.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">81.41</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b\" id=\"S5.T3.20.20.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.20.20.7.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">67.59</span></td>\n</tr>\n</tbody>\n</table>\n<figcaption class=\"ltx_caption ltx_centering\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S5.T3.31.4.1\" style=\"font-size:90%;\">Table 3</span>: </span><span class=\"ltx_text\" id=\"S5.T3.26.3\" style=\"font-size:90%;\">Accuracy of models trained with different methods on FH37K (left) and FH41K (right) dataset.  means the measurements consider the logical consistency. [Keys: <span class=\"ltx_text ltx_font_bold\" id=\"S5.T3.26.3.1\" style=\"color:#1A09F3;\">Best</span>, <span class=\"ltx_text\" id=\"S5.T3.26.3.2\" style=\"color:#E92341;\">60%</span>, <span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T3.26.3.3\">Second best</span>,  <svg class=\"ltx_picture\" height=\"16.6\" id=\"S5.T3.26.3.pic1\" overflow=\"visible\" version=\"1.1\" width=\"133.77\"><g fill=\"#000000\" stroke=\"#000000\" stroke-width=\"0.4pt\" transform=\"translate(0,16.6) matrix(1 0 0 -1 0 0)\"><g fill=\"#DFDFDF\" fill-opacity=\"1.0\"><path d=\"M 0 2.77 L 0 13.84 C 0 15.37 1.24 16.6 2.77 16.6 L 131 16.6 C 132.53 16.6 133.77 15.37 133.77 13.84 L 133.77 2.77 C 133.77 1.24 132.53 0 131 0 L 2.77 0 C 1.24 0 0 1.24 0 2.77 Z\" style=\"stroke:none\"></path></g><g fill=\"#DFDFDF\" fill-opacity=\"1.0\"><path d=\"M 0 2.77 L 0 13.84 C 0 15.37 1.24 16.6 2.77 16.6 L 131 16.6 C 132.53 16.6 133.77 15.37 133.77 13.84 L 133.77 2.77 C 133.77 1.24 132.53 0 131 0 L 2.77 0 C 1.24 0 0 1.24 0 2.77 Z\" style=\"stroke:none\"></path></g><g fill-opacity=\"1.0\" transform=\"matrix(1.0 0.0 0.0 1.0 2.77 5.19)\"><text color=\"#000000\" transform=\"matrix(1 0 0 -1 0 0)\">Logic involved methods</text></g></g></svg>].\n</span></figcaption>\n</figure>",
            "capture": "Table 3: Accuracy of models trained with different methods on FH37K (left) and FH41K (right) dataset.  means the measurements consider the logical consistency. [Keys: Best, 60%, Second best,  Logic involved methods].\n"
        },
        "4": {
            "table_html": "<figure class=\"ltx_table\" id=\"S5.T4\">\n<table class=\"ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle\" id=\"S5.T4.6\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S5.T4.6.7.1\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t\" id=\"S5.T4.6.7.1.1\" rowspan=\"2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.7.1.1.1\">Methods</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" colspan=\"3\" id=\"S5.T4.6.7.1.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">W/o considering logical consistency</td>\n<td class=\"ltx_td ltx_nopad_l ltx_align_center ltx_border_l ltx_border_t\" colspan=\"3\" id=\"S5.T4.6.7.1.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Considering logical consistency</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.6\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.1.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.2.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T4.3.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.4.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.5.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T4.6.6.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.8.2\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t\" id=\"S5.T4.6.8.2.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">AFFACT (original)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.6.8.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">81.25</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.6.8.2.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">95.72</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T4.6.8.2.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">66.78</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.6.8.2.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.11</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T4.6.8.2.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">93.55</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T4.6.8.2.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">64.67</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.9.3\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.9.3.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">ALM (original)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.9.3.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">81.97</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.9.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.25</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.9.3.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">69.69</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.9.3.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.04</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.9.3.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">91.04</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.9.3.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">67.03</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.10.4\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_tt\" id=\"S5.T4.6.10.4.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">AFFACT</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T4.6.10.4.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.71</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T4.6.10.4.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.6.10.4.3.1\">95.48</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_tt\" id=\"S5.T4.6.10.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">63.95</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T4.6.10.4.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">77.72</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T4.6.10.4.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.6.10.4.6.1\">93.31</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_tt\" id=\"S5.T4.6.10.4.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">62.12</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.11.5\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.11.5.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">ALM</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.11.5.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">80.53</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.11.5.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.10</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.11.5.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">66.95</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.11.