Introduction
Relation extraction (RE) aims to extract predefined relations between two marked entities in plain texts, and its success can benefit many knowledge base (KB) related tasks like knowledge base population (KBP) [11, 14], question answering (QA) [3, 15, 7] and etc.
Most existing works investigate the RE
task in a classification style. A sentence marked with a given pair of entities is fed to a classifier to decide their relationship, also called the
sentencelevel RE. Another related setup is to feed a group of sentences containing the given entity pair to the classifier, called the baglevel RE. We should note that both sentencelevel RE and baglevel RE make predictions for each entity pair individually and locally. However, when we look at the model outputs globally, there are always contradictions among different predictions, such as an entity is regarded as the object of both Country and City, two different cities have been labeled as Capitalfor one country and so on. To alleviate these local contradictions, chen2018encoding chen2018encoding collect constraints on the type and cardinality requirements of relations, such as whether two relations should not have the same type of subject (object), or whether a relation should not have multiple subjects (objects) given its object (subject). Further, in the inference stage, they use integer linear programming (
ILP) to filter and adjust the local predictions that are inconsistent with these constraints. Basically, ILP operates in a postprocessing way to copy with contradictory predictions, but there is no way to provide feedback to the original RE model.In fact, it would be of great importance to utilize those constraints to backwards improve the original RE models. For example, enhanced with various attention or pooling mechanisms, most current neural network extraction models have shown promising performance on benchmark datasets, but they still suffer from inconsistent local predictions [2]. If those relation constraints can be learned during model training, that will help to further improve the overall performance, and we may no longer need a separate postprocessing step as ILP does.
However, directly integrating relation constraints with NRE models is not a trivial task: (1) relation constraints are not defined regarding a single prediction, but often over combinations of instances, thus it is not easy to find appropriate representations for those constraints; (2) it is not easy to evaluate how well pairwise predictions match the constraints in a batch, and it is not clear how to feed the information back to the NRE models.
To tackle the challenges, we propose a unified framework to flexibly integrate relation constraints with NRE models by introducing a loss term Constraint Loss. Concretely, we develop two methods denoted as Coherent and Semantic to construct Constraint Loss from different perspectives. Coherent captures how well pairwise predictions match the constraints from an overall perspective, and Semantic pays more attention to which specific rule in the constraints the pairwise predictions should satisfy. In addition, we encode relation constraints into different representations for each method. Notably, Constraint Loss is regarded as a rulebased regularization term within a batch instead of regularizing each instance, since the relation constraints are often defined over combinations of local predictions. Moreover, our approach does not bring extra cost to the inference phase and can be adapted to most existing NRE models without explicit modifications to their structures, as it only utilizes the outputs from the NRE model as well as relation constraints to obtain Constraint Loss and provides feedback to the NRE model through backward propagation. Experiments on both Chinese and English datasets show that our approach can help popular NRE models learn from the constraints and outperforms stateoftheart methods even enhanced with ILP postprocessing. Moreover, jointing our approach and ILP achieves further improvement which demonstrates that our approach and the ILP postprocessing exploit complementary aspects from the constraints.
The main contributions of this paper include: (1) We propose a unified framework to effectively integrate NRE models with relation constraints without interfering the inherent NRE structure. (2) We develop two efficient methods to capture the inconsistency between local NRE outputs and relation constraints, which are used as a loss term to help the NRE training. (3) We provide thoroughly experimental study on different datasets and base models. The results show that our approach is effective and exploits the constraints from different perspectives with ILP.
Related Work
Since annotating highquality relational facts in sentences is laborious and timeconsuming, RE is usually investigated in the distant supervision (DS) paradigm, where datasets are automatically constructed by aligning existing KB triples ^{1}^{1}1We use , and to denote subject, object and relation for a KB triple, respectively, in the rest of this paper. with a large text corpus [9]. However, the automatically constructed dataset suffers the wrong labeling problem, where the sentence that mentions the two target entities may not express the relation they hold in KB, thus contains many false positive labels [10]. To alleviate the wrong labeling problem, RE is usually investigated in the multiinstance learning (MIL) framework which considers RE task at baglevel and holds the atleastone hypothesis, thinking that there exists at least one sentence which expresses the entity pair’s relation in its corresponding sentence bag [5, 12, 11].
