Duplex Sequence-to-Sequence Learning for Reversible Machine Translation

05/07/2021 ∙ by Zaixiang Zheng, et al. ∙ 0

Sequence-to-sequence (seq2seq) problems such as machine translation are bidirectional, which naturally derive a pair of directional tasks and two directional learning signals. However, typical seq2seq neural networks are simplex that only model one unidirectional task, which cannot fully exploit the potential of bidirectional learning signals from parallel data. To address this issue, we propose a duplex seq2seq neural network, REDER (Reversible Duplex Transformer), and apply it to machine translation. The architecture of REDER has two ends, each of which specializes in a language so as to read and yield sequences in that language. As a result, REDER can simultaneously learn from the bidirectional signals, and enables reversible machine translation by simply flipping the input and output ends, Experiments on widely-used machine translation benchmarks verify that REDER achieves the first success of reversible machine translation, which helps obtain considerable gains over several strong baselines.

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1 Introduction

Neural sequence-to-sequence (seq2seq

) learning has been extensively used in various applications of natural language processing, since such network design well matches many downstream tasks (e.g., machine translation), namely mapping sequences from the source side to the target side 

(Sutskever et al., 2014; Gehring et al., 2017; Vaswani et al., 2017). Given a source domain and a target domain , seq2seq problems naturally derive a symmetric pair of directional tasks, i.e., a source-to-target task and a target-to-source task, and two directional learning signals. Given parallel data of and , for instance, to learn the source-to-target mapping , a standard seq2seq neural network usually employs the encoder-decoder framework, which includes an encoder to acquire the representation from the source side, and a decoder to yield the target side outputs from the encoded source representation. The target-to-source mapping could be modeled and learned in the same way.

Figure 1: Illustration of different sequence-to-sequence neural models in regards to modeling direction and generation formulations.

We argue that the encoder-decoder framework cannot fully exploit the potential of bidirectional learning signals given by the seq2seq problems. Let us take machine translation as an example. (a) Encoder-decoder based seq2seq models typically only learn one directional signals to perform the corresponding unidirectional translation (Figure 1(a)). (b) Although multi-task learning could help the seq2seq models leverage both signals and perform bidirectional translation (Johnson et al., 2017a), by sharing one unidirectional networks (Figure 1(b)), they may suffer from the challenges of the parameter interference due to the limited network capacity (Arivazhagan et al., 2019; Zhang et al., 2021).

From the view of telecommunication111In telecommunications and computer networking, the simplex communication means the communication channel is unidirectional while the duplex communication is bidirectional., translation between languages resembles the duplex communication, whereas seq2seq models within the encoder-decoder framework are considered simplex. Thus we speculate that this discrepancy results in the aforementioned limitations of the encoder-decoder framework, making it not necessarily the best paradigm to model seq2seq problems.

Therefore intuitively, duplex seq2seq neural networks, which would leverage the duplex nature of seq2seq problems, could become better modeling alternatives. Conceptually, a duplex seq2seq neural network has two ends, each of which specialize ins a language and can both take inputs and yield outputs in that language (Figure 1(c)). Given a duplex neural network with source language and target language , it is expected to have an inverse , and satisfies the following reversibility:

The resulting duplex seq2seq model can take a sentence in the source language from the source end, and output a sentence in the target language to the target end (forward translation ). The same model is able to generate the reverse translation by taking a sentence in the target language from the target end to the source end (reverse translation ). In such a way, the bidirectional signals could be learned jointly by a duplex model, and the bidirectional translation can be achieved as a reversible and unified process. Thus both directions do not need to compete for the limited network capacity, but could learn together and boost each other.

However, building a duplex seq2seq neural network is yet under-studied and non-trivial. The intuition of designing such a duplex network lies in making the network reversible, as well as the computational process homogeneous for both forward and reverse directions. This is very challenging to achieve within the existing encoder-decoder paradigm for the following reasons: (a) a encoder-decoder network is irreversible. The decoder’s output end cannot take in input signals to exhibit the encoding functionality, and vice versa; (b) the encoder and decoder are heterogeneous. The decoder consists of extra cross attention modules while the encoder does not; plus, the typical decoder works autoregressively, while the encoder is non-autoregressive.

In this paper, we take the first step of building a duplex seq2seq neural network. We propose REDER 222The model name is a palindrome, which implies the model works from both ends., the Reversible Duplex Transformer, and apply it to reversible machine translation. To address the above problems, (a) for reversibility, we design REDER as a fully reversible Transformer inspired by Gomez et al. (2017); (b) for homogeneity, REDER has no division of encoder and decoder, and reads and yields sentence in a fully non-autoregressive fashion. Also, thanks to the reversibility inside the network, REDER could make use of cycle consistency to explicitly enhance intermediate layer representations.

