An Adversarial Transfer Network for Knowledge Representation Learning

Our framework extends shallow knowledge representation learning models with transfer learning and adversarial learning. As mentioned in Section 2, shallow models always define score functions based on triplets. The original translation-based model TransE (Bordes et al., 2013) defines a score function as Eq. (1). It follows a simple assumption that the addition of a head entity embedding and a relation embedding equals the tail entity embedding. This method still outperforms many latter shallow models with proper hyper-parameters.

Except for score functions, there are many skills proposed to improve knowledge representation learning. Negative sampling has been proved quite efficient in previous studies (Bordes et al., 2013; Trouillon et al., 2016). In this paper, we follow the “unif” strategy (Wang et al., 2014b): given a valid triplet ($h,r,t$), negative triplets ($h^{\prime},r,t^{\prime}$) are drawn by replacing the head or tail entity with an entity randomly sampled from $\mathcal{E}$ with an equal probability. The negative triplet set is denoted as $\mathcal{S}^{\prime}$ and the sampled distribution is $p_{s^{\prime}|(h,r,t)}$. We use the training objective from RotatE (Sun et al., 2019) for effectively optimizing distance-based models based on negative sampling loss (Mikolov et al., 2013):

where $\gamma$ is the fixed margin, $\sigma$ is the Sigmoid function, $p_{s}$ is the distribution of $\mathcal{S}$.

Shallow knowledge representation learning models always assume that knowledge graphs are dense enough. However, there are long-tail entities and relations and these corresponding representations are rarely updated in practice. Thus, the quality of learned representations declines as the number of triplets reduces. We introduce an embedding transfer module, which aims to transfer features learned in the teacher knowledge graph to the target one through the aligned entity set $\mathcal{C}$. Aligned entities and long-tail relations in the target knowledge graph could benefit from the transferred features. There are two ways to implement the transfer process.

First, we could construct a distance constraint based on the aligned entity set $\mathcal{C}$. Embeddings of aligned entity pair $(e_{t},e_{s})$ possibly have different dimensions $m$ and $n$. To handle this problem, teacher entity embeddings are fed to a transition network denoted as $W:\mathbb{R}^{m}\rightarrow\mathbb{R}^{n}$. In this case, teacher entity embeddings are projected into the target space by the transition network. Then the projected teacher embeddings are taken as soft targets of the corresponding target entities. We formulate such a constraint as a distance function $f_{d}(\mathbf{\mathcal{C}})$ defined with the projected teacher embeddings and the target embeddings of aligned entity pairs as follows:

where $\phi$ is a distance function to evaluate the distance between embeddings. We assume that the aligned entity embeddings in different knowledge graphs tend to be close in the target space when they are consistent with each other. We choose the Cosine distance as $\phi$, and it is defiend as $\phi(\bm{e_{t}},\bm{e_{s}})=1-\cos(W(\bm{e_{t}}),\bm{e_{s}})$.

Second, we can utilize relations and neighbour entities in the target knowledge graph. We assume that a target triplet assumption also holds after replacing one entity embedding with the corresponding projected teacher entity embedding. More specifically, given a triplet $(h,r,t)$ in the target knowledge graph $\mathcal{G}$, we assume that the aligned teacher entities $\{e_{t}\}$ should also comprise valid triplets {($e_{t},r,t$)} if $e_{t}$ aligns with $h$ or {($h,r,e_{t}$)} if $e_{t}$ aligns with $t$. We denote these valid triplets as transferred triplets. Similar to the first constraint, we project teacher embeddings to the target space through the transition network $W$. The goal is to make the transferred triplets fit the score function in the embedding module. Hence, we formulate the triplet constraint as Eq. (4), which is to minimize scores of the transferred triplets:

where $\gamma$ is the margin used in the embedding module, $p_{c}$ is the distribution of $\mathcal{C}$.

Finally, we define the training objective of the embedding module and the embedding transfer module as follows:

where $\alpha$ and $\beta$ are hyper-parameters to control the weights of the transferred embedding distance constraint and the transferred triplet constraint.

The transfer process is the key component of ATransN. However, semantic meanings of aligned entity pairs are not always consistent as illustrated in Figure 1. The more similar the neighbours are, the stronger supervision should the constraints provide. Thus, it is better to assign a dynamic weight to constraints during the embedding transfer according to the degree of consistency between an aligned entity pair.

