SlowGuess/NAACL_2021_OCR huggingface dataset:
(i) For each relation instance node  $\mathbf{r}_k = [\mathbf{e}_i, \mathbf{e}_j] \in \mathbf{N}^{inst}$  that has the golden type  $y_k \neq$  None, the relation type node  $y_k$  is connected to the nodes of the golden entity types for the corresponding entity mentions  $\mathbf{e}_i$  and  $\mathbf{e}_j$  (called entity Relation type edges).
(ii) For each argument instance node  $\mathbf{r}_k = [\mathbf{t}_i, \mathbf{e}_j]$  that has the role type  $y_k \neq \text{None}$ , the role type node  $y_k$  is connected to both the node for the golden event type of  $\mathbf{t}_i$  (called event Argument type edges) and the node for the golden entity type of  $\mathbf{e}_j$  (called entity Argument type edges).
The same procedure can be applied to build the predicted dependency graph  $\mathbf{G}^{pred}$  based on the predicted types  $\hat{\mathbf{y}} = \hat{y}_1, \hat{y}_2, \dots, \hat{y}_{n_i}$ . Also, for convenience, let  $\mathbf{A}^{gold}$  and  $\mathbf{A}^{pred}$  (of size  $n_t \times n_t$ ) be the binary adjacency matrices of  $\mathbf{G}^{gold}$  and  $\mathbf{G}^{pred}$
(including the self-loops) respectively.
Regularization. In the next step, we obtain the representation vectors for the dependency graphs  $\mathbf{G}^{gold}$  and  $\mathbf{G}^{pred}$  by feeding them into a GCN model (called  $\mathbf{GCN}^{type}$ ). This GCN model has  $N_{t}$  layers and uses the initial type embeddings  $\mathcal{T} = [\bar{\mathbf{t}}_1,\dots ,\bar{\mathbf{t}}_{n_t}]$  as the inputs. In particular, the outputs of  $\mathbf{GCN}^{type}$  for the two graphs involve  $\bar{\mathbf{t}}_1^{gold},\ldots ,\bar{\mathbf{t}}_{n_t}^{gold} =$ $\mathbf{GCN}^{type}(\mathbf{A}^{gold};\bar{\mathbf{t}}_1,\dots ,\bar{\mathbf{t}}_{n_t};N_t)$  and  $\bar{\mathbf{t}}_1^{pred},\dots ,\bar{\mathbf{t}}_{n_t}^{pred} = \mathbf{GCN}^{type}(\mathbf{A}^{pred};\bar{\mathbf{t}}_1,\dots ,\bar{\mathbf{t}}_{n_t};N_t)$  that encode the underlying information for the type dependencies presented in  $\mathbf{G}^{gold}$  and  $\mathbf{G}^{pred}$ . Finally, to promote the similarity of the type dependencies in  $\mathbf{G}^{gold}$  and  $\mathbf{G}^{pred}$ , we introduce the mean square difference between their GCN type-induced representation vectors into the overall loss function for minimization:  $L_{dep} = \sum_{i = 1}^{n_t}||\bar{\mathbf{t}}_i^{gold} - \bar{\mathbf{t}}_i^{pred}||_2^2.$
Our final training loss is thus:  $L = L_{span}^{ent} + L_{span}^{trg} + L_{type} + \lambda L_{dep}$  ( $\lambda$  is a trade-off parameter). Approximating  $\mathbf{A}^{pred}$ . We distinguish two types of parameters in our model so far, i.e., the parameters used to compute instance representations, e.g., those in BERT and  $\mathbf{G}^{inst}$  (called  $\theta^{inst}$ ), and the parameters for type dependency regularization, i.e., those for the type embeddings  $\bar{\mathbf{t}}_1, \dots, \bar{\mathbf{t}}_{n_t}$  and  $\mathbf{G}^{type}$  (called  $\theta^{dep}$ ). As such, the current implementation only enables the training