Despite the challenges from non-autoregressive modeling and non-encoder-decoder design, experiments show that enabling reversible machine translation, by jointly learning the two translation signals on the same parallel corpus, offers REDER significant accuracy gains (about 1.5 BLEU). REDER gives the top results among state-of-the-art non-autoregressive baselines, and outperform multi-task autoregressive methods regarding bidirectional translation, which verifies our motivation. Meanwhile, REDER closely approaches and is faster than typical autoregressive models. To our best knowledge, REDER is the first duplex seq2seq network and enables the first success of reversible machine translation, which is a completely brand-new paradigm to the machine translation community.

2 Related Work

Sequence-to-Sequence Models Exploiting Bidirectional Signals. Sequence-to-sequence problems naturally induce of a symmetric pair tasks of the opposite directions, a source-to-target mapping and a target-to-source mapping. Several studies try to capture such bidirectionality as constraint to improve sequence-to-sequence tasks such as machine translation (Cheng et al., 2016a, b). Additionally, dual learning (He et al., 2016; Xia et al., 2017)

leverage reinforcement learning to achieve the interaction between two separate directional translation models. Meanwhile,

Xia et al. (2018) propose a partially model-level dual learning that shares some components of similar underlying functionality of both models for forward task and reverse task. Zheng et al. (2020)

propose to model the two directional translation model with language models in a variational probabilistic framework. These approaches model two directional tasks by setting up two separate simplex models to consider the task bidirectionality. Different from them, REDER can unify direction pair within one duplex model and directly model the bidirectionality at a completely model level. In addition, another kind of work can also unify two directional tasks in a multilingual fashion 

(Johnson et al., 2017a; Chan et al., 2019) by sharing the same computational process of one simplex model, which would inevitably need to split the limited model capacity to learn to encode and decode two languages. In contrast, REDER can simultaneously formulate two directional tasks in one model by simply exchanging input and output ends, each of which specialize ins a language, thus bidirectional translation becomes a reversible process in which both directions do not need to compete for limited model capacity.

Non-autoregressive Sequence Generation. Non-autoregressive translation (NAT) models (Gu et al., 2018) significantly attract research interest due to the inefficiency of traditional autoregressive seq2seq models. The major research interest focuses on fully NAT models, which generate sequence in parallel within only one shot but sacrifice performance (Gu et al., 2018; Ma et al., 2019; Shu et al., 2020; Bao et al., 2019; Wei et al., 2019; Li et al., 2019; Wang et al., 2019; Qian et al., 2020; Gu & Kong, 2020)e. Besides, semi-autoregressive models greatly improve the performance of NAT models, which perform iterative refinement of translations based on previous predictions (Lee et al., 2018; Ghazvininejad et al., 2019; Gu et al., 2019; Kasai et al., 2020; Ghazvininejad et al., 2020; Shu et al., 2020). In this work, REDER takes the advantages of the probabilistic modeling of fully NAT models for resolving the designing challenge of computational homogeneity for both translation directions.

Reversible Neural Architectures.

Various reversible neural networks have been proposed for different purposes and based on different architectures. On one hand, reversible neural networks help model flexible probability distributions with tractable likelihoods 

(Dinh et al., 2014, 2017; Papamakarios et al., 2017; Kingma et al., 2016), which define a mapping between a simple, known density and a complicated desired density. Besides, reversibility can also assist to develop memory-efficient algorithms. The most popular approach is the reversible residual network (revnet, Gomez et al., 2017), which modifies the residual network for image classification and allows the activations at any given layer to be recovered from the activations at the following layer. Therefore layers can be reversed one-by-one as back-propagation proceeds from the output of the network to its input. Some follow-up work extends the idea of revnet to RNNs (MacKay et al., 2018) and Transformer (Kitaev et al., 2020) for natural language processing. In this paper, we borrow the idea of revnet as the basic unit of our proposed REDER, however, for different purposes. The aim of revnet and its variants lies in reducing memory consumption, while our purpose is to build a duplex seq2seq model, which can govern two directional tasks reversibly. In this line, van der Ouderaa & Worrall (2019)

propose a reversible GAN approach for image-to-image translation in computer vision, which to a certain extent shares the intuition with ours.

