reubencg@stanford.edu ngoodman@stanford.edu Abstract A desideratum of high-quality translation systems is that they preserve meaning, in the sense that two sentences with different meanings should not translate to one and the same sentence in another language. However, state-of-the-art systems often fail in this regard, particularly in cases where the source and target languages partition the meaning space in different ways. For instance, I cut my finger. and I cut my finger off. describe different states of the world but are translated to French (by both Fairseq and Google Translate ) as Je me suis coup  e le doigt., which is ambiguous as to whether the finger is detached. More generally, translation systems are typically many-to-one (non-injective) functions from source to target language, which in many cases results in important distinctions in meaning being lost in translation. Building on Bayesian models of informative utterance production, we present a method to define a less ambiguous translation system in terms of an underlying pretrained neural sequence-to-sequence model. This method increases injectivity, resulting in greater preservation of meaning as measured by improvement in cycle-consistency, without impeding translation quality (measured by BLEU score). Languages differ in what meaning distinctions they must mark explicitly. As such, translations risk mapping from a form in one language to a more ambiguous form in another. For example, the definite (1) and indefinite (2) both translate (under Fairseq and Google Translate ) to (3) in French, which is ambiguous in definiteness. Survey To evaluate the nature of this problem, we explored a corpus 1 of 500 pairs of distinct English sentences which map to a single German one (the evaluation language in section 2.3). We identify a number of common causes for the many-to-one maps. Two frequent types of verbal distinction lost when translating to German are tense (54 pairs, e.g. ...others { were, have been } introduced .) and modality (16 pairs, e.g. ...prospects for this year { could , might } be better.), where German konnen can express both epistemic and ability modality, distinguished in English with might and could respectively. Owing to En-glish's large vocabulary, lexical difference in verb (31 pairs, e.g. arise vs. emerge ), noun (56 pairs, e.g. mystery vs. secret), adjective (47 pairs, e.g. unaffected vs. untouched) or deic-tic/pronoun (32 pairs, usually this vs that) are also common. A large number of the pairs differ instead either orthographically, or in other ways that do not correspond to a clear semantic distinc-1 Generated by selecting short sentences from the Brown corpus (Ku  cera and Francis, 1967), translating them to German, and taking the best two candidate translations back into English, if these two themselves translate to a single German sentence. Translation in both directions was done with Fairseq. Our approach While languages differ in what distinctions they are required to express, all are usually capable of expressing any given distinction when desired. As such, meaning loss of the kind discussed above is, in theory, avoidable. To this end, we propose a method to reduce meaning loss by applying the Rational Speech Acts (RSA) model of an informative speaker to translation. RSA has been used to model natural language pragmatics (Goodman and Frank, 2016), and re-cent work has shown its applicability to image captioning (Andreas and Klein, 2016; Vedantam et al., 2017; Mao et al., 2016), another sequence-generation NLP task. Here we use RSA to define a translator which reduces many-to-one mappings and consequently meaning loss, in terms of a pretrained neural translation model. We introduce a strategy for performing inference effi-ciently with this model in the setting of translation, and show gains in cycle-consistency 2 as a result. Moreover, we obtain improvements in translation quality (BLEU score), demonstrating that the goal of meaning preservation directly yields improved translations. In the RSA framework, speakers and listeners, modeled as Bayesian agents, reason about each other in a nested fashion. We refer to listeners and speakers which do not reason about another agent as L 0 and S 0 respectively, and an agent which reasons about another agent as L 1 or S 1 . For instance, an informative speaker model S 1 is given a state 2 Formally, say that a pair of functions f : A  B , g : B  A is cycle-consistent if g  f = id , the identity function. If f is not one-to-one, then ( f, g ) is not cycle-consistent. (Note however that when A and B are infinite, the converse does not hold: even if f and g are both one-toone, ( f, g ) need not be cycle-consistent, since many-to-one maps between infinite sets are not necessarily bijective.) w  W , and chooses an utterance u  U to convey w to S 1 's model of a listener. By contrast, S 0 chooses utterances without a listener model in mind  its behavior might be determined by a semantics, or in our case, by a pretrained neural model. For translation, the state space W is a set of source language sentences (sequences of words in the language), while U is a set of target language sentences. S 1 's goal is to choose a translation u which allows a listener to pick out the source sentence w from among the set of distractors. This informative behavior discourages many-to-one maps that a non-informative translation model S 0 might allow. S 0 Model BiLSTMs with attention (Bahdanau et al., 2014), and more recently CNNs (Gehring et al., 