# Towards More Efficient Insertion Transformer with Fractional Positional Encoding

arXiv: https://arxiv.org/abs/2112.06295 · HTML: https://mlsanity.com/paper/2112.06295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 48 references that are in the map.
- First posted on arXiv 12 Dec 2021.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention](https://mlsanity.com/paper/1502.03044/) (2015)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [DialoGPT: Large-Scale Generative Pre-training for Conversational Response Generation](https://mlsanity.com/paper/1911.00536/) (2019)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Text Summarization with Pretrained Encoders](https://mlsanity.com/paper/1908.08345/) (2019)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [Depth-Adaptive Transformer](https://mlsanity.com/paper/1910.10073/) (2019)
- [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)
- [Language to Logical Form with Neural Attention](https://mlsanity.com/paper/1601.01280/) (2016)
- [A Transformer-based Approach for Source Code Summarization](https://mlsanity.com/paper/2005.00653/) (2020)
- [Insertion Transformer: Flexible Sequence Generation via Insertion Operations](https://mlsanity.com/paper/1902.03249/) (2019)
- [Understanding Knowledge Distillation in Non-autoregressive Machine Translation](https://mlsanity.com/paper/1911.02727/) (2019)
- [Fully Non-autoregressive Neural Machine Translation: Tricks of the Trade](https://mlsanity.com/paper/2012.15833/) (2020)
- [Grammar as a Foreign Language](https://mlsanity.com/paper/1412.7449/) (2014)

## Built on by (most cited first, 1 of 1)

- [Line-Coupled Language Model](https://mlsanity.com/paper/2609.07129/) (2026)

## Abstract (arXiv)

Auto-regressive neural sequence models have been shown to be effective across text generation tasks. However, their left-to-right decoding order prevents generation from being parallelized. Insertion Transformer (Stern et al., 2019) is an attractive alternative that allows outputting multiple tokens in a single generation step. Nevertheless, due to the incompatibility between absolute positional encoding and insertion-based generation schemes, it needs to refresh the encoding of every token in the generated partial hypothesis at each step, which could be costly. We design a novel reusable positional encoding scheme for Insertion Transformers called Fractional Positional Encoding (FPE), which allows reusing representations calculated in previous steps. Empirical studies on various text generation tasks demonstrate the effectiveness of FPE, which leads to floating-point operation reduction and latency improvements on batched decoding.