As neural networks have been widely used, an increasing number of researches for RE have been proposed under MIL
framework. zeng2014relation zeng2014relation use a convolution neural network (
CNN) to automatically extract features and zeng2015distant zeng2015distant use a piecewise convolution neural network (PCNN) to capture structural information by inherently splitting a sentence into three segments according to the two target entities. Furthermore, lin2016neural lin2016neural proposed sentencelevel attentionbased models (ACNN, APCNN) to dynamically reduce the weights of noisy sentences. And there also exists many NN based works improving the RE performance by utilizing external information, such as syntactic information [4], entity description [6], relation aliases [13] and etc.In addition, there are many works focusing on combining NNs
with precise logic rules to harness flexibility and reduce uninterpretability of the neural models. hu2016harnessing hu2016harnessing make use of firstorder logic (FOL) to express the constraints and propose a teacherstudent network that could project prediction probability into a ruleregularized subspace and transfer the information of logic rules into the weights of neural models. DBLP:conf/icml/XuZFLB18 DBLP:conf/icml/XuZFLB18 put forward a semantic loss framework, which bridges between neural output vectors and logical constraints by evaluating how close the neural network is to satisfying the constraints on its output with a loss term. And luo2018marrying luo2018marrying develop novel methods to exploit the rich expressiveness of regular expressions at different levels within a
NN, showing that the combination significantly enhances the learning effectiveness when a small number of training examples are available.However, using these frameworks on RE is not straightforward. Specifically, hu2016harnessing hu2016harnessing directly project prediction probability of instance as they can assess how well a single instance’s prediction satisfies the rules, while constraints in RE are nonlocal and we could not examine each instance individually for the violation of constraints. luo2018marrying luo2018marrying need the regular expressions to provide keyword information and get a priori category prediction, however, generating highquality regular expressions from RE datasets is not easy. For DBLP:conf/icml/XuZFLB18 DBLP:conf/icml/XuZFLB18, since our constraints are related to the combination of instances rather than a single instance, to utilize the semantic loss framework, we need to find appropriate representations for various relation constraints and evaluate the neural output in a pairwise way.
Relation Constraints
Since many KBs do not have a welldefined typing system and explicit argument cardinality requirements, similar in spirit with chen2018encoding chen2018encoding, our relation constraints are defined over the combination of two triples: and . ^{2}^{2}2The main difference is that our constraints are considered as positive rules where we expect the relation predictions to fall in, while the constraints in chen2018encoding chen2018encoding are considered as inviolate rules that the local predictions should not break. We derive the type and cardinality constraints from existing KB to implicitly capture the expected type and cardinality requirements on the arguments of a relation. One can surely employ human annotators to collect such constraints.
Type Constraints.
Type constraints implicitly express the types of subjects and objects that a specific relation could have. For example, the subject and object types for relation almaMater should be person and school, respectively, and we take positive rules [almaMater and knownFor could have the same subject type] and [almaMater and employer could have the same object type] to implicitly encode almaMater’s subject and object type requirements.
Specifically, we use entity sharing between different relations to implicitly capture the expected argument type of each relation. If the subject (or object) set of relation in KB has an intersection with those of , then we consider and could have the same expected subject (or object) type. We thereby assign relation pairs (, ) into if they are expected to have the same subject type, into if they are expected to have the same object type, and assign it into if the subject type of one relation is expected to be same as the object type of the other.
Cardinality Constraints.
Cardinality constraints indicate the cardinality requirements on a relation’s arguments. For example, relation almaMater could have multiple subjects (person) when its object (school) is given.
Specifically, for each predefined relation , we collect all triples containing , and count the number of the triples that have multiple objects (subjects) for each subject (object). Then, we assign relation into if it can have multiple subjects for a given object, into if it can have multiple objects for a given subject.
