Response to Reviewer bot2

Thank you for your encouraging evaluation and for the constructive suggestions. Below we address each concern in turn. Unless explicitly noted, all new results will be included in the camera-ready version and the public code release.

W1: Robustness of FFT-based Periodic Guidance

Our Periodic Guidance (PG) does not depend on a single, fixed cycle: we extract the top-k dominant frequencies per channel via an FFT power spectrum and fuse their contributions proportionally to their amplitudes . This multi-frequency design already captures moderate drift or co-existing cycles. Moreover, the meta-weight $\lambda$ learned by Meta Guidance automatically down-weights PG whenever periodic cues weaken, as confirmed by the markedly lower $\lambda$ on weak-seasonality datasets (e.g., Weather vs. HD) in Fig. 6 . Ablation on k further shows that adding or dropping secondary peaks has only a modest impact, indicating graceful behaviour even when periodicities are less regular . Together, the use of multiple FFT peaks plus adaptive blending ensures PG generalises beyond perfectly stable cycles; when periodic information becomes unreliable, NSG naturally takes the lead, preventing degradation.

W2: PatchTST & Non-stationary Transformer baselines

We conducted additional experiments by incorporating MG into PatchTST and the Non-stationary Transformer, and evaluated their performance across multiple datasets. The results are summarized below.

Across these strong baselines, MG consistently yields additional RMSE reductions of 7-23 %, confirming that our guidance layer complements both the patch trick and built-in non-stationary modelling.

Q1: Rationale for channel-independent NSG and PG

Each variable in a multivariate series often follows its own drift and cycle (e.g., temperature vs. wind speed). We therefore generate one guidance vector per channel so that (i) non-stationary level shifts and dominant periods are captured in the scale that is truly relevant to that variable, and (ii) heterogeneous units and magnitudes are not blended prematurely. Cross-channel relationships are still learned—but by the backbone's self-attention or diffusion layers, which are expressly designed for that purpose and can exploit richer, high-dimensional context than a lightweight guidance head.

To test whether this separation harms correlated variables, we conducted an additional experiment in which the MG from all channels are averaged and then applied to all channels:

Our new experiments confirm that the channel-independent MG does not impair—and in fact enhances—multivariate imputation. Keeping each variable's guidance separate lets the backbone attend to genuine inter-channel relations without conflating the distinct temporal dynamics of individual series, thereby delivering the strongest and most efficient performance.

Q2: Why single-point PG remains robust to noise

Although Eq.7 samples the central value at each previous period, PG actually weighted averages several periods before passing the signal to the backbone. This multi-period ensemble already dilutes an occasional outlier. Moreover, the meta-weight $\lambda$ is learned jointly with the backbone: if a periodic reference conflicts with nearby non-stationary neighbours, $\lambda$ shifts emphasis toward NSG, automatically down-weighting the noisy PG cue.

Dear Reviewer bot2,

Thank you very much for your thorough and insightful comments, and for recommending our paper for borderline accept. In our previous rebuttal we have already addressed every point you raised:

• PG robustness (W1): PG now blends the top-k FFT peaks per channel and is gated by $\lambda$; ablations show smooth performance even when cycles drift or weaken.

• Stronger baselines (W2): Adding MG to PatchTST and the Non-Stationary Transformer lowers error on every benchmark.

• Channel-specific guidance (Q1): Per-variable NSG/PG retains each signal's own drift/period; an averaged-guidance variant performs worse, confirming the design choice.

• Noise tolerance (Q2): PG averages multiple past periods, and $\lambda$ down-weights it when periodic cues conflict with NSG, preventing noise-induced errors.

We would be happy to provide further responses. Look forward to your feedback. Thanks for your comment again!

Best regards, All Authors

Response to Reviewer sQEU

We sincerely thank you for the thoughtful, detailed review. Below we respond point-by-point, following the order of your comments. All new analyses, figures and baselines are included in the updated appendix and will be integrated into the camera-ready version.

