{"id":"94dae976-d14c-499e-95b5-01da32116ffe","arxiv_id":"2411.17770","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"MTS-UNMixers forecasts multivariate time series by decomposing data into shared time and channel components with Mamba networks, and reports improved benchmark accuracy.","lead":"This paper introduces MTS-UNMixers, a neural network that forecasts several related time series at once by separating them into shared patterns over time and across channels. It reports accuracy gains over ten existing models on standard electricity, traffic, weather, and power transformer datasets.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table I's first-place tally is internally inconsistent (MTS-UNMixers 23 vs claimed 56; TimeXer 33) and omits the closest baseline MTS-Mixers, so the 'significantly outperform' claim lacks a reliable empirical basis.","rationale":"I read the paper as an empirical architecture paper whose central claim is state-of-the-art forecasting accuracy. The reader's weakest_assumption focuses on the stationarity of the shared decomposition (At and Sc) between history and future. That is a valid scientific concern about the model's interpretability and inductive bias, but it is not the most load-bearing issue for the central claim. The most load-bearing issue is the validity of the empirical comparison: Table I is internally inconsistent (the '1st Count' row sums to more than 56 and contradicts the text's '56 cases'), and the table omits the direct predecessor MTS-Mixers and the strong baseline iTransformer. If the comparison is unreliable, the 'significantly outperform' claim is unsupported no matter how elegant the unmixing formulation is. The stationarity concern could be tested by comparing prediction quality under distribution shift, but even if it fails, the model might still be empirically strong. I therefore agree with the reader's conditional verdict but for a different primary reason. I give credit for the provided code, the ablation study in Table II, and the varying-lookback experiments in Table III, which show the model is internally consistent and that longer history helps; however, those do not repair the external validity of Table I. The concrete test above would settle whether the headline performance claim survives contact with the data.","tokens_in":19916,"tokens_out":4756,"duration_ms":40051,"concrete_test":"Recompute Table I from the reported MSE/MAE values: for each dataset and horizon, determine which model is bold (first) and underlined (second), and compare the per-model first-place counts with the '1st Count' row and the text's '56 cases' claim. Separately, run MTS-Mixers and iTransformer under the same protocol (input length 96, horizons 96/192/336/720) and add them to the table. If the counts cannot be reconciled, or if either omitted baseline achieves lower MSE on any horizon, the 'significantly outperform' claim must be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that MTS-UNMixers 'significantly outperform[s] existing methods' on benchmark datasets. The sole quantitative support is Table I. That table contains an impossible '1st Count' row: MTS-UNMixers is credited with 23 first places, TimeXer with 33, and other models with additional firsts, while the text states the model 'ranked first in 56 cases' and 'consistently ranks within the top two in all scenarios.' Since Table I has 7 datasets × 4 horizons × 2 metrics = 56 cells, the reported counts cannot all be first-place cells. Either the bold/underline formatting is wrong or the count row is wrong, so the reader cannot determine which model actually wins. The comparison also omits MTS-Mixers (the direct predecessor, cited as [12]) and iTransformer (cited as [11]), despite the method being an explicit extension of MTS-Mixers with Mamba; the 'Comparison Methods' paragraph says nine models but lists ten. No error bars, seeds, or training details are given. These issues make the headline performance advantage unverifiable. The shared-basis stationarity assumption is a real concern, but it is secondary: even if that inductive bias were false, the architecture could still be empirically competitive, whereas if the comparison table is invalid, the central claim fails regardless.