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arxiv: 2606.08578 · v1 · pith:7CLQSMWQnew · submitted 2026-06-07 · 💻 cs.LG

Lost in the Non-convex Loss Landscape: How to Fine-tune the Large Time Series Model?

Pith reviewed 2026-06-27 19:04 UTC · model grok-4.3

classification 💻 cs.LG
keywords large time series modelsfine-tuningloss landscapenon-convex optimizationSmoothed Full Fine-tuningpre-trained modelstrainability
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0 comments X

The pith

Linear interpolation between pre-trained and random weights smooths the non-convex loss landscape to improve fine-tuning of large time series models.

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 pre-trained large time series models suffer from a poorly conditioned loss landscape that makes direct fine-tuning prone to overfitting and often worse than training from scratch. The proposed fix constructs an auxiliary randomly initialized model and linearly blends its weights with the pre-trained ones to produce a smoother landscape. This blending is claimed to improve trainability while retaining pre-trained knowledge. A sympathetic reader would care because it offers a way to make large pre-trained models usable on downstream tasks without losing the value of pre-training.

Core claim

Smoothed Full Fine-tuning (SFF) obtains a smoother loss landscape by linearly interpolating the weights of the pre-trained large time series model with those of an auxiliary model created via random initialization. From an optimization view, this perturbs sharp minima without significantly harming flat regions and helps the optimizer escape poor local basins toward smoother, more generalizable solutions. Experiments show consistent gains on eight representative models across diverse downstream tasks.

What carries the argument

Linear weight interpolation between a pre-trained large time series model and a randomly initialized auxiliary model, which produces the smoothed loss landscape used for fine-tuning.

If this is right

  • SFF enables effective use of pre-trained knowledge on downstream tasks where direct fine-tuning previously failed.
  • The method perturbs sharp minima while preserving flat regions, leading to more generalizable solutions.
  • Performance gains hold across eight representative LTSMs including Timer, TimesFM, MOMENT, UniTS, MOIRAI, Chronos, TTMs, and Sundial.
  • No task-specific adjustment of the interpolation ratio is needed for the smoothing effect.

Where Pith is reading between the lines

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

  • The same interpolation idea could be tested on large models in other modalities where non-convex fine-tuning landscapes are known to be problematic.
  • If the smoothing effect scales with model size, it might reduce the need for more complex regularization techniques during adaptation.
  • One could measure whether the interpolated landscape actually changes the distribution of Hessian eigenvalues at minima to confirm the claimed perturbation of sharp regions.

Load-bearing premise

Linear interpolation between pre-trained weights and randomly initialized weights produces a loss landscape that is both smoother and more amenable to generalization than the original, without requiring task-specific tuning of the interpolation ratio.

What would settle it

If SFF-tuned models show no consistent improvement over direct fine-tuning or training from scratch across the eight tested LTSMs and multiple benchmark tasks, the claim of improved trainability would be falsified.

Figures

Figures reproduced from arXiv: 2606.08578 by Peang Wang, Wei Wang, Xu Zhang.

Figure 1
Figure 1. Figure 1: Loss landscape comparisons based on the LTSM Timer and exchange rate dataset. Smoother [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Smoothed Full Fine-tuning (SFF). By linearly interpolating the pretrained and randomly initialized LTSMs, we obtain a smoothed model that preserves pretrained knowledge while exhibiting a smoother and more trainable loss landscape, thereby enabling more stable and effective fine-tuning. 3.1.1 INFLUENCE OF INTERPOLATION ON SHARP AND FLAT LOSS LANDSCAPE Given an MSE loss function L(Θ), where Θ denotes the mo… view at source ↗
Figure 3
Figure 3. Figure 3: MSE of different fine-tuning strategies on Timer with prediction length 96, across multiple [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test MSE over epochs for different fine-tuning methods on Timer in TSF with prediction [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Impact of interpolation coefficient α on zero-shot forecasting with prediction length 96. The “Re-initialize” model performs the worst, which is reasonable [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Fine-tuning Timer for TSF with prediction length 96 (100% training data) under different [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Loss landscape comparisons based on the LTSM Timer and weather dataset. The smoother [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Loss landscape comparisons based on the LTSM Timer and electricity dataset. The smoother [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Time series forecasting of the LTSM Timer on various datasets with 100% available data [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Time series imputation task on Timer with the mask ratio 25%. The experimental settings [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
read the original abstract

