{"id":"54ad0f5e-a083-421d-bf26-fb6c6593bba6","arxiv_id":"2507.12803","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"FLDmamba combines a learnable Fourier filter on Mamba's step size with a damped-sinusoid output layer and reports superior long-term forecasting accuracy on standard benchmarks.","lead":"FLDmamba is a new neural network for long-term time series forecasting that blends Mamba with Fourier and Laplace-inspired modules. It claims state-of-the-art results on nine benchmark datasets, but the Laplace part is mostly a learned damped-cosine layer rather than a true transform.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The SOTA claim rests on quoted baseline numbers that conflict with the stated tuning protocol; without re-running baselines under identical settings, the 60/72 win count is unverified.","rationale":"The reader's weakest assumption correctly identifies the load-bearing point: the central claim is empirical SOTA, and Table I is the sole quantitative support. The paper provides a code URL and ablations, which is real evidence, but the quoted-baseline protocol is the hinge. The internal contradiction between tuning hidden sizes and quoting published results is concrete and checkable, and it directly affects the 60/72 count. The inverse Laplace transform concern is real but secondary: even if the ILT module is a parameterized damped-cosine layer rather than a true inverse Laplace transform, the empirical superiority claim could still hold if the comparison were fair. That is why the baseline protocol, not the mathematical naming, is the most load-bearing uncertainty. The proposed check re-runs the key baselines under identical conditions and recomputes the win count; it settles whether the SOTA claim survives. Therefore the reader's CONDITIONAL verdict stands, and no change is needed.","tokens_in":21838,"tokens_out":3983,"duration_ms":47701,"concrete_test":"Re-run all Table I baselines using the official public implementations and the same data splits, lookback/horizon, normalization, GPU, and evaluation script as FLDmamba, with at least three seeds; then recompute the win count and report mean±std. Specifically, compare S-Mamba, iTransformer, RLinear, and PatchTST at both their published settings and hidden size 1024. If the corrected win count falls below 50%, or if FLDmamba's advantage over S-Mamba is within one standard deviation on ETTm1/ETTm2, the SOTA claim should be downgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV-A states that hidden dimensionality of all compared algorithms was tuned within [128, 256, 512, 1024, 2048] and that all baseline methods were evaluated using their predefined settings, while Table I's caption says all baseline results are obtained from [20] and [30]. These statements are mutually inconsistent: quoted numbers cannot reflect a hidden-size sweep, and a fair comparison requires identical data splits, lookback/horizon, normalization, seeds, and evaluation code. Since the headline claim is \"60 out of 72 (83.3%) SOTA\", the comparison table is the load-bearing evidence. If S-Mamba, iTransformer, RLinear, PatchTST, and other baselines are re-run at hidden size 1024 or at their original settings with the authors' own evaluation script, the win count could change materially; for instance, several FLDmamba margins in ETTm1/ETTm2 are within 0.005 MSE of S-Mamba, below typical seed noise. The absence of error bars further means the claimed majority could be within noise. This does not disprove the architecture, but it makes the SOTA assertion unsupported as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes FLDmamba, a state-space model for long-term multivariate time series forecasting. The architecture combines three ideas: an RBF kernel for input smoothing; a Fourier-filtered discretization step inside a 'FMamba' layer; and an 'inverse Laplace transform' output head that parameterizes a sum of damped cosines. The authors report MSE/MAE on nine benchmark datasets and claim state-of-the-art performance in 60 of 72 cases (83.3%) against 12 Transformer-, MLP-, and SSM-based baselines, along with ablations, robustness tests, efficiency measurements, and hyperparameter studies. Code and data are promised via a GitHub URL.","tokens_in":22080,"tokens_out":6775,"duration_ms":68083,"significance":"If the empirical claims survive a properly controlled comparison, the paper would contribute a competitive and efficient Mamba-based forecasting architecture, and the release of code/data would aid reproducibility. The main strengths are the breadth of benchmarks, the complexity analysis showing linear-time scaling, and the explicit ablation of each component. However, the significance is currently limited by two issues: the 'inverse Laplace transform' is not a mathematical inversion (coefficients are learned), and the headline SOTA claim relies on quoted baseline numbers under an inconsistent tuning protocol without error bars. These are fixable but require substantial revision rather than minor edits.","major_comments":[{"comment":"The claimed ILT derivation is not an inversion. Eq. (8) presents Ŷ(t)=Σ A_n e^{-σ_n t} cos(ω_n t+φ_n), which is the form a true inverse Laplace transform would take for first-order