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes MTS-UNMixers, a multivariate time series forecasting architecture that decomposes the input into temporal basis signals and channel coefficient matrices, and also into channel basis signals and temporal coefficient matrices. The historical and future windows are treated as a unified sequence that shares the temporal basis matrix At and the channel coefficient matrix Sc. A vanilla Mamba network estimates the time-dependent coefficients, while a bidirectional Mamba network estimates the channel-correlated bases. The authors claim that this dual unmixing plus sharing mechanism provides an explicit, physically interpretable mapping between history and future, and that it significantly outperforms existing methods on seven benchmark datasets (ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, Electricity) across four prediction horizons.","tokens_in":20239,"tokens_out":6446,"duration_ms":55033,"significance":"If the empirical claims were fully supported, the paper would make a useful contribution: it combines a relatively interpretable matrix-factorization view of time series with modern Mamba-based sequence models, and it includes an ablation study, a lookback-window analysis, and an efficiency comparison. The code is also made publicly available. However, the central claim of state-of-the-art or near-state-of-the-art performance currently rests on a single comparison table whose internal numbers are inconsistent, and the table omits the most directly relevant baselines. The shared-basis stationarity assumption is also a genuine conceptual risk, but it is secondary to the empirical verification problem. With corrected and completed experiments, the approach could merit publication; in its current form the evidence is not sufficient to support the headline claims.","major_comments":[{"comment":"The '1st Count' row in Table I is internally inconsistent. The table has 7 datasets x 4 horizons x 2 metrics = 56 cells, and the text states that MTS-UNMixers 'ranked first in 56 cases.' Yet the printed row gives 23 and 33 for MTS-UNMixers (which sums to 56 if read per metric), while also crediting TimeXer with 9 and 3, TimeMixer with 3, and DLinear with 1, for a total of 72 claimed first places. If the row is instead read as per-model totals, the sum is 23+33+9+3+3+1 = 72. Either way, the count cannot be correct, and the reader cannot determine which model actually wins which cells. This makes the headline performance advantage unverifiable.","section":"§V-B-b, Table I"},{"comment":"The comparison omits MTS-Mixers [12], the direct predecessor that this work explicitly extends, and iTransformer [11], a strong transformer baseline cited in the introduction. The 'Comparison Methods' paragraph says nine models but then enumerates ten (PatchTST, FEDformer, Autoformer, Stationary Transformer, TimeXer, DLinear, FITS, TiDE, TimesNet, TimeMixer). Without MTS-Mixers and iTransformer, the claim that MTS-UNMixers 'significantly outperform[s] existing methods' is not supported against the most relevant alternatives, and the discrepancy between 'nine' and ten listed models further undermines confidence in the comparison.","section":"§V-B-a, Table I"},{"comment":"No error bars, number of seeds, or statistical significance tests are reported anywhere in the experimental section. The word 'significantly' in the Abstract and Section V-B-b is not backed by any variance estimate or test. Please report at least mean and standard deviation over multiple seeds for the key comparisons, and, where possible, paired significance tests for the differences against the strongest baselines.","section":"§V-B, Table I and §V-C, Table II"},{"comment":"The sharing of At and Sc across historical and future windows is imposed by construction, not validated. If the latent mixing structure drifts between the observed and forecast windows, the shared-component constraint becomes a bias rather than a benefit. Because the network learns all factors from data, this sharing is an inductive bias, not a verified property of the data. Please add an experiment that relaxes the sharing (for example, separate basis/coefficient matrices for reconstruction and prediction) or otherwise measures the drift of the learned bases and coefficients across windows.","section":"§IV-C, Eqs. (7)-(9)"},{"comment":"The optimization problem in Eq. (11) imposes sum-to-one and non-negativity constraints on the coefficient matrices, but the network implementation only applies softmax to Sc, St, and Sp, while At, Ac, and Ap remain unconstrained, and the loss in Eq. (21) contains no constraint penalties. Please clarify how the constraints from Eqs. (3)-(6) are enforced in the implementation, or revise the formulation, because the paper's 'physical interpretability' claim depends on these constraints.","section":"§III-B-c and §IV-D"}],"minor_comments":[{"comment":"The section heading reads 'EXPERIMENT RESLUTS' and should be 'EXPERIMENT RESULTS'.","section":"§V heading"},{"comment":"The sentence 'we compared the proposed MTS-UNMixers with nine well-established