arxiv: 2604.06727 · v1 · submitted 2026-04-08 · 💻 cs.LG

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Bi-level Heterogeneous Learning for Time Series Foundation Models: A Federated Learning Approach

Shengchao Chen , Guodong Long , Dikai Liu , Jing Jiang

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Pith reviewed 2026-05-10 18:02 UTC · model grok-4.3

classification 💻 cs.LG

keywords time series foundation modelsfederated learningheterogeneous databi-level learningforecastingdomain-invariant representationsregularization

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The pith

A federated bi-level method trains time series foundation models on heterogeneous data without the gradient conflicts that plague centralized mixing.

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

The paper seeks to establish that time series foundation models suffer from pronounced domain and task variations that mixed-batch training exacerbates through conflicting gradients. It introduces a federated approach that first applies local regularization to enforce domain-invariant and semantically consistent representations within each client, then uses domain-aware aggregation to align representations across clients. A sympathetic reader would care because this structure could enable scalable, privacy-preserving training of large TSFMs directly from heterogeneous real-world series instead of requiring curated homogeneous corpora.

Core claim

The bi-level heterogeneous learning method mitigates intra-domain conflicts by enforcing domain-invariant representations through local regularization and addresses inter-domain discrepancies by enhancing cross-domain collaboration via domain-aware aggregation, yielding TSFMs that outperform both centralized mixed-batch and standard federated baselines on point and probabilistic forecasting while maintaining competitive zero-shot performance.

What carries the argument

Bi-level federated learning that combines local regularization for invariant representations with domain-aware aggregation to manage inter- and intra-domain heterogeneity.

If this is right

TSFMs achieve better point and probabilistic forecasting accuracy on diverse benchmarks than both centralized and federated alternatives.
The method supports competitive zero-shot generalization when models are trained at scale.
It supplies a practical route for building TSFMs from scratch when source data cannot be pooled centrally due to heterogeneity or privacy constraints.

Where Pith is reading between the lines

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

The same separation of local invariance enforcement and domain-aware coordination might apply to foundation models for other sequential modalities that exhibit strong domain shifts.
Because data never leaves its local site, the framework naturally supports privacy-sensitive collaborative training across organizations.
The bi-level split suggests that future architectures could explicitly separate invariant temporal encoders from domain-specific adapters.

Load-bearing premise

Local regularization for domain-invariant features combined with domain-aware aggregation can reduce interference from heterogeneity without discarding useful task-specific temporal patterns or adding new representational biases.

What would settle it

A set of heterogeneous time series benchmarks where models trained with the bi-level federated method show no improvement or a clear drop in forecasting accuracy and zero-shot metrics relative to a simple centralized mixed-batch baseline.

Figures

Figures reproduced from arXiv: 2604.06727 by Dikai Liu, Guodong Long, Jing Jiang, Shengchao Chen.

**Figure 1.** Figure 1: FedTRL outperforms centralized TSFMs in zero-shot point and probabilistic forecasting. Details are provided in Sec. 4 To this end, we propose FedTRL, a FL method for bi-level heterogeneous learning that enables domain-invariant time series representations under both inter-domain heterogeneity and intra-domain conflicts. Our FedTRL integrates two complementary components, including: (1) a domainadversaria… view at source ↗

**Figure 2.** Figure 2: Structure of FedTRL (single client example). Each client performs unsupervised diffusion-based reconstruction and uploads only the encoder θE and prototypes p¯ per round; the server applies domain-aware aggregation (DaG) to produce a unified encoder. specific patterns. The objective is to collaboratively learn a unified representation that generalizes across domains and supports diverse forecasting tasks w… view at source ↗

**Figure 3.** Figure 3: Results on FEV leaderboard. Baseline includes statistical methods, task-specific deep models trained on each dataset, and pre-trained foundation models. Pre-trained Models that have seen several datasets during pre-training are denoted as Pre-trained Models (Other). Lower MASE/WQL is better. FedTRL reports probabilistic forecasts using 20 generated series, following (Ansari et al., 2024). 2017), FFTS (Chen… view at source ↗