poles; however, the authors then state that A_n, σ_n, ω_n, and φ_n are 'directly parameterized as learnable functions of Y(t) from the previous layer.' No constraint links these parameters to the residues β_n and poles μ_n of the Laplace-domain signal, so the module is a learned parametric basis expansion, not the inverse Laplace transform. Consequently, the paper's claim that Laplace analysis enables transient-dynamics capture is not established by the derivation; the 'w/o ILT' ablation demonstrates only that the damped-cosine head helps, not that an ILT is being performed. Please either derive an actual inversion or rename and justify the module as a Laplace-motivated head.","section":"Section III-B5, Eq. (8)"},{"comment":"The comparison protocol is internally inconsistent. Section IV-A states that 'we modify the hidden dimensionality of all compared algorithms within [128, 256, 512, 1024, 2048] to achieve their reported best performance, which is consistently observed at 1024,' while the Table I caption says 'All baseline results are obtained from [20] and [30].' Numbers quoted from prior papers cannot reflect the authors' hidden-size sweep. Additionally, Section II declares Moirai ([30]) 'out-of-scope for our baselines,' yet Table I credits [30] as a source. Because the 60/72 SOTA claim is the paper's central empirical contribution, the authors must rerun all baselines under the same data splits, lookback/horizon, normalization, and seeds (or clearly state the results are quoted and justify comparability).","section":"Section IV-A and Table I caption"},{"comment":"No uncertainty quantification is provided for any table or figure. Many of FLDmamba's reported advantages are small (e.g., ETTm1-96 MSE 0.318 vs S-Mamba 0.333; ETTm2-96 MSE 0.173 vs 0.179; Electricity-336 MSE 0.182 vs S-Mamba 0.176; Electricity average 0.170 vs 0.170). Absent error bars or a significance test, the claim that FLDmamba wins 60/72 cases could reflect seed noise. Please report mean±std over multiple runs and state whether differences are statistically significant.","section":"Tables I and III; Figures 4-10"}],"minor_comments":[{"comment":"The paragraph preceding Figure 6 contains a long run of corrupted unicode sequences ('/uni0000001c/uni00000019/...') that makes the text unreadable; please repair the encoding.","section":"Section IV-E"},{"comment":"Algorithm 1 declares the output as Ŷ ∈ (B,L,V), but the problem statement in Section III-A defines predictions as (B,H,V) with horizon H; clarify how the ILT head maps to H time steps.","section":"Algorithm 1 and Section III-A"},{"comment":"The baseline taxonomy is inaccurate: DLinear is a linear/MLP model, not a Transformer-based method, and TimesNet is a 2D-variation CNN, not an MLP-based model.","section":"Section IV-A"},{"comment":"The text uses ξ_n for the decay parameter while Eq. (8) uses σ_n; standardize the notation.","section":"Section III-B5"},{"comment":"The statement that FLDmamba has '2.1× higher noise tolerance than iTransformer' is not defined; specify the metric and computation.","section":"Section IV-D"},{"comment":"Training time units (seconds per epoch?) and memory sizes are not stated in the figure or text; please specify.","section":"Section IV-G and Figure 9"},{"comment":"The sentence 'FLDmamba achieves state-of-the-art (SOTA) performance on of tasks' is incomplete; please correct to 'on the majority of tasks' or similar.","section":"Introduction, Contributions"}],"recommendation":"major_revision","confidential_remarks":"The two load-bearing issues are the baseline provenance and the ILT overclaim. If the authors cannot rerun the baselines, the SOTA claim should be downgraded to 'competitive with published numbers' and the ILT module should be renamed. The manuscript also needs substantial editorial cleanup (corrupted text, taxonomy errors, typos). I see no grounds for rejection if these are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: FLDmamba is a Mamba variant for long-term time series forecasting that puts a learnable FFT filter on Mamba's step-size parameter and finishes with a damped-cosine output layer. That combination is new relative to the cited baselines, and the paper ships code and data links, which is a real plus. If the results hold, it is a practical accuracy improvement for energy and traffic forecasting, not a new capability.\n\nWhat it does well: the FMM block (parallel FMamba and Mamba with residual summing) is a clean design, the RBF smoothing is a sensible preprocessing step, and the ablations show each component pulling its weight. The case studies and efficiency plots are standard but not sloppy. The method section is detailed enough to reimplement.\n\nNow the soft spots, in order of severity. The headline claim is 60/72 wins, but the benchmark protocol is internally contradictory. Section IV-A says they tuned the hidden dimensionality of all algorithms in [128, 256, 512, 1024, 2048] and found the best consistently at 1024. Two sentences later it says all baselines used their predefined settings from their publications. Table I's caption says all baseline results are obtained from S-Mamba and Moirai. You cannot both tune baselines and quote them. If the numbers are quoted, the tuning sentence is false; if they were tuned, the quoted numbers are stale. Either way, the 60/72 count is unsupported. Several FLDmamba margins over S-Mamba are below 0.005 MSE in ETTm1/ETTm2, which is within seed noise, and there are no error bars. This is the load-bearing flaw.