{"id":"f41c4fd4-bc78-400e-b73c-555b3ca6882d","arxiv_id":"2508.08919","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"APRNet forecasts time series by reconstructing Fourier amplitude and phase with a KAN-based local correlation module, reporting small improvements on ETT, Weather, Electricity, and Traffic benchmarks.","lead":"A new neural network, APRNet, forecasts time series by separately adjusting the amplitude and phase of frequency components using KAN-based local correlations. The authors report small but consistent accuracy gains over recent baselines on standard forecasting benchmarks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported SOTA margins are not reproducible from the paper's own tables: the claimed 13.95% zero-shot gain over 'second-best' is only 1.3% against the actual second-best in Table 4.","rationale":"The paper does include useful internal evidence: ablations for sequence/channel modeling, amplitude/phase modeling, KAN replacement, and MACs efficiency comparisons. So the method is not without support. The load-bearing weakness I identify is evidential and specific: the strongest quantified claims of superiority are contradicted by the paper's own tables, particularly the 13.95% zero-shot improvement over the 'second-best' result. This is more concrete than the reader's broader concern about missing error bars, though it points in the same direction. The appropriate verdict remains CONDITIONAL: the authors should correct the comparison protocol, identify the true second-best baseline, and report reproducible multi-seed results before the SOTA claim can be accepted. I partially agree with the reader because we reach the same overall conditional verdict, but the precise load-bearing concern here is arithmetic consistency of the headline margins rather than the theoretical justification of Eq. 6.","tokens_in":16639,"tokens_out":9754,"duration_ms":98112,"concrete_test":"Recompute every claimed relative improvement directly from Tables 1 and 4 using the table's actual second-best entry. For ETTh2→ETTm2: 1 - (0.296 / 0.300) = 1.3%, versus 1 - (0.296 / 0.342) = 13.5% against TimeMixer++. For ECL long-term: 1 - (0.156 / 0.161) = 3.1%, versus 4.9% against TimeMixer++. If the intended 'second-best' is TimeMixer++, rerun the full zero-shot and long-term benchmarks with CycleNet, FEDformer, FreTS, and PatchTST under the same protocol and report multi-seed mean ± std; if the corrected margins fall below a significance threshold, the SOTA claim should be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of 'superiority against SOTAs' rests largely on specific relative gains, but the two headline numbers do not match the tables. In the Zero-Shot Forecasting section, the text states that for ETTh2→ETTm2 'the MSE metric of APRNet improved by 13.95% compared to the second-best result.' Table 4 (ETTh2→ETTm2, Avg row) gives APRNet 0.296; the actual second-best baseline in that row is CycleNet at 0.300, which is only a 1.3% improvement. The 13.95% figure is not reproducible from any single baseline row; it is closest to comparing APRNet against TimeMixer++ (0.342, about 13.5%), which is not the second-best. Similarly, the Long-Term Forecasting section reports a 4.2% average error reduction on Electricity over 'sub-optimal' results; Table 1 (ECL Avg) shows APRNet 0.156 versus the next-best 0.161, about a 3.1% improvement, while 4.2% is closer to a comparison against TimeMixer++ (0.164, 4.9%). These discrepancies imply that the headline margins are computed against a selected baseline rather than the true strongest competitor. With no code, no error bars, and no multi-seed statistics, the quantified SOTA claim cannot be verified from the paper as written; the most favorable reading is that APRNet wins by small margins on some benchmarks, not that it achieves the stated double-digit improvement over the second-best method.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16984,"tokens_out":6936,"duration_ms":71707,"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":[{"comment":"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.","section":"Zero-Shot Forecasting, Table 4"},{"comment":"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.","section":"Long-Term Forecasting, Table 1"},{"comment":"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.","section":"Experiment Results, Tables 1-4"},{"comment":"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.","section":"Parameter Sensitivity and Eq. (6)"},{"comment":"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.","section":"Experiment Results, Baselines"}],"minor_comments":[{"comment":"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.","section":"Eq. (6)"},{"comment":"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.","section":"Datasets section"},{"comment":"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":"Eqs. (4)-(5)"},{"comment":"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.","section":"Section title, Methodology"},{"comment":"The related-work section contains duplicate entries for WaveForM and for Frequency Adaptive Normalization; these duplicate references should be consolidated.","section":"References"},{"comment":"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.","section":"Tables 1 and 4"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a plausible incremental contribution to frequency-domain forecasting. It decouples amplitude and phase in the Fourier domain and uses a KAN-based local correlation module to adjust them, then reconstructs the signal. That combination appears new, and the ablations give some credit: removing either the channel/sequence joint modeling or the amplitude/phase modeling hurts, and replacing KAN with linear or conv layers hurts. The efficiency table is also useful.