Dear Reviewer PB78,

Thank you very much for your valuable comments and positive support for our work. We will address your questions and concerns point by point.

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W1. More Detailed Analysis of Results

Thank you for the insightful comment. The relatively better performance of Crossformer on AQShunyi and AQWan may be attributed to its strength in jointly modeling temporal and inter-variable dependencies through attention mechanisms. In contrast, MAFS is instantiated with iTransformer in this experiment, which may have a comparatively weaker capacity to capture complex variable-wise correlations. Moreover, these two datasets exhibit strong global correlation patterns, where Crossformer's holistic modeling approach is particularly effective.

However, we would like to emphasize that MAFS is a model-agnostic framework. As demonstrated in our response to Q1, the agents in MAFS can be instantiated using different backbone models, and still lead to improved forecasting performance. We will include this clarification in our revised version to better explain the observed performance gap.

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W2. Minor Typos

Thank you for pointing this out. We have corrected the typos at line 270 (“MAS” → “MAFS”) and line 194 (“H^{L} _i” → properly formatted). We have also ensured that all decimal values in Table 1 are consistently rounded to three digits. These changes will be reflected in the revised version.

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W3. More analysis of Figure 5

Thank you for the insightful comment. We observe that the dominance of self-interaction weights reflects each agent's specialization in distinct forecasting aspects. Since each agent is assigned a decomposed task (e.g., specific variable groups or temporal patterns), it tends to rely more on its own features when making predictions. However, cross-agent interactions still play a supportive role, especially in capturing shared patterns across tasks. We will add this analysis to the revised version to clarify the observed attention distribution.

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Q1. Why was iTransformer chosen as the backbone for the agents in MAFS? Have other backbone networks been tried?

We chose iTransformer as the default backbone for MAFS because it represents a clean and standard Transformer-based architecture, without specialized designs. This makes it a suitable foundation to clearly demonstrate the benefits introduced by the MAFS multi-agent structure, without interference from model-specific enhancements.

To verify the generality of MAFS, we also integrated it with other representative backbones from different model families, including:

• PatchTST (former-based)
• TimeMixer (linear-based)
• SegRNN (RNN-based)

Across all 11 datasets, MAFS consistently outperforms their single-model counterparts, as shown below:

These results further demonstrate that MAFS acts as a general plug-and-play framework that consistently improves forecasting accuracy across diverse backbone models.

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Q2. What is the rationale behind this selection?

Thank you for the insightful question.

We select the four communication structures,graph, star, ring, and chain as representative topologies due to their diverse communication patterns and their interpretability:

• Graph: Fully connected communication offers an upper bound on information sharing.
• Star: Emphasizes centralized coordination, where a core agent integrates and disseminates information.
• Ring and chain: Represent decentralized topologies, with local or sequential message passing, mimicking diffusion-like processes.

While some performance differences exist, the variations are minor (e.g., on Weather, MSE difference between star and fully connected is under 0.01), with no sudden drops or instability observed. Overall, we recommend the star topology primarily for its balanced trade-off between performance and complexity, rather than as a sensitive hyperparameter that requires searching.

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Q3. Explanation of the Distribution-focused Agent Design

Thank you for this thoughtful question.

MAFS predict six separate statistical values (mean, standard deviation, min, max, skewness, kurtosis) to enable the agent to explicitly learn interpretable aspects of the future data distribution. This design offers several advantages:

1. Interpretability: Each predicted statistic corresponds to a distinct distributional property, making the agent's learning outcome transparent and easier to analyze.
2. Supervision efficiency: These statistics can be directly computed from ground-truth sequences, enabling effective supervised learning.
3. Modeling flexibility: Rather than assuming a specific parametric form (e.g., Gaussian), our approach allows the model to capture non-Gaussian characteristics, such as skewness or heavy tails.

While end-to-end distribution modeling (e.g., via normalizing flows or quantile regression) is an interesting alternative, our approach to strike a good balance between performance, stability, and interpretability. We appreciate your suggestion and consider distribution modeling methods an exciting direction for future exploration.

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Once again, we sincerely thank you for your valuable comments and kind support of our work. We hope that our responses have effectively addressed your concerns, and we truly appreciate your continued support.