3 Sequence-to-Sequence Models as Communication Channels

The standard sequence-to-sequence models. Sequence-to-sequence (seq2seq) tasks (Sutskever et al., 2014) such as machine translation (Bahdanau et al., 2015) typically adopt neural encoder-decoder models which aim to approximate the mapping function from source domain to target domain (). The encoder-decoder neural networks can be analogous to a simplex communication system in source-to-target direction (Figure 1 (a)): the encoder reads the source sequence from the source side and the decoder generates the target sequence from the target side. Reverse travel from the target to the source side is not allowed in such simplex models. In this paper, we focus on the most widely-used simplex model, the Transformer model (Vaswani et al., 2017). A Transformer-based model reads a source sequence and transforms to encoded representations by its encoder. The encoder is composed of stacked Transformer layers, each of which contains a self attention (San) and feed-forward networks (Ffn):

where is the sequence of word embeddings of , and for ease of understanding, we package layer normalization (Ba et al., 2016) inside residual blocks and omit its formulation details. Given the final encoded representation , the representations of each decoder layer are computed as:

where Can denotes the cross attention network that can fetch time-dependent context from the encoder, is the sequence of target word embeddings. Finally, it generates the corresponding target sequence autoregressively by (see Vaswani et al. (2017) for more details). Given the same parallel data, we can also learn a reverse mapping of the target-to-source direction () using another simplex model.

To leverage bidirectional learning signals, another possible choice is to employ multi-task learning to a simplex model to jointly model both directions, where both directions share the same model parameters () and from the same input end to the same output end. However, such models may suffer from the challenges of the parameter interference due to the limited network capacity (Arivazhagan et al., 2019; Zhang et al., 2021), where encoder and decoder are required to simultaneously understand and generate different languages, and the two different directional tasks compete for the limited shared network capacity.

Duplex sequence-to-sequence models. color=blue!40color=blue!40todo: color=blue!40(jjx: I still do not get the motivation of duplex based on current description for the following reasons. 1. I have no idea what is structure duality. 2. Why shared encoder-decoder can not achieve this goal? 3. Which advantages do duplex models have?) As we stated above, the standard sequence-to-sequence generation model resembles a simplex communication channel. Think of a scenario where one person from New York is making a phone call to another one in Berlin. The phone is simplex – it only takes voice input at New York, while only outputs voice at Berlin. This certainly reduced the benefit of two-way communication. Obviously, the everyday phone has the capability of taking voice input and producing voice output at both ends and transferring the signals in both communication directions. In analog, it will benefit sequence generation tasks such as machine translation by enabling a duplex sequence-to-sequence model.

Informally, a sequence-to-sequence model is duplex if it has two ends, both with sequence input and output capability, and share a same architecture to map from one sequence space to the other and vice versa.

Definition 1.

A sequence-to-sequence model with parameter is duplex if it satisfies the following: its network has two ends: a source end and a target end; both source and target ends can take input and output sequences; the network defines a forward mapping function and a reverse mapping function , where , are the vocabularies of the source and target domains , , and , are all possible sequences; essentially, it simultaneously induces both a forward sequence generation function and its mathematical inverse by reversely executing the network, i.e. and . In addition, these two functions should satisfy the following,

Notice that the forward function has the same model parameter as the reverse function . This sequence generation model following this definition behaves similarly to a two-way communication channel.

We can apply this definition on machine translation to get a reversible translation model. Such a reversible model will be able to take a sentence in the source language from the source end and to output a sentence in the target language to the target end. With the same model it will be able to generate the reverse translation by taking a sentence in the target language from the target end to the source end.

Remark.

A reversible machine translation model using duplex sequence-to-sequence is distinct from a multilingual MT model (e.g. multilingual Transformer). The multilingual Transformer takes input sentences in two (or more) languages only from the same end and outputs to the other end. Its output end cannot be used to receive input signals.

4 REDER for Reversible Machine Translation

Figure 2: The proposed REDER for duplex sequence-to-sequence generation. The bottom two diagrams show the computation of the regular and reverse forms of a reversible layer. Notice that, to make the whole model symmetric, we reverse the -th to -th layers, such that the overall computational operations of forward and reverse of REDER are homogeneous.

As in the well-known saying by Richard Feynman, ‘‘What I cannot create, I do not understand”, reversible natural language processing (Franck, 1992; Strzalkowski, 1993) and its applications in machine translation (van Noord, 1990) were proposed for the purpose of building machine models that understand and generate natural languages as a reversible, unified process. Such process resembles the mechanism of the ability that allows us human beings to communicate with each other via natural languages (Franck, 1992)

. However, the attempts were not so successful mainly due to the less powerful computational models then. With the great success of deep neural networks in machine translation, the idea of reversible machine translation is more likely to realized via neural machine translation, and brings further benefits to the translation performance.

