REVIEW 5 major objections 6 minor 2 references
Stationarity Exploration for Multivariate Time Series Forecasting
T0 review · 5 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read The paper claims that separately adjusting the amplitude and phase of Fourier components is what lets a forecaster extract stationary structure, and that APRNet outperforms prior methods across long-term, few-shot, short-term, and…
desk verdict A plausible frequency-domain forecasting architecture whose reported SOTA margins don't match its own tables; needs honest re-reporting before the claims can be trusted. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing mechanism is the APLC (Amplitude-Phase Local Correlation) module, which reconstructs each frequency component as $K_1 = \mathrm{IFFT}\big(\hat{F}_{a1}\odot F_{a1}\cos(\hat{F}_{p1}+F_{p1}) + j\,\hat{F}_{a1}\odot F_{a1}\sin(\hat{F}_{p1}+F_{p1})\big)$ and does the same along the channel dimension to produce $K_2$. Within it, the KLC module uses KAN B-spline functions $\phi(x)=\sum_k c_k B_k(x)$ to fit local correlations among frequencies, and the final output is $\hat{Y}=Z+\alpha K_1+\beta K_2$. The module's role is to let amplitude multiplication adjust energy contrast while phase addition corrects timing offsets, and its output is what the linear decoder turns into forecasts.
What would settle it
Train APRNet and an ablation that replaces the amplitude-phase split with a single learnable complex gain per frequency on a synthetic signal made of sinusoids with known drifting amplitudes and phases. If the ablation matches or beats APRNet, then separate amplitude and phase modeling is not what carries the reported improvement.
Extended reading notes
Core claim
The paper's central claim is that stationarity in multivariate time series can be exposed by reconstructing frequency-domain signals with amplitude scaled and phase shifted independently. APRNet applies Fourier transforms along both the sequence and channel dimensions, learns per-frequency adjustment coefficients for amplitude and per-frequency shifts for phase, and uses a KAN-based local correlation module to fit these adjustments as smooth univariate functions. The reconstructed signal is then fused with the encoded input and passed through a linear decoder with Reversible Instance Normalization. The authors argue that this amplitude-phase decoupling captures stationary information that existing frequency-domain methods miss, and they report best average results on long-term, few-shot, short-term, and zero-shot benchmarks.
Load-bearing premise
The load-bearing premise is that multiplying amplitudes and adding phases separately in Fourier space exposes stationary structure that a joint complex-domain adjustment would miss; if the reported gains come from extra model flexibility rather than from this decomposition, the paper's explanation collapses, and the benchmark results carry no error bars to rule that out.
Editorial extensions
If this is right
- Reported average MSE drops by 4.2% on Electricity and 2.2% on Weather compared with the second-best long-term result, with best averages also claimed on ETTm2 and Traffic.
- Few-shot forecasting with only 5% of ETTh1 training data reports a 35.1% error reduction over the second-best method, suggesting the amplitude-phase reconstruction transfers from limited data.
- On the M4 short-term benchmark, reported average SMAPE and OWA are the lowest among compared methods, with MASE second-best.
- The measured MACs on high-channel datasets are much lower than the primary baseline (2.09G vs 4.53G on Electricity, 17.78G vs 130.29G on Traffic), so the accuracy gains are not bought with raw compute.
- The authors' t-SNE visualization shows tighter clusters after APLC processing, which they interpret as evidence that the module turns non-stationary input into locally stationary features.
Reading between the lines
- The paper only tests APRNet as a complete model, so a natural next experiment is to attach the APLC module to other decoders; if the amplitude-phase reconstruction is the active ingredient, it should improve transformers and linear forecasters alike.
- The stationarity claim could be checked directly by measuring whether features after APLC have flatter or more time-invariant spectra than the input, since the paper currently offers only t-SNE clustering as evidence.
- Because the paper describes phase addition as correcting time-delay discrepancies, a synthetic experiment with known phase shifts on otherwise identical signals would isolate whether phase modeling or amplitude denoising drives the reported gains.
- Since Revin already removes level and scale shifts, part of APRNet's gain may come from frequency-domain denoising rather than from stationarization; distinguishing these would sharpen the mechanism claimed here.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes APRNet, an encoder-decoder forecasting model that operates on the frequency-domain representation of multivariate time series. The central idea is to decouple amplitude and phase in the complex Fourier spectrum, model them separately along sequence and channel dimensions with KAN-based local correlation (KLC) modules, and reconstruct the signal by element-wise amplitude scaling and phase addition (Eq. 6). The authors claim that this reconstruction extracts stationary information and improves forecasting. They report experiments in long-term, few-shot, short-term (M4), and zero-shot settings, along with ablations and an efficiency analysis. The headline claims are state-of-the-art performance, including an average MSE reduction of 4.2% on Electricity and 13.95% on ETTh2-to-ETTm2 zero-shot transfer.
