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arxiv: 2211.14730 · v2 · submitted 2022-11-27 · 💻 cs.LG · cs.AI

Recognition: 2 theorem links

· Lean Theorem

A Time Series is Worth 64 Words: Long-term Forecasting with Transformers

Yuqi Nie , Nam H. Nguyen , Phanwadee Sinthong , Jayant Kalagnanam
Authors on Pith no claims yet

Pith reviewed 2026-05-13 19:12 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords time series forecastingtransformerpatchingchannel independencelong-term forecastingself-supervised pretrainingmultivariate series
0
0 comments X

The pith

Splitting time series into subseries patches and processing channels independently lets a Transformer forecast long horizons more accurately than prior models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that dividing each time series into short consecutive patches turns those patches into the tokens a Transformer receives. It further treats every variable as its own independent univariate series while sharing the same embedding layer and Transformer weights across all of them. This keeps local patterns inside each patch, cuts the quadratic cost of attention maps, and lets the model look back farther in history without extra memory. The resulting PatchTST model therefore produces markedly lower error on long-term forecasting benchmarks than earlier Transformer designs. The same architecture also supports masked pre-training that transfers well across datasets and often beats training from scratch on large collections.

Core claim

By segmenting multivariate time series into subseries patches that serve as input tokens and enforcing channel independence with shared embeddings and weights, the model retains local semantic information, reduces attention computation quadratically for a given look-back window, and attends to longer history, delivering significantly higher long-term forecasting accuracy than state-of-the-art Transformer baselines.

What carries the argument

Subseries patches used as Transformer input tokens together with channel-independent processing that shares embeddings and weights across all univariate series.

Load-bearing premise

Dividing a time series into fixed-length patches keeps enough local information and does not break the cross-patch temporal dependencies needed for accurate long-range forecasts.

What would settle it

A controlled test on a dataset whose key predictive patterns cross the chosen patch boundaries, showing that the patched model loses accuracy relative to an otherwise identical non-patched Transformer given the same look-back window.

read the original abstract

We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces PatchTST, a Transformer architecture for multivariate long-term time series forecasting and self-supervised representation learning. It segments each univariate series into subseries patches that serve as input tokens and adopts channel-independence so that all channels share the same embedding and Transformer weights. The design is claimed to retain local semantics within patches, quadratically reduce attention cost for a given look-back window, and enable longer history, yielding significant accuracy gains over prior SOTA Transformer baselines. The paper also reports strong fine-tuning results after masked pre-training and successful transfer across datasets.

Significance. If the empirical gains are robust, the work would be significant for time-series modeling by demonstrating that a simple patch-based tokenization (analogous to ViT) combined with channel independence can make Transformers practical for long-horizon forecasting while lowering memory and compute. The public code release and the self-supervised pre-training results further increase its utility. The central empirical claim rests on direct comparisons rather than any parameter-free derivation.

major comments (2)
  1. [§3] §3 (Patching and embedding): the linear projection that maps each patch to a token embedding is presented as sufficient to retain local semantic information, yet the subsequent self-attention operates only across patches. No analysis is given of information loss inside a patch (e.g., high-frequency or non-stationary components). An ablation replacing the linear layer with a small MLP or varying patch length while holding look-back fixed would test whether this step is load-bearing for the reported gains.
  2. [§4] §4 (Experiments): the headline claim of “significant” improvement over SOTA Transformer models requires that baselines use identical look-back windows and that the reported advantage is not driven solely by the ability to use longer history. The manuscript should state the exact look-back lengths used for each baseline and include an ablation that isolates patching from the channel-independent design.
minor comments (2)
  1. [Title / §3.1] The title refers to “64 Words” but the manuscript does not explicitly justify the default patch length of 16 (or 64) in the main text; a short paragraph in §3.1 would clarify the hyper-parameter choice.
  2. [Figures in §4] Figure captions and legends in the experimental section would benefit from explicit mention of the number of runs and whether shaded regions represent standard deviation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the detailed review and the recommendation for minor revision. We have carefully considered the comments and provide point-by-point responses below. We will update the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (Patching and embedding): the linear projection that maps each patch to a token embedding is presented as sufficient to retain local semantic information, yet the subsequent self-attention operates only across patches. No analysis is given of information loss inside a patch (e.g., high-frequency or non-stationary components). An ablation replacing the linear layer with a small MLP or varying patch length while holding look-back fixed would test whether this step is load-bearing for the reported gains.

    Authors: We thank the referee for pointing this out. The choice of a linear projection for patch embedding is motivated by its efficiency and its ability to preserve local semantics, as validated by the overall performance gains. To investigate potential information loss, we will add an ablation study in the revision that replaces the linear layer with a small MLP. We will also include results varying the patch length while keeping the look-back window fixed to confirm the robustness of our design. revision: yes

  2. Referee: [§4] §4 (Experiments): the headline claim of “significant” improvement over SOTA Transformer models requires that baselines use identical look-back windows and that the reported advantage is not driven solely by the ability to use longer history. The manuscript should state the exact look-back lengths used for each baseline and include an ablation that isolates patching from the channel-independent design.