Finally, we get 5 subcategory constraint sets. We use to represent a single set, to represent a type constraint set, and to represent a cardinality constraint set. Note that our relation constraints are defined to examine whether a pair of subjectrelationobject triples can hold at the same time from different perspectives. To make our constraints clearer, we list some rules for each constraint set in Table 1.
Set  Sampled Positive Rules  










Our Approach
As shown in Fig. 1, our framework consists of two main components, a base NRE model and the Constraint Loss Calculator (CLC). The CLC module is designed to integrate the relation constraints with NRE models, which does not rely on specific NRE architectures and can work in a plugandplay fashion.
Base NRE Model
While our framework can work with most existing relation extractors, in this paper, we take the most popular neural relation extractors, ACNN and APCNN [8], as our base extractors. ^{3}^{3}3We do not use the most recently neural models, such as feng2018reinforcement feng2018reinforcement, qin2018dsgan qin2018dsgan and jia2019arnor jia2019arnor, as our base model, as they focused more on noise reduction which is not within the scope of this paper.
ACNN
uses convolution neural networks with maxpooling layer to capture the most significant features from a sentence. Then, an attention layer is used to selectively aggregate individual representations from a bag of sentences into a sentence bag embedding, which is fed to a softmax classifier to predict the relation distribution
.APCNN is an extension of ACNN. Specifically, APCNN divides the convolution output into three segments based on the positions of the two given entities and devises a piecewise maxpooling layer to produce sentence representation.
Constraint Loss Calculator (CLC)
Given the inherent nature of our relation constraints, the CLC can not evaluate a single subjectrelationobject prediction against our constraint sets, we thus operate our CLC in a minibatch wise way. Specifically, in each batch, we integrate the relation constraints with the NRE output by introducing a loss term, Constraint Loss, which is designed to regulate the NRE model to learn from those constraints, e.g., not to violate the positive rules in the constraints. As shown in Fig. 1, to calculate Constraint Loss, we first collect the NRE output probability within the batch, and then the CLC takes and relation constraints as input to obtain Constraint Loss, which should reflect the inconsistency among all local predictions according to our relation constraints. Finally, the total loss for back propagation consists of two parts: the original NRE loss () and the Constraint Loss ():
where is a weight coefficient.
Particularly, the key task of CLC is to evaluate how well the current NRE output probabilities satisfy our relation constraints. We solve this problem in two steps. We first calculate a local loss term for a pair of local predictions, i.e., and for the and instances, respectively, ^{4}^{4}4We use to represent the probability output of the neural model on the instance in a batch. against the constraint set . Secondly, we aggregate all local loss terms to obtain the batchwise Constraint Loss. Here, we develop two methods to calculate Constraint Loss from different perspectives, denoted as Coherent (Coh) and Semantic (Sem), respectively.
Coherent (Coh)
In this method, we calculate Constraint Loss by evaluating the coherence between the NRE output and a constraint set. Note that this method only requires the NRE outputs to be more consistent with one constraint set as a whole, but does not explicitly push the NRE model to update according to specific positive rules in this set.
Representing Constraint Sets.
We encode a constraint set into one single binary vector. Since the positive rules in the type and cardinality constraint set have different forms, we represent them in slightly different ways.
For a type constraint set , we construct a binary vector , where indicates whether relation pair belongs to , i.e., if and if . Take illustrated in Fig. 2 as an example, since , is set to 1.
For a cardinality constraint set , we construct a binary vector , where indicates whether relation belongs to , i.e., if and if . Again, in Fig.2, is set to 1, since .
Thus, for each one of the 5 subcategory constraint sets, we build one single representation vector, resulting in 5 vectors . And the dimensions of and are and , respectively, where is the size of the relation set.
Local Loss Calculation.
Now, we proceed to calculate the loss term for a pair of local predictions, e.g., the and instances, within a batch. Our expectation is that coherent local prediction pairs should satisfy our constraint sets. Again, we deal with the type constraint sets and cardinality constraint sets separately.