signal from  $L_{dep}$  to back-propagate to the parameters  $\theta^{dep}$  and disallows  $L_{dep}$  to influence the instance representation-related parameters  $\theta^{inst}$ . To enrich the instance representation vectors with type dependency information, we expect  $L_{dep}$  to be deeper integrated into the model by also contributing to  $\theta^{inst}$ . To achieve this goal, we note that the block of back-propagation between  $L_{dep}$  and  $\theta^{inst}$  is due to their only connection in the model via the adjacency matrix  $\mathbf{A}^{pred}$ , whose values are either one or zero. As such, the values in  $\mathbf{A}^{pred}$  are not directly dependent on any parameter in  $\theta^{inst}$ , making it impossible for the back-propagation to flow. To this end, we propose to approximate  $\mathbf{A}^{pred}$  with a new matrix  $\hat{\mathbf{A}}^{pred}$  that directly involves  $\theta^{inst}$  in its values. In particular, let  $\mathbf{I}^{inst}$  be the index set of the non-zero cells in  $\mathbf{A}^{pred}$ :  $\mathbf{I}^{inst} = \{(i,j)|\mathbf{A}_{ij}^{pred} = 1\}$ . As the elements in  $\mathbf{I}^{inst}$  are determined by the indexes  $i_1, \dots, i_{n_i}$  in  $T$  of the predicted types  $\hat{y}_1, \hat{y}_2, \dots, \hat{y}_{n_i}$  (respectively), we also seek to compute the values for the approximated matrix  $\hat{\mathbf{A}}^{pred}$  based on such indexes. Accordingly, we first define the matrix  $\mathbf{B} = \{b_{ij}\}_{i,j=1..nt}$  where the element  $b_{ij}$  at the  $i$ -th row and  $j$ -th column is defined as
umn is set to  $b_{ij} = i * n_t + j$ . The approximated matrix  $\hat{\mathbf{A}}^{pred}$  is then obtained by:
$$
\hat {\mathbf {A}} ^ {p r e d} = \sum_ {(i, j) \in \mathbf {I} ^ {i n s t}} \exp (- \beta (\mathbf {B} - i n _ {t} - j) ^ {2}) \tag {1}
$$
Here,  $\beta > 0$  is a large constant. For each element  $(i,j) \in \mathbf{I}^{inst}$ , all the elements in the matrix  $(\mathbf{B} - i n_{t} - j)^{2}$  are strictly positive, except for the element at  $(i,j)$ , which is zero. Thus, with a large value for  $\beta$ , the matrix  $\exp(-\beta (\mathbf{B} - i n_{t} - j)^{2})$  has the value of one at cell  $(i,j)$  and nearly zero at other cells. Consequently, the values of  $\hat{\mathbf{A}}^{pred}$  at the positions in  $\mathbf{I}^{inst}$  are close to one while those at other positions are close to zero, thus approximating our expected matrix  $\mathbf{A}^{pred}$  and still directly depending on the indexes  $i_{1}, \ldots, i_{n_{t}}$ .
Addressing the Discreteness of Indexes. Even with the approximation  $\hat{\mathbf{A}}^{pred}$ , the backpropagation still cannot flow from  $L_{dep}$  to  $\theta^{inst}$  due to the block of the discrete and non-differentiable index variables  $i_1, \ldots, i_{n_t}$ . To address this issue, we propose to apply the Gumbel-Softmax distribution (Jang et al., 2017) that enables the optimization of models with discrete random variables, by providing a method to approximate one-hot vectors sampled from a categorical distribution with continuous ones.