In this section, we introduce how to design a duplex neural seq2seq model, namely Reversible Duplex Transformer (REDER), that satisfies Definition 1, to realize reversible machine translation.

4.1 Challenges of Reversible Machine Translation

Designing neural architectures for reversible machine translation yet remains under-studied and has the following challenges:

  1. Reversibility. Typical encoder-decoder networks and their neural components, such as Transformer layers, are irreversible, i.e. one cannot just obtain its inverse function by flipping the same encoder-decoder network. To meet our expectation, an inverse function of the network should be derived from the network itself.

  2. Homogeneity. Intuitively, a pair of forward and reverse translation directions should resemble a homogeneous process of understanding and generation. However, typical encoder-decoder networks certainly do not meet such computational homogeneity due to extra cross attention layers in the decoder; and also because of the discrepancy that the decoder works autoregressively but the encoder does non-autoregressively. To meet our expectation, division of encoder and decoder should be no more exist in the desired network.

4.2 The Architecture of REDER

To solve the above challenges, we include two corresponding solutions in REDER to address the reversibility and homogeneity issues respectively, i.e., the reversible duplex Transformer layers, and the symmetric network architecture without encoder-decoder framework.

Figure 2 shows the overall architecture of REDER. As illustrated, REDER has two ends: the source end (left) and the target end (right). is the model parameter, shared by both directions. The architecture of REDER is composed of a series of identical Reversible Duplex Transformer layers, each of them contains a self attention and a feed-forward module. More concretely, when performing the source-to-target mapping , a source sentence (blue circles) 1) first transforms to its embedding and enters the source end; 2) then goes through the entire stacked layers and evolves to final representations

which are then normalized to probabilities; 3) finally its target translation (orange circles) will be generated from the target ends. The generation process is fully non-autoregressive.

Likewise, the target-to-source mapping is achieved by reversely executing the architecture of REDER from target end to source end. We will dive into the details of the key components of REDER in the following parts.

Reversibility: Reversible Duplex Transformer layers.  We adopt the idea of reversible residual network (revnet, Gomez et al., 2017; Kitaev et al., 2020) in the design of the reversible duplex Transformer layer. Each layer is composed of a multi-head self-attention block and a feedforward block with a special reversible design to ensure duplex behavior. Formally, the regular form of the -th layer performs as follow:

where is the concatenation of the embedding of . Accordingly, the reverse form of can be computed by subtracting (rather than adding) the residuals:

For better modeling the reordering between source and target languages, we employ relative self-attention (Shaw et al., 2018) instead of the original one (Vaswani et al., 2017).

Homogeneity: Symmetric network architecture without encoder-decoder framework. To meet our need to ensure homogeneous network computations for forward and reverse directional tasks, we therefore choose to discard the encoder-decoder paradigm.

Symmetric network. To achieve homogeneous computations, one solution is to make our network symmetric. Specifically, we let the -th to -th layers be the reverse form, whereas the latter -th to -th be the regular form:

where means a layer is connected to the next layer. Thereby the forward and reverse computational operations of the whole model become homogeneous: the forward computational operation series reads as a palindrome string and so does the reverse series, where and denote San and Ffn.

Fully non-autoregressive modeling. Note that without encoder-decoder division, the resulting model works in a fully non-autoregressive fashion for both forward and reverse directions. Thus, the conditional probability of a sequence pair becomes due to the introduced conditional independence assumption among target tokens. Once a forward computation is done, the concatenation of the output of the model serves as the representations of target translation. And then, a softmax operation is performed to measure the similarity between the model output and the concatenated embedding of ground-truth reference , to obtain the prediction probability:

We can likewise derive the procedure of for the target-to-source direction.

Modeling various-length input and output.  Encoder-decoder models can easily model various-length input and output of most seq2seq problems. However, discarding encoder-decoder separation imposes a new challenge: the width of all the layers of the network is depending on the length of the input, thus it is very difficult to allow various-length input and output, especially when the input is shorter than the output. We resort to the Connectionist Temporal Classification (CTC) (Graves et al., 2006) to solve this problem, a latent alignment approach with superior performance and the flexibility of variable length prediction. Given the conditional independence assumption, CTC is capable of efficiently finding all valid alignments which derives from the target by allowing consecutive repetitions and inserting blank tokens, and marginalizes log-likelihood:

where

is the collapse function that recovers the target sequence by collapsing consecutive repeated tokens, and then removing all blank tokens. Note that CTC requires that the length of source input should not be smaller than the target output, which is not the case in machine translation. To deal with this, we follow previous useful practice by upsampling the source tokens by 2 times 

(Saharia et al., 2020; Libovický & Helcl, 2018), and filter those examples when the target lengths are still larger than the one of upsampled source sentences.

