Many Minds, One Goal: Time Series Forecasting via Sub-task Specialization and Inter-agent Cooperation
Authors: Qihe Huang
Zhengyang Zhou
Yangze Li
Kuo Yang
Binwu Wang
Yang Wang
Venue: NeurIPS 2025 poster ()
Keywords: time series forecasting
Primary area: applications

Abstract: Time series forecasting is a critical and complex task, characterized by diverse temporal patterns, varying statistical properties, and different prediction horizons across datasets and domains. Conventional approaches typically rely on a single, unified model architecture to handle all forecasting scenarios. However, such monolithic models struggle to generalize across dynamically evolving time series with shifting patterns. In reality, different types of time series may require distinct modeling strategies. Some benefit from homogeneous multi-scale forecasting awareness, while others rely on more complex and heterogeneous signal perception. Relying on a single model to capture all temporal diversity and structural variations leads to limited  performance and poor interpretability. To address this challenge, we propose a Multi-Agent Forecasting System (MAFS) that abandons the one-size-fits-all paradigm. MAFS decomposes the forecasting task into multiple sub-tasks, each handled by a dedicated agent trained on specific temporal perspectives (e.g., different forecasting resolutions or signal characteristics).  Furthermore, to achieve holistic forecasting, agents share and refine information through different communication topology, enabling cooperative reasoning across different temporal views. A lightweight voting aggregator then integrates their outputs into consistent final predictions. Extensive experiments across 11 benchmarks demonstrate that MAFS significantly outperforms traditional single-model approaches, yielding more robust and adaptable forecasts.

Many Minds, One Goal: Time Series Forecasting via Sub-task Specialization and Inter-agent Cooperation
Qihe Huang", Zhengyang 2ho Yangze Li,, Kuo Yang", Binwu Wang
Yang Wang 1.8.as
University of Science and Technology of China (USTC), Hefei, China Suzhou Institute for Advanced Research, USTC, Suzhou, China
Email: (hgh.liyangzee.annkko)) @
(wbw2024, zzy0929, angyan) @ustc.edu.cn
Abstract
Time series forecasting is a critical and complex task, characterized by diverse temporal patterns, varying statistical properties, and different prediction horizons across datasets and domains. Conventional approaches typically rely on a single, unified model architecture to handle all forecasting scenarios. However, such monolithic models struggle to generalize across dynamically evolving time series with shifting patterns. In reality, different types of time series may require distinct modeling strategies. Some benefit from homogeneous multi-scale forecasting awareness, while others rely more complex and heterogeneous signal perception. Relying on a single model to capture all temporal diversity and structural variations leads to limited performance and poor interpretability. To address this challenge, we propose a Multi-Agent Forecasting System (MAFS) that abandons the one-size- fits-all paradigm. MAFS decomposes the forecasting task into multiple sub-tasks, each handled by a dedicated agent trained on specific temporal perspectives (e.g.. different forecasting resolutions signal characteristics). Furthermore, to achieve holistic forecasting, agents share and refine information through different commu- nication topology, enabling cooperative reasoning across different temporal views. A lightweight voting aggregator then integrates their outputs into consistent final predictions. Extensive experiments across 11 benchmarks demonstrate that MAFS significantly outperforms traditional single-model approaches, yielding more robust and adaptable forecasts. Code: https: http:///iituue /tggtttt....... com/h5505023922MMMF
Introduction
Time series forecasting [79, 78, 7,2, 11, 13, 53, 64] plays vital role in wide range of real-world applications, including finance, energy, healthcare, and intelligent transportation. Despite remarkable progress achieved by deep learning models such as RNNs [9, 24]. CNNs [55, 22]. and Transformers [60, 28, 23, 76, 25, 76]. many existing approaches rely on monolithic architectures that often struggle to generalize across ever-changing temporal patterns and continuously-evolwee signal characteristics inherent in time series [27, 16, 29,51].
Meanwhile, Multi-Agent Systems (MAS) [18, 48] have emerged a powerful paradigm for ad- dressing complex problems through collaboration among specialized agents [75]. This framework has achieved remarkable success in wide range of domains, including robotics [66], question
answering [65], and sequential decision-making [67]. Crucially, Multi-Agent Systems allow in- dividual agents to process information from distinct perspectives and coordinate their outputs
Yang Wang and Zhengyang Zhou corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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achieve common objective [74, 57]. This design promotes modularity, scalability, and robustness in solving eigh-dimensional and complex tasks [40, 5]. Inspired by these successes, a natural question arises: Can Multi-Agent Systems also benefit time series forecasting, particularly in scenarios with heterogeneous temporal patterns or task decomposition requirements?
However, directly applying multi-agent systems to time series forecasting remains non-trivial and faces three key challenges: (i) Task Decomposition for Specialized Modeling. Time series forecasting tasks are inherently unified and not easily divisible [8]. A critical question arises: how can we decompose a global forecasting task into meaningful sub-tasks that enable each agent to develop Comain-sspccipe expertise? Without proper decomposition, agents risk learning overlapping or redundant representations, which limits the benefits of specialization [68]. (ii) Limited Agent Perception. If an agent consistently operates within a narrow temporal scope, such as focusing only on local trends or periodic components, it may fail to capture important contextual signals needed for precise processing [74, 57]. A lack of holistic understanding can hinder the agent's s ability to generalize across variable temporal conditions. (iii) Forecasting Collaboration Bottlenecks. Even when agents are well-specialized, enabling effective collaboration among them remains substantial challenge [30, 4]. Agents must not only share information efficiently but also resolve potential confficts in their predictions. Poor coordination can lead to inconsistent or contradictory outputs, undermining the overall forecasting accuracy [47].
To bridge the gap between monolithic forecasting models and the need for adaptive, collaborative intelligence, we propose a novel Multi-Agent Forecasting System (MAFS) that introduces principled mechanisms for modular time series forecasting. Fundamentally, to enable each agent to specialize in modeling a distinct temporal attribute, MAFS explores two types of subtask decomposition: (i) forecasting across multiple homogeneous future horizons, and (ii) predicting heterogeneous signal features such as ceqquency-domain energy, statistical moments, periodicity, and trend. This design allows each agent to learn a well-defined aspect of the temporal structure. Furthermore, to expand each agent's s receptive field beyond local input views, we introduce inter-agent communication that allows information exchange at the representation level. This is implemented via structured message passing over predefined topologies, including Ring. Star, Chain, and Fully-Connected Graphs, enabling flexible and scalable coordination across agents. Third, to realize effective decision fusion across agents, MAFS incorporates a two-stage voting aggregator composed of: (i) an Agens Confidence Estimator that evaluates the confidence relevance of its own prediction; and (ii) Global Voter that aggregates forecasts across agents based on both their internal ratings and mutual assessments. This mechanism enables robust collaboration by assigning adaptive weights different agents during inference. Overall, MAFS is designed to fully harness the strengths of collective intelligence while maintaining scalability and generalization across a variety of forecasting scenarios. Our contributions are summarized as follows:
We propose Multi-Agent Forecasting System (MAFS), the first general-purpose time series forecasting framework based on Multi-Agent Systems, which leverages collective intelligence to tackle complex, evolving, and heterogeneous temporal patterns.
Within MAFS, we introduce two principled task decomposition strategies to enable each agent to specialize in distinct forecasting sub-tasks. Furthermore, we design an inter-agent communication module to enhance the generalization capacity of each agent through struc- tured message passing. Finally, two-stage voting aggregator combines self-assessments and global voting to facilitate robust and coordinated multi-agent forecasting.
Through agent specialization and structured collaboration, MAFS demonstrates superior forecasting performance. Extensive experiments on 11 real-world datasets demonstrate that MAFS consistently outperforms competitive basclines, achieving on average 6.35% % reduction in MSE and a 4.03% % reduction in MAE compared to its singlc-agent counterpart. MAFS also ranks first on 16 out of 22 metries, and secures a top-2 position on 20 out of 22 metrics, spanning both MSE and MAE evaluations.
2 Related Work
2.1
Time Series Forecasting
Time series forecasting is a foundational task in machine learning that aims to predict future values from past observations [63, 36, 50, 62, 21, 70, 35, 54, 56, 43, 32, 42, 10]. Traditional statistical

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Router
Aggregator
Collaboration
MMM Motilrr
EN
Specialization
Model
Model2
Model3
Model4
Adaptability
Shared Bottom
Task back--Decomosed
(a) Single-madel Forecasting
(b) Mixure-of-EEperts Forecasting
(c) Multi-Agent
Forecsating System
Figure 1: Illustration of different forecasting paradigms: (a) Single-model Forecasting, (b) Mixture- of-Experts Forecasting, and (c) Multi- Multi-Agent Forecasting System (MAFS). Compared to traditional paradigms, MAFS achieves better specialization, collaboration, adaptability, and interpretability.
models such as ARIMA [1] and VAR [31] are widely used for their simplicity, yet often struggle with capturing nonlinear and long-term dependencies. With the advent of deep learning, models such RNNs [9, 24], MLPs [58, 37, 29, 29, 34, 14], and Transformers [25, 44, 69, 77, 71, 76, 38, 33] have demonstrated remarkable improvements in modeling complex temporal dynamics. in Figure (a), these models typically adopt monolithic architectures, where single model is trained end-to-end to learn all patterns across the entire time series. However, such one-size-fitss approaches often underperform in heterogeneous nonstationary environments, where different segments the data may exhibit distinct behaviors or require different inductive biases [16].
shown
2.2 Mixture-of-Expert Forecasting
To improve modeling capacity and fiexibility, Mixture-of-Expert (MoE) [45] has been applied to time series forecasting, where multiple expert models are trained extract diverse high-level features from the input sequences. As shown in Figure ((b), Router mechanism is typically employed to dynamically select or weight experts for adaptive specialization across different temporal patterns. Time-MoE [46] introduces scalable autoregressive Transformer equipped with sparse mixture-of-experts, enabling billion-scale time series pretraining with reduced inference cost and flexible forecasting horizons. From frequency aspect, MOIRAI-MoE [26] eliminates the need human-defined frequency specialization by learning token-level expert routing within sparse MoE framework. Despite their strengths, MoE-based forecasting models typically operate within monolithic architecture and lack modular agent-level interpretability [20, 72].
2.3 Multi-Agent System
Multi-agent Systems (MAS) has emerged as a powerful paradigm for solving complex problems through the cooperation of multiple specialized agents [4]. the context machine learning, MAS enables agents to leam distinct competencies, share information, and coordinate actions to collectively solve tasks that are difficult for single model [30]. Recently, there has been growing interest in leveraging large language model agents for multi-agent collaboration in open-domain reasoning [75, 65], but its application to time series forecasting remains largely unexplored. As which implicitly routes inputs through
shown in in Figure I(c), in contrast to oixture-of-Fxpper fixed expert networks without agent awareness or coordination, multi-agent systems offer explicit control, communication, and division of labor. Thus, designing an MAS forecasting system offers promising pathway to harness specialization and collaboration for forecasting complex time series.
Problem Formulation
Time Series Forecasting We consider standard time series forecasting problem. Given historical input sequence = [x1,X, Xx,,,,,,,, Xy] ] E RT'xM with time steps and variables, the goal is to predict the future series Y [x X141,.442.00 xT+1] E Lx where L is future horizon.
Multi-agent System for Forecasting To improve forecasting performance and interpretability. introduce multi-agent forecasting system S {Agent, (-), Agentz()..... Agent (-))