and advanced models' is followed by a list of ten models; please correct the count.","section":"§V-B-a"},{"comment":"The model efficiency paragraph says the ranking is based on 'Informer, Autoformer, FEDformer, PatchTST, TimesNet, TimeXer, and our proposed MTS-UNMixers, totaling six models,' but seven models are listed.","section":"§V-E"},{"comment":"In the bidirectional Mamba equations, the symbol X is used both for the original historical sequence and for its linearly transformed version; please use distinct notation to avoid ambiguity.","section":"§IV-B-b"},{"comment":"Figure 2 contains a '???????' placeholder near the top, which should be replaced with the actual label or removed before publication.","section":"Fig. 2"},{"comment":"The captions contain typos: 'Infomer' should be 'Informer' and 'Transfomer' should be 'Transformer'.","section":"Fig. 6"},{"comment":"The phrase 'visualized in Figure 3' in the model efficiency analysis should refer to Figure 8, not Figure 3.","section":"§V-D"},{"comment":"The rows labeled 'A VG.' should be 'Avg.' for consistency with the other rows.","section":"Table I"}],"recommendation":"major_revision","confidential_remarks":"The paper is framed as an extension of MTS-Mixers, yet the closest baseline is absent from Table I and the comparison list itself is inconsistent (nine versus ten models). The '1st Count' row suggests the results table may have been assembled without careful verification. I would ask the authors to re-run or re-check all numbers, include the missing baselines, and add repeated-seed statistics before the paper can be considered for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the architecture is a legitimate, incremental extension of MTS-Mixers, swapping MLP mixing for vanilla and bidirectional Mamba and sharing bases/coefficients across history and future. That specific combination is new in the cited literature, and the ablations in Table II show both paths contribute. But the central empirical claim is currently unverifiable. Table I has an impossible '1st Count' row: 23 firsts for MTS-UNMixers plus 33 for TimeXer already accounts for all 56 cells, yet other models are also credited with firsts. The text says the model ranked first in 56 cases, which cannot be true given the row. The direct predecessor MTS-Mixers is missing from the comparison, iTransformer is cited but not compared, and there are no error bars or seeds. The 'nine baselines' paragraph lists ten models. Those are fixable, but they block any conclusion about 'significantly outperform.'\n\nThe modeling idea is worth engaging. Treating history and future as one sequence with shared temporal bases A_t and shared channel coefficients S_c is a clean inductive bias. The paper doesn't test whether those components actually stay stationary across the gap, so the 'physical interpretability' claim is stronger than the evidence. That's a secondary issue though: even if the shared-component assumption drifts, the architecture could still be empirically competitive.\n\nThe ablation study is the most useful part. Removing temporal unmixing hurts a lot, removing channel unmixing hurts less, and the Mamba versus Bi-Mamba comparison shows complementary roles. Those results are informative even if the headline numbers are shaky.\n\nWho this is for: someone working on Mamba-based forecasting or decomposable time series models. The paper ships code, a clear framework, and a testable hypothesis about shared components. It deserves a serious referee, but the referee will need the authors to fix the table, add MTS-Mixers and iTransformer, and report seeds and error bars before the accuracy gains can be trusted. Send it to review with a request for major revision.","headline":"A reasonable Mamba-based extension of MTS-Mixers, but the headline accuracy claims are unverifiable until Table I is fixed and the direct predecessor baselines are added.","tokens_in":20800,"tokens_out":2248,"would_cite":false,"duration_ms":20508,"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 treating history and future as one unmixed sequence with shared time bases and channel coefficients outperforms nine baselines in long-term multivariate forecasting.","keywords":["multivariate time series forecasting","unmixing","Mamba","bidirectional Mamba","state space models","shared components","long-term forecasting","channel-time decomposition"],"falsifier":"Train MTS-UNMixers on an early segment of a dataset and evaluate on a later segment whose channel correlations are known to shift, such as electricity demand before and after a structural change; if a version with separate history and future components matches or beats