# Byte Pair Encoding for Efficient Time Series Forecasting

arXiv: https://arxiv.org/abs/2505.14411 · HTML: https://mlsanity.com/paper/2505.14411/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 59 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series](https://mlsanity.com/paper/2401.03955/) (2024)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)
- [Moirai-MoE: Empowering Time Series Foundation Models with Sparse Mixture of Experts](https://mlsanity.com/paper/2410.10469/) (2024)
- [UniTS: A Unified Multi-Task Time Series Model](https://mlsanity.com/paper/2403.00131/) (2024)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version](https://mlsanity.com/paper/2204.13767/) (2022)
- [Toto: Time Series Optimized Transformer for Observability](https://mlsanity.com/paper/2407.07874/) (2024)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)

## Built on by (most cited first, 5 of 5)

- [OpenTSLM: Time-Series Language Models for Reasoning over Multivariate Medical Text- and Time-Series Data](https://mlsanity.com/paper/2510.02410/) (2025)
- [Understanding Transformers for Time Series: Rank Structure, Flow-of-ranks, and Compressibility](https://mlsanity.com/paper/2510.03358/) (2025)
- [Effective Data Pruning through Score Extrapolation](https://mlsanity.com/paper/2506.09010/) (2025)
- [A Systematic Evaluation of Sample-Level Tokenization Strategies for MEG Foundation Models](https://mlsanity.com/paper/2602.16626/) (2026)
- [Dywave: Event-Aligned Dynamic Tokenization for Heterogeneous IoT Sensing Signals](https://mlsanity.com/paper/2605.14014/) (2026)

## Abstract (arXiv)

Existing time series tokenization methods predominantly encode a constant number of samples into individual tokens. This inflexible approach can generate excessive tokens for even simple patterns like extended constant values, resulting in substantial computational overhead. Inspired by the success of byte pair encoding, we propose the first pattern-centric tokenization scheme for time series analysis. Based on a discrete vocabulary of frequent motifs, our method merges samples with underlying patterns into tokens, compressing time series adaptively. Exploiting our finite set of motifs and the continuous properties of time series, we further introduce conditional decoding as a lightweight yet powerful post-hoc optimization method, which requires no gradient computation and adds no computational overhead. On recent time series foundation models, our motif-based tokenization improves forecasting performance by 40% and boosts efficiency by 2314% on average. Conditional decoding further reduces MSE by up to 48%. In an extensive analysis, we demonstrate the adaptiveness of our tokenization to diverse temporal patterns, its generalization to unseen data, and its meaningful token representations capturing distinct time series properties, including statistical moments and trends.