W1: Clarifying MG's distinct contribution

Thank you for raising this point. In the methods you cite, periodicity or non-stationarity is built into the model itself: TimeCIB [1] incorporates a kernel term directly in its information-bottleneck loss, GP-VAE [2] places a Gaussian-process prior on the latent trajectory, and FGTI [3] learns separate latent variables for trend and seasonality. These method encode periodicity or non-stationarity as integral parts of the model architecture or training objective, rather than as detachable inductive hints.

By contrast, Meta Guidance remains entirely external to the backbone. Our non-stationary and periodic maps are delivered only as lightweight guidences, and a learnable gate $\lambda$ lets the model decide how much to trust each guidence. Nothing in the backbone or loss is changed, so MG acts as a detachable inductive bias that can be plugged into CIB, GP-VAE, FGTI, or almost any other deep-learning imputer. In the revised experiments we include these methods as baselines and show that simply adding MG to a vanilla Transformer reliably surpasses their performance.

[1] "Conditional information bottleneck approach for time series imputation.", ICLR.

[2] "Gp-vae: Deep probabilistic time series imputation.", AISTATS.

[3] "Frequency-aware generative models for multivariate time series imputation.", NeurIPS.

W2 & Q6: Additional baseline methods

We conduct additional experiments on three relevant methods [1,2,3], and the results show that our Transformer+MG approach consistently outperforms them, achieving the best overall performance. Below are the MSE results of the experiments under 10% missing rates:

Q1: Visualization of NSG and PG construction

Thank you for the suggestion. A full, step-by-step walkthrough already appears in Appendix H, accompanied by new figures that both illustrate how NSG and PG are built and show the final guidance maps after construction.

We realise this figure is easy to miss, so we will add a forward-reference from the main text in the camera-ready version.

Q2: Discussion on $\gamma$ parameters overfitting

To check whether the scaling factors $\gamma$ in Equations (3) and (8) simply memorise the training data, we ran an additional experiment. The table below reports (i) the Augmented Dickey–Fuller statistic (ADF: larger ⇒ more non-stationary) and (ii) the values learned for $\gamma$ on three representative datasets:

1. Above experimental results suggest that $\gamma^{NS}$ and $\gamma^{Per}$ effectively adapt to datasets with varying statistical properties. Specifically, for datasets with stronger non-stationarity (higher ADF test values), $\gamma^{NS}$ tends to be larger than $\gamma^{Per}$, and vice versa. This behavior aligns with expectations, further supporting the robustness of the proposed method.

2. The $\gamma$ parameter scales the original NSG and PG sequences by directly adjusting their values. However, this scaling effect is further regulated by the $\lambda$ parameter (Equation 11). As demonstrated in Figure 7 (Section 4.3), $\lambda$ dynamically adapts to different data characteristics. Moreover, additional experiments show that $\gamma$ exhibits minimal variation across different datasets, indicating that $\lambda$ remains the primary adjustment mechanism.

3. Overfitting is a common challenge in deep learning, particularly in meta-learning approaches. While limited method is entirely immune to this issue, our approach has been extensively evaluated on nine real-world datasets with diverse characteristics (Table 2, Section 4.2). These experiments demonstrate that MG exhibits strong generalization capabilities, effectively handling imputation tasks across various datasets.

Q3: Explaining when NSG and PG help

Our current results already hint at a clear pattern: datasets with pronounced level shifts (HD) gain most from the NSG, whereas those with strong seasonal peaks (Weather, Traffic) benefit chiefly from PG. As demonstrated in the ablation study in Section 4.3, the Augmented Dickey-Fuller (ADF) scores align closely with the guidance module that yields the most significant performance gain.

Q4: Time-varying missing patterns

To test MG in a setting where the gap rate itself changes over time, we injected a sinusoidally varying drop-probability:

$p(i) = 0.25 + 0.15 \cdot \sin\left(\frac{2\pi i}{T}\right)$ .

which swings the missing rate smoothly between 0.10 and 0.40. Even with this dynamically shifting pattern, MG delivers large error reductions:

The results show that MG continues to significantly improve model performance. This confirms that the Meta Guidance mechanism adapts effectively even when missingness itself follows a non-stationary, time-dependent process.

