We present a fast and scalable architecture called Explicit Modular Decomposition (EMD), in which we incorporate both classification-based and extraction-based methods and design four modules (for classification and sequence labelling) to jointly extract dialogue states. Experimental results based on the MultiWoz 2.0 dataset validates the superiority of our proposed model in terms of both complexity and scalability when compared to the state-of-the-art methods, especially in the scenario of multi-domain dialogues entangled with many turns of utterances. Dialogue state tracking (DST), responsible for extracting user goals/intentions from dialogues, is a core component in task-oriented dialogue sys-tems (Young et al., 2013). A dialogue state is commonly represented as a ( DOMAIN , SLOT TYPE , SLOT VALUE ) triplet, e.g., (hotel, people, 3). We show an illustrated example of a multi-domain dialogue in Figure 1, which involves two domains, i.e., TRAIN and HOTEL . Previous approaches for DST usually fall into the following four categories: (1) adopt encoder-decoder models to generates states (Kim et al., 2020; Ren et al., 2019; Li et al., 2019; Lee et al., 2019; Wu et al., 2019) ; (2) cast DST as a multi-label classification task when a full candidate-value list is available (Shan et al., 2020; Ramadan et al., 2018; Zhong et al., 2018; Ren et al., 2018); (3) employ span-based methods to directly extract the states (Chao and Lane, 2019; Gao et al., 2019); and (4) combine both classification-based and span-based methods to jointly complete the dialogue state extraction (Zhang et al., 2019). The most related work to ours is DS-DST (Zhang et al., 2019), a joint model which highlights the problem that using classification-based or span-Figure 1: A multi-domain dialogue example extracted from MultiWoz 2.0. The S-type slot values are marked in bold and the arrow points to a pair of C-type slots and its corresponding value. The domain discussed changes from train to hotel at the fourth turn. Refer to Section 2 for the definitions of C-type and S-type . based approach alone is insufficient to cover all cases of DST in the task-oriented dialogue. While DS-DST has achieved some promising result on dialogue state tracking and demonstrated the utility of combining these two types of methods, some problems still remain unaddressed. On one hand, since the model is conditioned on domain-slot pairs, the computational complexity is not constant and will grow as the number of domains and slots involved in dialogues increases. To be more specific, if there are 1000 domain-slot pairs, the model needs to run 1000 times to obtain the expected dialogue states for the current turn at each time, which is a huge computational overhead. On the other hand, previous works usually directly concatenate the history content and the current utterance as input, which is difficult to scale in the multi-turn scenarios, especially when the number of turns of a dialogue is large. Furthermore, we observe that generative approaches may generate some domain outlier 1 triplets due to lack of domain constraints. To tackle these issues, we propose a fast and 1 We refer a predicted result as domain outlier when slot types are out of the domain pertaining to current utterances. scalable method called EMD, where we decompose DST into three classification modules and one sequence labeling module to jointly extract the dialogue states. The benefits of our approach are summarised below:  Efficient : Different to the previous work, we employ a sequence labeling approach to directly annotate the domain-slot values in the utterance instead of iterating over all domain-slot pairs one by one, and thus greatly reduce the model complexity. Constrained output : To effectively model the relationship between the predicted domain and its associated slots, as well as to reduce the occurrence of domain outlier results, we propose a list-wise global ranking approach which uses Kullback-Leibler divergence to formulate the training objective. Scalable : Based on turn-level utterances rather than the whole history dialogue content, our proposed model offers better scalability, especially in tackling dialogues with multiple turns. Additionally, we employ a correction module to handle the changes of the states as the dialogue proceeds. Formally, a multi-turn dialogue is represented as T = { ( s 1 , u 1 , d 1 ) , ( s 2 , u 2 , d 2 ) ,    , ( s n , u n , d n ) } , d i  D , where s i , u i and d i refer to the system utterance, the user utterance, and the domain at turn i , respectively 2 , and D represents the set of all domains in the training dataset. The overall architecture of our model is shown in Figure 2. In our proposed model, we choose MT-DNN (Liu et al., 2019), pretrained model which has the same architecture as BERT but trained on multiple GLUE tasks (Wang et al., 2019). MT-DNN has been shown to be a better contextual feature extractor for downstream NLP tasks. Given dialogue utterances as input, we represent the output of MT-DNN as { H [ CLS ] , H 1 , H 2 ,    , H n } , where n is the length of the concatenation of the system and user utterances. As a sentence-level representation, H [ CLS ] is expected to encode the information of the whole input sequence (Devlin et al., 2019; Liu et al., 2019). Based on these contextual representations, we predict the domain (see 2.1) and belief 2 We assume that the turn-level utterances only contain one domain, and the Multiwoz 2.0 dataset we use in this paper also conforms to this assumption. Figure 1 shows a typical multi-domain dialogue example, from which we can