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">77.63</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.11.5.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">90.88</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.11.5.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">64.39</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.12.6\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.12.6.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.12.6.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">80.89</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.12.6.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.96</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.12.6.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">66.70</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.12.6.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">77.94</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.12.6.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">92.34</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.12.6.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">63.54</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.13.7\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.13.7.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE-MOON</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.13.7.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.13.7.2.1\" style=\"color:#1A09F3;\">87.13</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.13.7.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">87.95</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.13.7.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.13.7.4.1\" style=\"color:#1A09F3;\">86.32</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.13.7.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">74.76</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.13.7.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">76.24</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.13.7.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.13.7.7.1\" style=\"color:#1A09F3;\">73.28</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.14.8\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.14.8.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BF</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.14.8.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">76.44</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.14.8.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.14.8.3.1\" style=\"color:#1A09F3;\">96.77</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.14.8.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">56.11</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.14.8.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">75.28</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.14.8.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.14.8.6.1\" style=\"color:#1A09F3;\">95.82</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.14.8.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">54.75</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.15.9\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.15.9.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.1.1\" style=\"background-color:#DFDFDF;\">Semantic</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.15.9.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.2.1\" style=\"background-color:#DFDFDF;\">80.66</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.15.9.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.3.1\" style=\"background-color:#DFDFDF;\">94.61</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.15.9.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.4.1\" style=\"background-color:#DFDFDF;\">66.71</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.15.9.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.5.1\" style=\"background-color:#DFDFDF;\">77.72</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.15.9.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.6.1\" style=\"background-color:#DFDFDF;\">91.94</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.15.9.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.15.9.7.1\" style=\"background-color:#DFDFDF;\">63.50</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.16.10\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.16.10.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.1.1\" style=\"background-color:#DFDFDF;\">Constrained</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.16.10.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.2.1\" style=\"background-color:#DFDFDF;\">80.54</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.16.10.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.3.1\" style=\"background-color:#DFDFDF;\">94.91</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.16.10.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.4.1\" style=\"background-color:#DFDFDF;\">66.18</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.16.10.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.5.1\" style=\"background-color:#DFDFDF;\">77.81</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.16.10.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.6.1\" style=\"background-color:#DFDFDF;\">92.35</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.16.10.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.16.10.7.1\" style=\"background-color:#DFDFDF;\">63.27</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.17.11\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r\" id=\"S5.T4.6.17.11.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.17.11.1.1\" style=\"background-color:#DFDFDF;\">LCP</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.17.11.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.17.11.2.1\" style=\"background-color:#DFDFDF;\">81.91</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.17.11.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.17.11.3.1\" style=\"background-color:#DFDFDF;\">94.16</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T4.6.17.11.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.17.11.4.1\" style=\"background-color:#DFDFDF;\">69.66</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.17.11.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.6.17.11.5.1\" style=\"background-color:#DFDFDF;\">78.07</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T4.6.17.11.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.17.11.6.1\" style=\"background-color:#DFDFDF;\">90.26</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T4.6.17.11.