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arxiv: 2605.24911 · v1 · pith:WVVT6RVDnew · submitted 2026-05-24 · 💻 cs.LG · cs.AI

Factorize to Generalize: Retrieval-Guided Invariant-Dynamic Decomposition for Time Series Forecasting

Jinjin Chi , Lei Feng , Lulu Zhang , Yongcheng Jing , Yiming Wang , Ximing Li , Jialie Shen , Leszek Rutkowski
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Dacheng Tao
This is my paper

Pith reviewed 2026-06-30 12:12 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords time series forecastinginvariant-dynamic decompositionretrieval augmentationdistribution shiftszero-shot forecastingrepresentation learningdisentanglement
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The pith

Retrieval sequences guide decomposition of time series into invariant and dynamic components for better zero-shot robustness.

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

Retrieval in time series foundation models tends to produce oscillatory predictions that help on fluctuating series but reduce accuracy on smoother trend-dominated ones. The paper proposes using retrieved sequences as implicit samples from related environments to build a retrieval-aware representation and then route it via a guided mechanism into an invariant component for stable shared structure and a dynamic component for context-specific variations. These components are forecasted separately before fusion. The approach includes training objectives for invariant learning and disentanglement, with theory indicating that aggregation reduces variance to approximate supervised invariant learning. A sympathetic reader would care because the method aims to deliver more reliable forecasts across distribution shifts without needing explicit environment labels.

Core claim

The central claim is that rather than using retrieval as auxiliary predictive context, retrieved sequences serve as implicit environment samples to construct a retrieval-aware representation via attention-based aggregation. A retrieval-guided routing mechanism then decomposes this into an invariant component capturing stable shared structure and a dynamic component modeling context-dependent variations. These are forecasted separately and fused, supported by objectives that encourage invariant learning and disentanglement, plus theoretical insight that retrieval aggregation reduces variance and approximates invariant representation learning without explicit supervision. This yields improved

What carries the argument

The retrieval-guided routing mechanism that decomposes a retrieval-aware representation into an invariant component for stable shared structure and a dynamic component for context-dependent variations.

If this is right

  • The model improves robustness under distribution shifts compared to prior methods.
  • It outperforms existing time series foundation models and retrieval baselines in zero-shot forecasting.
  • Separate forecasting of invariant and dynamic components preserves transferable patterns while adapting to evolving dynamics.
  • Training objectives promote invariant learning and disentanglement of the two components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same retrieval-guided decomposition could apply to other sequential prediction tasks facing distribution shifts, such as in sensor data or financial series.
  • Retrieval may serve as a practical substitute for explicit environment labels in invariant representation methods across domains.
  • Performance could vary if retrieval sources differ substantially from the target distribution, suggesting a need to test retrieval quality thresholds.

Load-bearing premise

Retrieved sequences can be treated as implicit samples from related environments that enable decomposition into invariant and dynamic components without explicit environment labels or supervision.

What would settle it

An experiment on distribution-shifted time series data where the full decomposition method shows no gain or a loss in zero-shot accuracy compared to plain retrieval would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.24911 by Dacheng Tao, Jialie Shen, Jinjin Chi, Lei Feng, Leszek Rutkowski, Lulu Zhang, Ximing Li, Yiming Wang, Yongcheng Jing.