Significance. If the results are substantiated, the architecture is a worthwhile contribution to frequency-domain time-series forecasting: the explicit separation of amplitude and phase interactions, the joint modeling of sequence and channel dimensions, and the use of KAN-based local correlation for frequency coefficients are not standard in existing methods. The paper also provides ablations for the main components and an efficiency comparison. However, the quantitative evidence as written is not sufficient to establish the claimed superiority over SOTAs: two headline improvement figures are not reproducible from the paper's own tables, all benchmark tables report single deterministic runs without error bars or significance statistics, the stationarity claim rests on a qualitative, self-referential t-SNE visualization, and several relevant baselines are absent. The central idea is defensible, but the evidence needs substantial revision before the claims can be accepted.
major comments (5)
- [Zero-Shot Forecasting, Table 4] The stated 13.95% improvement on ETTh2→ETTm2 is not reproducible from Table 4. In the Avg row for ETTh2→ETTm2, APRNet has MSE 0.296, the actual strongest baseline CycleNet has 0.300 (a 1.3% gap), and TimeMixer++ has 0.342 (a 13.5% gap). The reported 13.95% therefore appears to be computed against TimeMixer++ rather than against the true second-best result. This is a load-bearing claim because the zero-shot result is a headline contribution and is repeated in the conclusion; the text must be corrected to state the margin against the strongest baseline, or the baseline selection must be justified.
- [Long-Term Forecasting, Table 1] The claim that APRNet reduces average error on Electricity by 4.2% is not supported by Table 1. In the ECL Avg row, APRNet has MSE 0.156, the next-best TQNet has 0.161 (a 3.1% gap), and TimeMixer++ has 0.164 (a 4.9% gap). Neither comparison yields 4.2%, so the reported improvement is not reproducible from the table. Since the long-term forecasting result is one of the paper's main empirical claims, the authors need to identify the exact baseline used for the percentage and recompute all reported margins.
- [Experiment Results, Tables 1-4] All benchmark tables report single MSE/MAE values without error bars, confidence intervals, multi-seed standard deviations, or significance tests. Many of the reported advantages are small: for example, ETTm2 Avg is 0.255 vs 0.258, Weather Avg is 0.222 vs 0.227, and several per-horizon zero-shot entries differ by less than 1%. With no code released and no indication of how many seeds or data splits were used, the central claim of consistent superiority over SOTAs cannot be verified. Statistical reporting is necessary here because the margins are frequently smaller than typical run-to-run variability in deep forecasting models.
- [Parameter Sensitivity and Eq. (6)] The paper's core conceptual claim is that amplitude scaling and phase addition in the frequency domain 'extract stationary information' and that APRNet 'explores stationarity,' but no formal definition or quantitative stationarity measure is provided. The only direct evidence is Fig. 3, which shows t-SNE visualizations of APRNet's own latent features; no baseline feature visualizations, no quantitative stationarity tests (e.g., ADF, KPSS, or spectral-stationarity metrics), and no comparison of reconstructed versus original spectra are reported. Because the title and the contributions are explicitly about stationarity, this evidence is too weak to support the claim as stated.
- [Experiment Results, Baselines] The SOTA comparison is incomplete relative to the paper's own framing. Well-known frequency-domain forecasting methods such as FEDformer and FreTS are absent from the benchmark tables, and the text in Long-Term Forecasting refers to Time-MoE, but Table 1 contains no Time-MoE column (the closest column is labelled TQNet). This makes the set of competitors unclear and weakens the 'superiority against SOTAs' conclusion. The authors should either add the missing baselines or explicitly state why they are excluded.
minor comments (6)
- [Eq. (6)] The notation in Eq. (6) is unclear: the reconstruction coefficients Fa1 and Fp1 are not distinguished from the original spectral inputs, and the dimensions or transpositions used after the channel-dimension FFT are not specified. Please define all symbols and the shape of each tensor.
- [Datasets section] The Datasets section lists SMD, SML, SMAP, SWaT, and PSM as being used for anomaly detection, but no anomaly-detection experiments or results appear anywhere in the paper; this promised comparison should either be added or removed.
- [Eqs. (4)-(5)] The symbol Y is used for both the intermediate projection in Eq. (4) and the final output in Eq. (5); renaming one of these would avoid confusion.
- [Section title, Methodology] The methodology heading calls the model the 'Amplitude-Phase Network', while the abstract and contributions use 'Amplitude-Phase Reconstruct Network'; the terminology should be consistent throughout.
- [References] The related-work section contains duplicate entries for WaveForM and for Frequency Adaptive Normalization; these duplicate references should be consolidated.
- [Tables 1 and 4] The average rows are embedded in the block of per-horizon rows without a visual separator, which makes it unnecessarily difficult to verify the reported margins; placing each average row on a clearly labelled line would improve reproducibility of the claims.