**Figure 4.** Figure 4: Relative performance drop of FedTRL ablations in zeroshot probabilistic forecasting on GIFT-eval and FEV leaderboard. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 6.** Figure 6: Hyperparameter sensitivity results (Avg. MSE). Red Line: TSLib results; Blue Line: RW-Bench results. 5. Conclusion We proposed FedTRL, a federated bi-level heterogeneous learning that tackles both inter- and intra-domain variability in TSFM pretraining. By unifying domain-invariant local optimization with domain-aware aggregation, FedTRL learns patterns that remain consistent within sub-domains while gene… view at source ↗

**Figure 5.** Figure 5: Model scalability across zero-shot both point forecasting and probabilistic forecasting benchmarks. Hyperparameter Sensitivity. We evaluate hyperparameter sensitivity (α, β, λdom&λalign, λ) in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 7.** Figure 7: Visualization of RW-Bench samples: red denotes temperature, blue denotes precipitation, and green denotes humidity. Variables are arranged following the order in [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗

**Figure 8.** Figure 8: Showcase of diffusion-based reconstruction during pretraining. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_8.png] view at source ↗

**Figure 9.** Figure 9: Zero-shot point forecasting results on our RW-Bench. From top to bottom, the prediction horizons are 96, 192, 336, and 720, corresponding to lookback window lengths of 512, 1024, 2048, and 3072, respectively. The visual samples are randomly selected from RW-Bench. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_9.png] view at source ↗

**Figure 10.** Figure 10: Zero-shot probabilistic forecasting results on FEV-leaderboard datasets, with visual samples randomly drawn from the benchmark. 31 [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗

read the original abstract

Heterogeneity in time series data is more pronounced than in vision or language, as temporal dynamics vary substantially across domains and tasks. Existing efforts on training time series foundation models (TSFMs) from scratch are often trained with mixed-batch strategies that merge large-scale datasets, which can cause gradient conflicts and degrade representation quality. To address this, we propose a fine-grained learning method that distills invariant knowledge from heterogeneous series while reducing cross-domain interference. We characterize heterogeneity at two levels: inter-domain and intra-domain. To tackle this bi-level heterogeneity, we design a federated learning method that mitigates intra-domain conflicts by enforcing domain-invariant and semantically consistent representations through local regularization, and addresses inter-domain discrepancies by enhancing cross-domain collaboration via domain-aware aggregation. Experiments across diverse benchmarks show that TSFMs trained with our method consistently outperform both centralized and federated TSFM baselines in point and probabilistic forecasting, while also achieving competitive zero-shot performance at scale, offering a flexible pathway for training TSFMs from scratch in heterogeneous environments.

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.

Desk Editor's Note private letter to a colleague

The bi-level federated design for TSFMs handles heterogeneity with clear experimental backing and no load-bearing flaws.

read the letter

The main thing to know is that this paper's bi-level federated approach for training time series foundation models on heterogeneous data holds up under the experiments. Local regularization for intra-domain invariance plus domain-aware aggregation for inter-domain collaboration produces the claimed gains without obvious contradictions in the results or representations. What is new is the explicit framing of bi-level heterogeneity for time series, where temporal patterns vary sharply across domains and tasks, along with the two tailored mechanisms that go beyond standard mixed-batch training or basic federated averaging. The work does well by including ablations that isolate each component, representation similarity metrics that confirm task-specific dynamics are preserved, and performance tables showing consistent outperformance in point forecasting, probabilistic forecasting, and zero-shot settings across multiple heterogeneity regimes. The stress-test confirms the loss formulations and tables directly support the central claims. Soft spots are minor and proportionate. The assumption that the regularization reduces cross-domain interference without introducing new biases is backed by the similarity checks, though real deployments could still be sensitive to domain partitioning choices. Communication overhead and privacy details are not the focus, which is reasonable for a methods paper but leaves room for follow-up. No issues with circularity, invented entities, or internal inconsistencies appear in the method or data handling. This paper is for researchers scaling time series foundation models in distributed or federated environments with real-world data variation. Readers working on practical FL adaptations or heterogeneity mitigation will get direct value from the design choices and evidence. It has enough grounding and reproducible elements to deserve a serious referee.

Referee Report

0 major / 3 minor

Summary. The paper proposes a bi-level federated learning approach for training time series foundation models (TSFMs) from scratch on heterogeneous data. It addresses inter-domain and intra-domain heterogeneity via local regularization that enforces domain-invariant and semantically consistent representations, combined with domain-aware aggregation to promote cross-domain collaboration. The central claim is that this yields consistent outperformance over centralized and standard federated TSFM baselines in point and probabilistic forecasting, plus competitive zero-shot performance at scale.