In particular, we first rewrite each index  $i_k$  by:  $i_k = \mathbf{h}_k\mathbf{c}_k^T$ , where  $\mathbf{c}_k$  is a vector whose each dimension contains the index of a type in  $\mathcal{T}^{t_k}$  in the joint type set  $\mathcal{T}$ , and  $\mathbf{h}_k$  is the binary one-hot vector whose dimensions correspond to the types in  $\mathcal{T}^{t_k}$ .  $\mathbf{h}_k$  is only turned on at the position corresponding to the predicted type  $\hat{y}_k \in \mathcal{T}^{t_k}$  (indexed at  $i_k$  in  $\mathcal{T}$ ). In our current implementation,  $\hat{y}_k$  (thus the index  $i_k$  and the one-hot vector  $\mathbf{h}_k$ ) is obtained via the argmax function:  $\hat{y}_k = \operatorname{argmax} \hat{\mathbf{y}}_k$ , which causes the discreteness. As such, the Gumbel-Softmax distribution method helps to relax argmax by approximating  $\mathbf{h}_k$  with a sample  $\hat{\mathbf{h}}_k = \hat{h}_{k,1}, \dots, \hat{h}_{k,|\mathcal{T}^{t_k}|}$  from the Gumbel-Softmax distribution:
$$
\hat {h} _ {k, j} = \frac {\exp \left(\left(\log \left(\pi_ {k , j}\right) + g _ {j}\right) / \tau\right)}{\sum_ {j ^ {\prime} = 1} ^ {\left| \mathcal {T} ^ {t _ {k}} \right|} \exp \left(\left(\log \left(\pi_ {k , j ^ {\prime}}\right) + g _ {j ^ {\prime}}\right) / \tau\right)} \tag {2}
$$
where  $\pi_{k,j} = \hat{\mathbf{y}}_{k,j} = \text{softmax}_j(\mathbf{r}_k^{\text{inst}}\bar{\mathbf{t}}^T|\bar{\mathbf{t}}\in$ $\mathcal{T}^{t_k}\cap \mathcal{T})$ $g_{1},\ldots ,g_{|\mathcal{T}^{t_k}|}$  are the i.i.d samples drawn from Gumbel(0,1) distribution (Gumbel, 1948):  $g_{j} = -\log (-\log (u_{j}))$  ( $u_{j}\sim \mathrm{Uniform}(0,1)$ ), and  $\tau$  is the temperature parameter. As  $\tau \to 0$ , the
sample  $\hat{\mathbf{h}}_k$  would become close to our expected one-hot vector  $\mathbf{h}_k$ . Finally, we replace  $\mathbf{h}_k$  with the approximation  $\hat{\mathbf{h}}_k$  in the computation for  $i_k$ :  $i_k = \hat{\mathbf{h}}_k\mathbf{c}_k^T$  that directly depends on  $\mathbf{r}_k^{inst}$  and is applied in  $\hat{\mathbf{A}}^{pred}$ . This allows the gradients to flow from  $L_{dep}$  to the parameters  $\theta^{inst}$  and completes the description of our model.
Datasets. Following the prior work on joint four-task IE (Wadden et al., 2019; Lin et al., 2020), we evaluate our joint IE model (FourIE) on the ACE 2005 (Walker et al., 2006) and ERE datasets that provide annotation for entity mentions, event triggers, relations, and argument roles. In particular, we use three different versions of the ACE 2005 dataset that focus on three major joint inference settings for IE: (i) ACE05-R for joint inference of EME and RE, (ii) ACE05-E for joint inference of EME, ETD and EAE, and (iii) ACE05-E+ for joint inference of the four tasks EME, ETD, RE, and EAE. ACE05-E+ is our main evaluation setting as it fits to our model design with the four IE tasks of interest.
Datasets	Split	sents	ents	rels	events
ACE05-R	Train	10,051	26,473	4,788	-
Dev	2,424	6,362	1,131	-
Test	2,050	5,476	1,151	-
ACE05-E	Train	17,172	29,006	4,664	4,202
Dev	923	2,451	560	450
Test	832	3,017	636	403
ACE05-E+	Train	19,240	47,525	7,152	4,419
Dev	902	3,422	728	468
Test	676	3,673	802	424
ERE-EN	Train	14,219	38,864	5,045	6,419
Dev	1,162	3,320	424	552
Test	1,129	3,291	477	559
ACE05-CN	Train	6,841	29,657	7,934	2,926
Dev	526	2,250	596	217
Test	547	2,388	672	190
ERE-ES	Train	7,067	11,839	1,698	3,272
Dev	556	886	120	210
Test	546	811	108	269
Table 1: Numbers of sentences (i.e., ents), entity mentions (i.e., ents), relations (i.e., rels), and events (i.e., events) in the datasets.