2016) and entirely attention based models (Vaswani et al., 2017) constitute the state-of-the-art architectures in neural machine translation . All of these systems, once trained end-to-end on aligned data, can be viewed as a conditional distribution 3 SWD 0 ( wd | w, c ) , for a word wd in the target language, a source language sentence w , and a partial sentence c in the target language. SWD 0 yields a distribution S SNT0 over full sentences 4 : S SNT0 ( u | w, c ) = (cid:89) t SWD 0 ( u [ t ] | w, c + u [: t ]) (4) S SNT0 returns a distribution over continuations of c into full target language sentences 5 . To obtain a sentence from S SNT0 given a source language sentence s , one can greedily choose the highest probability word from SWD 0 at each timestep, or explore a beam of possible candidates. We implement SWD 0 (in terms of which all our other models are defined) using Fairseq 's publicly available 6 pretrained Transformer models for English-German, and for German-English train a CNN using Fairseq . We first describe a sentence level, globally pragmatic model S SNT-GP1 for the simple case where 3 We use SWD 0 / 1 and SSNT 0 / 1 respectively to distinguish word and sentence level speaker models 4 Python list indexing conventions are used, + means concatenation of list to element or list 5 In what follows, we omit c when it is empty, so that S SNT0 ( u | w ) is the probability of sentence u given w 6 https://github.com/pytorch/fairseq a source language sentence needs to be distinguished from a presupplied distractor 7 (as in the pairs shown in figures (2) and (1)). We use this model as a stepping stone to one which requires an input sentence in the source language only, and no distractors. We begin by defining a listener L SNT1 , which receives a target language sentence u and infers which sentence w  W (a presupplied set such as the pair (1) and (2)) would have resulted in the pretrained neural model S SNT0 producing u : L SNT1 ( w | u )  S SNT0 ( u | w ) (cid:80) w (cid:48)  WS SNT0 ( u | w (cid:48) ) (5) This allows S SNT-GP1 to be defined in terms of L SNT1 , where U is the set of all possible target language sentences 8 : S SNT-GP1 ( u | w ) = SSNT 0 ( u | w ) L SNT1 ( w | u )  (cid:80) u (cid:48)  US SNT0 ( u (cid:48) | w ) L SNT1 ( w | u (cid:48) )  (6) The key property of this model is that, for W = { A, B } , when translating A , S SNT-GP1 prefers translations of A that are unlikely to be good translations of B . So for pairs like (1) and (2), S SNT-GP1 is compelled to produce a translation for the former that reflects its difference from the latter, and vice versa. Inference Since U is an infinite set, exactly computing the most probable utterance under S SNT-GP1 ( | w ) is intractable. Andreas and Klein (2016) and Mao et al. (2016) perform approximate inference by sampling the subset of U produced by a beam search from S SNT0 . Vedantam et al. (2017) and Cohn-Gordon et al. (2018) employ a different method, using an incremental model SSNT-IP 1 as an approximation of SSNT-GP 1 on which inference can be tractably performed. S SNT-IP1 considers informativity not over the whole set of utterances, but instead at each decision of the next word in the target language sentence. For this reason, the incremental method avoids the problem of lack of beam diversity encountered when subsampling from S SNT0 , which 7 Implementations for all models are available to https://github.com/reubenharry/ pragmatic-translation 8  is a hyperparameter of S SNT-GP1 ; as it increases, the model cares more about being informative and less about producing a reasonable translation. becomes especially bad when producing long sequences, as is often the case in translation. S SNT-IP1 is defined as the product of informative decisions, specified by SWD 1 (itself defined in terms of L WD1 ), which are defined analogously to (6) and (5). L WD1 ( w | wd , c )  SWD 0 ( wd | w, c ) (7) SWD 1 ( wd | w, c )  (8) SWD 0 ( wd | w, c )  L WD1 ( w | wd , c )  S SNT-IP1 ( u | w, c ) = (cid:89) t SWD 1 ( u [ t ] | w, c + u [: t ]) (9) Examples S SNT-IP1 is able to avoid many-to-one mappings by choosing more informative translations. For instance, its translation of (1) is Ces animaux courent vite ( These animals run fast.). See figures (1) and (2) for other examples of many-to-one mappings under S SNT0 avoided by S SNT-IP1 . While S SNT-IP1 can disambiguate between pairs of sentences, it has two shortcomings. First, it requires one (or more) distractors to be provided, so translation is no longer fully automatic. Second, because the distractor set W consists of only a pair (or finite set) of sentences, S SNT-IP1 only cares about being informative up to the goal of distinguishing between these sentences. Intuitively, total meaning preservation is achieved by a translation which distinguishes the source sentence w from every other sentence in the source language which differs in meaning. Both of these problems can be addressed by introducing a new cyclic globally pragmatic model S SNT-CGP1 which reasons not about L SNT1 but about a pretrained translation model from target language to source language, which we term L SNT0 . S SNT-CGP1 is like S SNT-GP1 , but its goal is to produce a translation which allows a listener model (now L SNT0 ) to infer the original sentence, not among a small set of presupplied possibilities, but among all source language sentences . As such, an optimal translation u of w under S SNT-CGP1 has high probability of being generated by S SNT0 and high probability of being