Remark.

Reversibility in REDER can be assured in the continuous representation level, where REDER can recover from output representations (last layer) to input embeddings (first layer), which is also the motivation and basis of the auxiliary learning signal, , in the next section. Reversibility might not hold in the discrete token level, because the irreversible argmax operation discretizes probabilities to tokens. But REDER still shows decent reconstruction capability in practice, as visually depicted in Figure 3.

4.3 Training

Given a parallel corpus and a single model , REDER can be jointly supervised by source-to-target and target-to-source translation for and , respectively. Thus both translation directions can be achieved in one REDER model. We refer this to bidirectional training, which is opposite to unidirectional training, where each translation direction needs a separate model. Moreover, the reversibility of REDER enables appealing potentials to exploit consistency/agreement between forward and reverse directions. We introduce two auxiliary learning signals as follows.

Cycle Consistency  Symmetry of a pair of sequence-to-sequence tasks enables the use of cycle consistency (He et al., 2016; Cheng et al., 2016a). Given a source sentence , the forward prediction of REDER is obtained, and then we use the reverse model on this prediction to reconstruct it to the source language:

Finally, we maximize the consistency or agreement between the original one and reconstructed one

. Thus, the loss function reads

We expect it can provide an auxiliary signal that a valid prediction should be loyal to reconstruct its source input. Here we use cross-entropy between the probabilistic prediction of the reverse model as distance to measure the consistency.

Layer-wise Forward-Backward Agreement

  Since REDER is fully reversible, which consists of a series of computationally inverse of intermediate layers, an interesting question arises: given the desired output (i.e., the target sentence), is it possible to derive the desired intermediate hidden representation by the backward target-to-source computation, and encourage the forward source-to-target intermediate hidden representations as close as possible to these “optimal” representations?

Given a source sentence , the inner representations of each layer in forward direction are:

and given its corresponding target sequence as the optimal desired output333for CTC-based model where the model prediction are the alignments, we instead extract the token sequence of the best alignment , predicted by the model, associated with the ground-truth as the optimal desired output., the inner representations of each layer in reverse direction are:

where and represent the representations of -th layer in forward and reverse models, respectively. As we consider these reverse inner layer representations as “optimal”, we try to minimize the cosine distance between the forward and backward corresponding inner layer representations:

where is stop-gradient operation.

A potential danger of both of the above auxiliary objective is model collapse, where it would probably cheat this task by simply learning an identity mapping. We solve this problem by setting a two-stage training scheme for them, where we first train REDER without using any auxiliary losses until a predefined updates, and then activate the additional losses and continue training the model until convergence.

Final Objective  Given a parallel dataset of i.i.d observations, the final objective of REDER is to minimize

where and are coefficients of auxiliary losses.

5 Experiments

Systems Speed WMT14 WMT16
En-De De-En En-Ro Ro-En
Simplex AT Transformer base (KD teacher) 62M 2 1.0 27.60 31.50 33.85 33.70
Reformer (Kitaev et al., 2020) 62M 2 1.0 27.60 - - -
Simplex models leveraging bidirectional signals Model-level DL big (Xia et al., 2018) - 28.90 31.90 - -
KERMIT (Chan et al., 2019) - 25.60 27.40 - -
KERMIT + mono (Chan et al., 2019) - 28.10 28.60 - -
MGNMT (Zheng et al., 2020) - 27.70 31.40 32.70 33.90
Simplex NAT vanilla enc-dec NAT (Gu et al., 2018) 15.6 17.69 21.47 27.29 29.06
CTC (Libovický & Helcl, 2018) - 16.56 18.64 19.54 24.67
CTC (Saharia et al., 2020) 18.6 25.70 28.10 32.20 31.60

CTC-based Imputer 

(Saharia et al., 2020)
18.6 25.80 28.40 32.30 31.70
GLAT+NPD (Qian et al., 2020) 15.3 26.55 31.02 32.87 33.51
GLAT+CTC (Gu & Kong, 2020) 16.8 27.20 31.39 33.71 34.16
Our work [1] vanilla enc-dec NAT 62M 2 16.3 19.50 24.95 29.49 29.86
[2]  + CTC 62M 2 15.6 26.11 30.24 33.25 33.68
[3] REDER (unidirectional training) 58M 15.5 25.55 29.54 - -
[4] REDER (bidirectional training) 58M 15.5 26.70 30.68 33.10 33.23
[5]  + beam20 + AT reranking 58M 5.5 27.36 31.10 33.60 34.03
Table 1: Comparisons between our models and existing models. The speed-up is measured on the WMT14 En-De test set. All NAT models are trained with KD. denotes models trained with distillation from a big Transformer. Separate training means two separate models trained for a pair of directions, while joint training means only one shared model is used.