Thus, for a type constraint set represented by , the local loss, , can be written as:
(1) 
where indicates whether to calculate . Take as an example, for triple pair and , we set , if which means the two triples have the same subject type and corresponding predicted relation pair should satisfy ; otherwise, we assign 0 to .^{5}^{5}5Detailed assignment for can be found in Appendix. can be considered as the probability that the base NRE model predicts relation and for the and instances, respectively.
For cardinality constraint set represented by , the local loss, , can be written as:
(2) 
where is an indicator similar to and is seen as the possibility that the base NRE predicts relation for both the and instances.
Aggregation.
To obtain the batchwise Constraint Loss, we simply sum all the local loss terms in a batch to get the total constraint loss (Eq. 3).
(3) 
Semantic (Sem)
In this method, we pay more attention to which specific rules in the constraint sets the pairwise local predictions should satisfy. Our intuition is that, for each of our constraint set, good local predictions should follow one rule in that set, while bad ones may not find any rules to satisfy. This may push the NRE model to effectively learn from specific rules in a more focused way.
Representing Constraints.
To represent the rules in the constraint sets more precisely, we encode each rule into a single binary vector , thus, the whole set is represented as a vector set , shown as in Fig. 2. Again, since the rules in and have different forms, we represent them in different ways.
For each type rule , the representation vector is a binary vector whose and dimensions are set to 1 and the rest are set to 0. Take in Fig. 2 as an example, the rule is encoded as a vector whose first two dimensions are set to 1.
For each cardinality rule , the representation vector is a binary vector whose dimension is set to 1 and the rest are set to 0. In Fig. 2, the rule is represented by a vector, where only the first dimension is set to 1.
Different from Coherent, here we construct one vector set to represent each subcategory constraint sets, resulting in 5 vector sets . And each single rule is represented by a dim binary vector.
Local Loss Calculation.
Inspired by the semantic loss function (
SL) introduced in DBLP:conf/icml/XuZFLB18 DBLP:conf/icml/XuZFLB18, which operates on a single output, we adapt the original SL to deal with pairwise instances over different kinds of constraints. We design the new local loss term as:(4) 
where is an indicator same as before and is a score function reflecting how well the pairwise predictions match a single rule . Since the rules in and are encoded in different ways, we calculate for type constraint sets and cardinality constraint sets separately.
Thus, for a rule in type constraint set , the score function can be calculated by:
(5) 
where is the vector representation of and is the probability that base NRE model predicts relation for at least one of the and the instances.
For a rule in cardinality constraint set , can be calculated by:
(6) 
where means the probability that NRE model predicts relation for both the and the instances.
Aggregation.
We use the same method as Coherent to perform aggregation according to Eq. 3.
Note that Coherent handles the constraint set as a whole and treats each single rule in that set equally, while Semantic treats all rules in a constraint set as mutually exclusive and makes the pairwise predictions more satisfying one certain rule in that set. Take as an example, in Eq. 2, Coherent just simply increases the probabilities of corresponding relation pairs for all positive rules, and each rule has the same influence on the summation. However, in Eq. 6, for a potentially satisfied rule, Semantic not only tries to increase the probabilities of its corresponding relation pair, but also lowers the probabilities of the rest. That is, there would not exist pairwise local predictions which satisfy two positive rules well in one constraint set at the same time, since if the high probabilities of a relation pair have the positive effect on one specific rule, it has negative effect on all the others.
Experiments
Our experiments are designed to answer the following questions: (1) whether our approach can effectively utilize the relation constraints to improve the extraction performance? (2) which CLC module performs better, Coherent or Semantic? (3) which is the better way to utilize the relation constraints, learning or postprocessing?
Datasets
We evaluate our approach on both English and Chinese datasets constructed by chen2018encoding chen2018encoding. The English one is constructed by mapping triples in DBpedia [1] to sentences in the New York Times Corpus. It has 51 relations, about 50k triples, 134k sentences for training and 30k triples, 53k sentences for testing. The Chinese dataset is built by mapping the triples of HudongBaiKe, a large Chinese encyclopedia, with four Chinese economic newspapers. It contains 28 relations, about 60k triples, 120k sentences for training and 40k triples, 83k sentences for testing.