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consisting of N specialized forecasting agents. Each Agent, (-) is responsible for solving distinct sub-task the forecasting problem. The agents interact and exchange information via predefined communication topology G {S, A, E). where A E {0, 1|NNNN is binary adjacency matrix, and E E TR. NxN denotes the edge weights. The agent outputs are aggregated by an Agent-rated Voting
Aggregator (- to produce the final forecasting result. The overall process is formulated as:
Y = AAVA(Com(((Aent) (X), AX) ..........nnnttte (X); G))
(1)
where Comm(:: G) represents the communication mechanism. Let θ사 = . d denote the parameters of all agents, Or the parameters of communication weight (i.e., E), and Op the parameters of the Agent-rated Voting Aggregator. The joint training objective to minimize the expected mean squared error (MSE) between the predicted and the truth:
min Exx,Y 0
||X
Y
(2)
where DD denotes the empirical data distribution.
Methodology
First Stage: Multi-agent Forecasting System Learning via Agent
Communication and Task Specialization
Forecating Agent
Chain
Communicate
Specialiss calllizaaio
Sub- Task
www
Ring
Graph
Star
Task Divide
Second Stage: Collaborating Multi Agents for Forecasting
Prodkne
Sar
Grggb
Agent-rated Voting Aggregator
Forecasting Task
Topology Aware Weight Adjuster
Figure 2: Overview of the two-stage learning in Multi-Agent Forecasting System.
As illustrated in Figure 2, the Multi-Agent Forecasting System (MAFS) is structured around two- stage learning paradigm. Stage 1: Specialization Pretraining, Each agent is assigned a distinct sub-task (e.g., different signal characteristics) and exchanges hidden states every layer using fixed communication graph with uniform weights. Only agent-specific parameters O are optimized in this stage, enabling each agent to specialize independently. Stage 2: Collaborative Forecasting. Agent parameters are frozen. Edge weights in communication is now learnable by Topology-awe aware Weight Adjuster with θ,. An Agent-rated Voting Aggregator (AVA) with parameters Op aggregates the communicated features to produce the final prediction.
4.1 Forecasting Agent Architecture
In the Multi-Agent Forecasting System (MAFS), as shown in Figure 3, each forecasting agent adopts pluggable encoder-based time series model as its backbone, enabling flexible integration with various architectures. Given an input sequence X E RTxM the encoding process is formulated as:
O)) = Emmeed(X]] ) (I+1) EncoderLayerr H()),
Ô
Head
(3)
Here, ( represents the hidden state at the i-th encoder layer. The Encoder can follow any standard design, making MAFS extensible to a wide range of forecasting backbones. is the agent output of specialized forecasting sub-task.

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Future Series
m0 0
O2
0g
TTrend
t Seasonality
Frequency
Distribution
Agent Head
Agent Head
Agent Head
Agent Head
Projection
I-th Encoder
Lath Encoder
L-th Encoder
L-th Encoder
Layer
Layer
Layer
Layer
Aggregator
*..
Global Voter
1-st Encoder
1-st Encoder
1-sf Encoder
1-st Encoder
Layer
Layer
Layer
Layer
Agent Confidence
Estimator
Embed
Embed
Embed
Embed
Figure 3: The overall architecture of MAFS. Each forecasting agent employs pluggable encoder- based time series model, and their representation are aggregated to produce the final forecast.
4.2 Agent Communication
Each agent is assigned with dedicated forecasting sub-task. While such specialization facil- itates inductive bias and modeling diversity, it inevitably leads to data bias. To mitigate this limitation and enable agents to form coherent and globally consistent predictions, we intro- duce an explicit communication mechanism. This communication can formally expressed as, Here, {HC), HCC, HC,, = Comm(H, H2 H G); H = LacooerLayerr(HHC))
H denotes the output of the I-th encoder layer of agent i, and HC; represents the updated repre- sentation after communication. The communication function Comm(-) is instantiated graph convolution operation, enabling structured message passing across agents connected via G. Specifi- cally, we implement the communication via Graph Convolutional Network [19].
HC =o
Aij A W. H JEN())
(4)
where (ii) is the set of connected agents of Agent,, Aij is the normalized adjacency matrix indicating communication strength between agents and j. W Rdassa is a learnable projection matrix, and (-) is a non-linear activation function. This formulation enables each agent to refine its hidden representation by aggregating contextual information from others, thereby overcoming the limitations of isolated modeling and improving coordination among agents.
4.3 Agent Specialization via Sub-task Decomposition
To promote diversity and specialization among agents, we design two sub-task decomposition strategies: (1) Multi-scale temporal forecasting (homogeneous setting): Each agent focuses on predicting different portion of the future horizon at increasing lengths, e.g., the Agent, predicts the first N I. steps. This encourages specialization across temporal scales, from short-term to long-term forecasting. (2) Multi-aspect signal forecasting (heterogeneous setting): Agents are assigned complementary signal analysis tasks, including trend extraction, scasonality modeling, spectral energy estimation, and statistical summary prediction. Each sub-task targets a distinct property of the future signal, fostering diverse and orthogonal representations. These decompositions enable the agent ensemble to capture rich temporal dynamics from multiple perspectives, improving overall forecasting accuracy. More details are availavle at Appendix A.
4.4 Topology-aware Weight Adjuster
In the second stage of training, we freeze the parameters of each forecasting agent and make the inter-agent communication weights learnable. Specifically, the fixed edge weight matrix E is replaced by a parameterized matrix Ee, E RNN.N, where each entry denotes the learnable communication strength between pair of agents.
5

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To retain the prior topology, we keep a fixed binary adjacency mask A E 0, 1 1xxN which encodes the initial traffic-aware structure. The learnable edge weights are modulated by this mask to obtain the soft communication graph, A' a (Ee,,) @ A, where a(-) is the sigmoid function and @ denotes element-ve wise multiplication. To ensure symmetric communication [19], we construct the normalized adjacency matrix as,
Anorm D (')A where A = ( AAA++" D = diag ΣAss
(5)
This topology-aware normalization allows information exchange be dynamically adjusted while preserving structural priors. Crucially, Ee, is optimized jointly with the forecasting objective via backpropagation, enabling the system to learn adaptive, task-specific communication topology that enhances coordination among agents and improves overall prediction performance.
4.5 Agent-rated Voting Aggregator
During forecasting phase, we aggregate the final embedding from all agents complete forecasting. To dynamically make decision-man making process adaptive to each agent, we design a two-stage voting aggregator (AVA), which include Agent Confidence Estimator and Global Voter.
Agent Confidence Estimator Let {H) H } denote the final output representations of all forecasting agents. The Agent Confidence Estimator evaluates the confidence of each agent through a ceffaassessment mechanism. Each H paired with a shared contextual embedding C,, and passed through learnable gating network to produce an element-wiss gate coefficient:
0₁ = a (Gate C1, C2...., Cxl))
(6)
The final gated representation computed as:
H. a H + (1-
(7)
Here, @ denotes element-win wise multiplication, a-)) is the sigmoid activation function, and Gate(.) is shared learnable network. This formulation enables each agent to adjust its output by blending its own prediction with the global context, based estimated confidence.
To further integrate the confidence-adjuster outputs from all agents, we introduce Global Voter that computes agent-wa wise collaboration weights CW TR- based on the encoded input X with MLP. These weights indicate the relative importance or contribution of each agent to final prediction. Each weight in CW is then broadcast to match the shape of its corresponding agent representation and used to perform weighted sum over {H{ H1..... H ). This results in unified latent representation Z, which captures the aggregated knowledge across all agents.
Global Voter
Finally, Z is projected through linear layer to produce the final multivariate time series forecast Y E R MxL, where L denotes the forecast horizon.
5 Experiments
5.1 Experimental Setups
Datasets We evaluate our model on 11 real-world datasets covering different domains. In Electricity domain, we use ETTh1, ETTh2, ETTml, and ETTm2 [77, 60). The Environment domain includes Weather [60], PM2.5 [59], AQShunyi and AQWan [41] The Nature domain consists of Czelan, ZafNoo [41] as well as Temp [59]. For the ETT datasets, we adopt a 6:2:2 train/validationftest split, and 7:1:2 split for the remaining datasets.
Implementation Details MAFS explores four distinct communication topologies for the agent interaction graph G, including ring, star, chain, and fully-connected structures. Each forecasting agent is implemented using iTransformer architecture [28]. MAFS is trained in two stages: the first stage independently optimizes each agent with a learning rate of 1e-3 for 10 epochs; the second stage freezes agent parameters and finetunes only the topology-aware weight adjuster and agent-rated voting aggregator for another 10 epochs with a reduced learning rate of le-4. We set hidden dimension of 128, and configure the encoder with layer for all datasets. The number of agents

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Table 1: Comparison of long-tern term time series forecasting methods on 11 datasets using MSE and
MAE (lower is better). Best results are marked in red second- best results are underlined in blue
Methods
MAFS
iTTrnsformer
TimeMixer
PTtchTST
Crossformer
TIDE
TimesNet
DLincar
Autoformer
Informer [2021]
(Ours)
[2024]
[2024]
[2024]]
[2023]
[2024]
[2023]
[2023]
[2021]
Datasets
MSE
MAB
MSE
MAE
MSE MAE
MSE MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE MAE
MSE MAB
ETTh1
0.433
0.437
0.467
0.466
0.447
0.44
(0.469
0.454
0.529
0.522 0.54] 0.507
(0.458
0.45
0.4456
0.452
(0.496
0,487
1.04
0,795
0.356
0.394
0.386
0.415
0.364
0.395
0.387
0.407
0.942
0.68-1 0.611 0.55
00:414
0.427
0.559
0.515
0.45
0,459
4.431
1.729
Er1ml
0,366
0.388
0.383
0,403
00.381
0.395
0.387
0.4
0.513
0,499
0.4
0.400
0:403
0:40:
00.588
0.517
0.961
0,734
mm
0,265 0.321
0.29
0.339
0..275
0.323
00.281
0.326
0.757
0.61 00,358
0,404
(0.291 0.333
0.35
0.401
00.327 0.371
1.41
0.81
Weather
0.233 0,267
0.2443
0,276
0..24
0.271
00.259
0.281
0.259
0.315 0.227 0.32 (0,259
0.287
0.265
0.317 00.338
0.382
0.634
0.548
AQSbunyi
0.701 0.509
0.723
0.515
00.799
0.529
(0,705
0.509
0.554 (0.726 0,516
(0,764 0.541
0.782 0,545
AQWan
0.802
0.503
0.:17
0,507
00.828
0.499
0.8812 0.499
0,786
0.49
0.856 0.536 (0.813 0.5
0.818
0.512 0.84
0.525
0.866 0.525
Czel.an
0.222
0.271
0:232
0.28
0.228
0.28
0.227
0.29
0.956
0.576 0.2237 0.303 0.2224 0,285
0:284
342
00.307 0.355
0.316 0.355
ZafNoo
0.451
0.541
0..338
0.44
0.511
0.569
0.498 (0.537
0.496
0.451
00.255
0.599
0.744
PM2.5
0.398
0.414
0.421
00,421
00:115
0.436
0.46
0.479
0.456
0.472
0.481 0,497 (0.473 0,492.
0:453
0:477
0,5115
0,524
0.539 0.561
Temp
0.14
0.288
0.173
0.321
0,146
0.304
0.147
0.306
0.206
0.423
0,164
0.338
(0,208 0.428
0.159
0.327
00.244
0.5
0.2388 0.492
N is selected from the range (4, 12, 16, 20,24) 24] to investigate the impact of varying agent scale. All experiments adopt a symmetric prediction setting, where the input sequence length equals the forecasting horizon [76]. More Details are available at Appendix C.
Baselines The proposed method is evaluated against a range of representative baselines, which can be categorized by model architecture. Transformer-basee based models include Informer [77], Auto- former [60]. Crossformer [76], PatchTST [38], and i'Transformer [28]. Linear-based models such as TixeMixer [58], TiDE [6] and DLinear [73] focus on efficient feature extraction and forecsating. Periodicity-baat based models, such as TimesNet [61], enhance forecasting performance by modeling multi-period temporal patterns.
5.2 Main Results
The experimental results are presented in Table 1, where we comprehensively evaluate the proposed MAFS against a range of SOTA models on long-term time series forecasting benchmarks. Experimen- tal results consistently demonstrate the superior performance and robustness of MAFS across diverse datasets and prediction horizons. Specifically, MAFS achieves an average improvement of 3.24% in MSE and 1.71% % in MAE over the recent SOTA model TimeMixer, confirming the effectiveness of our multi-agent collaborative framework. Furthermore, although MAFS adopts the iTransformer backbone, which is not the most competitive SOTA model in terms of forecasting accuracy, our multi-agent framework effectively overcomes this limitation. By leveraging agent specialization and structured inter-agent collaboration, MAFS achieves average improvement of 6.35% in MSE and 4.03% in MAE compared to iTransformer, successfully reaching across multiple benchmarks. In addition, MAFS ranks first on 16 out of 22 evaluation metrics and secures a top-2 ranking in 20 out of 22 metrics (covering both MSE and MAF across 11 datasets), showcasing its strong generalization capability across various application domains. In summary, MAFS breaks the limitations of monolithic forecasting models by introducing a flexible and adaptive multi-agent collaboration mechanism, delivering more accurate and reliable predictions across diverse and challenging time series forecasting scenarios. Full results are available at Appendix G.
of-the--rtr-tttttt performance
5.3 Ablation Analysis
To evaluate the effectiveness of each key component in our proposed MAFS framework, we conduct series of ablation studics. The experimental results are presented in Table 2. We evaluate the removal of three critical modules, 1) w/o Comm: Disables inter-agent communication by removing the shared semantic vector hes preventing collaborative reasoning. 2) w/o AVA: Removes the Agent-Ratee Voting Aggregator, directly averaging agent embeddings without adaptive gating and collaboration weights. 3) w/o STS: Disables Sub-task Specialization, assigning identical forecasting tasks to all agents instead of specialized sub-tasks.
Main results. (1) w/o Comm: Without communication, MSE and MAE increase by 4.18% and 2.62%, highlighting its role in enabling agents to share complementary temporal information. (2) Removing AVA leads to a significant MSE and MAE increase of 7.24% and 5.70%, confirming its importance in adaptively integrating agent outputs for accurate forecasting. (3) Without sub-task
7