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.17.11.7.1\" style=\"background-color:#DFDFDF;\">65.87</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T4.6.18.12\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r\" id=\"S5.T4.6.18.12.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.18.12.1.1\" style=\"background-color:#DFDFDF;\">Ours</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T4.6.18.12.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.6.18.12.2.1\" style=\"background-color:#DFDFDF;\">82.18</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T4.6.18.12.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.18.12.3.1\" style=\"background-color:#DFDFDF;\">93.74</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_rr\" id=\"S5.T4.6.18.12.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.6.18.12.4.1\" style=\"background-color:#DFDFDF;\">70.63</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T4.6.18.12.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.6.18.12.5.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">79.08</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T4.6.18.12.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T4.6.18.12.6.1\" style=\"background-color:#DFDFDF;\">90.89</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b\" id=\"S5.T4.6.18.12.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.6.18.12.7.1\" style=\"background-color:#DFDFDF;\">67.28</span></td>\n</tr>\n</tbody>\n</table>\n<figcaption class=\"ltx_caption ltx_centering\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S5.T4.12.2.1\" style=\"font-size:90%;\">Table 4</span>: </span><span class=\"ltx_text\" id=\"S5.T4.8.1\" style=\"font-size:90%;\">Accuracy of models trained with different methods on CelebA-logic dataset. \u201doriginal\u201d means the model is tested with the same images but using the original annotations. [Keys: <span class=\"ltx_text ltx_font_bold\" id=\"S5.T4.8.1.1\" style=\"color:#1A09F3;\">Best</span>, <span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T4.8.1.2\">Second best</span>,  <svg class=\"ltx_picture\" height=\"16.6\" id=\"S5.T4.8.1.pic1\" overflow=\"visible\" version=\"1.1\" width=\"133.77\"><g fill=\"#000000\" stroke=\"#000000\" stroke-width=\"0.4pt\" transform=\"translate(0,16.6) matrix(1 0 0 -1 0 0)\"><g fill=\"#DFDFDF\" fill-opacity=\"1.0\"><path d=\"M 0 2.77 L 0 13.84 C 0 15.37 1.24 16.6 2.77 16.6 L 131 16.6 C 132.53 16.6 133.77 15.37 133.77 13.84 L 133.77 2.77 C 133.77 1.24 132.53 0 131 0 L 2.77 0 C 1.24 0 0 1.24 0 2.77 Z\" style=\"stroke:none\"></path></g><g fill=\"#DFDFDF\" fill-opacity=\"1.0\"><path d=\"M 0 2.77 L 0 13.84 C 0 15.37 1.24 16.6 2.77 16.6 L 131 16.6 C 132.53 16.6 133.77 15.37 133.77 13.84 L 133.77 2.77 C 133.77 1.24 132.53 0 131 0 L 2.77 0 C 1.24 0 0 1.24 0 2.77 Z\" style=\"stroke:none\"></path></g><g fill-opacity=\"1.0\" transform=\"matrix(1.0 0.0 0.0 1.0 2.77 5.19)\"><text color=\"#000000\" transform=\"matrix(1 0 0 -1 0 0)\">Logic involved methods</text></g></g></svg>]</span></figcaption>\n</figure>",
            "capture": "Table 4: Accuracy of models trained with different methods on CelebA-logic dataset. \u201doriginal\u201d means the model is tested with the same images but using the original annotations. [Keys: Best, Second best,  Logic involved methods]"
        },
        "5": {
            "table_html": "<figure class=\"ltx_table\" id=\"S5.T5\">\n<table class=\"ltx_tabular ltx_centering ltx_align_middle\" id=\"S5.T5.3\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S5.T5.3.3\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Methods</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">5 O\u2019 S</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Bald</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Bangs</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.8\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Goatee</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.9\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Male</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.10\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Mustache</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.3.11\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">No_Beard</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.1.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">\n<sup class=\"ltx_sup\" id=\"S5.T5.1.1.1.1\">\u2217</sup>Hairline</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.2.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">\n<sup class=\"ltx_sup\" id=\"S5.T5.2.2.2.1\">\u2217</sup>Hat</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T5.3.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.4.1\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">AFFACT</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.4.1.2.1\">72.24</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.4.1.3.1\" style=\"color:#1A09F3;\">90.27</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">85.36</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">70.41</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.4.1.6.1\">95.51</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">61.86</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.8\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.4.1.8.1\">85.47</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.9\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.4.1.9.1\">65.69</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T5.3.4.1.10\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.4.1.10.1\" style=\"color:#1A09F3;\">93.93</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T5.3.4.1.11\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">80.08</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.5.2\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">ALM</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.5.2.2.1\" style=\"color:#1A09F3;\">76.34</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">81.81</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">85.08</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">74.27</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">93.88</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">64.51</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.8\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.5.2.8.1\" style=\"color:#1A09F3;\">87.66</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.9\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">62.84</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.5.2.10\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">90.62</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T5.3.5.2.11\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.67</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.6.3\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