Figure 1
Figure 1. Figure 1: Forecasted series of training w/o RAG (Base) and w/ RAG against the ground truth on [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of our proposed RIDDE. both invariant structure and dynamic variations, yet current methods typically fuse them into a single representation without explicitly disentangling these factors. Our work addresses this gap by using retrieval to guide invariant–dynamic decomposition for robust forecasting under distribution shifts. 3 Our Method Let D = {(xi , yi)} n i=1 denote a retrieval knowledge base,… view at source ↗
Figure 3
Figure 3. Figure 3: Top: Forecasting visualizations com￾paring our RIDDE (w/ IDD) and the ablative version removing the decomposition and Ldis (w/o IDD). Bottom: Forecasting visualizations comparing our RIDDE across Cross-RAG and TS-RAG. We present the forecasting visualizations of our RIDDE across ablative version and baseline methods. For ablation, we compare with the ab￾lative version removing our Invariant–Dynamic Decompo… view at source ↗
Figure 4
Figure 4. Figure 4: Sensitivity of the number of retrieved sequence [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Forecasted series of training w/o RAG (Base) and w/ RAG on FRED-ND with Chronos as [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Forecasted series of training w/o RAG (Base) and w/ RAG on Electricity with MLP as [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Forecasted series of training w/o RAG (Base) and w/ RAG on Electricity with MLP as [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Forecasted series of training w/o RAG (Base) and w/ RAG on Electricity with MLP as [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Forecasted series of training w/o RAG (Base) and w/ RAG on Electricity with Chronos as [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Forecasted series of training w/o RAG (Base) and w/ RAG on Electricity with MLP as [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visualization of forecasting results on ETTm1 between our RIDDE and the version [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Visualization of forecasting results on ETTh1 between our RIDDE and the version without [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Visualization of forecasting results on ETTm1 between our RIDDE and the version [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Visualization of forecasting results on ETTm1 between our RIDDE against RAG-based [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Visualization of the retrieved samples on ETTh1. [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Visualization of the retrieved samples on ETTh2. [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
read the original abstract

Time series foundation models (TSFMs) have recently achieved strong zero-shot forecasting performance through large-scale pretraining and retrieval-augmented prediction. However, our empirical analysis reveals a non-trivial limitation of retrieval-based forecasting: retrieval tends to induce more oscillatory predictions, improving performance on highly fluctuating series while degrading accuracy on smoother, trend-dominated ones. This suggests that retrieved information may be fused into prediction without explicitly distinguishing stable temporal structure from instance-specific variations, which can reduce robustness under distribution shifts. We propose a Retrieval-guided Invariant-Dynamic DEcomposition framework for time series forecasting. Rather than using retrieval as auxiliary predictive context, we leverage retrieved sequences as implicit samples from related environments to guide representation decomposition. Specifically, we first construct a retrieval-aware representation via attention-based aggregation, and then introduce a retrieval-guided routing mechanism to decompose it into an invariant component capturing stable shared structure and a dynamic component modeling context-dependent variations. These two components are forecast separately and fused for final prediction, enabling the model to preserve transferable patterns while remaining adaptive to evolving dynamics. We further design training objectives that encourage invariant learning and disentanglement, and provide theoretical insight showing that retrieval aggregation reduces variance and approximates invariant representation learning without explicit environment supervision. Extensive experiments demonstrate that our method consistently improves robustness under distribution shifts and outperforms existing TSFMs and retrieval-based baselines in zero-shot forecasting settings.

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

3 major / 2 minor

Summary. The manuscript proposes the RIDDE framework for time series forecasting. It first empirically observes that retrieval-augmented TSFMs produce oscillatory predictions that help fluctuating series but degrade smoother ones. The method treats retrieved sequences as implicit environment samples, constructs a retrieval-aware representation via attention aggregation, and applies a retrieval-guided routing mechanism to decompose the representation into an invariant component (stable shared structure) and a dynamic component (context-dependent variations). These are forecasted separately, fused for the final prediction, and trained with objectives that encourage invariant learning and disentanglement. A theoretical insight is offered that retrieval aggregation reduces variance and approximates invariant representation learning without explicit environment labels. Extensive experiments are claimed to show improved robustness under distribution shifts and superior zero-shot performance over TSFMs and retrieval baselines.