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Table 2: Ablation Study on the Contribution of Communication, Aggregation, and Specialization
Modules in MAFS. Bold values indicate the best performance.
Variant
Metric
ETTh1
ETTh2
ETTml
ETTm2
Weather
AQShunyi
AQWan
CzeLan
ZafNoo
PM2.5
Temp
MSE
0.433
0.356
0.366
0.265
0.233
0.701
0.802
0.222
0.520
0.398
0.144
MAFS
MAE
0.437
0.394
0.388
0.321
0.267
0.509
0.503
0.271
0.451
0.414
0.288
MSE
0.445
0.364
0.375
0.277
0.238
0.719
0.824
0.228
0.529
0.439
0.167
w/o Comm
MAE
0.446
0.402
0.398
0.335
0.273
0.517
0.513
0.279
0.456
0.427
0.312
MSE
0.454
0.373
0.379
0.288
0.265
0.722
0.845
0.253
0.536
0.421
0.158
w/o AVA
MAE
0.456
0.409
0.403
0.335
0.293
0.520
0.532
0.292
0.487
0.426
0.301
MSE
0.461
0.384
0.374
0.286
0.244
0.726
0.823
0.243
0.546
0.417
0.177
w/o STS
MAE
0.462
0.412
0.397
0.332
0.275
0.517
0,512
0.285
0.475
0.415
0.317
specialization, MSE and MAE rise by 6.97% and 3,93%, demonstrating that specialized agents improve representation and capture diverse signal characteristics.
5.4 Evaluating the Advantage of MAFS over Single Models
As shown in Figure 4, MAFS consistently outperforms the single-agent model across 11 datasets, achieving an average improvement of 6.35% in MSE and 4.03% in MAE, demonstrating the effec- tiveness of collaborative forecasting. The most significant improvement occurs on the Temp dataset, with 19.08% reduction in MSE and 10.28% MAE. This gain likely results from strong temporal patterns and variable dependencies in temperature data, which are better captured by specialized agents and collaborative reasoning. Overall, these results confirm that MAFS effectively realizes collective intelligence, enabling specialized agents to achieve superior forecasting accuracy, and highlighting the advantages of a multi-agent framework over monolithic models.
CrcLan
PM125
Teap
Weetber
ZaINoo
C0 Single Model
KDP
V
V
V
MAPS
AQShanyi
AQWas
ETTM
KTT32
XTTil
4.20
609
TV
MARS
Stack:
MAPS
Ntakk
MAPS
Figure 4: Performance comparison between single forecasting model and MAS forecasting system
5.5 Analysis of MAFS Scaling and Communication Structures
Tisk-Hon AQShuri
Hede Deta
Trok-Hote WetthWeather
Hele- Dits-ETTh!
4
4.70
1.50
0.50
0335
Ageat Namber
Agest Number
Aprat Number
Agcol Number
Figure 5: Performance comparison under varying agent numbers and communication structures
8

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The results are shown in Figure 5. (1) Agent Scaling: Increasing the number of agents generally improves performance by enhancing modeling diversity and specialization. However, beyond 16 agents, improvements become marginal, indicating a saturation point. Minor performance fluctuations are trivial and likely caused by random initialization or local optima. Full results are available at Appendix E. (2) Communication Structures: Among chain, ring, fully-connected, and star topologies, the star structure consistently yields better and more stable results. Its centralized design effectively integrates global information, reducing noise amplification and ensuring critical trends are shared across agents. conclusion, using agents with a star communication structure offers the best trade-off between performance and complexity for time series forecasting.
5.6 Impact of Sub-task Division Agent Specialization
ZafNoa
AQShems
ETiml!
Trap
100
Figure 6: Comparison of agent specialization under different sub-task division strategies
Figure shows the average forecasting accuracy under different sub-task divisions across prediction horizons. First, in most cases, the performance difference between homogeneous and heterogeneous task divisions is minor. For example, the performance gap remains within 1 1% between ZafNoo and AQShunyi, suggesting that task division strategies have limited influence under such data conditions. Second, for datasets with smaller variance and more stable patterns (e.g.. ETTml and Temp), homogeneous task division significantly outperforms heterogeneous division. This indicates that consistent modeling strategies are better suited for stable datasets without introducing unnecessary task diversity. summary, the choice sub-task division should consider the characteristics of the target dataset, with homogeneous division preferred for stable data and heterogeneous division applicable when greater diversity is required. Full results are available at Appendix
5.7 Case Study
As shown in Figure 7, we take ETTm2 illus- trate effectiveness of MAFS through sub-task evaluation, voting scores of different agents, and the learned com- munication weights. (1) Each agent can success- fully specialize and perform well on its assigned sub- task. (2) The voting results show that all agents actively contribute to the final deci- sion, avoiding issues such agent collapse reliance on a single expert. (3) In the second stage, the learned adaptive communication weights reflect task-aware information
0.080
1011170011141012211 1110 8 7
0.065
Agenti
0.060
Took Tonk
Tabk
Sub- Task Evaluation 62
0.055
0.000
00.45
-0000
Agent j
(b) Voting Score
Agent
(c) Learned Communication Weight
Figure 7: Case study of MAFS on ETTm2.
exchange, optimizing collaboration between agents under a fixed topology.
Conclusion
In this work, we propose MAFS, a novel multi-agent forecasting system that introduces collective intelligence into time series forecasting through principled task decomposition, structured inter-agent communication, and a two-stage voting aggregator. Extensive experiments on 11 real-world datasets demonstrate that MAFS consistently outperforms state-of-the-ar baselines, achieving significant

---

improvements in both accuracy and robustness. These results highlight the effectiveness of collabora- tive forecasting and offer new perspective for addressing the challenges of complex and evolving temporal patterns. This work can open new directions for modular, adaptive, and interpretable time series forecasting.
Acknowledgement
This paper is partially supported by the National Natural Science Foundation of China 08.62250488, No. 1227901,,,, Natural Science Foundation of Jiangsu Province (BK20240460), the grant from State Key Laboratory of Resources and Environmental Information System. The Al-driven experiments, simulations and model training were performed on the robotic Al-Scientist platform Chinese Academy of Sciences.
References
[1] George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung. Time Series Analysis: Forecasting and Control. John Wiley & Sons, 5th edition, 2015.
[2] Lu Chen, Qilu Zhong, Xiaokui Xiao, Yunjun Gao, Pengfei Jin, and Christian S Jensen. Price- and-time-aware dynamic ridesharing. In 2018 IEEE 34th international conference on data engineering (ICDE), pages 1061-1072. IEEE, 2018.
[3] Lu Chen, Yunjun Gao, Ziquan Fang, Xiaoye Miao, Christian Jensen, and Chenjuan Guo. Real-time distributed co-movement pattern detection on streaming trajectories. Proceedings of the VLDB Endowment, 12110):1008- 1220, 2019.
[4] Weize Chen, Yusheng Su, Jingwei Zuo, Cheng Yang, Chenfei Yuan, Chen Qian, Chi-Min Chan, Yujia Qin, Yaxi Lu, Ruobing Xie, et al. Agentverse: Facilitating multi-agent collaboration and exploring emergent behaviors in agents. arXiv preprint arXiv:2308. 108488 2(4):6, 2023.
[5] Weize Chen, Jiarui Yuan, Chen Qian, Cheng Yang, Zhiyuan Liu, and Maosong Sun. Optima: Optimizing effectiveness and efficiency for Ilm-based multi-agent system. arXiv preprint arXiv:2410.08// 2024.
[6] Abhimanyu Das, Weihao Kong, Andrew Leach, Shaan K Mathur, Rajat Sen, and Rose Yu. Long-term forecasting with tide: Time-series dense encoder. Transactions on Machine Learning Research, 2024.
[7] Xin Ding, Lu Chen, Yunjun Gao, Christian Jensen, and Hujun Bao. Ultraman: unified plat- form for big trajectory data management and analytics. Proceedings of the VLDB Endowment, 11(7):777779, 2018.
[8] Shanghua Gao, Teddy Koker, Owen Queen, Tom Hartvigsen, Theodoros Tsiligkaridis, and Marinka Zitnik. Units: A unified multi-task time series model. Advances in Neural Information Processing Systems, 37: 177589910414,,1, 2024.
[9] Felix Gers, Jürgen Schmidhuber, and Fred Cummins. Learning to forget: Continual prediction with Istm. Neural computation, 12(10):2451 22241122471, 2000.
[10] Qihe Huang, Lei Shen, Ruixin Zhang, Jiahuan Cheng. Shouhong Ding, Zhengyang Zhou, and Yang Wang. Hdmixer: Hierarchical dependency with extendable patch for multivariate time series forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38,
pages 12608-1621 12616, 2024.
[11] Qihe Huang, Lei Shen, Ruixin Zhang, Shouhong Ding, Binwu Wang, Zhengyang Zhou, and Yang Wang. Crossgnn: Confronting noisy multivariate time series via cross interaction refine- ment. Advances in Neural Information Processing Systems, 36, 2024.
[12] Qihe Huang, Zhengyang Zhou, Kuo Yang, Gengyu Lin, Zhongchao Yi, and Yang Wang. Leret: Language-empowerr retentive network for time series forecasting. In Kate Larson, editor, Proceedings of the Thirty-Thine International Joint Conference on Artificial Intelligence, IJCAI- 24, pages 4165-4173, International Joint Conferences Artificial Intelligence Organization, 8
10