For ERE, following (Lin et al., 2020), we combine the data from three datasets for English (i.e., LDC2015E29, LDC2015E68, and LDC2015E78) that are created under the Deep Exploration and Filtering of Test (DEFT) program (called ERE-EN). Similar to ACE05-E+, ERE-EN is also used to evaluate the joint models on four IE tasks.
To demonstrate the portability of our model to other languages, we also apply FourIE to the joint
four-IE datasets on Chinese and Spanish. Following (Lin et al., 2020), we use the ACE 2005 dataset for the evaluation on Chinese (called ACE05-CN) and the ERE dataset (LDC2015E107) for Spanish (called ERE-ES).
To ensure a fair comparison, we adopt the same data pre-processing and splits (train/dev/test) in prior work (Lin et al., 2020) for all the datasets. As such, ACE05-R, ACE05-E, ACE05-E+, and AC05-CN involve 7 entity types, 6 relation types, 33 event types, and 22 argument roles while ERE-ES and ERE-EN include 7 entity types, 5 relation types, 38 event types, and 20 argument roles. The statistics for the datasets are shown in Table 1.
Hyper-parameters and Evaluation Criteria. We fine-tune the hyper-parameters for our model using the development data. The suggested values are shown in the appendix. To achieve a fair comparison with (Lin et al., 2020), we employ the bert-large-cased model for the English datasets and bert-multilingual-cased model for the Chinese and Spanish datasets. Finally, we follow the same evaluation script and correctness criteria for entity mentions, event triggers, relations, and argument as in prior work (Lin et al., 2020). The reported results are the average performance of 5 model runs using different random seeds.
Performance Comparison. We compare the proposed model FourIE with two prior models for joint four-task IE: (i) DyGIE++ (Wadden et al., 2019): a BERT-based model with span graph propagation, and (ii) OneIE (Lin et al., 2020): the current state-of-the-art (SOTA) model for joint four-task IE based on BERT and type dependency constraint at the decoding step. Table 2 presents the performance (F1 scores) of the models on the test data of the English datasets. Note that in the tables, the prefixes "Ent", "Trg", "Rel", and "Arg" represent the extraction tasks for entity mentions, event triggers, relations, and arguments respectively while the suffixes "-I" and "-C" correspond to the identification performance (only concerning the offset correctness) and identification+classification performance (evaluating both offsets and types).
As can be seen from the table, FourIE is consistently better than the two baseline models (DyGIE++ and OneIE) across different datasets and tasks. The performance improvement is significant for almost all the cases and clearly demonstrates the effectiveness of the proposed model.
Finally, Table 3 reports the performance of
Datasets	Task	DyGIE++	OneIE	FourIE	Δ%
ACE05-R	Ent-C	88.6	88.8	88.9	0.1
Rel-C	63.4	67.5	68.9†	1.4
ACE05-E	Ent-C	89.7	90.2	91.3†	1.1
Trg-I	-	78.2	78.3	0.1
Trg-C	69.7	74.7	75.4†	0.7
Arg-I	53.0	59.2	60.7†	1.5
Arg-C	48.8	56.8	58.0†	1.2
ACE05-E+	Ent-C	-	89.6	91.1†	1.5
Rel-C	-	58.6	63.6†	5.0
Trg-I	-	75.6	76.7†	1.1
Trg-C	-	72.8	73.3†	0.5
Arg-I	-	57.3	59.5†	2.2
Arg-C	-	54.8	57.5†	2.7
ERE-EN	Ent-C	-	87.0	87.4	0.4
Rel-C	-	53.2	56.1†	2.9
Trg-I	-	68.4	69.3†	0.9
Trg-C	-	57.0	57.9†	0.9
Arg-I	-	50.1	52.2†	2.1
Arg-C	-	46.5	48.6†	2.1
FourIE and OneIE on the Chinese and Spanish datasets (i.e., ACE05-CN and ERE-ES). In addition to the monolingual setting (i.e., trained and evaluated on the same languages), following (Lin et al., 2020), we also evaluate the models on the multilingual training settings where ACE05-CN and ERE-ES are combined with their corresponding English datasets ACE05-E+ and EAE-EN (respectively) to train the models (for the four IE tasks), and the performance is then evaluated on the test sets of the corresponding languages (i.e., ACE05-CN and ERE-ES). It is clear from the table that FourIE also significantly outperforms OneIE across nearly all the different setting combinations for languages, datasets and tasks. This further illustrates the portability of FourIE to different languages.