We conduct extensive experiments on standard machine translation benchmarks to inspect REDER’s performance on sequence-to-sequence tasks. We demonstrate that REDER achieves competitive results, if not better, compared to strong autoregressive and non-autoregressive baseline. REDER is also the first approach that enables reversible machine translation in one unified model, where bidirectional training with paired translation directions surprisingly helps boost each them with a substantial margin.

5.1 Experimental Setup

Datasets. We evaluate our proposal on two standard translation benchmarks, i.e., WMT14 English (En) German (De) (4.5M training pairs), and WMT16 English (En) Romanian (Ro) (610K training pairs). We apply the same prepossessing steps as mentioned in prior work (EnDeZhou et al., 2020, EnRoLee et al., 2018). BLEU (Papineni et al., 2002) is used to evaluate the translation performance for all models.

Knowledge Distillation (KD). Following previous NAT studies (Gu et al., 2018; Zhou et al., 2020), REDERs are trained on distilled data generated from pre-trained auto-regressive Transformer models. The beam size is set to during generation.

Beam Search Decoding. We implement two kinds of inference policies. The first one is the most straightforward policy that adopts tokens with the highest probability at each position. For a fair comparison with other NAT studies, we also implement beam search to REDER with an efficient library of C++ implementation444https://github.com/parlance/ctcdecode. We adopt the first policy in the default setting.

Implementation Details. We design REDER based on the hyper-parameters of Transformer-base (Vaswani et al., 2017). The number of head is 8, the dimension of embedding size is 512, and the dimension of Ffn is 2048. REDER consists of 12 stacked layers. For both AT and NAT models, we set the dropout rate for WMT14 EnDe and WMT16 EnRo. We adopt weight decay with a decay rate and label smoothing with . By default, we upsample the source input by for CTC. We set and to 0.1 for all experiments. All models are trained for K updates using Nvidia V100 GPUs with a batch size of approximately K tokens. Following prior studies (Vaswani et al., 2017), we compute tokenized case-sensitive BLEU. We measure the validation BLEU scores every 2,000 updates, and average the best checkpoints to obtain the final model. As in previous NAT studies, we measure the GPU latency by running the model with a single sentence per batch on a single Nvidia V100 GPU. All models are implemented on fairseq (Ott et al., 2019).

5.2 Main Results

We compare REDER with previous AT and NAT models, as well as simplex models leveraging bidirectional learning signals. As shown in Table 1, the proposed REDER achieves competitive results compared with these strong baselines.

The proposed duplex network has a comparable capability as strong NAT models. Unlike conventional encoder-decoder models, since REDER has no division of encoder and decoder, we need to inspect the generalization ability of duplex architecture. It is surprising to see that the gap between REDER and traditional encoder-decoder NAT models (with CTC loss) is negligible within a half-point BLEU on WMT14 En-De translation ([3] vs [2]), verifying that REDER is reliable for further testing bidirectional tasks.

REDER enables reversible machine translation and better accuracy. We then show that a unified REDER trained on the same parallel data can simultaneously work in two directions. With auxiliary losses (i.e., the cycle consistency and layer-wise forward-backward agreement) enabled by the duplex reversibility, REDER surprisingly achieves more than 1 BLEU score improvements compared to its simplex version ([4] vs [3]). Finally, with the help of beam search and re-ranking, the performance of REDER is extremely close to that of the normal simplex AT models. These results verify our motivation that a duplex model can exploit the bidirectionality of sequence-to-sequence tasks in one unified model in such a way the two directions could boost each other. To the best of our knowledge, REDER is the first duplex approach that enables reversible machine translation in a unified model rather than separate simplex models.

Comparison with existing approaches. We first compare REDER with existing simplex approaches exploiting bidirectional signals (Xia et al., 2018; Zheng et al., 2020; Chan et al., 2019). These approaches need to deploy two separate simplex models for both directions (Xia et al., 2018; Zheng et al., 2020). REDER, in contrast, only needs one unified duplex model and coherently models two directions. REDER could achieve close performance compared to them despite the fact that non-autoregressive modeling is far more challenging in learning. Alternatively, Chan et al. (2019) use a same simplex network to achieve bidirectional translation via multi-task learning, needing to split limited capacity for both directions, which underperform REDER on parallel settings. We will present in-depth discussion with such multi-task approaches later ( § 5.4).