back-translated to w by L SNT0 . Incremental Model Exact inference is again intractable, though as with S SNT-GP1 , it is possible to approximate by subsampling from S SNT0 . This is very close to the approach taken by (Li et al., 2016), who find that reranking a set of outputs by probability of recovering input dramatically decreases the rate of dull and generic responses. in a question-answering task. However, because the subsample is small relative to U , they use this method in conjunction with a diversity increasing decoding algorithm. As in the case with explicit distractors, we instead opt for an incremental model, now S SNT-CIP1 which approximates S SNT-CGP1 . The definition of S SNT-CIP1 (12) is more complex than the incremental model with explicit distractors ( S SNT-IP1 ) since LWD 0 must receive complete sentences, rather than partial ones like L WD1 . As such, we need to marginalize over continuations k of partial sentences in the target language: SWD-C 1 ( wd | w, c )  SWD 0 ( wd | w, c )  (cid:88) k ( L SNT0 ( w | c + wd + k ) S SNT0 ( k | w, c + wd )) (11) S SNT-CIP1 ( u | w, c ) = (cid:89) t SWD-C 1 ( u [ t ] | w, c + u [: t ]) (12) Since the sum over continuations of c in (11) is intractable to compute exactly, we approximate it by a single continuation, obtained by greedily unrolling S SNT0 . The whole process of generating a new word wd of the translation from a sequence c and a source language sentence w is as follows: first use SWD 0 to generate a set of candidates for the next word (in practice, we only consider two, for efficiency). For each of these, use S SNT0 to greedily unroll a full target language sentence from c + wd , namely c + wd + k , and rank each wd by the probability L SNT0 ( w | c + wd + k ) . Our objective is to improve meaning preservation without detracting from translation quality in other regards (e.g. grammaticality). We conduct our evaluations on English to German translation, making use of publicly available pre-trained English-German and German-English Fairseq models. The pragmatic model we evaluate is S SNT-CIP1 since, unlike S SNT-IP1 , it is not necessary to hand-supply a distractor set of source language sentences. An example of the behavior of S SNT-CIP1 and S SNT0 on of our test sentences is shown below; S SNT0 is able to preserve the phrase world's eyes, which S SNT0 translates merely as world:  Source sentence: Isolation keeps the world's eyes off Papua. Reference translation: Isolation halt die Augen der Welt fern von Papua. S SNT0 : Die Isolation halt die Welt von Papua fern. SSNT-CIP 1 : Die Isolation halt die Augen der Welt von Papua fern. We use cycle-consistency as a measure of meaning preservation, since the ability to recover the original sentence requires meaning distinctions not to be collapsed. In evaluating cycle-consistency, it is important to use a separate target-source translation mechanism than the one used to define S SNT-CIP1 . Otherwise, the system has access to the model which evaluates it and may improve cycle-consistency without producing meaningful target language sentences. For this reason, we translate German sentences (produced by S SNT0 or S SNT-CIP1 ) back to English with Google Translate . To measure cycle-consistency, we use the BLEU metric (implemented with sacreBLEU (Post, 2018)), with the original sentence as the reference. However, this improvement of cycle consistency, especially with a high value of  , may come at the cost of translation quality. Moreover, it is unclear whether BLEU serves as a good metric for evaluating sentences of a single language. To further ensure that translation quality is not compromised by S SNT-CIP1 , we evaluate BLEU scores of the German sentences it produces. This requires evaluation on a corpus of aligned sentences, unlike the sentences collected from the Brown corpus in section 1 9 . 9 While we find that S SNT-CIP1 improves cycle-consistency for the Brown corpus over S SNT0 , we have no way to establish whether this comes at the cost of translation quality. 11 We use greedy unrolling in all models (using beam search is a goal for future work). For  (which represents the trade-off between informativity and translation quality) we use 0 . 1 , obtained by tuning on validation data. Results As shown in table (1), S SNT-CIP1 improves over SSNT 0 not only in cycle-consistency, but in translation quality as well. This suggests that the goal of preserving information, in the sense defined by S SNT-CGP1 and approximated by S SNT-CIP1 , is important for translation quality. We identify a shortcoming of state-of-the-art translation systems and show that a version of the RSA framework's informative speaker S 1 , adapted to the domain of translation, alleviates this problem in a way which improves not only cycle-consistency but translation quality as well. The success of S SNT-CIP1 on two fairly similar languages raises the question of whether improvements will increase for more distant language pairs, in which larger scale differences exist in what information is obligatorily represented this is a direction for future work. Thanks to the reviewers for their substantive comments, and to Daniel Fried and Jacob Andreas for many helpful discussions during the development of this project. 10 Our implementation of S SNT-CIP1 was not efficient, and we could not evaluate on more sentences for reasons of time. 11 http://www.statmt.org/wmt18/ translation-task.html References Jacob Andreas and Dan Klein.
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