We automatically collect relation constraints for English and Chinese datasets based on corresponding KBs. In total, we obtain 541 rules for the English dataset and 110 rules for the Chinese one.
Here we do not use the popular RE dataset created by riedel2010modeling riedel2010modeling, since it is produced with an earlier version of Freebase which is not available now, and makes it impossible to automatically collect the constraints. Secondly, Riedel’s dataset is dominated by three big relations: location/contains, /people/nationality and /people/place_lived, covering about 60% of all KB triples. Therefore, there are not enough data related to other relations for us to collect constraints.
Setup
Following common practice in the RE community [6, 4], we report the model performance by both precisionrecall (PR) curve and Precision@N (P@N). We also report the average score of P@N (Mean).
The main goal of our work is to explore whether our approach can help neural models effectively learn from discrete relation constraints. Therefore, the first baseline models are the two most popular base NRE models, ACNN and APCNN. We also compare with the base NRE models enhanced with a postprocessing ILP step, ACNN+ILP and APCNN+ILP, which can be considered as stateoftheart constraintbased RE solutions.
We use a grid search to tune our hyper parameters, including the weight coefficient . Details about our hyper parameters are reported in Appendix.
Main Results
English Dataset  Chinese Dataset  

Model Name  P@100  P@200  P@300  Mean  P@100  P@200  P@300  Mean  
ACNN  96.70  92.61  91.72  93.68  –  89.08  86.89  84.52  86.83  – 
ACNN(Coh)  97.39  93.78  90.69  93.96  +0.3  95.86  94.86  93.04  94.59  +7.8 
ACNN(Sem)  97.62  95.87  94.12  95.87  +2.2  95.97  94.61  93.53  94.70  +8.1 
ACNN+ILP  97.87  94.36  93.16  95.13  +1.5  93.75  92.18  90.10  92.01  +5.2 
ACNN(Coh)+ILP  97.73  94.51  91.29  94.51  +0.8  97.09  96.18  94.01  95.76  +9.0 
ACNN(Sem)+ILP  98.17  96.6  95.48  96.75  +3.1  97.73  96.40  94.43  96.18  +9.4 
APCNN  100  98.97  97.41  98.79  –  92.96  91.75  91.08  91.93  – 
APCNN(Coh)  100  99.57  97.33  98.97  +0.2  98.88  96.00  94.98  96.62  +4.7 
APCNN(Sem)  100  100  97.95  99.32  +0.5  100  96.97  93.42  96.80  +4.9 
APCNN+ILP  100  99.13  97.55  98.89  +0.1  96.06  95.15  94.63  95.28  +3.4 
APCNN(Coh)+ILP  100  100  98.03  99.34  +0.6  99.07  96.17  95.16  96.79  +4.9 
APCNN(Sem)+ILP  100  100  98.39  99.46  +0.7  100  97.67  94.25  97.31  +5.4 
Our main results are summarized in Fig. 3 and Table 2. As shown in Fig. 3, we can see that both the red and green dot lines are lifted above the solid black lines, showing that after equipped with our CLC modules, i.e., Coherent and Semantic, both ACNN and APCNN obtain significant improvement on the English and Chinese datasets. This indicates our CLC module actually helps the base NRE models benefit from properly utilizing the relation constraints, without interference to the base models.
However, we find that our approach obtains different levels of improvement on the two datasets. On the Chinese one, as shown in Table 2, with our Semantic version CLC, APCNN(Sem) gains 4.9% improvement in Mean compared to APCNN, but, on the English dataset, it only receives 0.5% in Mean. Similar trends are also found for the Coherent version and the ACNN base model. The better performance gain on the Chinese dataset is mainly because its relation definitions are more clear compared to that of the English dataset. For example, in English dataset, there are 8 relations whose object could be any location, such as birthPlace, while only 3 similar relations exist in Chinese dataset.