---

2024. doi: 10.24966//jccii222244466 URL https://doi.... http:////oooo.r////// org/ 24963/1 2a2.aaa2a..22220001 Main Track.
[13] Qihe Huang, Zhengyang Zhou, Kuo Yang, and Yang Wang. Exploiting language power for time series forecasting with exogenous variables. In Proceedings of the ACM on Web Conference 2025, WWW '25, page 4053-4052, New York, NY, USA, 2025. Association for Computing Machinery. ISBN 9798400712746. doi: 10. 0..145533694100.71479999 URL. 1145/3696444 33t
[14) Qihe Huang, Zhengyang Zhou, Kuo Yang. Zhongchao Yi, Xu Wang, and Yang Wang. Timebase: The power of minimalism in efficient long-term time series forecasting. In Forty-second International Conference on Machine Learning, 2025.
[15] Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y Zhang, Xiaoming Shi, Pin- Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, et Time-llm: Time series forecasting by reprogramming large language models. In The Twelfth International Conference on Learning Representations, 2024.
[16] Taesung Kim, Jinhee Kim, Yunwon Tae, Cheonbok Park, Jang-Ho Choi, and Jaegul Choo. Reversible instance normalization for accurate time-series forecasting against distribution shift. In International conference on learning representations, 2021.
[17] Diederik Kingma. Adam: method for stochastic optimization. arXiv preprint
arXiv:1412.6980, 2014.
[18] David Kinny and Michael Georgeff. Modelling and design of multi-agent systems. In Inter- national Workshop on Agent Theories, Architectures, and Languages, pages 1-20. Springer, 1996.
[19] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks, In International Conference on Learning Representations (ICLR), 2017. URL https: /tte:://araaa //trxvvaavvv////a///a//aaaaaaal .wrg/voooo////oooooooooooe abo/1609 02907.
[20] Jiachen Li, Xinyao Wang, Sijie Zhu, Chia-Wen Kuo, Lu Xu, Fan Chen, Jitesh Jain, Humphrey Shi, and Longyin Wen. Cumo: Scaling multimodal 11m with co-upcycled mixture-of-expeee Advances Neurul Information Processing Systems, 37:131224-131245, 2024.
[21] Xinyu Li, Yuchen Luo, Hao Wang. Haoxuan Li, Liuhua Peng. Feng Liu, Yandong Guo, Kun Zhang, and Mingming Gong. Towards accurate time series forecasting via implicit decoding. Advances in Neural Information Processing Systems, 2025.
[22] Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu. Diffusion convolutional recurrent neural network: Data-driven traffic forecasting, arXiv preprint 1r77vv1707.01920 2017.
[23] Shengsheng Lin, Weiwei Lin, Wentai Wu, Songbo Wang, and Yongxiang Wang. Petformer: Long-term time series forecasting via placeholder-enhancedd transformer. arXiv, 2023.
[24] Shengsheng Lin, Weiwei Lin, Wentai Wu, Feiyu Zhao, Ruichao Mo, and Haotong Zhang. Segrnn: Segment recurrent neural network for long-term time series forecasting. arXiv preprint arXiv:2308. 1200, 2023.
[25] Shizhan Liu, Hang Yu, Cong Liao, Jianguo Li, Weiyao Lin, Alex X Liu, and Schahram Dustdar. Pyraformer: Low-complexity pyramidal attention for long-range time series modeling and forecasting. In International conference on learning representations, 2021.
[26] Xu Liu, Juncheng Liu, Gerald Woo, Taha Aksu, Yuxuan Liang, Roger Zimmermann, Chenghao Liu, Silvio Savarese, Caiming Xiong, and Doyen Sahoo. Moirai-moe: Empowering time series foundation models with sparse mixture of experts. arXiv preprint arXiv:2410. 104..9999, 2024.
[27] Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Non-stationary transformers: Exploring the stationarity in time series forecasting. In Advances in Neural Information Processing Systems, 2022.

---

[28] Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. itransformer. Inverted transformers are effective for time series forecasting. In The Twelfth International Conference on Learning Representations, 2024.
[29] Yong Liu, Chenyu Li, Jianmin Wang, and Mingsheng Long, Koopa: Learning non-stationary time series dynamies with koopman predictors. Advances in Neural Information Processing Systems, 36, 2024.
[30] Zijun Liu, Yanzhe Zhang, Peng Li, Yang Liu, and Diyi Yang. A dynamic lIm-powered agent network for task-oriented agent collaboration. In First Conference on Language Modeling, 2024.
[31] Helmut Lütkepohl. New Introduction to Multiple Time Series Analysis. Springer Science & Business Media, 2005.
[32] Jiaming Ma, Zhiqing Cui, Binwu Wang. Pengkun Wang, Zhengyang Zhou, Zhe Zhao, and Yang Wang. Causal learning meet covariates: Empowering lightweight and effective nationwide air quality forecasting. 2025.
[33] Jiaming Ma, Binwu Wang, Qihe Huang, Guanjun Wang, Pengkun Wang, Zhengyang Zhou, and Yang Wang. Mofo: Empowering long-term time series forecasting with periodic pattern modeling. In Advances in Neural Information Processing Systems, 2025.
[34] Jiaming Ma, Binwu Wang, Guanjun Wang, Kuo Yang. Zhengyang Zhou, Pengkun Wang, Xu Wang, and Yang Wang. Less but more: Linear adaptive graph learning empowering spatiotemporal forecasting. In Advances in Neural Information Processing Systems, 2025.
[35] Jiaming Ma. Binwu Wang, Pengkun Wang, Zhengyang Zhou, Xu Wang, and Yang Wang. Bist: A lightweight and efficient bi-directional model for spatiotemporal prediction. Proceedings of the VLDB Endowment, 1866):6663-163 2025.
[36] Jiaming Ma, Binwu Wang, Pengkun Wang, Zhengyang Zhou, Xu Wang, and Yang Wang. Robust spatio-temporal centralized interaction for ood learning. In Forty-second International Conference on Machine Learning, 2025.
[37] Jiaming Ma, Binwu Wang, Pengkun Wang, Zhengyang Zhou, Yudong Zhang, Xu Wang, and Yang Wang. Mobimixer: A multi-scale spatiotemporal mixing model for mobile traffic prediction. IEEE Transactions on Mobile Computing, 2025.
[38] Yuqi Nie, Nam H Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A time series is worth 64 words: Long-term forecasting with transformers. In The Eleventh International Conference on Learning Representations, 2023.
[39] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high- high-performance deep learning library. Advances in neural information processing systems, 32, 2019.
[40] Tingrui Qiao, Caroline Walker, Chris Cunningham, and Yun Sing Koh. Thematic-lm: llm- based multi-agent system for large-scale thematic analysis. In Proceedings of the ACM on Web Conference 2025, pages 649-669966 2025.
[41] Xiangfei Qiu, Jilin Hu, Lekui Zhou, Xingjian Wu, Junyang Du Buang Zhang, Chenjuan Guo, Aoying Zhou, Christian S. Jensen, Zhenli Sheng, and Bin Yang. TFB: Towards comprehensive and fair benchmarking of time series forecasting methods. In Proc. VLDB Endow., pages 1163-2277,200 2024.
[42] Xiangfei Qiu, Zhe Li, Wanghui Qiu, Shiyan Hu, Lekui Zhou, Xingjian Wu, Zhengyu Li, Chenjuan Guo, Aoying Zhou, Zhenli Sheng, Jilin Hu, Christian S. Jensen, and Bin Yang. Tab: Unified benchmarking of time series anomaly detection methods. In Proc. VLDB Endow. pages 2775-2789, 2025.
[43] Xiangfei Qiu, Xingjian Wu, Hanyin Cheng, Xvyuan Liu, Chenjuan Guo, Jilin Hu, and Bin Yang. DBLoss: Dccomposition-basee loss function for time series forecasting. In NeurIPS, 2025.
12

---

[44] Xiangfei Qiu, Xingjian Wu, Yan Lin, Chenjuan Guo, Jilin Hu, and Bin Yang. DUET: Dual clustering enhanced multivariate time series forecasting. In SIGKDD, pages 1185-1196, 2025.
[45] Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, and Jeff Dean. Outrageously large neural networks: The sparsely-gate mixture-of mixture-of-experis layer. In International Conference on Learning Representations, 2017.
[46] Xiaoming Shi, Shiyu Wang, Yuqi Nie, Dianqi Li, Zhou Ye, Qingsong Wen, and Ming Jin. Time-moe: Billion-scale time series foundation models with mixture of experts. arXiv preprint arXiv:2409.1600 2024.
[47] Khanh-Tung Tran, Dung Dao, Minh-Duong Nguyen, Quoe- Viet Pham, Barry O' O'Sullivan, and Hoang D Nguyen. Multi-agent collaboration mechanisms: A survey of llss. arXiv preprint arXiv:2501.0632 2025.
[48] Wiebe Van der Hoek and Michael Wooldridge. Multi-agent systems. Foundations of Artificial Intelligence, 3:887-928, 2008.
[49] Binwu Wang, Yudong Zhang, Xu Wang, Pengkun Wang, Zhengyang Zhou, Lei Bai, and Yang Wang. Pattern expansion and consolidation on evolving graphs for continual traffic prediction. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 2223 2232, 2023.
[50] Hao Wang, Zhiyu Wang, Yunlong Niu, Zhaoran Liu, Haozhe Li, Yilin Liao, Yuxin Huang, and Xinggao Liu. An accurate and interpretable framework for trustworthy process monitoring. IEEE Transactions on Artificial Intelligence, 5(5):2241-22) 2023.
[51] Hao Wang, Haoxuan Li, Xu Chen, Mingming Gong, Zhichao Chen, et al. Optimal transport for time series imputation. In The Thirteenth International Conference on Learning Representations, 2025.
[52] Hao Wang, Lichen Pan, Yuan Shen, Zhichao Chen, Degui Yang, Yifei Yang, Sen Zhang, Xinggao Liu, Haoxuan Li, and Dacheng Tao. Fredf: Learning to forecast in the frequency domain. In The Thirteenth International Conference on Learning Representations, 2025.
[53] Hao Wang, Licheng Pan, Zhichao Chen, Xu Chen, Qingyang Dai, Lei Wang, Haoxuan Li, and Zhouchen Lin. Time-ol: Time-series forecasting needs transformed label alignment. Advances in Neural Information Processing Systems, 2025.
[54] Haotian Wang, Haoxuan Li, Hao Zou, Haoang Chi, Long Lan, Wanrong Huang, and Wenjing Yang. Effective and efficient varying counterfactual prediction with state-space models. In The Thirleenth International Conference on Learning Representations, 2025.
[55] Huiqiang Wang, Jian Peng, Feihu Huang, Jince Wang, Junhui Chen, and Yifei Xiao. Micn: Multi-scale local and global context modeling for long-term series forecasting. In The Eleventh International Conference on Learning Representations, 2023.
[56] Lei Wang, Shanshan Huang, Chunyuan Zheng, Jun Liao, Xiaofei Zhu, Haoxuan Li, and Li Liu. Mitigating data imbalance in time series classification based on counterfactual minority samples augmentation. In Proceedings of the s1 ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2. pages 2962-299299 2973, 2025.
[57] Shilong Wang, Guibin Zhang, Miao Yu, Guancheng Wan, Fanci Meng, Chongye Guo, Kun Wang, and Yang Wang. G-safeguard: A topology-guider security lens and treatment on llmebased multi-agent systems. arXiv preprint arXiv:2502.11 1277 2025.
[58] Shiyu Wang, Haixu Wu, Xiaoming Shi, Tengge Hu, Huakun Luo, Lintao Ma, James Y Zhang, and JUN ZHOU. Timemixer: Decomposable multiscale mixing for time series forecasting. In The Twelfth International Conference on Learning Representations, 2024.
[59] Shuo Wang, Yanran Li, Jiang Zhang, Qingye Meng, Lingwei Meng, and Fei Gao. Pm2. 5-gnn: A domain knowledge enhanced graph neural network for pm2. 5 forecasting. In Proceedings of the 28th international conference on advances in geographic information systems, pages 163-166, 2020.
13