the shared-component version, then the shared-component invariance, not the unmixing itself, is carrying the reported gains.","tokens_in":19707,"feed_emoji":"📈","tokens_out":8936,"duration_ms":73873,"temperature":0.7,"pith_summary":"Multivariate time series are hard to forecast because trends, cycles, and inter-variable correlations arrive mixed together, and because standard models map history to future without an explicit account of which parts carry over. This paper argues that both problems are solved by decomposing the entire series along two axes at once: time is a mixture of a few shared trend and cycle basis signals, and channels are a mixture of a few shared correlation bases that persist across the whole series. The proposed MTS-UNMixers learns these shared components with a causal Mamba encoder for time and a bidirectional Mamba encoder for channels, then reconstructs the past and predicts the future by recombining the same parts. On the ETT, Weather, Traffic, and Electricity benchmarks it reports top-two performance in every scenario and first place in 56 cases, with ablations showing the time unmixing module contributes the largest gain.","feed_headline":"A dual unmixing model ranks first in 56 benchmark forecast tests","feed_subtitle":"Sharing one temporal basis and one channel coefficient set between past and future lifts long-term forecast accuracy.","key_machinery":"The carrying object is the channel-time dual unmixing factorization, a pair of matrix decompositions applied to the same observed series. Along time, the data are written as $X = A_t S_t$ with $A_t$ a small set of trend and cycle basis signals; along channels, the data are written as $X = A_c S_c$ with $S_c$ a small set of tick-wise correlation bases. The key move is that $A_t$ and $S_c$ are shared between the historical and future windows, while the coefficient matrix $S_t$ and the channel basis $A_c$ are allowed to differ, so forecasting reduces to recombining components that were already extracted. A vanilla Mamba block, a linear-time selective state space model, estimates the time-dependent coefficients because time has a causal direction, and a bidirectional Mamba block estimates the channel-correlated bases because channel relations are noncausal; softmax enforces the two constraints on the coefficients, and an L1 loss trains reconstruction and prediction together.","core_discovery":"The central claim is that the historical and future windows are two views of one latent mixture, so the same temporal basis matrix $A_t$ and the same channel coefficient matrix $S_c$ can carry both reconstruction and prediction. Writing the observed series as $X = A_c S_c$ along channels and $X = A_t S_t$ along time, the future is produced as $\\hat{X} = A_t \\hat{S}_t$ and $\\hat{X} = \\hat{A}_c S_c$, with the shared components enforcing continuity of trends and of inter-variable relationships. The coefficient matrices are constrained to be non-negative and to sum to one, which the authors present as the source of physical interpretability. The paper's experiments compare this design against nine baselines on seven datasets at horizons 96, 192, 336, and 720, and report that the full model ranks first or second everywhere, that removing the time unmixing module causes the largest error increase, and that the bidirectional channel encoder matters most on the weather data.","pith_inferences":["Editorial inference: the same unmix-and-recombine decoder could be applied to other sequence tasks such as missing-value imputation and anomaly detection, because those tasks also need a shared representation that can regenerate an observed window.","Editorial inference: if the shared temporal basis is truly invariant, forecasting error should increase smoothly as the forecast window moves further from the training region, and a reader could test this by using the trained $A_t$ to decode windows far beyond the longest horizon evaluated.","Editorial inference: the strict sharing of $S_c$ is a strong prior, and a natural stress test is to allow the channel coefficient matrix to drift slowly with time and check whether accuracy improves on datasets whose channel correlations change between training and test periods."],"forward_implications":["Forecast horizons can be extended by recombining the same shared bases with new coefficients, so the model does not need to learn a separate decoder for each prediction length.","The shared components give a concrete inspection point: the learned trend and cycle bases and the per-channel loadings are directly readable as the model's explanation of what carries over from past to future.","Because the forecast is built from