As for non-autoregressive approaches (NAT), CTC (Saharia et al., 2020) and GLAT (Qian et al., 2020) are rather helpful. Among them, Gu & Kong (2020) explore the best technique combination for NAT, in which GLAT+CTC achieves by far one of the best NAT accuracy. In contrast, this paper focuses on a totally different idea of developing a duplex seq2seq model that can perform reversible MT, in which non-autoregressive modeling is one of all the technical solutions chose for our ultimate goal. Nevertheless, REDER approaches closely to the state-of-the-art Gu & Kong (2020), whose tricks can also supplement to enhance REDER. We leave this for exploration.

Figure 3: Case study. We first use the forward mapping of REDER to obtain a prediction in the target language, and then translate it back to the source language using the reverse model. REDER can reconstruct the input from output with mild differences to some extent.

Example. We also show an example regarding forward prediction and reconstruction of REDER in Figure 3.

5.3 Effects of Decoding and Re-ranking

Systems En-De De-En BP Speed
Transformer (AT, teacher) 27.20 31.00 0.980 1.0
 + beam=5 27.60 31.50 0.998 -
 + beam=20 27.65 31.12 0.954 -
GLAT (Qian et al., 2020) 25.21 29.84 - -
 + NPD=7 + AT reranking 26.55 31.02 - -
REDER (w/ ) 26.70 30.68 0.935 19.9
 + beam=20 26.90 30.72 0.985 6.8
 + beam=20 + AT reranking 27.36 31.10 1.000 5.5
 + beam=100 26.95 30.75 0.991 2.1
 + beam=100 + AT reranking 27.52 31.45 1.000 1.2
Table 2: Comparisons regarding decoding methods for REDER on WMT14 EnDe. The brevity penalty (BP) given by BLEU indicates the adequacy of translation: the lower the BP, the more inadequate the translation.

The performance of REDERs can be further boosted with additional (beam-search or re-ranking) techniques. For CTC beam search, we use the teacher model (AT base) to re-rank the translation candidates obtained by the beam search to determine the one with the best quality. As shown in Table 2, a larger beam size results in a smaller BP for AT models, meaning it produces shorter translations (Stahlberg & Byrne, 2019; Eikema & Aziz, 2020). For pure NAT models using the advanced glancing strategy (GLAT), noisy parallel decoding and re-ranking can provide significant improvements (1.3 for both En-De and De-En). In REDER, CTC beam search helps produce longer outputs (larger BPs) but only endows a little improvement. With beam search and AT reranking, REDER can generate more decent translations. These results imply that we need to find a better way to train REDER (and probably the NAT family) if we do not want to involve an extra AT for such a somewhat inconvenient re-ranking.

5.4 Does Duplex Network Really Matter for Bidirectional Translation?

Systems bidir. En-De De-En
AT (b=5) 62M2 27.60 31.50
AT (b=20) 62M2 27.65 31.12
AT-multi (b=5) 27.05 30.96 62M
NAT: GLAT+CTC (b=1) 27.49 31.10
NAT: GLAT+CTC (b=20) 62M 26.79 30.45
NAT-multi: GLAT+CTC (b=20) 62M 25.50 29.49
REDER (b=20) 58M 26.30 30.12
REDER-multi (b=20) 58M 25.89 29.32
REDER-reversible (b=20) 58M 27.36 31.10
Table 3: Comparisons on bidirectional translation with simplex AT and NAT models that use multi-task learning, on WMT14 EnDe. “bidir.” means whether models can perform bidirectional translation between two languages by itself, othewise unidirectional translation as usual. “-multi” means achieving bidirectional translation by multi-task learning via adding language-specific tokens, while “-reverible” means using reversible model, i.e., REDER. “GLAT+CTC” means our re-implementation of Gu & Kong (2020), while “” means results from their paper. All CTC-based models decode using beam search and AT-reranking. “b” is beam size.

