[Paper Review] On Learning Language-Invariant Representations for Universal Machine Translation

Han Zhao, Junjie Hu+1 more|arXiv (Cornell University)|Aug 11, 2020

Natural Language Processing Techniques4 citations

TL;DR

This paper provides the first theoretical analysis of language-invariant representations in universal machine translation, proving that without structural assumptions, any method learning shared representations must incur high translation error on at least one language pair. Under a natural encoder-decoder generative model, it shows that linearly many language pairs (rather than quadratically) suffice for good generalization across all unseen pairs, with performance degrading on longer paths in the language connection graph.

ABSTRACT

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an increasing interest in massively multilingual models, theoretical analysis on translation errors made by such universal machine translation models is only nascent. In this paper, we formally prove certain impossibilities of this endeavour in general, as well as prove positive results in the presence of additional (but natural) structure of data. For the former, we derive a lower bound on the translation error in the many-to-many translation setting, which shows that any algorithm aiming to learn shared sentence representations among multiple language pairs has to make a large translation error on at least one of the translation tasks, if no assumption on the structure of the languages is made. For the latter, we show that if the paired documents in the corpus follow a natural \emph{encoder-decoder} generative process, we can expect a natural notion of ``generalization'': a linear number of language pairs, rather than quadratic, suffices to learn a good representation. Our theory also explains what kinds of connection graphs between pairs of languages are better suited: ones with longer paths result in worse sample complexity in terms of the total number of documents per language pair needed. We believe our theoretical insights and implications contribute to the future algorithmic design of universal machine translation.

Motivation & Objective

• To understand the fundamental trade-off between learning language-invariant representations and achieving high translation accuracy in universal machine translation.
• To investigate the minimum number of parallel language pairs required to enable effective translation between any pair of languages.
• To characterize how the structure of language connections (e.g., graph distance) affects sample complexity and generalization performance.
• To establish theoretical guarantees for generalization in both deterministic and randomized settings under a generative model of parallel corpora.

Proposed method

• Formalizes universal machine translation as a problem of learning shared sentence representations across multiple language pairs.
• Introduces a theoretical framework using probability distributions over language-specific sentence distributions and defines translation error via expected reconstruction loss.
• Proves an impossibility result: in the absence of structural assumptions, any shared representation must incur high error on at least one translation task.
• Proposes a generative model where sentences are produced via a ground-truth encoder-decoder process, enabling theoretical analysis of generalization.
• Derives sample complexity bounds showing that linearly many language pairs suffice for good performance on all pairs, provided they are connected in the translation graph.
• Extends results to randomized models using denoising autoencoders and smoothness assumptions, maintaining generalization guarantees under relaxed conditions.

Experimental results

Research questions

• RQ1 What is the fundamental trade-off between language invariance and translation accuracy in universal machine translation?
• RQ2 How many parallel language pairs are necessary to achieve good generalization across all language pairs?
• RQ3 How does the structure of the language connection graph (e.g., path length) affect the sample complexity of learning universal translators?
• RQ4 Can we achieve generalization to unseen language pairs under a realistic generative model of parallel corpora?
• RQ5 How do randomized models (e.g., denoising autoencoders) affect the generalization and error bounds in universal machine translation?

Key findings

• Without any structural assumptions on language distributions, it is theoretically impossible to avoid high translation error on at least one language pair when learning language-invariant representations.
• Under a natural encoder-decoder generative model, a linear number of language pairs (rather than quadratic) is sufficient to learn good encoders and decoders for all language pairs.
• The quality of translation generalization degrades with longer paths between language pairs in the connection graph, as longer paths increase the required sample complexity.
• In the randomized setting with denoising mechanisms, generalization bounds are preserved under smoothness and boundedness assumptions on the model family.
• Theoretical error bounds scale with the sum of errors along the shortest path between source and target languages, indicating that direct or short-path connections are more sample-efficient.
• The results provide a formal justification for the empirical success of multilingual models and guide future algorithmic design by identifying favorable language graph structures.