Cross-lingual consistency should be considered to assess cross-lingual transferability, maintain the factuality of the model knowledge across languages, and preserve the parity of language model performance. We are thus interested in analyzing, evaluating, and interpreting cross-lingual consistency for factual knowledge.To facilitate our study, we examine multiple pretrained models and tuned models with code-mixed coreferential statements that convey identical knowledge across languages. Interpretability approaches are leveraged to analyze the behavior of a model in cross-lingual contexts, showing different levels of consistency in multilingual models, subject to language families, linguistic factors, scripts, and a bottleneck in cross-lingual consistency on a particular layer. Code-switching training and cross-lingual word alignment objectives show the most promising results, emphasizing the worthiness of cross-lingual alignment supervision and code-switching strategies for both multilingual performance and cross-lingual consistency enhancement. In addition, experimental results suggest promising result for calibrating consistency on test time via activation patching.

For multilingual training, we present CrossInit, an initialization method that initializes embeddings into similar geometrical structures across languages in an unsupervised manner. CrossInit leverages a common cognitive linguistic mechanism, Zipf’s law, which indicates that similar concepts across languages have similar word ranks or frequencies in their monolingual corpora. Instead of considering point-to-point alignments based on ranks, CrossInit considers the same span of consecutive ranks in each language as the Positive pairs for alignment, while others out of the span are used as Negative pairs. CrossInit then employs Contrastive Learning to iteratively refine randomly initialized embeddings for similar geometrical structures across languages. Our experiments on Unsupervised NMT, XNLI, and MLQA showed significant gains in low-resource and dissimilar languages after applying CrossInit.

In multilingual pre-training with the objective of MLM (masked language modeling) on multiple monolingual corpora, multilingual models only learn cross-linguality implicitly from isomorphic spaces formed by overlapping different language spaces due to the lack of explicit cross-lingual forward pass. In this work, we present CLPM (Cross-lingual Prototype Masking), a dynamic and token-wise masking scheme, for multilingual pre-training, using a special token [𝒞]_x to replace a random token x in the input sentence. [𝒞]_x is a cross-lingual prototype for x and then forms an explicit cross-lingual forward pass. We instantiate CLPM for the multilingual pre-training phase of UNMT (unsupervised neural machine translation), and experiments show that CLPM can consistently improve the performance of UNMT models on {De, Ro, Ne } ↔ En. Beyond UNMT or bilingual tasks, we show that CLPM can consistently improve the performance of multilingual models on cross-lingual classification.

Global co-occurrence information is the primary source of structural information on multilingual corpora, and we find that analogical/parallel compound words across languages have similar co-occurrence counts/frequencies (normalized) giving weak but stable self-supervision for cross-lingual transfer. Following the observation, we aim at associating contextualized representations with relevant (contextualized) representations across languages with the help of co-occurrence counts. The result is MLM-GC (MLM with Global Co-occurrence) pre-training that the model learns local bidirectional information from MLM and global co-occurrence information from a log-bilinear regression. Experiments show that MLM-GC pre-training substantially outperforms MLM pre-training for 4 downstream cross-lingual tasks and 1 additional monolingual task, showing the advantages of forming isomorphic spaces across languages.

In sequence modeling, certain tokens are usually less ambiguous than others, and representations of these tokens require fewer refinements for disambiguation. However, given the nature of attention-based models like Transformer and UT (universal transformer), all tokens are equally processed towards depth. Inspired by the equilibrium phenomenon, we present a lazy transition, a mechanism to adjust the significance of iterative refinements for each token representation. Our lazy transition is deployed on top of UT to build LT (lazy transformer), where all tokens are processed unequally towards depth. Eventually, LT is encouraged to oscillate around a relaxed equilibrium. Our experiments show that LT outperforms baseline models on several tasks of machine translation, pre-training, Learning to Execute, and LAMBADA.

A Multilingual model relies on language encodings to identify input languages because the multilingual model has to distinguish between the input and output languages or among all the languages for cross-lingual tasks. Furthermore, we find that language encodings potentially refine multiple morphologies of different languages to form a better isomorphic space for multilinguality. To leverage this observation, we present a method to compute a vocabulary-informed language encoding as the language representation, for a required language, considering a local vocabulary covering an acceptable amount of the most frequent word embeddings in this language. In our experiments, our method can consistently improve the performance of multilingual models on unsupervised neural machine translation and cross-lingual embedding.

Translation quality can be improved by global information from the required target sentence because the decoder can understand both past and future information. However, the model needs additional cost to produce and consider such global information. In this work, to inject global information but also save cost, we present an efficient method to sample and consider a semantic draft as global information from semantic space for decoding with almost free of cost. Unlike other successful adaptations, we do not have to perform an EM-like process that repeatedly samples a possible semantic from the semantic space. Empirical experiments show that the presented method can achieve competitive performance in common language pairs with a clear advantage in inference efficiency. We will open all our source code on GitHub.