SlowGuess/NAACL_2022_OCR huggingface dataset:
We run experiments on a Linux machine with a single GeForce RTX 2080 Ti GPU with 11 GB GPU memory and a Intel(R) Xeon(R) Gold 6240 CPU @ 2.60GHz. The operating system of our machine is Ubuntu 18.04.2 LTS. The major software packages used are as follows: TensorFlow 1.12; CUDA 10.1; Python 3.6; NumPy 1.18.1; SciPy 1.4.1. Our source code is available in the attachment for reproducible experiments.
C Hyperparameter Settings
To ensure a fair comparison, we follow the hyperparameter settings of the base alignment model (i.e., MTransE and AliNet) and the base dangling detection loss (i.e., MR and BR) reported in the previous work (Sun et al., 2021). For our proposed methods, in WGAN, we use a two-layer FNN with 500 hidden units for the critic. As suggested by Arjovsky et al. (2017), we adopt weight clipping to ensure K-Lipschitz for WGAN and train the critic more than the generator (i.e., the transformation matrix). Besides the hyperparameter stated in Section 4.1, we tune other hyperparameters within a search space as follows:
- The number of nearest targets  $k$ : {5, 10, 15}
The number of nearest sources  $m$ :  $\{5, 10, 15\}$
- Batch size: \{4096, 8192, 10240, 20480\}
D More on Experiments
As shown in Sun et al. (2021), AliNet (Sun et al., 2020b) performs much worse than MTransE (Chen et al., 2017) in dangling-aware entity alignment. Dangling entity detection would also suffer as a result of the poor alignment performance. However, in this section, we still present the results of MHP with AliNet as the base alignment model to demonstrate that MHP is model-agnostic and has a good robustness.
Consolidated evaluation. Tab. 7 shows that, using AliNet as the base model, MHP still outperforms baselines in terms of F1 scores on dangling detection. We can see that baselines sometimes achieve better precision with the sacrifice of recall, which leads to unsatisfactory F1 scores. Comparing our two variants  $\mathrm{MHP} + \mathrm{MR}$  and  $\mathrm{MHP} + \mathrm{BR}$ , there is no one consistently achieving better performance than the other one. We report the performance of
Methods	ZH-EN	EN-ZH	JA-EN	EN-JA	FR-EN	EN-FR
Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1
MR	.752	.538	.627	.828	.505	.627	.779	.580	.665	.854	.543	.664	.552	.570	.561	.686	.549	.609
BR	.762	.556	.643	.829	.515	.635	.783	.591	.673	.846	.546	.663	.547	.556	.552	.674	.556	.609
MHP + MR	.750	.711	.730	.838	.726	.778	.743	.702	.722	.831	.714	.768	.541	.601	.571	.638	.661	.649
MHP + BR	.748	.718	.733	.841	.721	.776	.738	.702	.719	.833	.711	.767	.556	.568	.562	.681	.590	.632
Table 7: Dangling entity detection results on DBP2.0. MR refers to marginal ranking and BR refers to the background ranking (Sun et al., 2021). The base alignment model is AliNet (Sun et al., 2020b).
Methods	ZH-EN	EN-ZH	JA-EN	EN-JA	FR-EN	EN-FR
Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1	Prec.	Rec.	F1
MR	.207	.299	.245	.159	.320	.213	.231	.321	.269	.178	.340	.234	.195	.190	.193	.160	.200	.178
BR	.203	.286	.238	.155	.308	.207	.223	.306	.258	.170	.321	.222	.183	.181	.182	.164	.200	.180
MHP + MR	.259	.280	.269	.222	.298	.254	.266	.288	.276	.225	.305	.259	.204	.186	.195	.197	.189	.193
MHP + BR	.258	.274	.265	.223	.305	.257	.261	.281	.271	.224	.306	.258	.183	.180	.182	.172	.201	.185
Table 8: Two-step entity alignment results on DBP2.0. The base alignment model is AliNet.
Methods	ZH-EN	EN-ZH	JA-EN	EN-JA	FR-EN	EN-FR
H@1	H@10	MRR	H@1	H@10	MRR	H@1	H@10	MRR	H@1	H@10	MRR	H@1	H@10	MRR	H@1	H@10	MRR
AliNet	.332	.594	.421	.359	.629	.451	.338	.596	.429	.363	.630	.455	.223	.473	.306	.246	.495	.329
w/ MR	.343	.606	.433	.364	.637	.459	.349	.608	.438	.377	.646	.469	.230	.477	.312	.252	.502	.335
w/ BR	.333	.599	.426	.357	.632	.451	.341	.608	.431	.369	.636	.461	.214	.468	.298	.238	.487	.321
MHP + MR	.346	.613	.439	.375	.645	.469	.354	.617	.444	.379	.654	.473	.228	.477	.311	.253	.496	.335
MHP + BR	.339	.611	.432	.373	.635	.464	.346	.614	.437	.367	.638	.460	.218	.473	.303	.244	.504	.331
Table 9: Entity alignment results in the relaxed setting on DBP2.0. The base alignment model is AliNet.
two-step entity alignment on Tab. 8. In general, MHP offers better performance on two-step alignment compared with baselines that do not consider high-order proximities. We observe that when we choose AliNet as the base model, the improvement over the baselines is less than the improvement when using MTransE as the base model. The reason could be that AliNet generally performs worse than MTransE, even only with MR or BR. For example, combining Tab. 1 and 7, MTransE+MR can achieve 0.740 F1 score, while AliNet+MR only obtains 0.627 F1 score. The observation is also pointed out by Sun et al. (2021). The inherent inferiority of AliNet in dangling-aware entity alignment can hinder our new proposed techniques. Therefore, we suggest to use MTransE as the base alignment model for dangling-aware entity alignment. Future work could investigate other advanced alignment models on this setting.
Relaxed evaluation. Tab. 9 demonstrates the results of entity alignment in the relaxed setting. We observe that AliNet without any dangling detection technique performs the worst. By applying dangling detection techniques, the alignment per
formance increases, indicating that learning to detect dangling entities can indirectly help alignment. MHP with two different base dangling losses (i.e., MR and BR) generally outperforms the corresponding baselines without our proposed techniques. For our two variants,  $\mathrm{MHP} + \mathrm{MR}$  slightly outperforms  $\mathrm{MHP} + \mathrm{BR}$  variants in most cases.
E Computational Cost
Note that, similar with the MR loss (Sun et al., 2021), MHP also relies on nearest neighbor search (NNS) for training. Therefore, MHP can reuse the results of NNS obtained by MR during the training phase, and cause negligible additional overhead. On ZH-EN, MHP averagely spends around 60 seconds training an epoch. When the efficiency is of importance in some real-time applications, we can adopt the large-scale efficient similarity search library faiss (Johnson et al., 2021) which uses GPUs for fast NNS. Additionally, we could also maintain a cache unit to store the results of NNS and only lazily update the results every ten or twenty epochs during training.
We notice that many prior studies on conventional entity alignment consider the side information of entities (e.g., names, descriptions and attributes) (Chen et al., 2018b; Trisedya et al., 2019; Zhang et al., 2019; Xu et al., 2019b; Wang et al., 2020; Wu et al., 2020). However, on dangling-aware entity alignment, the pioneer work (Sun et al., 2021) proposes a framework that only considers the structure information of entities since most KGs are built around relation triples. Thus, for a fair comparison, we follow their setting and do not utilize side information of entities. Future work could investigate how to effectively incorporate side information for dangling-aware entity alignment in the proper way and with a fair evaluation.