mlsanityData to 7 Oct 2026

One Patch, Three Roles: What Is Actually Coupled in Autoregressive Time-Series Forecasting?

arXiv 2609.23686 ↗First posted 20 Sep 2026cs.LGcited by 0

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Abstract (arXiv)

Patch-based autoregressive time-series forecasting often ties input representation, learned transitions, and recursive execution to one patch length. We ask which of these roles can be adjusted separately. A supporting atomic-encoding study finds greater sensitivity to model width than to atom grouping on the evaluated grid. Our main finding is that a frozen parent's recursive trajectory is easier to fit than the observed future with lightweight parallel exits. Autoregressive Trajectory Distillation (ATD) turns this into selectable ATD-1/2/4/8 execution, with ATD-1 exactly recovering the parent. On a paired four-data-set comparison, ATD-8 reaches 5.54× end-to-end speedup with stable quality across widths. Fewer calls do not automatically remove the parent's existing forecast error: ATD improves trajectory fidelity in all 21 seed runs but forecast accuracy in only 15 against matched clean-future supervision. We further find a correctable residual projection along a train-selected periodic history direction. Spectrum Tangent applies this correction without adding neural parameters or Transformer calls. At horizon 720, it reduces mean squared error (MSE) and mean absolute error (MAE) by 2.54% and 2.33% over seven data sets and two output widths, while remaining 3.24× faster than recursive inference. Level and shape projections sometimes disagree. Trajectory compressibility, the fidelity-accuracy mismatch, and the correction recur across three public AR parents. Together these results separate representation, transition, and execution as AR design axes. Code is available at https://github.com/RowanFFF/ATD-Spectrum-Tangent.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 33 of its 40 references that are in the map. First posted on arXiv 20 Sep 2026.

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33 of 40 references.

References · 33

  1. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  2. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  3. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
  4. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,654
  5. 2022Fast Inference from Transformers via Speculative Decodingcited by 1,615
  6. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
  7. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,200
  8. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
  9. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  10. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 906
  11. 2024Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Headscited by 821
  12. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 779
21 more
  1. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 744
  2. 2024Chronos: Learning the Language of Time Seriescited by 712
  3. 2023A decoder-only foundation model for time-series forecastingcited by 650
  4. 2024Unified Training of Universal Time Series Forecasting Transformerscited by 588
  5. 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 385
  6. 2024Better & Faster Large Language Models via Multi-token Predictioncited by 344
  7. 2024TimeMixer: Decomposable Multiscale Mixing for Time Series Forecastingcited by 333
  8. 2023Long-term Forecasting with TiDE: Time-series Dense Encodercited by 327
  9. 2018Blockwise Parallel Decoding for Deep Autoregressive Modelscited by 318
  10. 2024Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Expertscited by 280
  11. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 205
  12. 2025Sundial: A Family of Highly Capable Time Series Foundation Modelscited by 168
  13. 2025TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learningcited by 107
  14. 2024Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecastingcited by 102
  15. 2024Timer-XL: Long-Context Transformers for Unified Time Series Forecastingcited by 83
  16. 2025Moirai 2.0: When Less Is More for Time Series Forecastingcited by 59
  17. 2026Timer-S1: A Billion-Scale Time Series Foundation Model with Serial Scalingcited by 24
  18. 2024UniTST: Effectively Modeling Inter-Series and Intra-Series Dependencies for Multivariate Time Series Forecastingcited by 13
  19. 2025Fast and Accurate Causal Parallel Decoding using Jacobi Forcingcited by 11
  20. 2025Semantic-Enhanced Time-Series Forecasting via Large Language Modelscited by 2
  21. 2026T-LLM: Teaching Large Language Models to Forecast Time Series via Temporal Distillationcited by 2

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