In addition, we investigate the performance improvement when applying our CLC module to different base NRE models. Although both ACNN and APCNN are improved by our CLC module in various datasets, we can still observe that ACNN generally receives more performance improvement compared with the APCNN base model. Taking the Semantic method as an example, as shown in Table 2, on the English dataset, ACNN(Sem) obtains 2.2% performance improvement in Mean against ACNN, while APCNN(Sem) only fetches 0.5% improvement. And similar trends can be found in the Coherent method and on the Chinese dataset. The more improvement when taking the ACNN as base NRE model is because, compared with ACNN, APCNN itself is designed to take the entityaware sentence structure information into account, thus can extract more effective features that, to some extent, can implicitly capture part of the arguments’ type and cardinality requirements of a relation, leaving relatively less space for our CLC module to improve.
Comparing Coherent and Semantic
This paper presents two different methods, Coh and Sem, to represent and integrate the relation constraints, both of which can lead to substantial improvement with both base models and datasets. Specifically, as shown in Table 2, Sem brings slightly more improvement than Coh in most of the settings, e.g., on Chinese dataset, APCNN(Sem) obtain about 0.2% more gains (4.9% vs 4.7%) in Mean than APCNN(Coh). We think the reason is that Sem provides a more precise treatment for the constraints, e.g., embedding each rule with a vector and trying to evaluate the NRE output against one specific rule, while Coh represents all rules in a subcategory with one single vector and evaluates the output against whole set of rules, which is admittedly a more coarse fashion.
Learning? or Postprocessing?
Previous works show that ILP can effectively solve the inconsistency among predictions in a postprocessing fashion [2].
Now we discuss which is the better way to utilize the relation constraints, our CLC module or traditional ILP postprocessing. As shown in Table 2, both APCNN(Sem) and APCNN(Coh) outperforms APCNN+ILP by at least 0.1% on the English dataset and 1.0% on the Chinese dataset. Similar trends can be also found for ACNN(Sem) and ACNN(Coh). This shows that helping base NRE models to learn from the relation constraints can generally bring more improvement, thus utilizes the constraints more effectively compared to utilizing those constraints in a postprocessing way.
We can also apply ILP as a postprocessing step to our approach, since our CLC module works in the model training phase, and leaves the testing phase as it is. Interestingly, as shown in Table 2, with an extra ILP postprocessing, both Coh and Sem obtain further improvement with different base NRE models on different datasets. This indicates that our CLC module still may not fully exploit the useful information behind the relation constraints. The reasons may be that our approach and the ILP postprocessing exploit the relation constraints from different perspectives. For example, our CLC operates in a minibatch level during training, that is a relatively local view, but ILP postprocessing directly optimizes the model output in a slightly global view.
Moreover, in Table 3, we find that applying ILP to our CLC enhanced model receives relatively less gain compared to applying ILP to the base model, e.g., 0.5% for APCNN(Sem) v.s. 3.4% for APCNN on the Chinese dataset. This observation may indicate that our approach has pushed NRE base models to learn part of the useful information behind relation constraints, leaving fewer inconsistent outputs for ILP postprocessing to filter out. On the other hand, this observation shows again that our CLC approach and the ILP postprocessing exploit complementary aspects from the relation constraints, and our CLC module could be further improved by taking more global optimization into account.
English  Chinese  

Mean  Mean  
ACNN  93.68  +1.5  86.83  +5.2 
ACNN(Coh)  93.86  +0.6  94.59  +1.2 
ACNN(Sem)  95.87  +0.9  94.70  +1.5 
APCNN  98.79  +0.1  91.93  +3.4 
APCNN(Coh)  98.97  +0.4  96.62  +0.2 
APCNN(Sem)  99.32  +0.1  96.80  +0.5 
More Analysis
To better understand what our approach learns from the constraints, we take a deep look at the outputs of APCNN and APCNN(Sem) on the test split of the Chinese dataset. First, we count the total number of contradictory pairwise predictions and find that applying our Semantic method to APCNN achieves a reduction of 5,966 violations, 28.0% of the total^{6}^{6}6Detailed numbers per category are reported in Appendix.. This indicates our approach has pushed the base NRE models to learn from the relation constraints. However, there are still many remaining violations since our approach operates during training in a soft and local way, compared to ILP during testing.