\n\nBut the headline numbers do not survive contact with the paper's own tables. The abstract says the method beats SOTAs; the zero-shot section says ETTh2→ETTm2 improves MSE by 13.95% over the second-best. The actual second-best in Table 4 is CycleNet at 0.300, and APRNet is 0.296, which is 1.3%. The 13.95% figure only works if you compare to TimeMixer++ at 0.342, which is not second-best. Same story for Electricity: the text claims 4.2% over sub-optimal, but the next-best is 0.161 vs APRNet's 0.156, about 3.1%. These are not rounding errors; the claimed margins are computed against a cherry-picked baseline.\n\nThere are other soft spots. Some standard baselines (FEDformer, FreTS) are missing from the experiments even though the paper discusses them. There are no error bars, no multi-seed results, and no code, so the small gains could be noise. The 'stationarity' evidence is qualitative — a t-SNE plot of the model's own features — and the paper never defines what 'stationary information' means in a measurable way. There's also a citation error: the paper cites 'Ren et al. 2024' for Informer, but the reference is about camera-shake deblurring.\n\nNone of this is fatal to the underlying idea. The architecture is coherent and the ablations are the right kind of evidence. But as written, the paper overstates its results and under-reports its setup. It is a serious engineering contribution that deserves a careful referee, provided the authors are asked to fix the reporting: release code, add error bars, include the missing baselines, and correct the claimed improvements.\n\nI would not cite it in its current form, but I'd read a revised version.\n\nRecommendation: send to peer review, but expect major revisions.","headline":"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.","tokens_in":17470,"tokens_out":2515,"would_cite":false,"duration_ms":23598,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["multivariate time series forecasting","frequency domain analysis","amplitude-phase decomposition","stationary information","Kolmogorov-Arnold Network","long-term forecasting","zero-shot forecasting","few-shot forecasting"],"falsifier":"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.","tokens_in":16441,"feed_emoji":"📈","tokens_out":9905,"duration_ms":94257,"temperature":0.7,"pith_summary":"This paper is trying to establish that frequency-domain forecasters fail on non-stationary multivariate series because they treat amplitude and phase as one complex quantity, preventing the model from separating how large a frequency is from when it occurs. It proposes APRNet, which decouples Fourier components into amplitude and phase, models local correlations between them with a KAN-based spline module, and reconstructs the signal before decoding. If the claim holds, a small architectural change in the frequency domain can improve forecasts across horizons and datasets, including transfer settings where the model never sees the target series. The paper reports average MSE reductions of 4.2% on Electricity and 13.95% on the ETTh2-to-ETTm2 zero-shot transfer relative to prior results.","feed_headline":"APRNet beats time-series forecasters by splitting amplitude and phase","feed_subtitle":"Modeling the size and timing of wave components separately cuts forecast error on electricity, weather, and transfer benchmarks.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the Kolmogorov-Arnold Network B-spline functions that the KLC module uses to fit local amplitude-phase correlations.","marker":"Liu et al. 2025"},{"why":"Provides Reversible Instance Normalization, the normalization wrapper that handles distribution shift before and after frequency modeling.","marker":"Kim et al. 2021"},{"why":"TimeMixer++ is the primary state-of-the-art comparison and the efficiency baseline that APRNet claims to beat.","marker":"Wang et al. 2025b"},{"why":"FEDformer is the frequency-enhanced transformer baseline that motivates the frequency-domain approach and serves as a comparison on long-term tasks.","marker":"Zhou et al. 2022"},{"why":"DLinear is the decomposition-based locally stationary baseline that APRNet compares against on long-term and zero-shot tasks.","marker":"Zeng et al. 2023"},{"why":"Autoformer supplies the Weather, Electricity, and Traffic benchmark datasets and acts as a long-term forecasting baseline.","marker":"Wu et al. 2021"}],"fun_headline_variants":["APRNet splits amplitude and phase to reveal stationarity","Decoupling wave components in frequency domain improves forecasts","APRNet uses KAN local correlation to capture time-varying patterns","Amplitude-phase separation beats state-of-the-art forecasters"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["APRNet splits amplitude and phase to reveal stationarity","Decoupling wave components in frequency domain improves forecasts","APRNet uses KAN local correlation to capture time-varying patterns","Amplitude-phase separation beats state-of-the-art forecasters"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000223,"raw_usage":{"total_tokens":1416,"prompt_tokens":861,"completion_tokens":555,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":477,"completion_tokens_details":{"reasoning_tokens":487}},"tokens_in":477,"tokens_out":555,"duration_ms":5929,"temperature":1.0,"reasoning_tokens":487,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:31:43.798616+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}