Yours sincerely,

Authors of Paper 474

Dear Reviewer VZEb,

Thank you very much for your review and valuable insights. We will address your questions and concerns point by point.

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W1. Instability in Volatile Datasets.

Thank you for the insightful question. We would like to clarify that the observed instability is not due to a fundamental flaw of MAFS, but rather arises from specific dataset characteristics. For example, predicting 720 steps ahead on PM2.5 and Temperature data (sampled every 3 hours) equates to 90-day forecasting, which is inherently challenging for all models.

The table below further supports the stablity of MAFS, when the dataset is more reasonable, MAFS performs stably and often improves as the number of agents increases.

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W2&Q2. Efficiency Analysis

Thank you very much for raising this important point. Efficiency is also one of the core design principles of MAFS, and we deeply appreciate your attention to this aspect. Specifically:

1. Lightweight Design: The multi-agent design aims to replace a single large model with several lightweight agents collaborating, rather than stacking or ensembling heavy models. We set a much smaller hidden dimension (e.g., 16 or 32 vs. 128/256 in typical models), aiming to use multiple lightweight agents to outperform a single large model with lower cost.
2. Parallel Accleration: Unlike many LLM-based agent systems, our agents communicate in parallel using graph-based matrix operations on feature vectors, greatly improving parallel training and inference efficiency.

As shown, MAFS achieves a favorable balance of accuracy and efficiency, with only slightly higher latency than iTransformer, and far lower computational cost than Time-MoE or TimeMixer, while outperforming all in accuracy metrics.

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W3. Optimal Topology

Thank you for your valuable feedback. MAFS is not as sensitive (or instable) to communication topology. We test multiple structures, including fully connected, chain, ring, and star structure. While some performance differences exist, the variations are minor (e.g., on Weather, MSE difference is under 0.01), with no sudden drops or instability observed. Therefore, topology is not a sensitive hyperparameter that requires extensive tuning. From both efficiency and performance perspectives, we recommend the star topology as the default setting.

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W4. Theoretical Analysis

Thank you for your interest in theory. As this is an application track, we focus on pratical results in the initial version. We now provide a tighter generalization bound for MAFS under similar empirical risk.

Definition 1 (Single-model)

Let X be the input space and Y the output space. A single predictive model is defined as:

$$f_{mono}: X \to Y, \quad f_{mono} \in F_{mono},$$

where $F_{mono}$ is a high-complexity function class that captures the full modeling space.

Definition 2 (Multi-Agent Forecasting System)

The MAFS model is defined as: $\hat{Y} = AVA( Comm(\{Agent_1(X), \dots, Agent_N(X)\}; G) ),$ The overall function class is: $F_{MAFS} = AVA \circ Comm ( F_1 \times \cdots \times F_N ).$ Definition 3 (Empirical risk and function class complexity)

Given training data $(x_i, y_i)_{i=1}^n$, Empirical risk:

$\hat{L}(f) = \frac{1}{n} \sum_{i=1}^n \ell(f(x_i), y_i)$

Rademacher complexity: $R_n(F) = E_{\sigma}[ \sup_{f \in F} \frac{1}{n} \sum_{i=1}^n \sigma_i f(x_i)],$ where $\sigma_i \in \{-1, +1\}$ are Rademacher variables and $\ell(f(x), y)$ is 1-Lipschitz and bounded.

Theorem 1 (Generalization bound)

For any $\delta \in (0, 1)$, if the loss function is Lipschitz and bounded, then with probability at least $1 - \delta$: $E[\ell(f(x), y)] \leq \hat{L}(f) + 2 R_n(F) + 3 \sqrt{\frac{\log(2/\delta)}{2n}}.$ Theorem 2 (Model complexity)

Let $F_{mono}$ represent a full-capacity function class over high-dimensional inputs X. Assume each sub-model $F_i$ satisfies $R_n(F_i) \leq r$, and both Comm and AVA are L-Lipschitz. Then there exists a constant $c_0 > 0$: $R_n(F_{mono}) \geq c_0 \cdot \dim(X) > \sum_{i=1}^N R_n(F_i) + R_n(Comm) + R_n(AVA).$ Theorem 3 (Tighter generalization bound for MAFS)

As the monolithic model space $F_{mono}$ has significantly higher complexity than the modularized structure, the overall Rademacher complexity satisfies: $R_n(F_{MAFS}) \leq \sum_{i=1}^N R_n(F_i) + R_n(C) + R_n(AVA) < R_n(F_{mono}),$ which implies that, under comparable empirical risk, MAFS enjoys a tighter generalization bound and thus stronger generalization ability.

