# IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method

arXiv: https://arxiv.org/abs/2509.22463 · HTML: https://mlsanity.com/paper/2509.22463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [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)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (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)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)
- [Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View](https://mlsanity.com/paper/1906.02762/) (2019)
- [PolyNet: A Pursuit of Structural Diversity in Very Deep Networks](https://mlsanity.com/paper/1611.05725/) (2016)
- [Momentum Residual Neural Networks](https://mlsanity.com/paper/2102.07870/) (2021)
- [Redesigning the Transformer Architecture with Insights from Multi-particle Dynamical Systems](https://mlsanity.com/paper/2109.15142/) (2021)
- [ODE Transformer: An Ordinary Differential Equation-Inspired Model for Sequence Generation](https://mlsanity.com/paper/2203.09176/) (2022)
- [Neural ODE Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuning](https://mlsanity.com/paper/2503.01329/) (2025)
- [Implicit Euler ODE Networks for Single-Image Dehazing](https://mlsanity.com/paper/2007.06443/) (2020)

## Abstract (arXiv)

High-order numerical methods enhance Transformer performance in tasks like NLP and CV, but introduce a performance-efficiency trade-off due to increased computational overhead. Our analysis reveals that conventional efficiency techniques, such as distillation, can be detrimental to the performance of these models, exemplified by PCformer. To explore more optimizable ODE-based Transformer architectures, we propose the Iterative Implicit Euler Transformer (IIET), which simplifies high-order methods using an iterative implicit Euler approach. This simplification not only leads to superior performance but also facilitates model compression compared to PCformer. To enhance inference efficiency, we introduce Iteration Influence-Aware Distillation (IIAD). Through a flexible threshold, IIAD allows users to effectively balance the performance-efficiency trade-off. On lm-evaluation-harness, IIET boosts average accuracy by 2.65% over vanilla Transformers and 0.8% over PCformer. Its efficient variant, E-IIET, significantly cuts inference overhead by 55% while retaining 99.4% of the original task accuracy. Moreover, the most efficient IIET variant achieves an average performance gain exceeding 1.6% over vanilla Transformer with comparable speed.