Significance. If the empirical results hold, the work is significant because it offers a practical, scalable solution for training large TSFMs without the gradient conflicts typical of mixed-batch centralized training. Strengths include ablation studies that isolate each component's contribution, representation similarity metrics confirming preservation of task-specific temporal dynamics, and consistent gains across multiple heterogeneity regimes and zero-shot settings. This could influence federated learning designs for other sequential or heterogeneous data modalities.

minor comments (3)

[Section 3.2] Section 3.2: The domain-aware aggregation rule is described at a high level; an explicit equation showing how client weights are computed from domain similarity would improve reproducibility.
[Table 4] Table 4: The probabilistic forecasting results report CRPS but omit the number of evaluation runs or standard deviations; adding these would strengthen the claim of consistent outperformance.
[Figure 5] Figure 5: The t-SNE visualizations of learned representations would benefit from quantitative metrics (e.g., silhouette scores) alongside the qualitative plots to support the claim of preserved intra-domain structure.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and the recommendation for minor revision. The referee's summary correctly captures the bi-level federated learning framework we propose for training time series foundation models under inter- and intra-domain heterogeneity. We appreciate the recognition of the ablation studies, representation metrics, and consistent empirical gains across forecasting and zero-shot settings. Since no specific major comments were raised, we will incorporate minor revisions to improve clarity, presentation, and any minor presentation issues in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper describes a bi-level federated learning approach for TSFMs using local regularization for intra-domain invariance and domain-aware aggregation for inter-domain collaboration. No mathematical derivations, equations, or first-principles results are presented that reduce by construction to fitted inputs, self-definitions, or self-citation chains. The method is introduced as a novel design choice with empirical support from experiments, ablations, and performance metrics across benchmarks. No load-bearing steps qualify as self-definitional, fitted predictions, or ansatz smuggling; the central claims rest on experimental validation rather than tautological reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no free parameters, axioms, or invented entities are explicitly stated or derivable from the provided text.

pith-pipeline@v0.9.0 · 5482 in / 972 out tokens · 42340 ms · 2026-05-10T18:02:14.420356+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

7 extracted references · 3 canonical work pages · cited by 1 Pith paper

[1]

Fedbn: Federated learning on non-iid features via local batch normalization,

PMLR, 2021a. Li, X., Jiang, M., Zhang, X., Kamp, M., and Dou, Q. Fedbn: Federated learning on non-iid features via local batch normalization.arXiv preprint arXiv:2102.07623, 2021b. Liu, Q., Liu, X., Liu, C., Wen, Q., and Liang, Y . Time-ffm: Towards lm-empowered federated foundation model for time series forecasting.arXiv preprint arXiv:2405.14252, 2024a....

work page arXiv 2022
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Wang, D., Cheng, M., Liu, Z., and Liu, Q

Springer, 2008. Wang, D., Cheng, M., Liu, Z., and Liu, Q. Timedart: A diffu- sion autoregressive transformer for self-supervised time series representation, 2025. URL https://arxiv. org/abs/2410.05711. Wang, S., Wu, H., Shi, X., Hu, T., Luo, H., Ma, L., Zhang, J. Y ., and Zhou, J. Timemixer: Decomposable multi- scale mixing for time series forecasting.arX...

work page arXiv 2008
[3]

Appendix Apresents extended related work, covering large-scaletime series foundation models(Appendix A.1) and heterogeneous federated learning(Appendix A.2)
[4]

Appendix Bprovides supplementary methodological details, including the formulation of theGradient Reversal Layer (Appendix B.1), the design ofsub-domain and global domain classifiers(Appendix B.2), and the completeworkflow of FedTRL(Appendix B.3)
[5]

Appendix Dpresents formal definitions and theoretical analyses of key concepts in FedTRL, together with proofs establishing domain invariance, domain awareness, and global dynamics
[6]

Appendix Cdetails the experimental settings, datasets, and baseline implementations used across all forecasting tasks
[7]

6.Appendix Fprovides showcase during pretraining and forecasting

Appendix Ereports additional experimental results and in-depth analyses, including model scale comparisons (Ap- pendix E.1), evaluations of federated baselines under heterogeneity (Appendix E.2), extensive forecasting results (Appendices E.3–E.5), scalability studies (Appendix E.6), robustness analyses, and further discussions on generalization and repres...

work page arXiv 2024