Recently, large time series models (LTSMs) have gained increasing attention due to their similarities to large language models, including flexible context length, scalability, and task generality, outperforming advanced task-specific models. However, prior studies indicate that pre-trained LTSMs may exhibit a poorly conditioned non-convex loss landscape, leading to limited trainability. As a result, direct fine-tuning tends to cause overfitting and suboptimal performance, sometimes even worse than training from scratch, substantially diminishing the benefits of pre-training. To overcome this limitation, we propose Smoothed Full Fine-tuning (SFF), a novel fine-tuning technology. Specifically, we construct an auxiliary LTSM via random initialization to obtain a smoother loss landscape, and then linearly interpolate its weights with those of the pre-trained model to smooth the original landscape. This process improves trainability while preserving pre-trained knowledge, thereby enabling more effective downstream fine-tuning. From an optimization perspective, SFF perturbs sharp minima without significantly harming flat regions, facilitating escape from poor local basins toward smoother and more generalizable solutions. Extensive experiments on benchmark datasets demonstrate consistent improvements across eight representative LTSMs, including Timer, TimesFM, MOMENT, UniTS, MOIRAI, Chronos, TTMs, and Sundial, on diverse downstream tasks. The code is available at the link: https://github.com/Meteor-Stars/SFF.

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 / 0 minor

Summary. The paper claims that pre-trained large time series models (LTSMs) suffer from poorly conditioned non-convex loss landscapes that cause direct fine-tuning to overfit or underperform training from scratch. It proposes Smoothed Full Fine-tuning (SFF), which builds an auxiliary randomly initialized LTSM and linearly interpolates its weights with the pre-trained model to smooth the landscape by perturbing sharp minima while preserving flat regions. This is asserted to improve trainability and generalization without task-specific tuning of the interpolation ratio. Experiments are said to show consistent gains across eight LTSMs (Timer, TimesFM, MOMENT, UniTS, MOIRAI, Chronos, TTMs, Sundial) on diverse downstream tasks.

Significance. If the mechanism and empirical gains are validated, SFF would supply a lightweight, architecture-agnostic fine-tuning procedure that could make pre-trained LTSMs more reliably usable, addressing a practical bottleneck in the emerging LTSM literature. The public code release is a clear strength for reproducibility.

major comments (2)
  1. [§3] §3: The core claim that linear interpolation produces a smoother loss landscape (rather than acting as generic regularization or changed initialization scale) is load-bearing for the method's justification, yet the manuscript provides no quantitative landscape diagnostics such as Hessian trace, sharpness metrics, or barrier heights along the interpolation line, and no ablation that isolates the geometric effect.
  2. [Experiments] Experiments (throughout): The abstract asserts 'consistent improvements' and 'extensive experiments' across eight models, but supplies no numerical results, baseline comparisons, statistical tests, or controls; without these, it is impossible to determine whether the data support the central claim that SFF enables more effective downstream fine-tuning.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive feedback. We address each major comment below and will revise the manuscript to strengthen the claims where needed.

read point-by-point responses
  1. Referee: [§3] §3: The core claim that linear interpolation produces a smoother loss landscape (rather than acting as generic regularization or changed initialization scale) is load-bearing for the method's justification, yet the manuscript provides no quantitative landscape diagnostics such as Hessian trace, sharpness metrics, or barrier heights along the interpolation line, and no ablation that isolates the geometric effect.

    Authors: We agree that quantitative landscape analysis would strengthen the geometric justification. Section 3 motivates the smoothing effect via optimization arguments (perturbing sharp minima while preserving flat regions), but lacks explicit metrics. In revision we will add Hessian trace, sharpness, and barrier height measurements along the interpolation path, plus ablations against pure regularization and rescaled initialization to isolate the interpolation geometry. revision: yes

  2. Referee: [Experiments] Experiments (throughout): The abstract asserts 'consistent improvements' and 'extensive experiments' across eight models, but supplies no numerical results, baseline comparisons, statistical tests, or controls; without these, it is impossible to determine whether the data support the central claim that SFF enables more effective downstream fine-tuning.