Another observation is that our approach actually reduces the violations related to each relations, and especially does better when there are tighter requirements on the relation’s arguments. For example, APCNN(Sem) reduces 89.6% violations for relation locationState compared to APCNN, but for locationRegion, it only reduces 36.3%. This is because the relation constraints may indicate more clear arguments’ type requirements for locationState than those of locationRegion, which are captured by our CLC module to push into the base NRE during training.
Conclusion
In this paper, we propose a unified framework to effectively integrate discrete relation constraints with neural networks for relation extraction. Specifically, we develop two approaches to evaluate how well NRE predictions satisfy our relation constraints in a batchwise, from both general and precise perspectives. We explore our approach on English and Chinese dataset, and the experimental results show that our approach can help the base NRE models to effectively learn from the discrete relation constraints, and outperform popular NRE models as well as their ILP enhanced versions. Our study reveals that learning with the constraints can better utilize the constraints from a different perspective compared to the ILP postprocessing method.
Acknowledgments
We thank anonymous reviewers for their valuable suggestions. This work is supported in part by the National HiTech R&D Program of China (2018YFC0831900) and the NSFC Grants (No.61672057, 61672058). For any correspondence, please contact Yansong Feng.
Appendix A Appendix
Parameter Settings
In the experiment, both ACNN and APCNN use convolution window size 3, sentence embedding size 256, position embedding size 5 and batch size 50. The word embedding size is 50 and 300 for the English and Chinese dataset, respectively. We use Adam with learning rate 0.001 to train our model. And we finetune the constraint loss coefficients for each experimental settings, reported in Table 4
English dataset  Chinese dataset  

ACNN  APCNN  ACNN  APCNN  
Sem  
Coh 
Local Loss Calculating Indicators
In this section, we list the assignment methods for all which indicates whether to calculate local loss term for the combination of the and instances, and , within a batch.
(7) 
where means the two triples have the same subject type, thus, corresponding predicted relation pair may be contradictory with .
(8) 
where means the two triples have the same object type, thus, corresponding predicted relation pair may be contradictory with .
(9) 
where means the subject type of one relation is same as the object type of the other, thus, corresponding predicted relation pair may be contradictory with .
(10) 
where means that for a given object, there are multiple subjects, thus, corresponding predicted relation pair may be contradictory with .
(11) 
where means that for a given subject, there are multiple objects, thus, corresponding predicted relation pair may be contradictory with .
Statistics on Violations for Each Constraint Set
In this section, we collect the number of violations for each specific constraint set among the relation predictions of APCNN and APCNN(Sem) on Chinese dataset, shown as in Table 5.
Total  

APCNN  850  11,183  7,636  1,464  209  21,342 
APCNN(Sem)  596  6,772  6,573  1,259  176  15,376 
Further Discussions on Training Procedure
First, adjusting the coefficient of our constraint loss by a dynamic mechanism during training would be helpful. Particularly, we use Eq.12 to dynamic adjust .
(12) 
where is a constant which represents the max value of , and
represent the current epoch number and the total epoch number, respectively. By Eq.
12, we make first rise and then fall, since we think the NRE model should more focus on the original loss at the start of training, and the influence of relation constraints should decrease after the NRE model has learned relation constraints pretty well. We apply this dynamic mechanism on English dataset with APCNN as base model, and achieve 99.33% compared to 99.32% of constant in Mean. We think may be a more nicely dynamic mechanism which captures the inherent of combining relation constraints with NRE models could fetch more improvement.In addition, organizing related instances into a same minibatch seems to be helpful too, while how to make the reorganized data evenly distributed and maintaining the randomness of data at the same time, is very challenging. We leave this modification into the future work.
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