Circularity Check
No derivation-chain circularity: APRNet's benchmark claims are empirical; the only circular moment is a minor self-referential t-SNE validation of stationarity extraction.
-
other
[Experiment / Parameter Sensitivity (discussion of Fig. 3)]
"We illustrate the capture of stationary information following analysis by the APLC module in Fig 3. The three t-SNE results depicted in the figure demonstrate the clustering phenomenon of stationary segments we observed in the feature space. The model can effectively capture stationary information, and then the data points corresponding to the stationary information will form tightly clustered shapes in low-dimensional space."
The t-SNE plots are computed from features produced by APRNet's own APLC module, and no independent labeling or external stationarity criterion is provided. The claimed demonstration therefore observes the model's own output and reads clustering as evidence of the very capability the model was designed to implement. This is self-referential evidence rather than an independent test, so it cannot by itself establish that stationary information has been extracted. It is not load-bearing for the benchmark MSE/MAE claims, which stand or fall on the tables and experimental protocol.
full rationale
The central claims of this paper are empirical benchmark results for a learned forecasting architecture, not first-principles derivations. Equations (1)-(10) define a trainable network, and no fitted parameter is renamed as a prediction; the long-term, few-shot, short-term, and zero-shot results are standard train/test comparisons. The only self-referential moment is the t-SNE analysis in Fig. 3, where APRNet's own features are used as evidence of stationarity extraction; this is a visual interpretation and does not enter the reported metrics. The citations with overlapping authors, such as Fang et al. 2025 used only for MSE/MAE conventions, are not load-bearing. The reported discrepancies in headline percentage improvements relative to the tables are reproducibility and correctness concerns, not circularity. Overall, the core empirical claims are self-contained and not forced by definition or self-citation, so the circularity score is low.
Assumptions & free parameters
free parameters (4)
- Revin affine parameters gamma, beta =
learned
- Fusion parameters alpha, beta =
learned
- KAN spline coefficients c_k =
learned
- Linear projection f and output weight W_t =
learned
assumptions (3)
- standard math Fourier transform is invertible and IFFT of modified spectrum yields a valid time-domain representation
- domain assumption KAN B-spline basis functions can approximate the local relationships between amplitude and phase
- ad hoc to paper Element-wise amplitude scaling and phase addition in the frequency domain correspond to meaningful signal modifications that enhance stationarity
Cite this review
Pith. "Pith review of Stationarity Exploration for Multivariate Time Series Forecasting." pith.science (2026). https://pith.science/paper/JWKBYZV3
@misc{pith2026250808919,
author = {Pith},
title = {Pith review of: Stationarity Exploration for Multivariate Time Series Forecasting},
year = {2026},
howpublished = {\url{https://pith.science/paper/JWKBYZV3}},
note = {Machine review of arXiv:2508.08919}
}
read the original abstract
Deep learning-based time series forecasting has found widespread applications. Recently, converting time series data into the frequency domain for forecasting has become popular for accurately exploring periodic patterns. However, existing methods often cannot effectively explore stationary information from complex intertwined frequency components. In this paper, we propose a simple yet effective Amplitude-Phase Reconstruct Network (APRNet) that models the inter-relationships of amplitude and phase, which prevents the amplitude and phase from being constrained by different physical quantities, thereby decoupling the distinct characteristics of signals for capturing stationary information. Specifically, we represent the multivariate time series input across sequence and channel dimensions, highlighting the correlation between amplitude and phase at multiple interaction frequencies. We propose a novel Kolmogorov-Arnold-Network-based Local Correlation (KLC) module to adaptively fit local functions using univariate functions, enabling more flexible characterization of stationary features across different amplitudes and phases. This significantly enhances the model's capability to capture time-varying patterns. Extensive experiments demonstrate the superiority of our APRNet against the state-of-the-arts (SOTAs).
Figures
Figures from the paper (1 more)
Reference graph
Works this paper leans on
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[2021]
In International conference on learning representations
Reversible instance normalization for accurate time- series forecasting against distribution shift. In International conference on learning representations. Kim, T.; Kim, J.; Tae, Y .; and et al. 2022. Reversible In- stance Normalization for Accurate Time-Series Forecasting against Distribution Shift. In International Conference on Learning Representation...
arXiv 2022
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[2025]
LLM-TS Integrator: Integrating LLM for Enhanced Time Series Modeling. Trans. Mach. Learn. Res., 2025. Cinar, Y . G.; Mirisaee, H.; Goswami, P.; and et al. 2018. Period-aware content attention RNNs for time series fore- casting with missing values. Neurocomputing, 312: 177– 186. Fang, Z.; Zhu, X.; Yang, C.; Zhou, H.; Qin, J.; and Yin, X.-C. 2025. Aligning ...
work page 2025
Reviewed August 15, 2026 · model on record in the stance chip above.
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