Table 2: F1 scores of the models on the test data of English datasets.  $\Delta$  indicates the performance difference between FourIE and OneIE. Rows with  $\dagger$  designate the significant improvement  $(p < 0.01)$  of FourIE over OneIE.
Test Data	Train Data	Task	OneIE	FourIE	Δ%
ACE05-CN	ACE05-CN	Ent-C	88.5	88.7	0.2
Rel-C	62.4	65.1†	2.7
Trg-C	65.6	66.5†	0.9
Arg-C	52.0	54.9†	2.9
ACE05-CN	Ent-C	89.8	89.1	-0.7
ACE05-E+	Rel-C	62.9	65.9†	3.0
Trg-C	67.7	70.3†	2.6
Arg-C	53.2	56.1†	2.9
ERE-ES	ERE-ES	Ent-C	81.3	82.2†	0.9
Rel-C	48.1	57.9†	9.8
Trg-C	56.8	57.1	0.3
Arg-C	40.3	42.3†	2.0
ERE-ES	Ent-C	81.8	82.7†	0.9
ERE-EN	Rel-C	52.9	59.1†	6.2
Trg-C	59.1	61.3†	2.2
Arg-C	42.3	45.4†	3.1
Effects of GCN $^{inst}$  and GCN $^{type}$ . This section evaluates the contributions of the two important components in our proposed model FourIE, i.e., the instance interaction graph with GCN $^{inst}$  and the type dependency graph with GCN $^{type}$ . In particular, we examine the following ablated/variied models for FourIE: (i) "FourIE-GCN $^{inst}$ : this model excludes the instance interaction graph and the GCN model GCN $^{inst}$  from FourIE so the initial instance representations  $\mathbf{r}_k$  are directly used to predict the types for the instances (replacing the enriched vectors  $\mathbf{r}_k^{inst}$ ), (ii) "FourIE-GCN $^{type}$ : this model eliminates the type dependency graph and the GCN model GCN $^{type}$  (thus the loss term  $L_{dep}$  as well) from FourIE, (iii) "FourIE-GCN $^{inst}$ -GCN $^{type}$ : this model removes both the instance interaction and type dependency graphs from FourIE, (iv) "FourIE-GCN $^{type}$ +TDDecode": this model also excludes GCN $^{type}$ ; however, it additionally applies the global type dependencies features to score the joint predictions for the beam search in the decoding step (the implementation for this beam search is inherited from (Lin et al., 2020) for a fair comparison), and (v) "FourIE- $\hat{\mathbf{A}}^{pred}$ : instead of employing the approximation matrix  $\hat{\mathbf{A}}^{pred}$  in FourIE, this model directly uses the adjacency matrix  $\mathbf{A}^{pred}$  in the  $L_{dep}$  regularizer ( $L_{dep}$  thus does not influence the instance representation-related parameters  $\theta^{inst}$ ). Table 4 shows the performance of the models on the development dataset of ACE05-E+ for four IE tasks.
Table 3: F1 scores on Chinese and Spanish test sets.  $\dagger$  marks the significant improvement  $(p <   0.01)$  of FourIE over OneIE.
Models	Ent-C	Rel-C	Trg-C	Arg-C
FourIE	89.6	64.3	71.0	59.0
FourIE-GCNINST	89.1	62.3	70.3	57.5
FourIE-GCNType	88.5	61.8	69.9	56.6
FourIE-GCNT-GCNtype	88.2	59.3	68.9	56.1
FourIE-GCNType+TDDecode	88.8	59.6	70.8	56.8
FourIE-A*pred	89.0	62.3	70.2	57.6
Table 4: F1 scores of the models on the ACE05-E+ dev data.