">65.88</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">75.68</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.6.3.4.1\">86.69</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">76.73</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.78</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">87.80</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.8\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">80.68</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.9\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.6.3.9.1\" style=\"color:#1A09F3;\">67.28</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T5.3.6.3.10\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">89.96</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_tt\" id=\"S5.T5.3.6.3.11\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">80.61</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.7.4\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BCE-MOON</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">69.79</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">70.77</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">82.22</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.7.4.5.1\" style=\"color:#1A09F3;\">80.73</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">82.09</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">82.73</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.8\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">77.40</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.9\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">59.67</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.7.4.10\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">84.20</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T5.3.7.4.11\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">76.62</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.8.5\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">BF</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">59.38</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">78.05</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">78.52</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">69.33</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.8.5.6.1\" style=\"color:#1A09F3;\">96.82</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">87.59</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.8\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">83.12</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.9\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">62.88</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.8.5.10\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.8.5.10.1\">92.13</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T5.3.8.5.11\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">78.65</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.9.6\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.1.1\" style=\"background-color:#DFDFDF;\">Semantic</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.2.1\" style=\"background-color:#DFDFDF;\">65.34</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.3.1\" style=\"background-color:#DFDFDF;\">77.78</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.4.1\" style=\"background-color:#DFDFDF;\">86.87</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.5.1\" style=\"background-color:#DFDFDF;\">76.95</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.6.1\" style=\"background-color:#DFDFDF;\">94.36</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.7.1\" style=\"background-color:#DFDFDF;\">88.21</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.8\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.8.1\" style=\"background-color:#DFDFDF;\">80.54</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.9\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.9.1\" style=\"background-color:#DFDFDF;\">64.98</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.9.6.10\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.10.1\" style=\"background-color:#DFDFDF;\">89.96</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T5.3.9.6.11\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.9.6.11.1\" style=\"background-color:#DFDFDF;\">80.55</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.10.7\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.1.1\" style=\"background-color:#DFDFDF;\">Constrained</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.2.1\" style=\"background-color:#DFDFDF;\">66.61</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.3.1\" style=\"background-color:#DFDFDF;\">78.82</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.4.1\" style=\"background-color:#DFDFDF;\">85.73</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.5.1\" style=\"background-color:#DFDFDF;\">71.73</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.6.1\" style=\"background-color:#DFDFDF;\">94.76</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.7.1\" style=\"background-color:#DFDFDF;\">87.76</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.8\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.8.1\" style=\"background-color:#DFDFDF;\">80.42</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.9\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.9.1\" style=\"background-color:#DFDFDF;\">65.50</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.10.7.10\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.10.1\" style=\"background-color:#DFDFDF;\">91.06</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T5.3.10.7.11\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.10.7.11.1\" style=\"background-color:#DFDFDF;\">80.26</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.11.8\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.1.1\" style=\"background-color:#DFDFDF;\">LCP</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.2.1\" style=\"background-color:#DFDFDF;\">69.83</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.3.1\" style=\"background-color:#DFDFDF;\">82.91</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.4.1\" style=\"background-color:#DFDFDF;\">84.00</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.5.1\" style=\"background-color:#DFDFDF;\">75.33</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.6.1\" style=\"background-color:#DFDFDF;\">92.72</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.11.8.7.1\" style=\"background-color:#DFDFDF;\">88.54</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.8\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.8.1\" style=\"background-color:#DFDFDF;\">81.30</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