Motivated by this idea, we add an adversarial adaption module to evaluate the degree of consistency between an aligned entity pair, where the discriminator gives the consistency score, and the generator generates noisy transferred embeddings to improve the discriminator (Goodfellow et al., 2014). A naive generator generates fake examples $z$ from a noise prior distribution $p_{z}$ and hopes $G(z)$ could become a good estimator of the target entity distribution $p_{e}$. It simply initializes the distribution $p_{z}$ as a uniform distribution or normal distribution if there is no prior knowledge. However, the entity embedding space is unlimited so that such a method always fails. Inspired by the Conditional GAN (Mirza and Osindero, 2014), we assume the prior noise distribution is a standard uniform distribution $\mathcal{U}(-1,1)$, and use a linear layer with input $e$ and the sampled uniform noise to shape the conditional distribution $p_{z|e}$:

where $z$ is a sampled from the standard uniform distribution $p_{z}$, $G(\bm{e},\bm{z})$ is a conditional signal following $p_{z|e}$, $D$ is a discriminator is used to measure the embedding consistency of two aligned entities, $D(\bm{e},G(\bm{e},\bm{z}))$ is a score to the degree of consistency. A new issue is that the embedding space may be not closed so that $p_{z|e}$ arises the instability problem. Hence, we also add the cosine distance constraint between the $\bm{e}$ and $\bm{z}$. The binary cross-entropy is used to train the discriminator as Eq. (7). Once we get the output of the discriminator, we can use the score as the weight of the embedding transfer module. A larger score means two entities are more consistent so that features in the teacher knowledge graph are more useful.

Therefore, Eq. (3) and Eq. (4) can further benefit from the discriminator. The discriminator output can guide whether the aligned embeddings could help target knowledge graph representation learning. We add the output as the weights for Eq. (3) and Eq. (4). Eq. (8) is the adjusted distance function, and Eq. (4) can also be adjusted in the similar way.

Knowledge graph completion aims to predict the missing entity in a triplet, namely to predict $h$ given ($r,t$) or $t$ given ($h,r$) as defined in (Bordes et al., 2013). It reflects the expressiveness of the embeddings learned by a model. For each positive test triplet ($h,r,t$), we replace the head (or tail) entity with all entities in $\mathcal{E}$ to construct corrupted triplets. Then we compute the triplet scores of the ground-truth triplet and its corresponding corrupted triplets. Scores are further sorted in ascending order so that we can obtain metrics based on ranking. We report the results on four metrics, including Mean Rank (MR), Mean Reciprocal Rank (MRR), Hits@3, and Hits@10, where Hits@$K$ denotes the proportion of correct entities ranked in top $K$. A lower Mean Rank, a higher Mean Reciprocal Rank, or a higher Hits@$K$ usually means better performance. Since a corrupted triplet might also exist in the target knowledge graph, these metrics will be adversely affected. To avoid underestimating the performance of models, we remove all the corrupted triplets that already exist in the target knowledge graph (including training, validation, and test parts) and take the filtered rank of the positive triplet, which denoted as the “filter” setting (Dettmers et al., 2018).

We conduct experiments on three benchmarking datasets, CN3l (EN-DE), WK3l-15k (EN-FR) (Chen et al., 2017)¹¹1https://github.com/muhaochen/MTransE, and DWY100k (Sun et al., 2018)²²2https://github.com/nju-websoft/BootEA, all of which are originally constructed for the entity alignment task. Table 1 summarizes data statistics. In this paper, each dataset is randomly split into three parts where 60% triplets as the training data, 20% triplets as the validation data, and 20% triplets as the test data.

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  CN3l (EN-DE) is constructed from ConceptNet (Speer et al., 2017), containing an English knowledge graph and a German knowledge graph. The aligned entities are linked according to the relation TranslationOf in ConceptNet. As there are fewer German triplets per entity, we take the English knowledge graph as the teacher and learn embeddings with methods such as TransE. Then, we use ATransN to learn entities and relation embeddings based on the German triplets as well as the entity embeddings of the English knowledge graph.

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  WK3l-15k (EN-FR) is created from Wikipedia, including an English knowledge graph and a French knowledge graph. The aligned entity set is constructed by verifying the inter-lingual links. As the English knowledge graph has more triplets than the French, we also use the English knowledge graph as the teacher knowledge graph and the French knowledge graph as the target.

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  DWY100k contains two large-scale datasets constructed from three data sources, DBpedia, Wikidata and YAGO. The two datasets are denoted by DBP-WD and DBP-YG, where all entities are 100% aligned. Although the YAGO knowledge graph has more triplets, we both take the DBpedia knowledge graph as the teacher knowledge graph here.

We compare ATransN with several competitive baselines mentioned in Section 2, including TransE (Bordes et al., 2013), DistMult (Yang et al., 2015), ComplEx (Trouillon et al., 2016), and RotatE (Sun et al., 2019). Score functions of these models are listed in Table 2. We implement all models under PyTorch³³3https://pytorch.org framework.