---

[60] Haixu Wu, Jiehui Xu, Jianmin Wang. and Mingsheng Long, Autoformer: Decomposition trans- formers with auto-correlation for long-term series forecasting. Advances in Neural Information Processing Systems, 34:22419- 22440,, 2021.
[61] Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. In International Conference on Learning Representations, 2023.
[62] Xingjian Wu, Xiangfei Qiu, Hanyin Cheng. Zhengyu Li, Jilin Hu, Chenjuan Guo, and Bin Yang. Enhancing time series forecasting through selective representation spaces: A patch perspective. In NewrIPS, 2025.
[63] Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, and Chenjuan Guo. VA A koopman-kalman enhanced variational autoencoder for probabilistic time series forecasting. In ICML, 2025.
[64] Xingjian Wu, Xiangfei Qiu, Zhengyu Li, Yihang Wang, Jilin Hu, Chenjuan Guo, Hui Xiong, and Bin Yang. CATCH: Channel-aware multivariate time series anomaly detection via frequency patching. In ICLR, 2025.
[65] Zhao Xinjie, Fan Gao, Rui Yang, Yingjian Chen, Yuyang Wang, Ying Zhu, Jiacheng Tang, and Irene Li. Reagent: Reversible multi-agent reasoning for knowledge-enhanced multi-hop qa. arXiv preprini arXiv:2503.0695/ 2025.
[66] Vladyslav Yevsiciev. Using Multi-Agent Systems in the Management of Collaborative Robots. PhD thesis, 2025.
[67] Yangyang Yu. Zhiyuan Yao, Haohang Li, Zhiyang Deng, Yuechen Jiang, Yupeng Cao, Zhi Chen, Jordan Suchow, Zhenyu Cui, Rong Liu, et al. Fincon: A synthesized Ilm multi-agent system with conceptual verbal reinforcement for enhanced financial decision making. Advances in Neural Information Processing Systems, 37:137010-137045, 2024.
[68] Tongxin Yuan, Zhiwei He, Lingzhong Dong, Yiming Wang. Ruijie Zhao, Tian Xia. Lizhen Xu, Binglin Zhou, Fangqi Li, Zhuosheng Zhang, et al. R-judge: Benchmarking safety risk awareness for IIm agents. arXiv preprint arXiv:2401.10011 2024.
[69] Wenzhen Yue, Xianghua Ying. Ruohao Guo, DongDong Chen, Ji Shi, Bowei Xing, Yuging Zhu, and Taiyan Chen. Sub-adjacent transformer: Improving time series anomaly detection with reconstruction error from adjaeet neighborhoods. arXiv preprint arXiv:2404. 18948, 2024.
[70] Wenzhen Yue, Yong Liu, Hao Wang, Haoxuan Li, Xianghua Ying. Ruohao Guo, Bowei Xing, and Ji Shi. Olinear: A linear model for time series forecasting in orthogonally transformed domain. Advances in Neural Information Processing Systems, 2025.
[71] Wenzhen Yue. Yong Liu, Xianghua Ying, Bowei Xing, Ruohao Guo, and Ji Shi. Freeformer: Frequency enhanced transformer for multivariate time series forecasting. arXiv preprint arXiv:2501.1398) 2025.
[72] Ted Zadouri, Ahmet Üstün, Arash Ahmadian, Beyza Ermiş, Acyr Locatelli, and Sara Hooker. Pushing mixture of experts to the limit: Extremely parameter efficient moe for instruction tuning. arXiv preprint 209.02200, 2023.
[73] Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are transformers effective for time series forecasting? In Proceddnggs of the AAAI conference on artificial intelligence, volume 37, pages 11121-11128, 2023.
[74] Guibin Zhang, Luyang Niu, Junfeng Fang, Kun Wang, Lei Bai, and Xiang Wang. Multi-agent architecture search via agentic supernet. arXiv preprint arXiv:2502.04188 2025.
[75] Yao Zhang, Zijian Ma, Yunpu Ma, Zhen Han, Yu Wu, and Volker Tresp. Webpilot: versatile and autonomous multi-agent system for web task execution with strategic exploration. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 23378-23388 2025.
14

---

[76] Yunhao Zhang and Junchi Yan. Crossformer: Transformer utilizing cross cross-dimense dimension dependency for multivariate time series forecasting. In International Conference on Learning Representa- lions; 2023.
[77] Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond efficient transformer for long sequence time series forecasting. In Proceedings of the AAAI conference on artificial intelligence, volume 35, pages 11106-11115,
2021.
[78] Zhengyang Zhou, Qihe Huang, Gengyu Lin, Kuo Yang, LEI BAI, and Yang Wang. GReto: Remedying dynamic graph topology-tast -ask discordance via target homophily. In The Eleventh International Conference on Learning Representations, 2023. URL https: /ttp://////ee.....e/ net/forum? ttt/forrm?id-8duT[30 id=8duT3mi_5m
[79] Zhengyang Zhou, Qihe Huang, Binwu Wang, Jianpeng Hou, Kuo Yang, Yuxuan Liang, Yu Zheng, and Yang Wang. Coms2t: complementary spatiotemporal learning system for data- adaptive model evolution. IEEE Transactions on Pattern Analysis and Machine Intelligence, 47 (10):8506-8523, 2025. doi: 10.1109/TPAM..222.33777
Appendix
A Details of Forecasting Sub-task Decomposition
Homogeneous sub-task Decomposition: Multi-Scale Temporal Forecasting. Under the homo- geneous setting, each agent is tasked with predicting future values at a distinct temporal resolution. Specifically, the i-th agent forecasts a future subsequence of length (L/K) i, where L is the full prediction horizon and K is the number of agents. Formally, the prediction from agent i is denoted as
Ó = Agent, (X); Ô E (R(L/K)iXM
where X T is the multivariate historical sequence of length T and M is the number of variables. This design ensures that each agent captures forecasting dynamics at a specific temporal scale, ranging from short-term fluctuations to long-term evolution, thereby forming multi-resolution ensemble.
Heterogeneous sub-task Decomposition: Multi-Aspect Signal Forecasting. To capture different latent components the future signal, we further design a heterogencous sub-task scheme, where each agent is specialized on predefined signal property. This enables orthogonal learning objectives across agents, contributing complementary views to the ensemble. We define four types forecasting sub-tasks in this setting:
We first define the future sequence as Y R. where is the prediction horizon. Let each agent process Y to extract distinct forecasting targets.
(1) Trend forecasting. We estimate the low-frequency trend component by applying temporal average pooling over a padded version Y:
A AvgPool(Padd()) e T
where P.d(.) aligns the length of Y with the pooling window and AvgPool(.) computes segment- wise means. This sub-task enables the agent focus on slowly evolving components in the signal.
(2) Seasonality forecasting. Seasonal dynamics are extracted by removing the estimated trend from the original signal:
where F TrendModel((Y),
15

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with F being smoothed version of Y, either computed or learned. This task guides the agent to attend periodic or residual structures.
(3) Spectral energy forecasting. To encode frequency-domate characteristics, we apply the real-valued Fast Fourier Transform (FFT) and take the magnitude:
E FFT(Y) 121//2+1)xM
The resulting spectral energy profile provides insights into dominant frequencies and periodicities in the future signal.
(4) Statistical descriptor forecasting. summarize using a fixed set of descriptive statisties, capturing distributional properties as follows:
D = ju, a, R. Maxx Mmin] E IR 6x
where
1 (=-MeanY))) =Std(YY), Y Skewness(Y),, K KurtosissY) (Y),
and
mmax max [ Ymin min Y
This task allows the agent to model global signal characteristics a compact form.
More Dataset Details
Table 3: Summary of the 11 datasets used in our experiments, covering diverse domains, temporal resolutions, and feature dimensions.
Dataset
Variate
Input Length
Predict Length
Information
Frequency
Split
ETThl
720
720
Electricity
15mins
6:2:2
ETTh2
720
720
Electricity
15mins
6:2:2
ETTml
720
720
Electricity
15mins
6:2:2
ETTm2
720
720
Electricity
15mins
6:2:2
Weather
21
720
96 720
Environment
10mins
7:1:2
Temperature
108
720
96 720
Environment
3hours
7:1:2
AOShunyi
11
96
720
96 720
Environment
lhour
7:1:2
AQWan
11
96
720
96 720
Environment
1hour
7:1:2
PM2.5
108
96 720
96 720
Nature
3hours
7:1:2
ZafNoo
11
96
720
96
720
Nature
30mins
7:1:2
CzeLan
96
720
96
720
Nature
30mins
7:1:2
As shown in Table 3, we evaluate our framework on 11 multivariate time series datasets spanning three real-world application domains: Electricity, Environment, and Nature. These datasets exhibit diverse characteristics in terms of feature dimensionality, sampling frequency, and domain semantics, offering a comprehensive benchmark for assessing forecasting performance under different temporal patterns and data complexities. The Electricity domain includes four ETT datasets: ETTh1, ETTh2, ETTml, and ETTm2 [77, 60]. Each contains 7 variates recorded at 1 15-minute intervals, primarily reflecting industrial power consumption dynamics. The Environment domain covers Weather [60], Temperature [59], AQShunyi, and AQWan [41]. Weather contains 21 meteorological variables sampled every 10 minutes, while Temperature and PM2.5 have higher dimensionality (108 variates) coarser 3-hour frequency. AQShunyi and AQWan offer l-dimensional hourly air quality
readings from different regions in Beijing. The Nature domain consists of PM2.5 [59], ZafNoo, and
16

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CzeLan [41], all of which represent long-range environmental trends collected over various regions, with sampling frequencies ranging from 30 minutes to 3 hours. Across datasets, the input and prediction sequence lengths are consistently selected from the range 96 to 720 to ensure uniform temporal coverage across tasks. For the ETT datasets, we follow prior work and adopt a 6:2:2 split for training, validation, and testing. For the remaining datasets, we use a 7:1:2 split. This ensures both consistent evaluation and fair comparison with previous studies.
C More Implementation Details
All experiments conducted on server equipped with 8 NVIDIA A100 GPUs (80GB memory each). MAFS is implemented using PyTorch 1.13.0 [39] and optimized using the Adam opti- mizer [17] with L2 loss. We investigate four distinct communication topologies for the agent interaction graph G, including ring, star, chain, and fully-connected structures. Each forecasting agent instantiated using the iTrrnsformee architecture [28], with a unified configuration across all experiments: a fixed learning rate of le-3, a hidden dimension of 128, and 2 encoder layers. To evaluate the scalability of MAFS, we vary the number of agents N {4.8, 12, 16, 20, 24). MAFS training is conducted in two stages. In the first stage, each agent is independently optimized on its assigned sub-task using& learning rate of 1e-3 for 10 epochs. In the second stage, we freezee the parameters of all forecasting agents and jointly finetune only the topology-awan weight adjuster and the agent-rated voting aggregator. This stage also runs for 10 epochs, using smaller learning rate of le-4 to enable stable convergence during topology adaptation and collaborative forecasting. For all tasks, we adopt symmetric prediction setting where the historical input length equals the forecasting horizon, following the protocol in [76], to enable consistent evaluation across datasets. To ensure fair comparison, we re-run iTransformer under our unified setting (including learning rate, hidden size, and number of layers). For all baselines other than iTransformer, we use reported results from the iTransformer and TFB [41] papers, except for the temp and pm2. 5 datasets, where we re-run all identified and corrected bug in the original evaluation process: the
baseline models. Importantly, test_loade _oaddordrrrrrr was configured with srop_last=Trus during testing, which led to the exclusion of final test batches. We explicitly drop False ensure fair and complete evaluation [41].
D Full Results of Comparison Between Two Types of Sub-tasks Division
Figure to Figure 18 present a comprehensive comparison of homogeneous--orrelatee and heteroggeneous-corelaatee sub-task configurations across all 11 datasets. The results demonstrate that each configuration exhibits distinct advantages under different data characteristics, emphasizing the need for adaptive task decomposition in multi-agent forecasting.
Apent=4 Datased= AQShaayi
Agent-8 Dataset-AQShuny
Apent-12 AQQhuni
1716
0717
6.112
MSE
4.700
4.794
6:790
144
Reg
145
K44
CMd4
Kig
Agent=16 DatasttAQShuuy
Agent=20 20 Dataset-ASShuny
Agent 24 Datase= AQShunyi
0.71
8712
6380
MISE
MSE
0.764
0.78
3.10
0.60
0330
Figure 8: Performance comparison Thomogencous--orrellaed and heterogenneous-corrrlatteee sub- tasks on AQShunyi.
17

