# Predictor-Corrector Enhanced Transformers with Exponential Moving Average Coefficient Learning

arXiv: https://arxiv.org/abs/2411.03042 · HTML: https://mlsanity.com/paper/2411.03042/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 73 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [fairseq: A Fast, Extensible Toolkit for Sequence Modeling](https://mlsanity.com/paper/1904.01038/) (2019)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [COMET: A Neural Framework for MT Evaluation](https://mlsanity.com/paper/2009.09025/) (2020)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Abstractive Text Summarization Using Sequence-to-Sequence RNNs and Beyond](https://mlsanity.com/paper/1602.06023/) (2016)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [Improving Massively Multilingual Neural Machine Translation and Zero-Shot Translation](https://mlsanity.com/paper/2004.11867/) (2020)
- [Adaptive Input Representations for Neural Language Modeling](https://mlsanity.com/paper/1809.10853/) (2018)

## Built on by (most cited first, 4 of 4)

- [Beyond Decoder-only: Large Language Models Can be Good Encoders for Machine Translation](https://mlsanity.com/paper/2503.06594/) (2025)
- [Corrector Sampling in Language Models](https://mlsanity.com/paper/2506.06215/) (2025)
- [Neural CDEs as Correctors for Learned Time Series Models](https://mlsanity.com/paper/2512.12116/) (2025)
- [IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method](https://mlsanity.com/paper/2509.22463/) (2025)

## Abstract (arXiv)

Residual networks, as discrete approximations of Ordinary Differential Equations (ODEs), have inspired significant advancements in neural network design, including multistep methods, high-order methods, and multi-particle dynamical systems. The precision of the solution to ODEs significantly affects parameter optimization, thereby impacting model performance. In this work, we present a series of advanced explorations of Transformer architecture design to minimize the error compared to the true ``solution.'' First, we introduce a predictor-corrector learning framework to minimize truncation errors, which consists of a high-order predictor and a multistep corrector. Second, we propose an exponential moving average-based coefficient learning method to strengthen our higher-order predictor. Extensive experiments on large-scale machine translation, abstractive summarization, language modeling, and natural language understanding benchmarks demonstrate the superiority of our approach. On the WMT'14 English-German and English-French tasks, our model achieved BLEU scores of 30.95 and 44.27, respectively. Furthermore, on the OPUS multilingual machine translation task, our model surpasses a robust 3.8B DeepNet by an average of 2.9 SacreBLEU, using only 1/3 parameters. Notably, it also beats LLama models by 5.7 accuracy points on the LM Harness Evaluation.