    Authors: We agree that it is crucial to use identical look-back windows for fair comparison. In our experiments, the look-back window was set to the same value for PatchTST and all baselines (details are provided in the appendix, and we will move this to the main text). The ability to use longer history is an additional benefit enabled by the reduced complexity of patching, but our primary results use matched settings. We will also add an ablation that isolates the effect of patching from the channel-independent design by comparing against a channel-dependent variant. revision: yes

Circularity Check

0 steps flagged

No significant circularity: empirical architecture evaluated against external baselines

full rationale

The paper introduces patching of time series into subseries tokens and channel-independent processing as explicit architectural choices, then reports forecasting accuracy via direct head-to-head experiments on standard public datasets against prior published SOTA Transformer models. No equation or claim reduces a fitted internal parameter to a 'prediction' of itself, no load-bearing premise rests on a self-citation chain, and the design motivations (local semantics, quadratic attention reduction, longer history) are stated independently of the numerical results. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The design rests on the domain assumption that local patch semantics are sufficient for long-range forecasting and on standard Transformer inductive biases; no free parameters or invented entities are introduced beyond ordinary hyperparameters.

axioms (2)
  • domain assumption Segmenting a univariate time series into fixed-length patches preserves sufficient local semantic information for downstream forecasting.
    Invoked to justify the patching design in the abstract.
  • domain assumption Channel independence with shared weights is a valid modeling choice for multivariate series.
    Stated as a core component without further justification in the abstract.

pith-pipeline@v0.9.0 · 5501 in / 1226 out tokens · 40011 ms · 2026-05-13T19:12:20.078362+00:00 · methodology

discussion (0)

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    segmentation of time series into subseries-level patches which are served as input tokens to Transformer; patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history

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    A.4.2 V ARYING LOOK -BACK WINDOW Here we provide a full benchmark of quantitative results in Table 9 for varying look-back window in supervised PatchTST/42 regarding Figure 2 in the main text. Generally speaking, our model gains performance improvement with increasing look-back window, which show the effectiveness of our model in learning information from...

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    A full benchmark regarding Table

    16 Published as a conference paper at ICLR 2023 Models PatchTST FEDformerP+CI CI P Original Metric MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE Weather 96 0.152 0.199 0.164 0.2130.168 0.2230.177 0.2360.238 0.314 192 0.197 0.243 0.205 0.2500.213 0.2620.221 0.2700.275 0.329 336 0.249 0.283 0.255 0.2890.266 0.3000.271 0.3060.339 0.377 720 0.320 0.335 0.327 0.3430...

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    The best results are inbold and the second best are underlined

    17 Published as a conference paper at ICLR 2023 ModelsPatchTST/64 (+in)PatchTST/64 (-in)PatchTST/42 (+in)PatchTST/42 (-in)FEDformerAutoformerInformer Metric MSE MAE MSE MAE MSE MAE MSE MAE MSE MAEMSE MAEMSE MAE Weather 96 0.149 0.198 0.161 0.219 0.152 0.199 0.156 0.210 0.238 0.3140.249 0.3290.354 0.405 192 0.194 0.241 0.201 0.254 0.197 0.243 0.199 0.250 0...

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    The mean and standard derivation of the results are reported in Table

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    Models PatchTST DLinear FEDformer Autoformer InformerFine-tuning Lin

    The best results are in bold. Models PatchTST DLinear FEDformer Autoformer InformerFine-tuning Lin. Prob. Sup.Metric MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE Weather 96 0.145 0.195 0.163 0.216 0.152 0.1990.176 0.237 0.238 0.314 0.249 0.329 0.354 0.405192 0.193 0.243 0.205 0.252 0.1970.243 0.220 0.282 0.275 0.329 0.325 0.370 0.419 0.434336 0...

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    The best results are in bold. A.6.2 R ESULTS WITH DIFFERENT MODEL PARAMETERS To see whether PatchTST is sensitive to the choice of Transformer settings, we perform another ex- periments with varying model parameters. We vary the number of Transformer layersL ={3, 4, 5} and select the model dimension D ={128, 256} while the inner-layer of the feed forward ...

    work page arXiv 2023

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    The model is run with supervised PatchTST/42 to forecast 96 steps

    are orderly labeled from 1 to 6 in the figure. The model is run with supervised PatchTST/42 to forecast 96 steps. For Traffic and Electricity datasets, we reduce the maximum number of epochs to 50 to save computational time. A.7 C HANNEL -INDEPENDENCE ANALYSIS Intuitively, channel-mixing models should outperform the channel-independent ones since they have ...

    work page 2023

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    The best trained models are determined by validation data, which are approximately the lowest points in the test loss curves

    Channel-mixing models show over- fitting after a few initial epochs, while channel-independent models continue optimizing the loss with more training epochs. The best trained models are determined by validation data, which are approximately the lowest points in the test loss curves. It is clear that the forecasting performance of channel-independent models...

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    The channel-independent technique can improve the forecasting performance of those models generally. Although they are still not able to outperform PatchTST which is based on vanilla attention mechanism, we believe that more performance boost and computational reduction can be obtained with more advanced attention designs incorporating the channel-indepen...

    work page 2023

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    Left Panel: Test loss vs train size

    We plot the mean values and error bars with 5 differ- ent random seeds:{2019, 2020, 2021, 2022, 2023}. Left Panel: Test loss vs train size. Here, train size denotes the fraction of the training data that is used to learn the model from scratch. Channel- independence contributes to a quicker convergence as more training data is available. Right Panel: Test...

    work page 2019