.9\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.9.1\" style=\"background-color:#DFDFDF;\">63.57</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T5.3.11.8.10\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.11.8.10.1\" style=\"background-color:#DFDFDF;\">89.70</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T5.3.11.8.11\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.11.8.11.1\" style=\"background-color:#DFDFDF;\">80.88</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T5.3.12.9\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.1\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.12.9.1.1\" style=\"background-color:#DFDFDF;\">Ours</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.2\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.12.9.2.1\" style=\"background-color:#DFDFDF;\">68.10</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.3\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.12.9.3.1\" style=\"background-color:#DFDFDF;\">86.03</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.4\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.12.9.4.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">87.79</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.5\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.3.12.9.5.1\" style=\"background-color:#DFDFDF;\">79.05</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.6\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.12.9.6.1\" style=\"background-color:#DFDFDF;\">94.54</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.7\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.12.9.7.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">89.40</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.8\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.12.9.8.1\" style=\"background-color:#DFDFDF;\">81.45</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.9\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.12.9.9.1\" style=\"background-color:#DFDFDF;\">65.55</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T5.3.12.9.10\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T5.3.12.9.10.1\" style=\"background-color:#DFDFDF;\">91.39</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b\" id=\"S5.T5.3.12.9.11\" style=\"background-color:#DFDFDF;padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.3.12.9.11.1\" style=\"color:#1A09F3;background-color:#DFDFDF;\">82.59</span></td>\n</tr>\n</tbody>\n</table>\n<figcaption class=\"ltx_caption ltx_centering\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S5.T5.15.4.1\" style=\"font-size:90%;\">Table 5</span>: </span><span class=\"ltx_text\" id=\"S5.T5.9.3\" style=\"font-size:90%;\">Accuracy values of the attributes that have strong logical relationships in CelebA-logic with considering the logical consistency. 5 O\u2019 S, <sup class=\"ltx_sup\" id=\"S5.T5.9.3.1\">\u2217</sup>Hairline, and <sup class=\"ltx_sup\" id=\"S5.T5.9.3.2\">\u2217</sup>Hat are 5 O\u2019clock Shadow, Receding Hairline and Wearing Hat. [Keys: <span class=\"ltx_text ltx_font_bold\" id=\"S5.T5.9.3.3\" style=\"color:#1A09F3;\">Best</span>, <span class=\"ltx_text ltx_framed ltx_framed_underline\" id=\"S5.T5.9.3.4\">Second best</span>,  <svg class=\"ltx_picture\" height=\"16.6\" id=\"S5.T5.9.3.pic1\" overflow=\"visible\" version=\"1.1\" width=\"133.77\"><g fill=\"#000000\" stroke=\"#000000\" stroke-width=\"0.4pt\" transform=\"translate(0,16.6) matrix(1 0 0 -1 0 0)\"><g fill=\"#DFDFDF\" fill-opacity=\"1.0\"><path d=\"M 0 2.77 L 0 13.84 C 0 15.37 1.24 16.6 2.77 16.6 L 131 16.6 C 132.53 16.6 133.77 15.37 133.77 13.84 L 133.77 2.77 C 133.77 1.24 132.53 0 131 0 L 2.77 0 C 1.24 0 0 1.24 0 2.77 Z\" style=\"stroke:none\"></path></g><g fill=\"#DFDFDF\" fill-opacity=\"1.0\"><path d=\"M 0 2.77 L 0 13.84 C 0 15.37 1.24 16.6 2.77 16.6 L 131 16.6 C 132.53 16.6 133.77 15.37 133.77 13.84 L 133.77 2.77 C 133.77 1.24 132.53 0 131 0 L 2.77 0 C 1.24 0 0 1.24 0 2.77 Z\" style=\"stroke:none\"></path></g><g fill-opacity=\"1.0\" transform=\"matrix(1.0 0.0 0.0 1.0 2.77 5.19)\"><text color=\"#000000\" transform=\"matrix(1 0 0 -1 0 0)\">Logic involved methods</text></g></g></svg>]</span></figcaption>\n</figure>",
            "capture": "Table 5: Accuracy values of the attributes that have strong logical relationships in CelebA-logic with considering the logical consistency. 5 O\u2019 S, \u2217Hairline, and \u2217Hat are 5 O\u2019clock Shadow, Receding Hairline and Wearing Hat. [Keys: Best, Second best,  Logic involved methods]"
        },
        "6": {
            "table_html": "<figure class=\"ltx_table\" id=\"S5.T6\">\n<table class=\"ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle\" id=\"S5.T6.6\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S5.T6.6.7.1\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t\" id=\"S5.T6.6.7.1.1\" rowspan=\"2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text\" id=\"S5.T6.6.7.1.1.1\">Methods</span></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" colspan=\"3\" id=\"S5.T6.6.7.1.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">W/o considering logical consistency</td>\n<td class=\"ltx_td ltx_nopad_l ltx_align_center ltx_border_l ltx_border_t\" colspan=\"3\" id=\"S5.T6.6.7.1.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Considering logical consistency</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.6\">\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.1.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.2.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T6.3.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.4.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.5.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T6.6.6.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.8.2\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_t\" id=\"S5.T6.6.8.2.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Adversarial learning (preds)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.6.8.2.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">82.63</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.6.8.2.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">93.42</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_t\" id=\"S5.T6.6.8.2.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">71.83</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.6.8.2.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">65.94</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T6.6.8.2.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">74.18</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T6.6.8.2.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">57.70</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.9.3\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r\" id=\"S5.T6.6.9.3.