Q5: Related work positioning

We agree the current survey is too generic. Since MG is a modular component that can be integrated into most deep learning methods, our approach is most appropriately positioned in Section 2.2, line 79, under "Deep Learning-Based Imputation." In the next version, we will refine the paper's structure, including the Related Work section, to better align with the core contributions and enhance overall clarity and readability.

Q7: Down-stream predictive value of MG-imputed data

To test whether MG's gains translate into better forecasting accuracy, we trained two standard forecasters—TimesNet and iTransformer—on the Weather dataset under two input conditions:

The substantial MAE drops confirm that MG not only reduces reconstruction error but also enhances the predictive signal needed for downstream tasks.

Dear Reviewer sQEU,

Thank you very much for your thorough and insightful comments. In our previous rebuttal we have already addressed every point you raised:

• MG's contribution (W1) – clarified its plug-and-play design. NSG & PG are zero-parameter sequence gated by a learnable parameters $\lambda$.

• Extra baselines (W2 & Q6) – added TimeCIB, GP-VAE, FGTI as baseline; Transformer + MG still achieves the lowest MSE.

• Guidance visualisation (Q1) – Appendix H already contains a step-by-step NSG/PG walkthrough with new figures.

• $\gamma$ overfitting (Q2) – ADF-aligned $\gamma$ values and $\lambda$-controlled scaling confirm robustness across all datasets.

• When NSG and PG helps (Q3) – ablations plus ADF scores explain dataset-specific gains.

• Time-varying gaps (Q4) – MG still reduces Transformer error by a large margin.

• Related-work placement (Q5) – will refine Section 2.2 for clearer positioning.

• Down-stream value (Q7) – Forecasting models trained on MG-imputed series achieve noticeably lower errors than those trained on missing data, confirming MG’s practical utility.

We would be happy to provide further responses. Look forward to your feedback. Thanks for your comment again!

Best regards,

All Authors

Response to Reviewer i1nN

We sincerely thank you for the detailed and constructive feedback. Unless explicitly noted, all new results will be included in the camera-ready version and the public code release.

W1 & Q4: Missing comparisons with simple baselines

Following Q4's recommendation, we added a simple pre-processing baseline (de-trending) and an additional deep-learning baseline (Non-Stationary Transformer [1]). The experimental results are shown below, and the results show that our Transformer+MG approach consistently outperforms them, achieving the best overall performance.

[1] "Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting", NeurIPS

W2: Making r and sigma learnable

To further investigate this issue, we conducted additional experiments in which the hyperparameter r and the standard deviation of the normal distribution were treated as learnable parameters. The results are presented in the table below.

These results reinforce our decision to keep a simple fixed radius, which delivers the strongest accuracy with minimal complexity; nonetheless, the learnable options remain available in the public code for users who wish to experiment on other data regimes.

W3: Could channel-independent guidance mislead multivariate imputation?

Our design intentionally keeps NSG/PG channel-specific so that each variable receives the most relevant temporal neighbours, while the backbone (e.g., Transformer or Diffusion) still performs full cross-channel mixing through self-attention or shared latent states. To test whether this separation harms correlated variables, we conducted an additional experiment in which the MG from all channels are averaged and then applied to all channels:

Our new experiments confirm that the channel-independent MG does not impair—and in fact enhances—multivariate imputation. Keeping each variable's guidance separate lets the backbone attend to genuine inter-channel relations without conflating the distinct temporal dynamics of individual series, thereby delivering the strongest and most efficient performance.

W4: Experiments on the additional dataset

We conduct additional experiments on the PhysioNet and PM25 dataset, and the method with MG also achieve excellent results. Below are the MSE results of the experiments under different missing rates:

W5: Minor and Typos

Thank you for the detailed presentation-quality remarks.

• The anonymous code repository has been made publicly available.
• Figure 1 will be redrawn in higher resolution and consistent styling; a legend will clarify that yellow dots denote the current missing point and pink squares mark the reference points located at the same value positions (periodic neighbours).
• We will define MAE (Mean Absolute Error) and RMSE (Root Mean Square Error) on first use and note that they are the prevailing point-estimate metrics in imputation research; CRPS targets probabilistic forecasts, which are beyond our scope.
• The caption of Table 11 will state that boldface marks the best score in each column.
• For Table 8 we will clarify that each entry is the standard deviation over three independent training runs for the corresponding experiment reported in Table 10 and 11.