By definition, learning bidirectional translation with a duplex network results in reversible machine translation. Meanwhile, multi-task learning can also help to learn two or more translation directions in one simplex model, resulting in bi- or multi-lingual NMT models. Here we refer them to multi-task simplex models in the investigated bilingual scenarios. Such multi-task simplex models share the encoder/decoder for all involved languages, which are shown to be helpful for low-resource languages but hurtful for high resource languages in multilingual machine translation scenarios (Johnson et al., 2017b; Arivazhagan et al., 2019; Zhang et al., 2020). Thus, one may ask: given such models, does duplex model really matter in performing a bidirectional task? To answer this we conduct a comparison with multi-task approaches with shared encoders and decoders for both translation directions. As shown in Table 3, (1) Multilingual-style models suffer from sharing capacity thus their performance shrink ([2] vs [3], [5] vs [6] and [7] vs [8]), which verifies our motivation of the concern of limited model capacity of multi-task models. (2) When using beam search, reversible machine translation makes REDER outperform multi-task AT regarding bidirectional translation ([9] vs [3]). REDER can even achieve very close result to unidirectional AT ([9] vs [1]/[2]), while REDER can translate both direction in one model. In addition, all of the NAT models are faster than AT models. This evidence shows the advantage and practical value of the proposed REDER. It also indicates that reversible machine translation s more decent solution for performing bidirectional translation.

5.5 Ablation Study of Components

KD CTC revnet R-San BLEU
11.40
19.50
16.90
25.01
25.55
25.90
26.20
26.70
26.65
26.89
Table 4: Ablation on WMT14 EnDe test set with different combinations of techniques. R-San denotes relative self attention.

REDER is developed on the top of various components in terms of data (knowledge distillation), learning objective (CTC), architecture (revnet, relative attention), and auxiliary losses endowed by reversibility of REDER. We analyze their effects through various combinations in Table 4. We first consider training REDER for a single direction to seek the best practice to run REDER for sequence-to-sequence tasks. KD and CTC are essential to training REDER, as suggested by previous NAT studies (Saharia et al., 2020; Gu & Kong, 2020). Meanwhile, we notice the benefit of relative self-attention. We therefore use these three techniques by default for all of the proposed models. As for the duplex variants of models that learn both directions simultaneously, they can further improve the translation accuracy by substantial margins. These results verify our motivation that the paired translation directions could be better learned in a unified reversible model. Reversibility enables us to utilize layer-wise forward-backward agreement and cycle consistency, which are also shown to boost improvement considerably.

6 Conclusion and Future Work

In this paper, we propose REDER, the reversible duplex Transformer for reversible sequence-to-sequence problem and apply it to machine translation that for the first time shows the feasibility of a reversible machine translation system. REDER is a fully reversible model that can transform one sequence to the other one forth and back, by reading and generating through its two ends. We verify our our motivation and the effectiveness of REDER on several widely-used NMT benchmarks, where REDER shows appealing performance over strong baselines.

As for promising future directions, REDER can be applied to monolingual, multilingual and zero-shot settings, thanks to the fact that each “end” of REDER specializes a language. For instance, given trained REDERs and , we combine last half layers (the De end) of and the Ja end of to obtain a zero-shot , translating between German and Japanese. Likewise, composition of an English end and its reverse results in

, which can learn from monolingual data like an autoencoder. This compositional fashion resembles the LEGO, which manipulates only a linear number of language ends. Therefore, while adding a new language to a multilingual REDER system (in a form of composition of ends of involved languages), we would probably not need to re-train the whole system like we do for a current multilingual NMT system, which reduces the difficulty and cost to train, deploy and maintain a large scale multilingual translation system.

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Appendix A Additional Empirical Results

a.1 Impact of Knowledge Distillation

Systems En-De De-En #data
all raw 17.85 19.68 /
EnDe KD (only De distillated) 25.49 26.57 /
DeEn KD (only En distillated) 23.04 28.82 /
mixture KD 25.80 28.89 2/2
separate KD [final model] 26.70 30.68 /
Table 5: Performance regarding KD on WMT14 EnDe. #data means the amount of data points for each direction.

Like other NAT approaches, we find that REDER heavily relies on knowledge distillation. We report the performance of models trained on raw data and distilled data generated from AT models in Table 5. As we can see, without KD, the accuracy of REDER significantly drops. Then, we aim to explore the most proper way to integrate KD data. We observe that if we only use KD data of one direction (only target-side data are KD’ed, e.g., German sentences in En-De), it only mostly benefits a single direction. These results imply that we need to provide KD data of both directions to train REDER, and we then try to figure how to do so. We notice that if we mix the KD data of both directions by concatenating them directly, it somehow improves results compared to the policy only using single-direction KD data. Finally, we find the best way is to separately feed KD data in accordance to directions, i.e., feeding En-De KD data when training the En-De direction and providing De-En KD data when training the reverse direction De-En.