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Reward model (BoL)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.9.3.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">81.90</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.9.3.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">93.04</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T6.6.9.3.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">70.77</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.9.3.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">65.04</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.9.3.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">73.23</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T6.6.9.3.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">56.86</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.10.4\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r\" id=\"S5.T6.6.10.4.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">LogicNet (preds + BoL)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.10.4.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.10.4.2.1\" style=\"color:#1A09F3;\">83.65</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.10.4.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.10.4.3.1\" style=\"color:#1A09F3;\">93.46</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T6.6.10.4.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.10.4.4.1\" style=\"color:#1A09F3;\">73.83</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.10.4.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.10.4.5.1\" style=\"color:#1A09F3;\">71.55</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.10.4.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.10.4.6.1\" style=\"color:#1A09F3;\">79.37</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T6.6.10.4.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.10.4.7.1\" style=\"color:#1A09F3;\">63.73</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.11.5\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_tt\" id=\"S5.T6.6.11.5.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Adversarial learning (preds)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.11.5.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.11.5.2.1\" style=\"color:#1A09F3;\">85.72</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.11.5.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.12</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_tt\" id=\"S5.T6.6.11.5.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.11.5.4.1\" style=\"color:#1A09F3;\">77.32</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.11.5.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">72.83</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.11.5.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.38</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_tt\" id=\"S5.T6.6.11.5.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">66.28</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.12.6\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r\" id=\"S5.T6.6.12.6.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Reward model (BoL)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.12.6.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">85.48</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.12.6.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.05</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T6.6.12.6.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">76.91</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.12.6.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">73.03</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.12.6.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">79.96</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T6.6.12.6.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">66.11</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.13.7\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r\" id=\"S5.T6.6.13.7.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">LogicNet (preds + BoL)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.13.7.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">85.66</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.13.7.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.13.7.3.1\" style=\"color:#1A09F3;\">94.23</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T6.6.13.7.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">77.10</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.13.7.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.13.7.5.1\" style=\"color:#1A09F3;\">74.50</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.13.7.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.13.7.6.1\" style=\"color:#1A09F3;\">81.41</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T6.6.13.7.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.13.7.7.1\" style=\"color:#1A09F3;\">67.59</span></td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.14.8\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_tt\" id=\"S5.T6.6.14.8.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Adversarial learning (preds)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.14.8.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">81.46</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.14.8.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.14.8.3.1\" style=\"color:#1A09F3;\">94.42</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr ltx_border_tt\" id=\"S5.T6.6.14.8.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">68.49</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.14.8.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">77.95</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_tt\" id=\"S5.T6.6.14.8.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">91.07</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_tt\" id=\"S5.T6.6.14.8.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">64.82</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.15.9\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_r\" id=\"S5.T6.6.15.9.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Reward model (BoL)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.15.9.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">80.65</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.15.9.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">94.18</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_rr\" id=\"S5.T6.6.15.9.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">67.12</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.15.9.