# ngram-OAXE: Phrase-Based Order-Agnostic Cross Entropy for Non-Autoregressive Machine Translation

arXiv: https://arxiv.org/abs/2210.03999 · HTML: https://mlsanity.com/paper/2210.03999/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 41 references that are in the map.
- First posted on arXiv 8 Oct 2022.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [A Call for Clarity in Reporting BLEU Scores](https://mlsanity.com/paper/1804.08771/) (2018)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [Levenshtein Transformer](https://mlsanity.com/paper/1905.11006/) (2019)
- [Deterministic Non-Autoregressive Neural Sequence Modeling by Iterative Refinement](https://mlsanity.com/paper/1802.06901/) (2018)
- [Analyzing Uncertainty in Neural Machine Translation](https://mlsanity.com/paper/1803.00047/) (2018)
- [Understanding Knowledge Distillation in Non-autoregressive Machine Translation](https://mlsanity.com/paper/1911.02727/) (2019)
- [Deep Encoder, Shallow Decoder: Reevaluating Non-autoregressive Machine Translation](https://mlsanity.com/paper/2006.10369/) (2020)
- [Glancing Transformer for Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/2008.07905/) (2020)
- [Fully Non-autoregressive Neural Machine Translation: Tricks of the Trade](https://mlsanity.com/paper/2012.15833/) (2020)
- [Non-Autoregressive Machine Translation with Latent Alignments](https://mlsanity.com/paper/2004.07437/) (2020)
- [FlowSeq: Non-Autoregressive Conditional Sequence Generation with Generative Flow](https://mlsanity.com/paper/1909.02480/) (2019)
- [Improved Natural Language Generation via Loss Truncation](https://mlsanity.com/paper/2004.14589/) (2020)
- [End-to-End Non-Autoregressive Neural Machine Translation with Connectionist Temporal Classification](https://mlsanity.com/paper/1811.04719/) (2018)
- [Aligned Cross Entropy for Non-Autoregressive Machine Translation](https://mlsanity.com/paper/2004.01655/) (2020)
- [Fast Structured Decoding for Sequence Models](https://mlsanity.com/paper/1910.11555/) (2019)
- [Latent-Variable Non-Autoregressive Neural Machine Translation with Deterministic Inference Using a Delta Posterior](https://mlsanity.com/paper/1908.07181/) (2019)
- [Order-Agnostic Cross Entropy for Non-Autoregressive Machine Translation](https://mlsanity.com/paper/2106.05093/) (2021)
- [Minimizing the Bag-of-Ngrams Difference for Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1911.09320/) (2019)
- [Non-Autoregressive Neural Machine Translation with Enhanced Decoder Input](https://mlsanity.com/paper/1812.09664/) (2018)
- [A Study of Non-autoregressive Model for Sequence Generation](https://mlsanity.com/paper/2004.10454/) (2020)
- [Hint-Based Training for Non-Autoregressive Machine Translation](https://mlsanity.com/paper/1909.06708/) (2019)
- [Rethinking the Value of Transformer Components](https://mlsanity.com/paper/2011.03803/) (2020)
- [An EM Approach to Non-autoregressive Conditional Sequence Generation](https://mlsanity.com/paper/2006.16378/) (2020)
- [On the Language Coverage Bias for Neural Machine Translation](https://mlsanity.com/paper/2106.03297/) (2021)
- [Bag-of-Words as Target for Neural Machine Translation](https://mlsanity.com/paper/1805.04871/) (2018)

## Built on by (most cited first, 8 of 8)

- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [Chain of Preference Optimization: Improving Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2406.09136/) (2024)
- [A Survey on Parallel Text Generation: From Parallel Decoding to Diffusion Language Models](https://mlsanity.com/paper/2508.08712/) (2025)
- [Reinforcement Retrieval Leveraging Fine-grained Feedback for Fact Checking News Claims with Black-Box LLM](https://mlsanity.com/paper/2404.17283/) (2024)
- [Directed Acyclic Transformer Pre-training for High-quality Non-autoregressive Text Generation](https://mlsanity.com/paper/2304.11791/) (2023)
- [Improving Non-autoregressive Machine Translation with Error Exposure and Consistency Regularization](https://mlsanity.com/paper/2402.09725/) (2024)
- [On the Information Redundancy in Non-Autoregressive Translation](https://mlsanity.com/paper/2405.02673/) (2024)
- [Reconsidering Positional Supervision in Masked Diffusion Language Model Training](https://mlsanity.com/paper/2601.22947/) (2026)

## Abstract (arXiv)

Recently, a new training oaxe loss has proven effective to ameliorate the effect of multimodality for non-autoregressive translation (NAT), which removes the penalty of word order errors in the standard cross-entropy loss. Starting from the intuition that reordering generally occurs between phrases, we extend oaxe by only allowing reordering between ngram phrases and still requiring a strict match of word order within the phrases. Extensive experiments on NAT benchmarks across language pairs and data scales demonstrate the effectiveness and universality of our approach. %Further analyses show that the proposed ngram-oaxe alleviates the multimodality problem with a better modeling of phrase translation. Further analyses show that ngram-oaxe indeed improves the translation of ngram phrases, and produces more fluent translation with a better modeling of sentence structure.