Significance. If the routing mechanism produces a genuine, validated decomposition into invariant and dynamic factors (rather than an arbitrary split) and the theoretical approximation is non-circular, the work would provide a concrete mechanism for improving robustness in retrieval-augmented forecasting without requiring environment labels. The zero-shot gains would be noteworthy if shown to arise specifically from the disentanglement rather than richer context alone.

major comments (3)
  1. [Abstract] Abstract (theoretical insight paragraph): the claim that 'retrieval aggregation reduces variance and approximates invariant representation learning without explicit environment supervision' is stated without any derivation, equations, variance-reduction proof, or comparison to standard invariant-risk minimization; this is load-bearing for the central claim that the method enables label-free invariant learning.
  2. [Abstract] Abstract and experiments description: no invariance metric (e.g., prediction stability across shifts), mutual-information measure between components, or ablation removing the routing mechanism is mentioned; without such evidence the robustness gains cannot be attributed to the claimed decomposition rather than simply richer retrieval context.
  3. [Abstract] Abstract (weakest-assumption paragraph): the assumption that retrieved sequences can be treated as implicit samples from related environments enabling unsupervised decomposition is presented without any supporting diagnostic (e.g., environment-similarity statistics or routing visualization); this directly underpins the entire retrieval-guided routing design.
minor comments (2)
  1. [Abstract] The abstract introduces the acronym RIDDE only implicitly; spelling out the full name on first use would improve readability.
  2. [Abstract] The empirical observation about oscillatory vs. smooth series is described qualitatively; a brief quantitative summary (e.g., performance delta on trend-dominated vs. fluctuating subsets) would strengthen the motivation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We appreciate the emphasis on strengthening the theoretical presentation and empirical attribution of gains. We respond to each major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract (theoretical insight paragraph): the claim that 'retrieval aggregation reduces variance and approximates invariant representation learning without explicit environment supervision' is stated without any derivation, equations, variance-reduction proof, or comparison to standard invariant-risk minimization; this is load-bearing for the central claim that the method enables label-free invariant learning.

    Authors: The abstract summarizes the insight concisely due to length limits. The full manuscript contains a dedicated theoretical section deriving the variance-reduction property of retrieval aggregation and relating it to invariant-risk minimization without environment labels. We will revise the abstract to include a brief parenthetical reference to this analysis for improved clarity. revision: partial

  2. Referee: [Abstract] Abstract and experiments description: no invariance metric (e.g., prediction stability across shifts), mutual-information measure between components, or ablation removing the routing mechanism is mentioned; without such evidence the robustness gains cannot be attributed to the claimed decomposition rather than simply richer retrieval context.

    Authors: We agree this evidence would strengthen attribution. The current experiments emphasize forecasting accuracy under shifts but omit explicit invariance or disentanglement metrics. In revision we will add an ablation removing the routing mechanism, plus metrics for prediction stability across shifts and mutual information between the invariant and dynamic components. revision: yes

  3. Referee: [Abstract] Abstract (weakest-assumption paragraph): the assumption that retrieved sequences can be treated as implicit samples from related environments enabling unsupervised decomposition is presented without any supporting diagnostic (e.g., environment-similarity statistics or routing visualization); this directly underpins the entire retrieval-guided routing design.

    Authors: We concur that diagnostics would better support the modeling assumption. The revised version will incorporate environment-similarity statistics between retrieved and query sequences together with routing visualizations demonstrating separation of invariant and dynamic factors. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and excerpts describe a retrieval-guided decomposition framework with a claimed theoretical insight that retrieval aggregation reduces variance and approximates invariant learning. No equations, derivations, or self-citations are exhibited that reduce any prediction or result to its inputs by construction, nor do any load-bearing steps rely on fitted parameters renamed as predictions or uniqueness theorems imported from the same authors. The central claims rest on the proposed architecture, training objectives, and empirical validation, which remain independent of the inputs in the given text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.1-grok · 5801 in / 986 out tokens · 29377 ms · 2026-06-30T12:12:16.983090+00:00 · methodology

discussion (0)

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Reference graph

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7 extracted references · 6 canonical work pages · 3 internal anchors

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