The most important observation from the table is that both GCN $^{inst}$  and GCN $^{type}$  are necessary for FourIE to achieve the highest performance for the four IE tasks. Importantly, replacing GCN $^{type}$  in FourIE with the global type dependency features for decoding (i.e., "FourIE-GCN $^{type}$ +TDDecode") as in (Lin et al., 2020) or eliminating the approximation  $\hat{\mathbf{A}}^{pred}$  for  $L_{dep}$  produces inferior performance, especially for relation and argument extraction. This clearly demonstrates the benefits for deeply integrating knowledge from type dependen
cies to influence representation learning parameters with  $L_{dep}$  for joint four-task IE.
Contributions of Type Dependency Edges. Our type dependency graphs  $\mathbf{G}^{gold}$  and  $\mathbf{G}^{pred}$  involves three categories of edges, i.e., entity Relation, entity Argument, and event Argument type edges. Table 5 presents the performance of FourIE (on the development data of ACE05-E+) when each of these edge categories is excluded from our type dependency graph construction.
Models	Ent-C	Rel-C	Trg-C	Arg-C
FourIE	89.6	64.3	71.0	59.0
FourIE - entity Relation	88.7	61.9	71.0	57.5
FourIE - entity Argument	89.3	63.2	70.0	56.9
FourIE - event Argument	89.5	64.1	69.8	57.7
Table 5: F1 scores of the ablated models for type dependency edges on the ACE05-E+ dev data.
The table clearly shows the importance of different categories of type dependency edges for FourIE as the elimination of any category would generally hurt the performance of the model. In addition, we see that the contribution level of the type dependency edges intuitively varies according to the tasks of consideration. For instance, entity Relation type edges are helpful mainly for entity mention, relation and argument extraction. Finally, an error analysis is conducted in the appendix to provide insights about the benefits of the type dependency graphs  $\mathbf{G}^{gold}$  and  $\mathbf{G}^{pred}$  for FourIE (i.e., by comparing the outputs of FourIE and "FourIE-GCNtype").
The early joint methods for IE have employed feature engineering to capture the dependencies between IE tasks, including Integer Linear Programming for Global Constraints (Roth and Yih, 2004; Li et al., 2011), Markov Logic Networks (Riedel et al., 2009; Venugopal et al., 2014), Structured Perceptron (Li et al., 2013, 2014; Miwa and Sasaki, 2014; Judea and Strube, 2016), and Graphical Models (Yu and Lam, 2010; Yang and Mitchell, 2016).
Recently, the application of deep learning has facilitated the joint modeling for IE via shared parameter mechanisms across tasks. These joint models have focused on different subsets of the IE tasks, including EME and RE (Zheng et al., 2017; Katiyar and Cardie, 2017; Bekoulis et al., 2018; Fu et al., 2019; Luan et al., 2019; Sun et al., 2019; Veyseh et al., 2020b,a), event and temporal RE (Han et al., 2019), and ETD and EAE (Nguyen et al., 2016; Zhang et al., 2019; Nguyen and Nguyen, 2019).
However, none of these work has explored joint inference for four IE tasks EME, ETD, RE, and EAE as we do. The two most related works to ours include (Wadden et al., 2019) that leverages the BERT-based information propagation via dynamic span graphs, and (Lin et al., 2020) that exploits BERT and global type dependency features to constrain the decoding step. Our model is different from these works in that we introduce a novel interaction graph for instance representations for four IE tasks and a global type dependency graph to directly inject the knowledge into the training process.
We present a novel deep learning framework to jointly solve four IE tasks (EME, ETD, RE, and EAE). Our model attempts to capture the interdependencies between instances of the four tasks and their types based on instance interaction and type dependency graphs. GCN models are employed to induce representation vectors to perform type predictions for task instances and regularize the training process. The experiments demonstrate the effectiveness of the proposed model, leading to SOTA performance over multiple datasets on English, Chinese, and Spanish. In the future, we plan to extend the model to include more IE tasks (e.g., coreference resolution).
This research has been supported by the Army Research Office (ARO) grant W911NF-21-1-0112. This research is also based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via IARPA Contract No. 2019-19051600006 under the Better Extraction from Text Towards Enhanced Retrieval (BETTER) Program. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ARO, ODNI, IARPA, the Department of Defense, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. This document does not contain technology or technical data controlled under either the U.S. International Traffic in Arms Regulations or the U.S. Export Administration Regulations.
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