The training process of ATransN is summarized in Algorithm 1. The transition network $W$ that maps teacher entity embeddings into target entity embedding space consists of two linear layers to handle the complex transformation. The generator $G$ that generates the noisy fake embeddings is a two-layer MLP with a LeakyReLU activation after the first layer; the discriminator $D$ that tries to distinguish whether two distributions are similar consists of one linear layer followed by a LeakyReLU activation and layer normalization, and one linear layer followed by a Sigmoid activation. We select the best models based on the sum of $\frac{100}{\text{MR}}$, MRR, Hits@3, and Hits@10 on the validation data. We use the same strategy for the teacher knowledge graph training. Then we take the target entity and relation embeddings for the knowledge graph completion task.

Embeddings are initialized following the uniform distributions $\mathcal{U}(-\frac{\gamma+\epsilon}{n},\frac{\gamma+\epsilon}{n})$ where $\epsilon$ is a hyperparameter fixed as 2 (Sun et al., 2019), $n$ is the dimension of the specific embedding module. The dimension $n$ for TransE, DistMult, ComplEx, RotatE are set as 200, 200, 100, and 100 respectively for a fair comparison because the latter two are in the complex space, containing both real vectors and imaginary vectors. Parameters of the transition network $W$ are initialized orthogonally (Saxe et al., 2014), while other parameters are initialized uniformly (He et al., 2015).

We choose TransE as the embedding module of ATransN and Adam (Kingma and Ba, 2015) to optimize ATransN and other baselines. The optimizer for the generator only updates parameters of $G$; the optimizer for the discriminator updates parameters of both $D$ and $W$; the optimizer for the embedding module updates parameters of knowledge graphs representations as well as $W$. To mitigate the performance impact of adversarial and transfer learning on the target data, we add the cyclical cosine annealing scheduler for $\alpha$ and $\beta$ (Fu et al., 2019) and the learning rate scheduler to warm up the learning rates for the first 1% steps. Detailed hyper-parameter searching and settings are described in Appendix A.

The empirical results on two standard multi-lingual datasets CN3l, WK3l-15k, and the multi-source dataset DWY100k are shown in Tables 3 and 4. And teacher performance is listed in Appendix B. These tables report MR, MRR, Hits@3, and Hits@10 results of four different baseline models and ATransN on each dataset.

We first compare our ATransN with the four baselines. ATransN has the best performance on WK3l-15k, DBP-YG, and DBP-WD across all metrics. On CN3l, ATransN outperforms all the baselines on all metrics except MRR. In this case, ATransN is still competitive with RotatE on MRR and significantly surpassing RotatE on other metrics. Comparing with TransE, ATransN improves the Hits@3 and Hits@10 by notable margins of 7.47% and 10.72% on CN3l, substantial margins of 8.89% and 10.73% on DBP-YG, and remarkable margins of 9.31% and 11.80% on DBP-WD. In addition, ATransN can help make relevant head or tail entities come top in ranks, reflected by significant decreases of MR among all data. This would be very helpful for the knowledge graph completion because models with transfer learning tend to have higher recall scores. From these results, we show that ATransN successfully transfers knowledge from an auxiliary knowledge graph, and improves representation expressiveness on the target knowledge graph.

Second, the improvement of WK3l-15k is not as significant as others. There are two possible reasons. One is that compared with the other three target knowledge graphs, the French knowledge graph on WK3l-15k is much denser, where the average degree of entities is about 11 while others are no greater than 5. The representations learned on the target triplets have already been good enough. Thus, the auxiliary knowledge graph contributes little. The other is that the entity alignment ratio is quite small on the WK3l-15k data, while ratios on the other two datasets reach 90% and even 100%. A smaller alignment ratio usually indicates a larger difference between the two knowledge graphs.

We conduct extensive ablation studies to prove the effectiveness of each module in ATransN. To verify the validity of the distance constraint and the triplet constraint, models with the best $\alpha$ and $\beta$ are searched when the other hyper-parameter is set as 0. To verify the necessity of the adversarial adaptation module, we implement a baseline CTransE, which only adds the two constraints in the training objective like Eq. (5) with constant weights. The consistency degree of two aligned entities is no longer considered in CTransE.

The experimental results on four different datasets are reported in the first block of Table 5. ATransN almost achieves the best performance when $\alpha>0$ and $\beta>0$, which means two constraints in Eq.(5) really contribute to the embedding learning process. Furthermore, ATransN w/ $\beta=0$ has competitive results with ATransN on CN3l, WK3l, DBP-YG, and DBP-WD, which shows that the distance constraint plays a more important role in the transfer learning. We find that ATransN w/ $\alpha=0$ can still outperforms TransE at the bottom. The triplet constraint mainly improves MR on CN3l and WK3l but Hits@3 and Hits@10 on DWY100k. The assumption behind the triplet constraint is too strong as it requires a teacher entity embedding to fit all triplets of its corresponding aligned entity in the target knowledge graph. When data are not in the same domain, it does not work; when data are in the same domain, it may duplicate triplets. On the contrary, the distance constraint seems looser as it only makes two aligned entity embeddings have similar directions instead of the same elements. WK3l-15k is a denser and less-aligned dataset, and the results of ATransN w/ $\alpha=0$ are much closer to ATransN. Two constraints perform similarly because target entity and relation representations can be trained well and supervisions from constraints are dispelled by target triplets. In this case, the general contributions of the two constraints become roughly equal.