    Authors: The manuscript reports results across eight LTSMs and diverse tasks with comparisons to direct fine-tuning and scratch training, supported by the released code. To improve clarity we will expand the experimental section with full numerical tables, additional baseline controls, and statistical tests (e.g., paired t-tests with p-values) in the revision. revision: yes

Circularity Check

0 steps flagged

No circularity: method defined independently and evaluated via external experiments

full rationale

The paper introduces SFF as an explicit procedure (random auxiliary model + linear interpolation of weights) whose claimed benefit is then tested on eight external LTSMs across downstream tasks. No derivation step reduces a claimed outcome to a fitted parameter or self-referential definition; the smoothing effect is asserted as a geometric consequence of the interpolation construction and is not used to justify its own inputs. No self-citations appear in the provided text as load-bearing premises, and the experimental results are presented as independent validation rather than tautological outputs. The absence of Hessian diagnostics is a limitation of evidence strength, not a circularity in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal rests on the unproven domain assumption that random-weight interpolation yields a usefully smoother landscape; no free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption Linear interpolation of weights between a pre-trained LTSM and a randomly initialized model produces a smoother loss landscape that improves generalization
    This premise is invoked to justify why SFF works but receives no derivation or external validation in the abstract.

pith-pipeline@v0.9.1-grok · 5780 in / 1176 out tokens · 21876 ms · 2026-06-27T19:04:19.016014+00:00 · methodology

discussion (0)

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Forward citations

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Reference graph

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    By combining the strengths of the randomly initialized LTSM (good trainability with a smoother loss landscape) and the pretrained LTSM (good pretrained knowledge), the convergence of the smoothed LTSM can be improved during fine-tuning. A.3 MORE DETAILS ABOUT REPRODUCING PAPER RESULTS Datasets.In forecasting and imputation, we conduct extensive experiment...

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    for anomaly detection. 15 Published as a conference paper at ICLR 2026 Algorithm 1:Smoothing the loss landscape of the pre-trained LTSM for fine-tuning defSmoothing_Landscape ( model1 , model2 ) : " " " model1 : pre − t r a i n e d LTSM, model2 : randomly i n i t i a l i z e d LTSM" " " f o rparam1 , param2i n z i p( model1 . p a r a m e t e r s ( ) , mod...

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    Based on the limited computing resources and settings supported by each model, the input lengths for MOMENT and TimesFM are 512 and 256, while the forecast lengths are 96, and 128, respectively. Following Timer (Liu et al., 2024), the fine-tuning epochs are fixed at 10, and we report the best metric in all epochs. The learning rate is 3e-5 and the optimiz...

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    Hourly These datasets used in this paper are extensively used for TSF algorithm evaluation, including exchange rate forecasting in the financial field, electricity consumption forecasting in the energy field, climate parameter forecasting in the weather domain, and machine parameter (e.g., loads and oil temperature) forecasting in the industrial field: • ...

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    All datasets can be downloaded from the link11

    • Traffic10 dataset contains the occupation rate of freeway systems in California, USA. All datasets can be downloaded from the link11. A.5 ADDITIONAL EXPERIMENT RESULTS AND DISCUSSIONS The experiments in the appendix serve as supplements to those in the main paper, including complete standard deviations, MAE results, and interpolation experiments. All fi...

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    flat” and “sharp

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    Avg. on 1%, 2%, 3%

    “-” indicates that the preprocessed dataset is not included (Chronos) or out of memory (Sundial). MOIRAI +Smooth Chronos +Smooth TTMs +Smooth Sundial +Smooth ETTh1 0.4390.447 - - 0.4210.424 0.4370.453 ETTh2 0.3860.4 - - 0.4040.408 0.4090.417 ETTm1 0.6010.603 - - 0.4350.439 0.4090.417 ETTm2 0.4070.438 - - 0.4090.41 0.3970.408 Weather 0.3990.424 - - 0.3280....