[1] Vapnik V. The nature of statistical learning theory. Springer science & business media, 2013

[2] Bartlett, P. Rademacher and Gaussian Complexities: Risk Bounds and Structural Results. Journal of Machine Learning Research, 3, 463–482, 2002.

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W5. Could multiple specialized agents lead to overfitting?

Thank you for your thoughtful question. In fact, The multi-agent design in MAFS aims to reduce overfitting. Each agent specializes in capturing distinct temporal patterns, promoting diverse representations. Importantly, during communication, agents correct biases and suppress noise, acting as implicit regularization that improves generalization.

To further support this, we conduct zero-shot experiments where MAFS consistently outperform strong single-model baselines like iTransformer and PatchTST, demonstrating its ability to avoid overfitting and effectively capture intrinsic data patterns.

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Q1. Why multiple agents are needed for TSF?

• Diverse temporal characteristics: Time series data, though domain-specific, often exhibit diverse temporal patterns (e.g., short-/long-term dynamics, seasonality, trend, etc.). MAFS assigns different agents to specialize in different scales or sub-patterns, enabling more structured and effective learning than a single model.
• Theoretical grounding: Theorem 3 (see W4) shows that model splitting leads to a tighter generalization bound, reducing overfitting risk and improving learning stability.
• Pratical superiority: By integrating strong single-model forecasters (e.g., PatchTST, TimeMixer, SegRNN) into the MAFS framework, we observe consistent performance improvements across 11 datasets. This consistent improvement indicates MAFS' better generalization across diverse temporal patterns.

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Q3. Why no consider transfer learning?

Thank you for the question. Transfer learning is indeed a valuable technique, especially in low-resource or cross-domain scenarios. It typically aims to enhance performance by leveraging external datasets, which is a complementary but orthogonal direction to MAFS.

As a supplement, we also experimented with combining MAFS and transfer learning in the form of zero-shot forecasting (see W5), and observed strong out-of-distribution generalization, demonstrating that MAFS enables stable, interpretable, and adaptive modeling within the target domain.

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Q4.Robustness of MAFS

The multi-agent architecture allows each agent to specialize in specific patterns ( stable and easy subtasks), thereby reducing task complexity and enhances learning robustness compared to a single DL model. This decoupling is especially valuable for unseen data, as agents can reuse domain-specific knowledge while dynamically adapting to new patterns. Combined with Agent-rated Voting Aggregator module, the system further boosts adaptability and robustness by selecting the most relevant agents on demand.

To more thoroughly address your concern, we conducted systematic experiments to empirically validate the robustness of our proposed method:

• Zero-shot Forecasting (see W5): MAFS significantly outperforms iTransformer and PatchTST on multiple unseen datasets, demonstrating strong out-of-distribution generalization.

• Increasing Unseen Ratio Experiments: As training data decreases to simulate distribution shift, all models’ performance drops, but MAFS shows the smallest decline, demonstrating superior robustness.

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Thank you again for your valuable feedback. We hope our responses have clarified your concerns and welcome any further questions you may have.

Yours Sincerely,

Authors of Paper 474

Dear reviewer,

The discussion phase is soon coming to an end. It will be great if you could go over the rebuttal and discuss with the authors if you still have outstanding concerns. Thank you for being part of the review process.

Regards,

Area Chair

Dear Reviewer HBiT,

Thank you for taking the time to review our paper and for your valuable suggestions. All added model variants (Ensemble/MAFS) and baselines (Time-MoE, CycleNet, xLSTM-Mixer, S-Mamba) have been added to the original anonymous code repository.

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W1&Q4 Provide a Comparison to MoE / Ensemble Baselines

Thank you for your comment. Since Time-MoE is a pretrained model on 300B data mainly for zero-shot tasks, we initially do not compare it with our end-to-end MAFS. To better show MAFS’s effectiveness, we have now included comparisons with Time-MoE and several ensemble baselines.