---

Agent-12
0230
0.812
1.11
MSE.
0.110
0.00
6:800
K0ng
Agrné-16 Datase-AQQWas
Agent-20 InfawitAAQia
Agani-24 AQWan
0331
0.111
MSS
0.800
01445
144
Cbun
Fab
K4g
C.44
Falp
30a
Bing
Figure 9: Performance comparison of comnogencous--corrllttee and heterogeencous-correlaaddd sub- tasks on AQWan.
Agent-4 (relsnt-Cee.on
Agent-8 Datatet-Ceelan
Agent-12 Dataset-Ceel
6310
1250
MIE
0.238
0.33
0221
6:30
Agent-16
Dataset-CeeLan
Agent-24
0110
0.234
MIS..
MSE
0.244
Paffs
King
Figure 10: Performance comparison of homooenecous-corccatce and beterogeencous-correladde sub- tasks on CzeLan.
Apented Dataset-ETTh
Agent-R Dataet-ETTh
Agent-12 Dataset-ETTh.
0.441
E40
0442
0.411
MSV.
8430
0.43
0.33
0.43
Ring
140
Krng
140
K14
Apent=16 Pataser-KTTTI
Agent-20 Pataset-ETThh
Agent=24 Datasct-E1 E.T
11443
0.20
04455
0.431
11SE:
MISE
0.422
E4250
0.072
0,050
0.33
Figure 11: Performance comparison of homogeneous--corelattee and heterogeneous-correeene sub- tasks on ETTh1.
18

---

Agent-B
Agent-12
0.50
0.79
MSE
0.372
0.240
0.34
6360
Kig
Bag
Agent-16 PTTh
Agral-20 Datavi-FTThh
Agent-24 -TTh
0.712
0.54
MSS
0.54
0357
01445
144
Cbun
Fab
Falp
Big
Figure 12: Performance comparison of homogenneous-corrlltte and leterogeencous-correladdd sub- tasks on ETTh2.
Agent-4 Dataser-ETImi
Agent-8 Datase-ETiml
Agenr-12 Dataser-
0..73
6311
AISE
0.71
MSE
8370
MINE
0370
0.57
0.60
0.50
Agent-16
0.00
03312
MES.
MSE
6.300
0.75
0.572
Figure 13: Performance comparison of homogeneoos--corccatee and heterogenccous-corclaaaee sub- tasks on ETTml.
Apente4 DatasetFFTTm!
Apent-8 Dataset-ETTer
Agent-12 Dataset-ETTmn
035
A17715
MSE
0.778)
0.300
C.24
Brng
F4b
CM44
K0ng
Apenr-16 Dataset-ETTmi
Agent=20 20 Daraset -TTT
Apent-24 Dataset-ETTI ETTm
0.279
6370
MINE
4.77
MSE
0.273
630
Figure 14: Performance comparison hwwogeneous-coreeeeeeee and heterogeneous-corre.eeee sub- tasks on ETTm2.
19

---

0.43
MSE.
MSE
0.41
4.11
6412
1.60
0.48
6480
King
Agent-16 Datasrt-PM2.5
Agret-20 PMta
Agent-24 Datasei- PMI.5
E410
4.40
MIS
6-112
1412
0.400
0.402
01445
144
Cbun
Fal
CBs4
Falp
BIng
Figure 15: Performance comparison of homogenneous-corrllltd and beterogenecous-correladdd sub- tasks on pm2.5.
Agent- Dataset Temp
A Demm
Agent-12 Dataset-
119
0.171
MSE
MINE
0.18
0.141
Rize
Agent-16
Temp
Agent-24 Dataset-Temp
0.194
0.17
6166
1174
MSF.
0.100
0.14
6.155
maady
King
Bing
Figure 16: Performance comparison of hhomoeencous--corclatd and beterogenccou--corrlladdd sub- tasks on temp.
Agent-4 Dataset-Weather
Apent-X Detawet-Warther
Agent-12 DatheetWWather
0.343
MSE
MSE
0.38
0.24
Reg
0.300
640
382
Krg
0.27
Cisls
380
Kig
Apear-16 WeatherWWather
Apent-20
-eatterr
Apent-24 Weather
03412
1.358
MSE
03335
MSE
A342
02480
82409
42212
Figure 17: Performance comparison of hwwogeneous-coreeeeeeee and heterogeneous-coreelnee sub- tasks on weather.
20

---

Agent-4
Dalio
Agent-12 Datavet-ZalNoo
0540
1.50
0.54
MSE.
6.55
4.53
8.235
0.50
0.32
King
Agrnt-16 Dataset-Zaaoo
Agen-20 DalawttZafNoo
Agrnt-24 Zatavet-ZaNoon
0.54
624)
0.51
0.53
0.53
0.58
8:5
144
Cbun
Fall
Fall
Figure 18: Performance comparison of homogeneeous--orrclaaeeee and heterogeneeous-correlace sub- tasks on ZafNoo.
E Full Results of Different MAFS Scales
Figure 19 to Figure 29 show the full results of MAFS under varying numbers of agents across all datasets. Overall, we observe that increasing the number agents generally leads to more stable forecasting performance, with reduced variance across different runs. Although more agents do not always yield the best accuracy, the ensemble effect tends to enhance robustness. This finding supports the scalability of MAFS in diverse time series scenarios and highlights the trade-off between performance and computational overhead when scaling agent populations.
Hae--Harm Clein Dats-
Trak:
AQSlmnd
MST.
MSF
Agest
Agest
Agost
Agent
Tade-fiit Chnm-Chhth Boirr
Tedbefler Cram-Tdll Bate-AQNurst
Task-fletz CanmeBier
Took-llete Compebirr Baterk
MSR
MSE
NSE
Ageat Number
Ageat Number
Ageat Number
Agest Nomber
Figure 19: Performance comparison of different agent numbers on AQShunyi.
MSS.
MSR
MSE
MSC
Agest Number
Agest Number
Agest Number
Agest Number
Tadksthut LinneCaah 1atan30/Was
Tasbettm Omnehstt DateeA
Tobeilelr Commetting AWWan
Iinkslietc Commetter Bates
1152
SINE
SISE
Aprst Number
Aprat Number
Aprat Number
Aprat Number
Figure 20: Performance comparison different agent numbers on AQWan.
21

---

Tack Herre Chrte-Chele Dutp-Cad 10
Ted--lieoo Conte Full. Dura-Cal 15
Deb--Blette Cxtre-Rnn Daty:Crlan
Tedi-flama CammerSur Bute
MAR.
Number
Agest Number
Number
Number
3155
NEW
Aprat Number
Aprat Number
Aprnt Number
Agent Number
Figure 21: Performance comparison of different agent numbers on CzeLan.
Tec- Nei--ieess Cants-Chais Der--111
Tec--Hetee Cottre-Full bata ETTh
Toce Edde-Blaess Coner-Ring Datee
Tesl Hiero Conteraa Bai
MAT.
Number
Agent Number
Number
Number
11NE
Agont
Agost
Agont
Agent
Figure 22: Performance comparison of different agent numbers on ETThl.
Iak--Heette CortenChala Dith-EThe
Tac--Here Crmme-Fuh Piia-ETThe
Taab-fllerss CommenRiyy Data
Bado-Baams Camme Nar Date
Number
Number
Number
Number
MISP
MISE
Apont Number
Agont Number
Apent Number
Apent Number
Figure 23: Performance comparison of different agent numbers on ETTh2.
Tac--Hoen Cones-Chais Dan-ETTal
Tede-Hore Call Dura-
Tock Takk-lleess Comm--ity Date-ETTni
Tedi-flam Camm-Sar Dun---ii
MNN.
Number
Number
Number
Tesl: Number
Hele
Hete. Faly.
Agest
Agest
Agent
Agent
Figure 24: Performance comparison of different agent numbers on ETTml.
22

---

Tak--Berte Chrre-Chels Dite ETTn
Ted-lhero Conne Ful Dun-ETTin
Tede-flam Camm-Sar Bite-
MAR.
Number
Number
Number
Number
Dia-ETled
1158
SISE
NIN
Aprst Number
Aprat Number
Apent Number
Aprnt Number
Figure 25: Performance comparison of different agent numbers on ETTm2.
Tach-Bleess Chrne-hhsh PNtL
Took iitees ConersiFully Dai--PM5
Test- Hiero Correr Ring Durx-PA125
Tock- Hoato Commesaar Dats-PMD.5
MNT.
MAE
MSC
Agent Number
Agent Number
Number
Number
Dair-PME25
MINE
MISE
Agont
Agost
Agont
Agent Number
Figure 26: Performance comparison of different agent numbers pm2.5.
Daak -llerr Char Date-Torp
Tack-llerns Chers-Fudl Data-Terp
Tralo-Elames Consenitin Datar Temps
Tack-lbemt Commeter Bate-hup
MSR
MSR
MSE
Agrst Number
Agest Number
Agest Number
Number
Tisk-Heek:
Tede-litte
1153
Apont Number
Agont Number
Agent Number
Agent Number
Figure 27: Performance comparison of different agent numbers temp.
Tak--Here Chazs Bur--Weather
Tadl- Homno Commo Full Dats-Waather
Tab--llems Cenrs Rit Date-Woather
Teeb-flamm Cammeder Banth
MANE
MSE
MSE
Number
Apest Number
Number
Number
Weather
Teal
Tesh: Het
Hetr
MSN
MSE
MSE
Agost
Agest
Agost
Agest
Figure 28: Performance comparison of different agent numbers on weather.
23

---

Tul-Ihrmn Canteolall Cldn BeteeTaftte
Dabelllm Camm-Fally Daterafft
Tabellere Conee-Rias Date-Zafaes
Iak-illms Conn-dtu DanrZaPaa
Autines
MAN.
MSE
Agrat Number
Number
Number
Number
Tek-Hlitr
Date-ZafSaa
1155
Agont Number
Agent Number
Agent Number
Agent Number
Figure 29: Performance comparison of different agent numbers ZafNoo.
Limitation
This work introduces MAFS, novel multi-agent forecasting system that successfully leverages collective intelligence to enhance long-term time series forecasting. Through specialized agent design, structured communication, and adaptive decision fusion, MAFS achieves consistent performance provements across diverse datasets and forecasting horizons, demonstrating its strong generalization and robustness. However, despite these promising results, multi-agent forecasting still faces certain limitations. Specifically, the system exhibits occasional instability during training, particularly when the number of agents increases or when dealing with highly volatile datasets. This instability may arise from conflicting agent objectives or suboptimal communication structures that hinder effective information integration.
In future work, we plan to further improve MAFS from the following perspectives:
Adaptive Communication Topologies: Develop dynamic topology learning mechanisms
that can automatically adjust inter-agent connections based on data characteristics and task complexity, reducing reliance on manually defined structures.
Diverse Task Decomposition Strategies: Explore more fine-grained and semantically meaningful task divisions, enabling agents to specialize in richer forecasting aspects such as uncertainty estimation, anomaly detection,
event prediction.
We believe these directions will further enhance the stability, adaptability, and forecasting capability of multi-agent systems in real-world scenarios.
24