All of these revisions will appear in the camera-ready version.

Q1: Explanation of the "loss" in MLP

The two-layer MLP inside each guidance module does not introduce an additional, standalone loss term. Its parameters are trained end-to-end with the backbone via the same imputation objective (MSE on masked values). We follow the common meta-learning rationale: by propagating gradients only through the main task, the MLP learns the neighbour weights that best serve the ultimate imputation goal, instead of optimising a surrogate signal that may mis-align with overall error. Furthermore, for each missing entry we know the true value we must recover, but we do not know the "correct" neighbour weights that should be assigned by the MLP.

Q2: Meaning of "three independent runs"

We fully retrain each model three times under identical hyper-parameter settings but with different random seeds (affecting weight initialisation, data shuffling, and mask generation). The reported values are the mean of these three complete runs.

Q3: Do the extra MG embeddings require more training epochs?

No—models with MG are trained for exactly the same number of epochs as the original backbones and reach their optimal validation error within that schedule.

I thank the authors for answering my questions.

I still have some concerns about W1 & Q4 answer, as a simple detrending has a very close performance to MG. I believe for some tasks the overhead from MG may not be justified, and simple approches could be better.

I keep the score.

Response to Reviewer NQxZ

We sincerely thank you for the thorough and insightful review and for recommending a borderline accept. Unless explicitly noted, all new results will be included in the camera-ready version and the public code release.

W1 & L2 & L4: Broader Scope to missing pattern

In Appendix D, we have explored the missing patterns other than MCAR, includingMissing At Random (MAR) and Missing Not At Random (MNAR). To further investigate the performance of MG under time-varying missing patterns, we conduct additional experiments with a dynamically changing missing rate. Specifically, the missing probability of a data point is modeled as a time-dependent function, with the missing rate oscillating between 0.1 and 0.4 over time.

$p(i) = 0.25 + 0.15 \cdot \sin\left(\frac{2\pi i}{100}\right)$ .

We additionally conducted experiments under a consecutive missing setting. Specifically, we randomly removed continuous segments of length 10 until the overall missing rate reached 10%. The experimental results are presented below.

The results show that MG continues to significantly improve model performance, even in the presence of complex, time-varying missing patterns.

W2 & W8 & Q6: Dataset suitability for hyper-parameter study

Thank you for your suggestion. Following your advice, we conducted additional hyperparameter experiments with k on the Weather and Traffic datasets, and with r on the HD dataset. The results are as follows:

As presented in the table, the performance remains relatively stable across different values of hyperparameters $k$ and $r$, highlighting the robustness of our approach. This indicates that our method requires minimal hyperparameter tuning in real-world deployments.

W3 & Q4: Insufficient analysis of $\lambda$'s impact

In response to your suggestion, we introduced an additional variant in the ablation study (Section 4.3), denoted as "MG w\o $\lambda$", where NSG and PG are combined by directly averaging their outputs instead of using the weighting factor $\lambda$. The results, presented in the table below, show a performance drop without $\lambda$, underscoring the necessity of the weighted summation.

W4 & L5: Code repository

The anonymous code repository has been made publicly available and can be accessed through the link provided in Section 4.

W5: Context for Baselines

We recognize that readers unfamiliar with time-series imputation may need clearer baseline context; in the revision we will add a concise "baseline" table to make our contributions easier to situate.

W6 & L1: Need evaluation on synthetic data

We designed a preliminary synthetic dataset composed of a trend component and multiple periodic components, formulated as follows.

$$f(t)=0.01\ t +1.5\ \sin(0.002\,t) +2.0\ \sin\left(\frac{2\pi t}{50}+\frac{\pi}{6}\right) +1.2\ \sin\left(\frac{2\pi t}{120}+\frac{\pi}{4}\right) +0.8\ \sin\left(\frac{2\pi t}{300}+\frac{\pi}{2}\right) +\varepsilon_t \qquad \varepsilon_t\sim\mathcal{N}\left(0,\ 0.3^{2}\right)$$

We sampled 1,000 points from this signal to construct the dataset. Experimental results demonstrate that our MG module consistently improves baseline performance, even on data with manually controlled trends and periodicities. We leave a more comprehensive investigation of MG's behavior on synthetic data for future work.