\n\nThe ILT module is a second, smaller issue. The paper says \"we derive\" Eq. (8) from stipulating first-order singularities, then immediately says the coefficients are directly parameterized as learnable functions. That is fine as a parametric output layer, but calling it an inverse Laplace transform overstates the mathematics. It is a damped-cosine basis with learned coefficients. The ablation shows it helps, but the mechanism is fitting, not inversion.\n\nMinor: some earlier frequency-enhanced Mamba work is not cited, and the blanket claim that Mamba cannot capture multi-scale periodicity is too strong. There are also obvious PDF text-extraction artifacts in the manuscript, but I do not count those against the science.\n\nWho is this for? Researchers working on SSM-based forecasting will get a useful architectural idea, and the paper is a good case study for a reading group on benchmarking pitfalls. It deserves a serious referee: the idea is plausible, the code is promised, and the flaws are correctable. I would recommend major revision with a demand for a consistent baseline protocol, re-run numbers, and error bars, plus a rename or honest reframing of the ILT module.","headline":"A plausible incremental architecture for Mamba-based forecasting, but the SOTA claim rests on a contradictory benchmark protocol and needs a re-run before it is taken seriously.","tokens_in":22597,"tokens_out":3157,"would_cite":true,"duration_ms":34177,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"FLDmamba claims that adding Fourier-filtered step sizes and an inverse Laplace output layer to Mamba captures multi-scale periodicity, transient dynamics, and noise robustness, yielding state-of-the-art long-term time series forecasting…","keywords":["time series forecasting","Mamba","state space models","Fourier transform","Laplace transform","long-term prediction","noise robustness"],"falsifier":"Re-run the 12 baselines under the paper's own protocol (lookback windows of 96/192/336/720, hidden sizes searched over {128,...,2048}, same learning rate schedule) and compare against FLDmamba on the same nine datasets; if the win rate drops below the reported 60 of 72, the claim fails. Alternatively, train FLDmamba with the Fourier filter disabled but every other component intact: if the performance gap does not widen as claimed, the filter mechanism is not doing the work.","tokens_in":21674,"feed_emoji":"📈","tokens_out":6526,"duration_ms":61999,"temperature":0.7,"pith_summary":"FLDmamba claims that Mamba-based time-series forecasting can be made state-of-the-art by adding two transform stages: a Fourier filter that cleans and separates multi-scale periodic patterns from noise, and an inverse Laplace output layer that represents predictions as damped oscillations, capturing both transient fluctuations and long-term cycles. The paper reports that this design outperforms 12 Transformer-, MLP-, and Mamba-based baselines on 60 of 72 (83.3%) task/dataset combinations across nine real-world benchmarks, while preserving Mamba's linear-time complexity. The practical stake is that long-term forecasting could get both higher accuracy and better efficiency than current attention-based models, and better robustness to noisy data.","feed_headline":"Mamba with Fourier-Laplace transforms wins 60 of 72 forecast tasks","feed_subtitle":"The new architecture captures multi-scale cycles and short-term transients while resisting noisy data, at Mamba-class cost.","key_machinery":"The load-bearing object is the FMamba-Mamba (FMM) block with a Fourier-filtered step size. In standard Mamba, the input-dependent step size $\\Delta$ gates information flow through the hidden state; FLDmamba computes $\\Delta_F$ by taking the FFT of $\\Delta$, multiplying by a learnable kernel $\\widetilde{W}$, and applying the inverse FFT, then uses $\\Delta_F$ to discretize the state matrices $\\bar{A}_F$ and $\\bar{B}_F$. The other load-bearing object is the inverse Laplace transform output layer, which writes the prediction as a sum of damped cosines $A_n e^{-\\sigma_n t}\\cos(\\omega_n t + \\varphi_n)$, directly representing both transient and periodic structure. An RBF kernel smooths the input before both encoders, and the two encoders run in parallel with their outputs summed, in a residual-block style.","core_discovery":"The paper's central claim is that FLDmamba, by filtering the selective state-space step size $\\Delta$ through the Fourier transform and by decoding through an inverse Laplace transform, overcomes three known weaknesses of Mamba for time-series: it captures multi-scale periodicity, it models transient dynamics, and it resists data noise. Concretely, the Fourier-filtered step size $\\Delta_F$ replaces the raw $\\Delta$ when discretizing the state matrices $\\bar{A}_F$ and $\\bar{B}_F$, so the selective state space only propagates frequency components that a learnable kernel marks as relevant. The output layer then parameterizes the forecast as $\\hat{Y}(t) = \\sum