components observed in history, the model is structurally prevented from inventing channel relationships that never appeared in the training window.","The ablation results point to time unmixing as the dominant source of accuracy, so improvements to the temporal basis estimation should yield larger gains than further channel modeling.","If the shared-component design generalizes, the same reconstruction-and-prediction decoder can be applied to any horizon on all four benchmark families without retraining the encoder."],"supporting_citations":[{"why":"Supplies the causal selective state-space encoder used to estimate the shared time-dependent coefficients.","marker":"[24]"},{"why":"Earlier factorized temporal and channel mixing model whose shared-component idea this paper extends with an explicit mapping.","marker":"[12]"},{"why":"TimeMixer is the decomposable multiscale mixing baseline that MTS-UNMixers most often beats and is compared against directly.","marker":"[10]"},{"why":"PatchTST is the patch-based Transformer baseline that anchors the channel-independence comparison.","marker":"[13]"},{"why":"TimesNet supplies the benchmark protocol, including prediction horizons 96, 192, 336, and 720, and is a CNN baseline.","marker":"[20]"},{"why":"TimeXer is the cross-variable attention model that outperforms MTS-UNMixers on the Traffic dataset, bounding the claim.","marker":"[29]"},{"why":"DLinear provides the linear decomposition baseline that motivates representing series as basis and coefficient mixtures.","marker":"[18]"},{"why":"FITS is the compact frequency-domain baseline used for efficiency and accuracy comparisons.","marker":"[33]"}],"fun_headline_variants":["Channel-time unmixing via Mamba improves forecast accuracy","Shared bases between past and future lift time series prediction","MTS-UNMixer decomposes series for interpretable multivariate forecasting","Dual unmixing with Mamba outperforms baselines on benchmarks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the historical and future windows share the same temporal basis signals and the same channel coefficient matrix, so the components learned from the past are still the right components for the future.","fun_headline_variants_meta":{"raw":{"variants":["Channel-time unmixing via Mamba improves forecast accuracy","Shared bases between past and future lift time series prediction","MTS-UNMixer decomposes series for interpretable multivariate forecasting","Dual unmixing with Mamba outperforms baselines on benchmarks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000327,"raw_usage":{"total_tokens":1862,"prompt_tokens":1010,"completion_tokens":852,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":626,"completion_tokens_details":{"reasoning_tokens":782}},"tokens_in":626,"tokens_out":852,"duration_ms":9078,"temperature":1.0,"reasoning_tokens":782,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:23:17.389468+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train MTS-UNMixers on an early segment of a dataset and evaluate on a later segment whose channel correlations are known to shift, such as electricity demand before and after a structural change; if a version with separate history and future components matches or beats the shared-component version, then the shared-component invariance, not the unmixing itself, is carrying the reported gains.","supporting_citations":[{"cited_title":"TimeMixer: Decompos- able Multiscale Mixing for Time Series Forecasting","cited_arxiv_id":null,"evidence_quote":"TimeMixer is the decomposable multiscale mixing baseline that MTS-UNMixers most often beats and is compared against directly."},{"cited_title":"A Time Series is Worth 64 Words: Long-term Forecasting with Transformers","cited_arxiv_id":null,"evidence_quote":"PatchTST is the patch-based Transformer baseline that anchors the channel-independence comparison."},{"cited_title":"TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis","cited_arxiv_id":null,"evidence_quote":"TimesNet supplies the benchmark protocol, including prediction horizons 96, 192, 336, and 720, and is a CNN baseline."},{"cited_title":"Are transformers effective for time series forecasting? In Proceedings of the AAAI Conference on Artificial Intelligence , volume 37, number 9, pages 11121–11128, 2023","cited_arxiv_id":null,"evidence_quote":"DLinear provides the linear decomposition baseline that motivates representing series as basis and coefficient mixtures."},{"cited_title":"FITS: Modeling Time Series with 10k Parameters","cited_arxiv_id":null,"evidence_quote":"FITS is the compact frequency-domain baseline used for efficiency and accuracy comparisons."}],"review_version":1}