observe that some slot values can be directly found from utterances (e.g. cambridge and london ), while other slot values are implicit which are more challenging to discover, e.g., requiring classification to infer the values (e.g. internet:Yes ). We divide slots into two categories that are handled by two two separate modules: S-type slots whose values could be extracted from dialogue utterances, and C-type slots whose values do not appear in utterances and are chosen from one of the three values { yes, no, don't care } . In a multi-domain dialogue, the target domain may change as the dialogue proceeds. Different from some previous works (Chen et al., 2019; Castel-lucci et al., 2019), which directly use the first hidden state ( H [ CLS ] ), in our model, apart from H [ CLS ] , we additionally incorporate D l , the domain result of the last turn into the our domain prediction module. The rationale behind is that when the domain of current utterances is not explicit, D l can provide useful reference information for domain identification. Formally, the domain is predicted as: y d = softmax ( W d [ H [ CLS ] ; E ( D l )]) (1) D c = arg max( y d ) , D c  D (2) where ; denotes the concatenation operation and E (  ) embeds a word into a distributed representation using fixed MT-DNN (Liu et al., 2019). D c is the predicted domain result. Domain-slot-matching constraints R To prevent our model from predicting some slots not belonging to the current domain, we generate a domain constrained contextual record R  R 1  ( s +1) , where s is number of S-type slots of all domains 3 . Concretely speaking, R is a distribution over all S-type slots and [EMPTY] using R = softmax ( WR [ H [ CLS ] ; E ( D l ]) (3) 3 We add a [EMPTY] , the value of which is expected to be 1 when there is no slot needed to be predicted. In particular, LR , the loss for R is defined as the Kullback-Leibler (KL) divergence between Div ( R real || R ) , where distribution R real from the ground truth is computed as follows:  If there is no slot required to be predicted, R real [ EMPTY ] receives a probability mass of 1 for the special slot [EMPTY] . If the number of slots needed to be predicted is k (  1) , then corresponding k slot positions receive an equal probability mass of 1 /k . Next, we employ a sequence labeling approach to directly annotate the domain-slot values in the utterance instead of iterating over all domain-slot pairs one by one. Specifically, to tag S-type slots of the given input, we feed the final hidden states of H 1 , H 2 ,    , H n into a softmax layer to classify all the S-type slots, y si = softmax ( W s H i ) , i  [1 , 2 ,    , N ] (4) Instead of directly predicting S-type slot results based on y si , we introduce a domain-slot-matching constraint R , which helps avoid generating S-type slots that do not belong to the predicted domain. The multiplication operation is given below,  y si = R (cid:12) y si (5) where (cid:12) is the element-wise multiplication. Given the currently predicted domain result D c we build a set CD c which contains all C-type slots from all domains D . If CD c is empty, it indicates that there is no C-type slot needed to be predicted in the current domain. Otherwise, we classify each slot c D c i in CD into one of the following following categories, i.e., {yes, no, don't care}, with the classification function below. Previous models such as TRADE (Wu et al., 2019) and COMER (Ren et al., 2019) requires that all dialogue states need to be predicted from scratch at each turn, including those dialogue states that have already been predicted at previous turns. This poses a big challenge to the model in terms of scalability, especially when the number of dialogue turns increases. Conversely, the input of our model consists of the system utterance and the user utterance at the current turn, so our model only outputs the estimates of the dialogue states for the current turn, and the previous dialogues are directly included where no re-prediction is needed. However, there is an issue with direct inclusion of previously predicted results in that some states may need to be updated or removed as the dialogue proceeds. For example, a user firstly looks for a hotel located in the center area, then a state (hotel, area, center) is estimated. Subsequently, the user utters a specified hotel name, e.g.  I wanna the King House , then the previous state (hotel, area, center) is outdated and should be removed. To this end, we design the dialogue state correction module to update previously predicted results in order to improve the precision of the outputted dialogues states at each turn. Similar to the C-type classification module, we cast this situation as a classification task, and for each triple tuple p from the previous dialogue states, the classifier is formulated as y p = sigmoid ( W p [ p ; E ( D l ); H [ CLS ] ]) (7) Here each item in p is embedded using E (  ) and  p is the embedding sum of the three items in p . During training, we use cross entropy loss for y d , y c , y s and y p , which are represented as L y d , L y c , L y s and L y p , respectively. The loss for R (denoted as LR ) is defined as Kullback-Leibler (KL) divergence between R real and R (i.e, KL ( R real || R ) ). All parameters are jointly trained by minimizing the weighted-sum of five losses (  ,  ,  ,  , (cid:15) are hyper-parameters), Loss = L y d + L y c + L y s + L y p + (cid:15)L R (8) 2.5 Analysis of model complexity Table 1 reports the Inference Time Complexity (ITC) proposed by (Ren et al., 2019), which is used to measure the model complexity. ITC calculates how many