When removing the adversarial adaptation module, numbers of CTransE in Table 5 drop a lot on all metrics, which proves that measuring the consistency degree is vital during the transfer process. In other words, the embedding transfer process without the adversarial adaption module is not very effective and even has a negative influence as the results of CTransE with $\alpha=0$ shown on CN3l. Therefore, it is the predictions of the discriminator as the dynamic weights that bring significant improvement. For the CTransE baseline, we also report the best results when $\alpha$ and $\beta$ are zero respectively to explore how the distance constraint and the triplet constraint work during the transfer process. On the two datasets in DWY100k, CTransE without the triplet constraint has the same results as CTransE. On CN3l, the combination of two constraints is of help for the learning process. However, on the WK3l-15k dataset, combining the two constraints is not helpful. Besides, CTransE w/o the triplet constraint performs better than CTransE w/o the distance constraint on most data, but the difference is small. In conclusion, the distance constraint has a similar effect to the triplet constraint when the constraint weight is constant. And the combination of the two constraints could affect each other in this case.

To further analyze how the entity overlap ratio would influence the experimental results, we design more experiments on subsets of DWY100k (DBP-WD). Figure 3 shows performance curves on three metrics under 5 different overlap ratios {20%, 40%, 60%, 80%, 100%}. The total number of entities in the teacher and target are 50,000 in each setting and we remain the same target knowledge graph for a fair comparison. The difference is the teacher part, where the aligned entities are transitive. That is, if an aligned entity pair appears in the aligned set of 20% ratio, then it must exist in the set of 40%, and so on. As we can see, all metrics become better steadily as the overlap ratio increases. Furthermore, to show the upper bound of improvement brought by introducing the teacher, we designed the TransE(joint), which is trained on the target triplets and teacher triplets after id mapping. Embedding module is learned on the merged training set, but the original target validation and test data are used to choose and report models. The gaps between curves of ATransN and TransE(joint) corresponding to the same metric become smaller with the rise of the overlap ratio. However, the margins between ATransN and TransE cannot be ignored gradually (in fact, curves of TransE are not changed because validation and test data are the same). Thus, introducing the teacher knowledge graphs does improve target representation learning, and the performance grows rapidly as the entity overlap increases.

Two important hyper-parameters $\alpha$ and $\beta$ are involved for constants in our previous experiments. It is unknown how sensitive the performance of ATransN is to these two parameters. Thus, we perform sensitivity analysis in this section to explore the effect of $\alpha$ and $\beta$ in our framework. We choose ATransN and CTransE and two representative datasets CN3l and WK3l-15k. Figure 5 provides heat maps of results on three metrics, namely, MR, MRR, and Hits@10.

On CN3l, we consider the weight of the distance constraint $\alpha\in\{0,1,5,10,20,30\}$, the weight of the triplet constraint $\beta\in\{0.0,0.1,0.2,0.4,0.8.\}$. It is easy for us to see the trend that a larger $\alpha$ can result in better performance. When $\beta$ increases, MR becomes better but MRR becomes worse. It is also clear to see the best $\beta$ value for Hits@10 is around 0.1 or 0.4. This proves that the distance constraint is effective enough to transfer entity features but the triplet constraint can slightly adjust. However, from the results of CTransE on CN3l, the most immediate observation is each metric has its own optimal configuration. And it is infeasible to find a pattern for Hits@10. That suggests that $\alpha$ and $\beta$ become very sensitive without the adversarial adaptation module. It requires careful hyper-parameter searching. But CTransE with even the best configuration is still far worse than ATransN with a proper but not the best configuration.

As the entity alignment ratio on WK3l-15k is much smaller, we consider $\alpha\in\{0.0,0.1,0.2,0.4,0.8\}$ and $\beta\in\{0.0,0.1,0.2,0.4\}$. Heat maps plotted in the third line of Figure 5 is not as regular as the first line on CN3l, but we can still find some trends on MR and MRR. In general, the best value of $\alpha$ is between 0.1 and 0.2, while the best value for $\beta$ is about 0.4. Besides, there is no consistent pattern in heat maps of CTransE in the last line, let alone the performance. In conclusion, the two parameters of ATransN is not as sensitive as those of CTransE. And the adversarial adaptation module makes ATransN appropriate to different scenarios in a general way.