---

G
Full Long-term Time Series Forecasting Results
Table 4: Comparison of long-ter term time series forecasting methods on 11 datasets using MSE and
MAE (lower is better). Best results are marked in red second- best results are underlined in blue
MAFS
(Transtormer
TimeMixer
PatchTST
Crossformer
TIDE
TemesNet
DI.inear
Autofommer
Informer
Methods
(Ours)
[2024]
[2024]
[2024]
[2023]
[2024]
[2023]
[2025]
[2021]
[2021]
Danasets
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MAE
MSE
MAE
MSE
MSE
MAE
MSE MAE
MSE
MAE
MAR
96
0.381
0,399
0.392
0.4
0.414
0.419
0,423
0.448
0,479
0,464
0,384
0:402
(0.366
0.449
0.459
0.865
0.713
192
0.424
0.442
0.442
0.421
0,46
0.445
0.474
0.525
0.492 0:436
0..437 0.432
0.5 0.482
1.008 0.792
336
0.444
0.442
0.483
0.473
0.484
0:458
0.501
0.466
0.57
0.546
0.,565
0.515 0:491
0:469
0:481 0:459
(0.521
0.496
1.107 0.809
720
0.478
0.484
0.552
0.537
0.498
0..882
0.488
0.653
0.621
01.594
0.558
0.521
[0:519 0.516
(0:514 0.512
1.181 0.865
Avg
0.433
0.437
0.467
0.466
0.447
0.44
0.469
0.454
0.529
0.522
0..44L
0.507
0.458
0.45
0.445 0.452
0.496
0.487
1.04 0.795
96
0.2899
0.341
D.3004
0.353
012299
D 14341
0.302
0.348
0,745
0,566
0.4 0,44 0:34
0.374
(0.558 0. 387
01,346 0.388
3,755 1,525
192
0.358
0.391
0.399
0.417
0:372
0.392
0.388
0.4
0.877
0.656
(1,328
0,509
0,402
0,414
(0.477 0.476
(0:456
0.452
5.602
1,931
ETTh2
336
0.372
0.406
0:41
0.429
0.386
0.414
0.426
0.433
1,043
0.731
01.643
0.571 0,452
0,452
(0,594 0,541
00:482
0.486
4.721 1.835
720
0.405
0.438
0.433
0.463
0:412
0.433
0.431
0.446
1.104
0,763
(1.874
0.679 0.462
0.468
(0.831 0.657
(0.515
0.511
3.647 1.625
Avg
0..56
0.799
0.386
0,415
0.364
0.395
0.387 0.407
0.942
0.684
(1.611
0.55 0.414
0.427
(0,559 0.515
0.45
0.459
4.431 1,729
96
0.323
0.361
0,336
0,372
0.32
0.357
0.329 0.367
0.404
0.412
0..36
0.387 0.338
0.375
00.345 0,372
0.500
0.475
0.672 0.571
192
0.344
0.373
0,366
0.39
0
0.381
0.367 0.385
0.45
0.451
0.399
0.404
0.374
0.387
0.38
0.389
0.553
0.496
0.795 0.669
ETTml
0.372
0,393
0.38%
0:403
0.39M
0,41
0.533 0.51.
01,4288
0:41
0.411
0.:43
(0.621 0.537
1,212
0.4428
0.426
0.442
0:441
0.454
0:439
0,589
01:487
0,461
0,478
(0:474
(0.671 0.561
1.166
Avg
0.366 0.385
0,383
0.395
0.387
0.4
0.196
0.,119
0.119
0.1 0.106
00:103 0.407
(0.588 0.517
0,961
0.117
0.26
0.188 0.266
0.255
0.125
0.259
0..287
0.366
0..007
0,305
0:187
0.267
10:193 0:292
(0:255 0.339
00,365 0.453
192
0.239 0.302
0.256 0.317
0.237
0.299
0.241
0.302
0.414
0.492
0.29
0.364 0,219 0.309 00.284 0.362
0.2281 0.34
0.533 0.563
BTTm2
336
0.277
0.329
0,313
0.355
0.298
0.34
0.305
0.343
0.997
0.542
0.337
0.422 0.321 0.351 (0.369 0.427
0.339 0.372
1,363 0.887
720
0.369
0.395
0.407
0.417
0.391
0.396
0.402
0.4
1.73
1.042
0.555 0.524 0.408 0.403
(0.554
0.522
0.433 0.432
3.379 1.338
Arg
(0,665
0,321
0.29
0.339
0:275
0.323
0.281
0.526
0.757
0.61
00,358
0,404 0,291 0,353 0.35 0.401
00,327 0,371
1.41 0.81
96
0.166
0.206
0,175
0.215
0.163
0.209
0.177
0.218
0.158
0.23
0.200 0.261 0.172 0.22 19.196 0.255
0.266 0.336
0.3 0.384
192
0.2001
0.244
0.214
0.254
0.208
0.25
0.225
0.259
0.200
0.277
0.242 0.298 0.219 0.261 (0.237 0. 0.296
(0,307 0.367
0.598
0.544
Weather
336
0.2246
0.282
0.252
0.288
0:251
0.287
0.278
0.297
0.272
0.335
(1.787
0,335 0.28 0.306
(0.283
0.335
(0,359
0.395
00.578 0,523
720
0.318
0.338
0.331
0,348
0.339
0.341
0.354
0.348
0.398
0.418
0.35L
0.386 0.365
0.359 0.345 0.381
0.441 0.428
1.059 0.741
Avg
0,233
0.267
0.243
0,276
0.24
0.271
0.259
0.281
0.259
0.315
0.271
0.32 0.259
0.287
0.2265 0,317
0.338
0.382
0.634 0,548
0.711
0.499
0.742
0.533
0.652
0.488
0.708
0.658
0:651
0.7736
0.529
01.754 0.542
192
0.697
0.502
0.507
00.667
0.501
0.774
0.569
0.707
[0.691
0.512
0.733 0.535
0.759 0.536
AQShunyi
0.668
0.506
0.687
0.564
0.711
0.515
0.704
0.515
0.822
0.785
(0.716
0.529
0.83 0.566
0.837 0.56
720
0.728
0.533
0.752
0.539
0.749
0.554
0.77
0.538
0.247
0.518
0.8003
0.566 0.755
0.527
(0.765
0.556
(.7754
0.532
(1.777 0.543
Avg
03.701
0.500
0.723
0.515
0.719
0.529
0.705
0.509
0.504
0.7778
0.554 0.726
0.516
(0:706
0.522
(1.764
01541
(3.782 0.545
96
0.8004
0.44
0.814
0.491
0.829
00.456
0.745
0..4
0.75
0.465
01833
0.524 0.791
0.48%
(1.756
0.488
0.858
0.518
(3.901 0,522
192
0.786
0.496
0.801
0.497
0.88
0.501
0.7792
0.491
0.762
0.479
0180 0,516 0.777
0.49
0.8
0.500
00.803
0.513
(18333 0.521
AQWian
336
0.765
0.49
0.786
0.502
0.791
0.538
0.819
0.503
0.802
0,504
018558
0.552 0.814
0.505
(0.823
0.516
0.8826
0.523
0.844 0.525
720
0.854
0.529
0.868
0.536
0.883
00.499
0.89
0.533
0.83
0.511
0.913
0.551 0.869
0.5
(0.891
0.548
(0.872
0.547
00.883 0.532
Avg
0.802
0.503
D.817
0.507
0.828
0.499
0.812
0.499
0.786
0.49
(18856
0,536 0.813
0.5
(08818
0.512
0.84
0.525
(.8666 0.525
96
0.199
0.248
0.21
0,255
0.202
0.263
0.183
0.251
0.581
0.443
0.186
0.256 0.176
0.237
0.211
0. 0.289
0.238
0.294
0,25 0,305
192
0.214
0.258
0.231
0.275
0.22
0.288
0.208
0.271
0.503 0.705
0.226
0.29 0.215
0.279
0.252
0.323
0.29 0.341
0.295 0.337
CeeLam
336
0.229
0.281
0.243
0..66
0.244
0.302
0.971
(1.238
0.224
0,288
(0.317 1.366
(0,322
01,33
0.29%
0.245
0.254
0.302
0.335
1.566
0,762
01.295
0.363
0,282
(0.358
0. 0.392
0..379
0.427
00,384 0.416
Avg
0.271
0.232
0.228
0.28
0.227
0.29
0.956
0.576
0.2337
0.303
0.224
0.285
(0.284
0.342
0.330 0.355
0.311 0.355
0.466
0.411
0.476
0.419
0.481
10.404
0.444
0.426
0.432
0.419
00.508
0.479
0.424
0.434 0.411
(0.524 0.468
0..541 0.473
192
0.505
0.439
0.529
0.457
0.527
0.154
0.998
0.156
0.479
0.149
0.536
0.191 0.191
0.116
0:184
0.444
0.687
0.558
0.708 0.575
ZafNoo
336
0.541
0.465
0.568
0.488
0.56
0.444
0.53
0.48
0.521
0.469
0.592
0.519 0.551 0.479
0.518
0.464
0.8835
0.669
0.851 0.661
720
0.567
0.494
0
0.509
0.585
0.46
0.574
0.499
0.543
0.483
0.642
0.533 0.627 0.511 0.548
0.486
0.854
0.702
0.876 0.699
Arg
0.52
0.451
0.541
0.468
0.538
0.44
0.511
0.465
0.494
0.455
(1,569
0,,488 0,537
0.465
0.496
0.451
(0.725
0.599
01.744 0.602
96
0.428
0.428
0.438
0.432
0.445
0.48
0.46
0.468
0.451
0.46
0..475
0.484 0.481 0.481
[0.453
0.466
(0.525
0.512
00.88 1 0.594
192
0..42
0.425
0.436
0.429
0.45
0.408
0.462
0.449
0.463
0.446
(0.493
0.476 0.455 0.446 (0.447
0.431
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0.502
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0.379
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0.412
0.417
0.395
0.441
0.466
0.505
0.447
0.449
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0.473 0.409
0.508 (0.451 0.485
0.53
0.553
(0.524 0,546
720
0.357
0.399
0.4
0.408
0.37
0.414
0.452
0,493
0.464
0,514
0..19
0.554 0.19 0.535
0.4158 0.524
00,485
0.53
0.419 0,566
Avg
0.398
0.414
0.421
0.421
0.41.5
0.436
0.46
0.479
0.472 0.456
0.488 0.497 0.473 0.492 0.445 0.477
0.515
0.524
0.539 0.561
0.139
0.282
0.1.38
0.144
0.306
0.144
0.3
0.186
0.377
0.155
0.323
0.162
0.329
(0.152 0.317
(0185
0.373
0.199 0..455
0.279
0.145
0.317
0.309
0.203
0.435
0.157
0.173 0.374 (0.155 0.322
00.213
0.45
0.199 0.429
Temp
336
00.138
0.289
0.205
0.352
0.297
0.147
0.313
0.209
0.435
0.1669
0.357 0.185 0.387
10.162 0. 0.342
(0:331
0.492
0.243 0.506
720
0.151
0.3
0.204
0.352
00.298
0.153
0.303
0.224
0.445
0..173
0.312
(0.167 0.329
0.347
0.683
0.311 0.627
Avg
0.14
0.288
0.173
0.321
D.146
0:3014
0.147
0.306
0.206
0.423
00.164
0.338
0.208
0.478
(0:159 0:327
01.24
0.2338 0,492
25

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The abstract and introduction clearly state the main contributions and scope of the paper. In particular, the introduction outlines the motivation for applying multi-agent systems time series forecasting, explicitly presents the key challenges, and summarizes the core solutions proposed by MAFS, including sub-task decomposition, inter-agent com- munication, and voting aggregation. These claims consistent with the overall scope and objectives of the work.
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32