times inference must be performed to complete a prediction of the belief state in a dialogue turn. By comparison, we can observe that our model achieves the lowest complexity, O (1) , attributed to the modular decomposition and the usage of the sequence label based model. Dataset We evaluate our model performance based on the MultiWoZ 2.0 dataset (Budzianowski et al., 2018), which contains 10 , 000 dialogues of 7 domains and 35 domain-slot pairs. Detailed dataset statistics is summarised in Table 2. Evaluation metrics We utilize joint goal accuracy (JGA) (Henderson et al., 2014) to evaluate the model performance. Joint goal accuracy is the accuracy of the dialogue state of each turn and a dialogue state is regarded as correct only if all the values of slots are correctly predicted. Implementation details The hyper-parameters of our model go as follows: both the embedding and the hidden size is 1024 ; we used a learning rate of 0.0001 with a gradient clip of 2.0, mini-batch SGD with a batch size of 32 , and Adam optimizer (Kingma and Ba, 2014) for 50 epoch training. We set a value of 1 to the five weighted hyper-parameters:  ,  ,  ,  , (cid:15) . Overall comparison We compare our models against six strong baselines on the multi-domain dataset MultiWoz. Results are reported in Table 3 based on joint goal accuracy (JGA). Our model achieves the best performance of 50 . 18% in the multi-domain testset, while the accuracy achieved in the single-domain is on par with the state-of-the-art results, which demonstrates the superiority of our model. Analysis of model scalability We select 200 samples from the testing dataset, in which each dialogue has more than 8 turns of utterances between the system and the user. Then, taking the turn number 6 as a threshold, we divide the dialogue content into two categories, i.e., COLD and Turn Previous States Domain Target states Predicted states for the current turn COMMER TRADER EMD 1 {} Hotel (hotel, internet, yes) (hotel, internet, yes) (hotel, internet, yes) (hotel, internet, yes)        3 (hotel, internet, yes) (hotel, name, holiday inn) Taxi (hotel, internet, yes) (hotel, name, holiday inn) (taxi, destination, holiday inn) (hotel, internet, yes) (hotel, name, holiday inn) (train, destination, holiday inn) (hotel, internet, yes) (hotel, name, holiday inn) (taxi, destination, holiday inn) (hotel, internet, yes) (hotel, name, holiday inn) (taxi, destination, holiday inn)  ...      8 (hotel, internet, yes) (hotel, name, holiday inn) (taxi, destination, holiday inn) Taxi (hotel, internet, yes), (hotel, name, holiday inn), (taxi, destination, holiday inn) (hotel, internet, yes) (hotel, name, holiday inn) (train, destination, holiday inn) (hotel, internet, no) (hotel, name, holiday inn) (taxi, destination, holiday inn) (hotel, internet, yes) (hotel, name, holiday inn) (taxi, destination, holiday inn) Figure 3: Case study of predicated states by our model and two baselines. From Table 4, we observe that the model performance has a big drop for the four baseline models, but our model achieves a relatively stable performance, achieving 51.01% in HOT and 51 . 89% in COLD , respectively. This demonstrates that our model is not only fast in terms of inference speed (cf. 2.5), but also has a good scalability which can maintain a high accuracy even when the dialogue proceeds into more turns and the input length becomes larger. Ablation study We conduct two ablation experiments to investigate the impacts of D l and R . We introduce a metric, called outlierslot ratio (OSR), denoting the proportion of slots predicted by our model that do not belong to the current domain. From Table 5, we notice that adding D l improves the domain accuracy, where one possible reason is that some utterances may not have a clear domain attribute, and thus the incorporated previous domain is believed to provide useful guiding information in domain prediction. Besides, by comparing OSR with and without using R , we can observe that using R reduces the proportion of generating slots that do not align to the predicted domain, which further improves the model performance. itatively, we show an exemplary dialogue and illustrate some generated results by EMD and two baseline models in Figure 3. At turn 3 when the dialogue domain change from hotel to taxi , COMMER fails to capture the domain information and generates a domain outlier,  train , which does not conform to the current context. Conversely, dialogue generated by our model always conforms to the domain at the current turn, which may benefit from the incorporation of the domain constrained contextual record R . Besides, another observation is that as the dialogue proceeds to the turn 8 when the history dialogue content accumulates, TRADER makes an incorrect prediction in the hotel-internet slot, which is correctly identified at the turn 1 . One possible reason is that it becomes more challenging for the model to correctly predict all dialogue state from scratch when both the history dialogue content and states involved increase. Instead of repeatedly generating those previously predicted states at each turn, our model only outputs the states for the current turn, and updates previous dialogue states with a separate module. In this paper, we propose to decompose DST into multiple submodules to jointly estimate dialogue states. Experimental results based on the MultiWoz 2.0 dataset show that our model not only reduces the model complexity, but also gives high scalability in coping with multi-domain and long task-oriented dialogue scenarios.
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