W7 & L3: Missing comparisons with simple baselines

Following your suggestions in the Limitations and Suggestions section, we incorporated three additional baselines: Linear Interpolation, KNN Imputation and Seasonal Historical Averages. The experimental results are shown below. While Linear Interpolation achieves surprisingly strong performance on certain datasets, our MG module consistently outperforms all baselines, further demonstrating its effectiveness.

Q1: Similarity to Existing Solutions

Period Guidance (PG) represents a fundamental departure from existing imputation methods. Whereas conventional deep learning imputers treat seasonality as an implicit pattern to be rediscovered and re-encoded within model weights through training, PG explicitly extracts dominant periods using a lightweight FFT-based peak detection module and feeds them back as zero-parameter guidance. This "hint" can be seamlessly integrated into any backbone model and toggled on or off without retraining. To the best of our knowledge, no prior imputation method offers such detachable, plug-and-play seasonal guidance. If relevant work exists, we would sincerely appreciate the citation and will gladly acknowledge it in the final manuscript.

Q2: Why MG brings only marginal gains to TimesNet / CSDI

Although the raw differences look modest—e.g., CSDI at 0.027 vs CSDI+MG at 0.024 may only be a 0.003 improvement—this translates to an 11.1 % relative error reduction, and MG delivers an average 15.6 % improvement across all CSDI datasets. For TimesNet, its built-in FFT already captures much of the periodic signal, leaving less headroom; even so, MG still yields a notable 11.9 % boost on ETTm1. In short, the perceived "limited benefit" stems from low baseline errors, but on a percentage basis MG provides consistent, meaningful gains.

Q3: About hyperparameters $r$

The normal distribution function used to generate NSG and PG is the standard normal distribution, characterized by a mean of 0 and a variance of 1. Since 99.7% of a standard normal distribution lies within [-3, 3], setting r = 3 effectively captures nearly all informative neighbors. In practice, larger values yield no measurable improvement. Using a shared radius helps minimize the hyperparameter budget and ensures consistency across datasets.

Q4: Clarifying the wording around Lines 271-275

We agree the current phrasing is ambiguous. Line 275 was intended to summarise Table 10, which compares three groups: (i) earlier baselines (e.g., Transformer), (ii) recent advances (e.g., CSDI, SAITS), and (iii) our MG-enhanced models. Both groups (ii) and (iii) outperform the older baselines on the highly non-stationary HD dataset—but only group (iii) contains MG, so the sentence conflates two separate observations. In the camera-ready version we will replace it with:

"Table 10 shows that (a) recent architectures already reduce HD error relative to older baselines, and (b) adding MG yields a further 15-25% reduction, highlighting MG's specific contribution to non-stationarity mitigation."

This revision explicitly separates the effects of modern backbones from the additional gains brought by MG, eliminating the contradiction.

Additional Clarification about Q7 & Q8 & L5

We confirm that every wording adjustment highlighted by the reviewer will be incorporated into the camera-ready version. Moreover, all baselines in our experiments were executed with their original default hyper-parameters as released in the corresponding papers or official repositories. No extra tuning was applied, ensuring that the observed performance gains arise exclusively from the proposed Meta Guidance mechanism.

Dear Reviewer NQxZ,

Thank you very much for your thorough and insightful comments, and for recommending our paper for borderline accept. In our previous rebuttal we have already addressed every point you raised:

• Broader Scope to Missing Patterns (W1, L2, L4) – new time-varying, and consecutive-gap experiments.

• Dataset Suitability for Hyper-parameter Study (W2, W8, Q6) – additional $k$ and $r$ sweeps on Weather, Traffic, and HD showing robustness.

• Impact of $\lambda$ (W3, Q5) – new "MG w/o $\lambda$" ablation highlighting its necessity.

• Code Availability (W4, L5) – anonymous repository link now public.

• Baseline Context (W5) – concise table to be added in the revision.

• Synthetic-Data Evaluation (W6, L1) – preliminary synthetic-signal study confirming MG's gains.