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">78.15</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r\" id=\"S5.T6.6.15.9.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.15.9.6.1\" style=\"color:#1A09F3;\">91.72</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center\" id=\"S5.T6.6.15.9.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">64.58</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T6.6.16.10\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_r\" id=\"S5.T6.6.16.10.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">LogicNet (preds + BoL)</th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T6.6.16.10.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.16.10.2.1\" style=\"color:#1A09F3;\">82.18</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T6.6.16.10.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">93.74</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_rr\" id=\"S5.T6.6.16.10.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.16.10.4.1\" style=\"color:#1A09F3;\">70.63</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T6.6.16.10.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.16.10.5.1\" style=\"color:#1A09F3;\">79.08</span></td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r\" id=\"S5.T6.6.16.10.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">90.89</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b\" id=\"S5.T6.6.16.10.7\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"><span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.6.16.10.7.1\" style=\"color:#1A09F3;\">67.28</span></td>\n</tr>\n</tbody>\n</table>\n<figcaption class=\"ltx_caption ltx_centering\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S5.T6.9.1.1\" style=\"font-size:90%;\">Table 6</span>: </span><span class=\"ltx_text\" id=\"S5.T6.10.2\" style=\"font-size:90%;\">Ablation study for training a logic discriminator resulting in the accuracy of the classifier. The testing sets are FH37K (Top), FH41K (Middle), CelebA-logic (Bottom). [Keys: <span class=\"ltx_text ltx_font_bold\" id=\"S5.T6.10.2.1\" style=\"color:#1A09F3;\">Best</span>]</span></figcaption>\n</figure>",
            "capture": "Table 6: Ablation study for training a logic discriminator resulting in the accuracy of the classifier. The testing sets are FH37K (Top), FH41K (Middle), CelebA-logic (Bottom). [Keys: Best]"
        },
        "7": {
            "table_html": "<figure class=\"ltx_table\" id=\"S5.T7\">\n<table class=\"ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle\" id=\"S5.T7.1\">\n<tbody class=\"ltx_tbody\">\n<tr class=\"ltx_tr\" id=\"S5.T7.1.2.1\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_th ltx_th_row ltx_border_r ltx_border_t\" id=\"S5.T7.1.2.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T7.1.2.1.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">baseline</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T7.1.2.1.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Semantic</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T7.1.2.1.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Constrained</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_r ltx_border_t\" id=\"S5.T7.1.2.1.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">LCP</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_t\" id=\"S5.T7.1.2.1.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">Ours</td>\n</tr>\n<tr class=\"ltx_tr\" id=\"S5.T7.1.1\">\n<th class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r ltx_border_t\" id=\"S5.T7.1.1.1\" style=\"padding-left:1.4pt;padding-right:1.4pt;\"></th>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r ltx_border_t\" id=\"S5.T7.1.1.2\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">1.78h</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r ltx_border_t\" id=\"S5.T7.1.1.3\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">8.12h</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r ltx_border_t\" id=\"S5.T7.1.1.4\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">9.77h</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_r ltx_border_t\" id=\"S5.T7.1.1.5\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">5.32h</td>\n<td class=\"ltx_td ltx_nopad_l ltx_nopad_r ltx_align_center ltx_border_b ltx_border_t\" id=\"S5.T7.1.1.6\" style=\"padding-left:1.4pt;padding-right:1.4pt;\">3.6h</td>\n</tr>\n</tbody>\n</table>\n<figcaption class=\"ltx_caption ltx_centering\"><span class=\"ltx_tag ltx_tag_table\"><span class=\"ltx_text\" id=\"S5.T7.3.1.1\" style=\"font-size:90%;\">Table 7</span>: </span><span class=\"ltx_text\" id=\"S5.T7.4.2\" style=\"font-size:90%;\">Training time for 20 epochs on CelebA-logic. Hardware: 4 RTX6000 GPUs. Backbone: ResNet50. Baseline: BCE method.\n</span></figcaption>\n</figure>",
            "capture": "Table 7: Training time for 20 epochs on CelebA-logic. Hardware: 4 RTX6000 GPUs. Backbone: ResNet50. Baseline: BCE method.\n"
        }
    },
    "image_paths": {
        "1": {
            "figure_path": "2311.11208v2_figure_1.png",
            "caption": "Figure 1: Regular and logical tests on two model types. Model 1 and Model 2 trained without and with logical relationships between predicted results, respectively. In real-world deployment, Model 2 provides more reliable predictions.",
            "url": "http://arxiv.org/html/2311.11208v2/extracted/5870621/images/teaser_figure.png"
        },
        "2": {
            "figure_path": "2311.11208v2_figure_2.png",
            "caption": "Figure 2: Strong logical relationship between attributes in CelebA. The attributes are split to three categories. Strong: Impossible in most cases. Weak: Rarely possible in some cases. Independent/Ambiguous: The attributes are either ambiguous on definitions [47, 27]. The latter two are in the Supplementary Material.",
            "url": "http://arxiv.org/html/2311.11208v2/extracted/5870621/images/strong-rela.png"
        },
        "3": {
            "figure_path": "2311.11208v2_figure_3.png",
            "caption": "Figure 3: The proposed LogicNet. The weights of multi-attribute classifier and discriminator are updated alternatively. Y\u2032superscript\ud835\udc4c\u2032Y^{\\prime}italic_Y start_POSTSUPERSCRIPT \u2032 end_POSTSUPERSCRIPT is either the predictions of the classifier or the poisoned labels from BoL algorithm. Yl\u2062o\u2062g\u2062i\u2062csubscript\ud835\udc4c\ud835\udc59\ud835\udc5c\ud835\udc54\ud835\udc56\ud835\udc50Y_{logic}italic_Y start_POSTSUBSCRIPT italic_l italic_o italic_g italic_i italic_c end_POSTSUBSCRIPT is the logical consistency label vector.",
            "url": "http://arxiv.org/html/2311.11208v2/extracted/5870621/images/algorithm.png"
        }
    },
    "validation": true,
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