• Time-MoE: We use pretrained weights and fine-tune autoregressively for 10 epochs on each test dataset before evaluation.
• Ensemble: Following your Q4 suggestion, we implement ensembles for four models, iTransformer, TimeMixer, PatchTST, and SegRNN, combining them via a learnable linear layer.

The results show that the MAFS architecture outperforms both the current state-of-the-art multi-expert baseline TimeMoE and various ensemble strategies based on different backbones. This indicates that MAFS, which decomposes forecasting tasks and coordinates multi-agent system, is beneficial for improving predictive accuracy.

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W2&Q3 MAFS vs. Ensemble with Different Backbones

Thank you for your constructive suggestions, which help us further validate MAFS. We compare three representative methods, TimeMixer, PatchTST, and SegRNN, under single model, simple ensemble, and MAFS settings. Results show MAFS>Single>Ensemble, indicating:

1. MAFS’s multi-agent architecture effectively activates different backbones’ potential, serving as a plug-and-play accuracy booster (also see Figure 4, Page 8).
2. Simple ensembles may cause instability due to lack of task specialization or overfitting, while MAFS’s task decomposition leads to more stable and reliable predictions.

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W3 Compared to CycleNet,xLSTM-Mixer,S-Mamba

Thank you for your suggestion. With many new models emerging each year, we can only select 10 representative SOTA models for the main paper. To further validate MAFS, we additionally compare it with CycleNet, xLSTM-Mixer, and S-Mamba, showing MAFS consistently outperforms each.

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W4 Improve Figure 1

Thank you for your insightful suggestion. We will add '(d) Multi-Model Ensemble Forecasting' to enhance the completeness of Figure 4.

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W5 Minor concerns

Thank you for your suggestions. We will revise Figures 5 and 6 accordingly.

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Q1 Relation to Hierarchical Forecsating & Reconciliation Constraints

Thank you for the insightful question.

• Relation to Hierarchical Forecsating: Homogeneous horizon split indeed shares conceptual similarities with hierarchical or multi-resolution forecasting frameworks likecoarse-to-fine stages in TimeMixer. Importantly, our formulation does not explicitly impose a hierarchical dependency across stages; each agent in MAFS focuses on a specific horizon segment and contributes to the final prediction.
• Reconciliation Constraints: MAFS incorporates two key mechanisms that implicitly address reconciliation needs. First, Agent Communication enables information exchange among agents, fostering context-aware interactions and gradual alignment where appropriate. Second, the Agent-Rated Voting Aggregator evaluates each agent’s output both locally and globally, adaptively weighting their contributions to ensure a coherent and accurate final forecast. Together, these mechanisms offer a flexible yet effective alternative to hard reconciliation constraints, supporting both diversity and consistency in final forecasting.

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Q2 Are Sub-task ever Changing?

Thanks for your constructive question.

• Whether sub-tasks change per agent during training: In MAFS, each agent’s sub-task is fixed to encourage specialization and effective collaboration. Fixed roles are a common practice in multi-agent systems, and task migration is usually not applied.
• Benefit for generalization or overfitting: Although our original setup does not use task migration, we explore dynamic task assignment by cyclically rotating agents’ sub-tasks during training. Results show that this improves generalization in zero-shot transfer scenarios (MAFS_Dynamic), while the original MAFS remains more stable and accurate in full-shot tasks.

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Q5 More Ablations

In the main text (Page 8, Table 2), we conduct ablation studies on three key MAFS components (w/o Comm, AVA, STS). Following your insightful comment, we extend the ablation to evaluate each module individually, adding one module at a time on top of a base Ensemble iTransformer:

The results show that STS yields the most significant improvement, with a 7.47% reduction in MSE, indicating that task decomposition greatly enhances the collaborative forecasting ability of different models. In contrast, AVA achieves a smaller 4.85% reduction, indicating hierarchical integration helps only if strong task specialization exists.

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Thank you once again for your valuable suggestions to improve the quality of our paper. We have incorporated these insights into a new revised version.

Yours sincerely,

Authors of Paper 474