• Simple Baseline Comparisons (W7, L3) – Linear, KNN, and Seasonal baselines now included.

• Clarifications (Q1-Q4) – clarified MG/PG's novelty, quantified consistent gains on strong backbones, justified rr, and fixed ambiguous wording.

We would be happy to provide further responses. Look forward to your feedback. Thanks for your comment again!

Best regards,

All Authors

Thank you for your detailed explanations and the additional experiments/results. I appreciate the time you've taken to address these points, and I apologize for my late response.

Hyper-parameter Study Observations

Regarding the top-k frequency selection method, I'm somewhat surprised by the results. Based on my understanding, I would have expected high seasonal datasets to show improvement as $k$ increases. However, this doesn't appear to be the case in your results. This makes me wonder whether:

• Top-k might not be the optimal method for selecting important frequencies, or
• I might be missing something in my interpretation of the results

Could you please provide additional clarification on this aspect?

Implementation of Simple Baselines

I was somewhat surprised that the Seasonal Historical Average baseline didn't perform better. To better understand these results, could you please explain how you implemented this baseline? Unfortunately, I'm still unable to access the Git repository (the page remains stuck on the "loading..." screen and the I have an "error" screen), which prevents me from examining the implementation details directly (if you provided it).

Presentation of Marginal Gains

If you wish to emphasize the gains achieved by your proposal, I would recommend computing the metrics using non-normalized values. This approach differs from what is typically done in most papers, but it could potentially make the improvements more apparent and impactful to readers.

At this point, I don't have any additional questions as I'm satisfied with the answers provided. However, I was interested in seeing reviewer i1nN's comments on your rebuttal.

Additionally, regarding reviewer i1nN's comment:

There is no comparison against other approaches handling [...] periodicity.

I believe they were suggesting comparisons of your Periodic Guidance (PG) component against other models that specifically address periodicity, such as:

• CycleNet [1]
• PerimidFormer [2]
• FRNet [3]

These comparisons could provide valuable context for evaluating the effectiveness of your periodicity handling approach.

[1] Lin, et al. "Cyclenet: Enhancing time series forecasting through modeling periodic patterns."

[2] Wu, et al. "Peri-midformer: Periodic pyramid transformer for time series analysis."

[3] Zhang, et al. "FRNet: Frequency-based Rotation Network for Long-term Time Series Forecasting."

Thank you for providing these additional explanations and results.

Regarding Periodicity-Specific Models

While I'm not highly familiar with FRNet, I understand that CycleNet is designed to learn the main cycles in a dataset and has a similar usage to iTransformer. Given this similarity, it seems that using CycleNet shouldn't be significantly more difficult than how you've already incorporated iTransformer.

Questions About Top-k Frequency Analysis

Let me summarize my understanding to ensure I've grasped the concept correctly:

• The frequency domain analysis identifies the importance of each top frequency for the dataset in question
• The previous table showing results with varying k (from 1 to 20) demonstrates your proposal's performance across different numbers of top frequencies included

If this understanding is correct, I notice that while there's approximately a 10% difference in importance between the top-1 and top-4 frequencies, your proposal's performance actually decreases as we consider more frequencies. This seems counterintuitive given that:

most useful periodic information is already captured by the first few peaks

However, your proposal doesn't appear to benefit from the important information provided by the second, third, and fourth peaks, even though they make significant contributions. Could you provide any interpretation or explanation for this observation?

Regarding Non-Normalized Performance

I can't access your repository, so it is difficult to judge; but usually:

1. Input data are normalized before passing it to the model
2. Normalized outputs are then obtained from the model
3. (Most papers) Calculate metrics on these normalized values (which, in my opinion, don't fully reflect real-world performance) But it is not that complicated to inverse normalized the obtained values, compare them to the actual and report metrics on these unnormalized comparisons.

I'm somewhat confused by the authors' mention of needing to retrain models for this purpose. Models like iTransformer typically include an inverse_transform function in their data_loader, it should be possible to obtain these unnormalized performance metrics without significant computational expense.

In any case, it is just a suggestion to make the performance of your proposal more visually impactful and meaningful for readers, I understand if you choose not to address this in the current phase of revision.