M_n A_n e^{-\\sigma_n t}\\cos(\\omega_n t + \\varphi_n)$, whose cosine factors encode periodicity and whose exponential factors encode transient decay. The paper further claims that the RBF kernel contributes noise robustness and that the parallel FMamba-Mamba block keeps the overall complexity at $O(BLVN)$.","pith_inferences":["The paper does not analyze which frequency bands the learned Fourier kernel actually selects; visualizing $\\widetilde{W}$ per dataset would reveal whether the gain comes mainly from denoising or from periodicity extraction.","The damped-cosine decoder is reminiscent of exponential-sinusoidal decomposition, and a natural extension the authors do not explore is to impose sparsity on the number of terms or to allow the decay rates to vary over time.","Because the baseline numbers are quoted from other papers, the decisive external test is a from-scratch re-implementation of all baselines under the identical protocol; until that is done, the 60-of-72 claim should be read as conditional on those quoted numbers."],"forward_implications":["Existing Mamba-based forecasters can adopt the Fourier-filtered step size and the inverse Laplace output layer without changing asymptotic running time, since both additions cost at most $O(BLN\\log L)$.","FLDmamba could serve as a drop-in replacement for Transformer-based long-term forecasters in settings where quadratic attention cost is a bottleneck, if the reported win rate holds up.","The reported noise-robustness advantage suggests that deployment on noisy sensor streams could see smaller forecast degradation under data corruption.","The damped-cosine output representation gives an interpretable decomposition of a forecast into periodic cycles and decaying transients, which could aid post-hoc analysis."],"supporting_citations":[{"why":"The Mamba state-space backbone that FLDmamba modifies.","marker":"[19]"},{"why":"The main Mamba-based baseline and the source of many baseline results quoted in Table I.","marker":"[20]"},{"why":"The iTransformer baseline whose tokenization limitation motivates the frequency-domain design.","marker":"[16]"},{"why":"Prior frequency-enhanced Transformer that motivates using Fourier analysis for periodicity.","marker":"[28]"},{"why":"Provides the ETT datasets used across the evaluation.","marker":"[21]"},{"why":"Source of baseline results for comparison in Table I.","marker":"[30]"},{"why":"Source of the real-world benchmark datasets used in the experiments.","marker":"[35]"},{"why":"The residual connection idea behind the FMM block's parallel summation.","marker":"[33]"}],"fun_headline_variants":["Fourier and Laplace steer Mamba's step size for better forecasts","Mamba with frequency-filtered step size wins 60 of 72 forecast tasks","Cycle-aware Mamba: Fourier and Laplace improve time series accuracy","Laplace decay plus Fourier cycles: Mamba outperforms on 72 tasks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The state-of-the-art claim depends on the baseline numbers taken from S-Mamba and Moirai papers being comparable to FLDmamba's own runs; if those baselines were tuned or evaluated under a different protocol, the 60-of-72 advantage could be inflated.","fun_headline_variants_meta":{"raw":{"variants":["Fourier and Laplace steer Mamba's step size for better forecasts","Mamba with frequency-filtered step size wins 60 of 72 forecast tasks","Cycle-aware Mamba: Fourier and Laplace improve time series accuracy","Laplace decay plus Fourier cycles: Mamba outperforms on 72 tasks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000381,"raw_usage":{"total_tokens":2049,"prompt_tokens":1003,"completion_tokens":1046,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":966}},"tokens_in":619,"tokens_out":1046,"duration_ms":11406,"temperature":1.0,"reasoning_tokens":966,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:38:09.360220+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the 12 baselines under the paper's own protocol (lookback windows of 96/192/336/720, hidden sizes searched over {128,...,2048}, same learning rate schedule) and compare against FLDmamba on the same nine datasets; if the win rate drops below the reported 60 of 72, the claim fails. Alternatively, train FLDmamba with the Fourier filter disabled but every other component intact: if the performance gap does not widen as claimed, the filter mechanism is not doing the work.","supporting_citations":[{"cited_title":"Is mamba effective for time se- ries forecasting?","cited_arxiv_id":null,"evidence_quote":"The main Mamba-based baseline and the source of many baseline results quoted in Table I."},{"cited_title":"Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting,","cited_arxiv_id":null,"evidence_quote":"Prior frequency-enhanced Transformer that motivates using Fourier analysis for periodicity."},{"cited_title":"Informer: Beyond efficient transformer for long sequence time-series forecasting,","cited_arxiv_id":null,"evidence_quote":"Provides the ETT datasets used across the evaluation."},{"cited_title":"Expanding the prediction capacity in long sequence time-series forecasting,","cited_arxiv_id":null,"evidence_quote":"Source of the real-world benchmark datasets used in the experiments."}],"review_version":1}