Reviews:
[{"review_id": "xQe8WWnCmx", "reviewer": "Reviewer_HBiT", "summary": "The authors propose a multi-agent forecasting system (MAFS) that tackles shortcomings of single-model forecasters, particularly under non-stationary conditions. MAFS splits the overall task into several subtasks such as different segments of the prediction horizon so each agent can specialize. Agents share information through structured message-passing graph, and their outputs are combined by a global voter weighted by per-agent confidence scores. With iTransformer serving as the backbone encoder, MAFS outperforms a range of baseline models.", "questions": "- Q1. Relation to hierarchical and multi-resolution forecasting: Could your homogeneous horizon split be viewed as a special hierarchical forecast (e.g., TimeMixer’s coarse-to-fine stages)? How would MAFS handle reconciliation constraints in hierarchical series?\n- Q2 \"Each agent is assigned a distinct sub-task (e.g., different signal characteristics)\" Do the sub-tasks change per agent across the training? If not do tasks ever migrate between agents during training. Would this be beneficial for generalization or overfitting on a task?\n- Q3 Please see W4, could you provide your framework for the different baselines with different enncoders.\n- Q4 Could you provide a Comparison to MoE / bagging, i.e. could you add a strong MoE baseline (e.g., Time-MoE) and a simple ensemble of K independently initialised iTransformers with learned linear weighting. How much of the gain comes purely from ensembling?\n- Q5 I don't think your ablation is sufficient, it would be significant to see how beneficial certain aspects are in isolation, i.e. the message-passing communication in an ensemble (w/o STS)", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths:** \n- S1 The authors clearly articulate three key challenges in multi-agent forecasting—task decomposition, limited perception, and collaboration bottlenecks—and address each one.\n    \n- S2 The framework is modular and extensible: agents are plug-and-play encoders, and the communication graph is topology-agnostic, so the system should adapt to future backbones or larger agent pools.\n    \n- S3 The experiments cover multiple data sets, communication topologies, agent scales, and task-division schemes.\n    \n- S4 Figure 1 is especially helpful and well designed; overall, the figures are clean and easy to follow.\n\n\n\n**Weaknesses:** \n- W1 At a high level (this is very simplified) MAFS resembles an ensemble. The paper positions itself against Mixture-of-Experts but stops short of an empirical comparison with a strong MoE baseline or standard bagging/stacking ensembles.\n- W2 Empirical scope feels narrow (and a bit unfair): The technical story checks out, but in practice the authors only ever wrap one encoder—iTransformer—inside MAFS. That leaves me wondering whether the gains come from the multi-agent trick or just from picking a lucky backbone. If, as you claim, _any_ encoder can slot in, then please show it: TimeMixer + MAFS, PatchTST + MAFS, maybe even an old RNN + MAFS. Stack those side-by-side with their vanilla counterparts the same way iTransformer is treated in Table 1. Seeing that full matrix would make the numbers feel a lot more convincing (and, frankly, would shut down the \"it’s just an ensemble\" objection). Right now the comparison feels lopsided, and it’s hard to judge how much credit belongs to the framework itself.\n- W3 Currently, recent SOTA are sparsely covered. Models such as CycleNet, xLSTM-Mixer, (_not as encoder_ MoEs) and State Space Models (e.g., S-Mamba, Chimera) are absent from Table 1, leaving open whether MAFS still leads when competitive encoders are used.\n- W4 Following up on S4. Including multi-model forecasting (i.e., ensembles) in the figure would provide the entire picture.\n\n\n**Minor concerns**\n- **Figure 5** is barely readable, and the green curve is hard to distinguish. Consider a shared legend, fewer plots in the main text (move the rest to the appendix), and larger fonts.\n    \n- **Figure 6**: spell out _Heterogeneous_ and _Homogeneous_.\n\n\n**Overall assessment**\nThe method is sensible, but the experimental comparison skips equally expressive ensemble baselines and alternative backbones, so the quantitative claims aren’t fully substantiated. The writing is mostly clear and the figures are well crafted. MAFS is potentially valuable, yet incremental relative to MoE/ensemble literature; its impact hinges on demonstrating backbone-agnostic benefits. While applying a multi-agent lens to time-series forecasting is interesting, the ingredients—task splitting, GCN message passing, confidence-weighted voting—are familiar.", "was_revised": true, "final_justification": "The new experiments add all missing baselines (Time-MoE, CycleNet, xLSTM-Mixer, S-Mamba, plus four strong ensemble backbones), and MAFS now wins or ties almost everywhere. Detailed ablations show where the gains come from—i.e., task splitting is the main driver—and the TEMP-720 case study pinpoints underfitting as the cause of the earlier ensemble dip, not overfitting or cherry-picking. The authors also compare two-stage vs. end-to-end ensembles and trace their failures to temporal covariate shift, explaining why naïve ensembling isn’t enough. Their evaluation techniques are, after a round of clarification, scientifically sound.\nThe method remains backbone-agnostic across iTransformer, PatchTST, TimeMixer, and SegRNN. Minor issues remain, and obviously, we cannot check whether the figure updates were made accordingly. However, I believe the authors will manage to do so. Nothing is a major blocker. Overall, the paper now offers a solid, well-substantiated contribution to long-horizon time-series forecasting.", "rebuttal": "Dear Reviewer HBiT,  \n\nThank 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.**\n\n---\n>**W1&Q4 Provide a Comparison to MoE / Ensemble Baselines**\n\nThank 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.**\n* **Time-MoE**: We use pretrained weights and fine-tune autoregressively for 10 epochs on each test dataset before evaluation.\n* **Ensemble**: Following your Q4 suggestion, we **implement ensembles for four models**, iTransformer, TimeMixer, PatchTST, and SegRNN, combining them via a learnable linear layer.\n\n||MAFS(iTrans)|Time-MoE|Ensemble(iTrans)|Ensemble(TimeMixer)|Ensemble(PatchTST)|Ensemble(SegRNN)|\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|ETTh1|**0.433 0.437**|0.452 0.449|0.457 0.486|0.448 0.446|0.472 0.452|0.461 0.464|\n|ETTh2|**0.356 0.394**|0.375 0.405|0.364 0.402|0.377 0.412|0.378 0.395|0.367 0.407|\n|ETTm1|**0.366 0.388**|0.412 0.435|0.442 0.459|0.489 0.488|0.401 0.423|0.403 0.431|\n|ETTm2|**0.265 0.322**|0.297 0.337|0.369 0.404|0.451 0.455|0.313 0.379|0.315 0.370|\n|weather|**0.233 0.268**|0.270 0.294|0.240 0.288|0.246 0.290|0.238 0.284|0.237 0.288|\n|AQShunyi|**0.701 0.510**|0.799 0.541|0.739 0.557|0.796 0.578|0.718 0.548|0.723 0.523|\n|AQWan|**0.802 0.503**|0.879 0.531|0.853 0.555|0.896 0.566|0.820 0.541|0.830 0.515|\n|CzeLan|**0.222 0.271**|0.242 0.293|0.275 0.335|0.296 0.335|0.277 0.308|0.350 0.406|\n|ZafNoo|**0.520 0.452**|0.551 0.448|0.539 0.474|0.555 0.481|0.565 0.491|0.530 0.462|\n|pm2_5|**0.398 0.414**|0.454 0.446|0.453 0.493|0.430 0.459|0.537 0.573|0.544 0.577|\n|temp|**0.140 0.288**|0.169 0.316|0.283 0.414|0.201 0.352|0.304 0.419|0.447 0.523|\n\nThe 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.**\n\n---\n>**W2&Q3 MAFS vs. Ensemble with Different Backbones**\n\nThank 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:\n1. MAFS’s multi-agent architecture effectively activates different backbones’ potential, **serving as a plug-and-play accuracy booster (also see Figure 4, Page 8)**.\n2. **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.\n\n||MAFS(PatchTST)|Ensemble(PatchTST)|Single(PatchTST)|\n|:-:|:-:|:-:|:-:|\n|ETTh1|**0.437 0.439**|0.472 0.452|0.469 0.455|\n|ETTh2|**0.373 0.394**|0.378 0.395|0.387 0.407|\n|ETTm1|**0.371 0.39**|0.401 0.423|0.387 0.4|\n|ETTm2|**0.265 0.318**|0.313 0.379|0.281 0.326|\n|weather|**0.231 0.272**|0.238 0.284|0.259 0.28|\n|AQShunyi|**0.678 0.496**|0.718 0.548|0.705 0.509|\n|AQWan|**0.774 0.483**|0.82 0.541|0.812 0.499|\n|CzeLan|**0.217 0.273**|0.277 0.308|0.227 0.29|\n|ZafNoo|**0.494 0.453**|0.565 0.491|0.512 0.465|\n|pm2_5|**0.407 0.42**|0.537 0.573|0.46 0.479|\n|temp|**0.142 0.289**|0.304 0.419|0.147 0.306|\n\n||MAFS(TimeMixer)|Ensemble(TimeMixer)|Single(TimeMixer)|\n|:-:|:-:|:-:|:-:|\n|ETTh1|**0.434 0.426**|0.448 0.446|0.447 0.44|\n|ETTh2|**0.353 0.382**|0.377 0.412|0.365 0.395|\n|ETTm1|**0.368 0.381**|0.489 0.488|0.381 0.396|\n|ETTm2|**0.264 0.314**|0.451 0.455|0.275 0.323|\n|weather|**0.231 0.264**|0.246 0.29|0.24 0.272|\n|AQShunyi|**0.695 0.502**|0.796 0.578|0.719 0.53|\n|AQWan|**0.781 0.478**|0.896 0.566|0.828 0.499|\n|CzeLan|**0.22 0.273**|0.296 0.335|0.228 0.28|\n|ZafNoo|**0.518 0.425**|0.555 0.481|0.538 0.441|\n|pm2_5|**0.401 0.416**|0.43 0.459|0.415 0.436|\n|temp|**0.139 0.291**|0.201 0.352|0.146 0.305|\n\n||MAFS(SegRNN)|Ensemble(SegRNN)|Single(SegRNN)|\n|:-:|:-:|:-:|:-:|\n|ETTh1|**0.43 0.438**|0.461 0.464|0.442 0.45|\n|ETTh2|**0.368 0.399**|0.367 0.407|0.389 0.42|\n|ETTm1|**0.369 0.39**|0.403 0.431|0.38 0.405|\n|ETTm2|**0.262 0.32**|0.315 0.37|0.27 0.327|\n|weather|**0.227 0.272**|0.237 0.288|0.237 0.275|\n|AQShunyi|**0.686 0.498**|0.723 0.523|0.701 0.504|\n|AQWan|**0.774 0.481**|0.83 0.515|0.8 0.496|\n|CzeLan|**0.218 0.268**|0.35 0.406|0.23 0.284|\n|ZafNoo|**0.504 0.446**|0.53 0.462|0.512 0.451|\n|pm2_5|**0.397 0.41**|0.544 0.577|0.421 0.426|\n|temp|**0.146 0.295**|0.447 0.523|0.207 0.341|\n\n---\n>**W3 Compared to CycleNet,xLSTM-Mixer,S-Mamba**\n\nThank 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**.\n\n| |MAFS(iTrans)|CycleNet|S-Mamba|SegRNN|xLSTM-Mixer|\n|:-:|:-:|:-:|:-:|:-:|:-:|\n|ETTh1|**0.433 0.437**|0.458 0.452|0.463 0.465|0.442 0.45|0.441 0.443|\n|ETTh2|**0.356 0.394**|0.364 0.401|0.381 0.41|0.389 0.42|0.366 0.404|\n|ETTm1|**0.366 0.388**|0.375 0.394|0.4 0.415|0.38 0.405|0.373 0.394|\n|ETTm2|**0.265 0.322**|0.271 0.327|0.295 0.34|0.27 0.327|0.271 0.326|\n|weather|**0.233 0.268**|0.237 0.274|0.247 0.279|0.237 0.275|0.236 0.271|\n|AQShunyi|**0.701 0.51**|0.712 0.519|0.717 0.517|0.701 0.504|0.717 0.513|\n|AQWan|**0.802 0.503**|0.819 0.506|0.824 0.51|0.8 0.496|0.819 0.508|\n|CzeLan|**0.222 0.271**|0.23 0.277|0.25 0.298|0.23 0.284|0.232 0.275|\n|ZafNoo|**0.52 0.452**|0.53 0.46|0.549 0.473|0.512 0.451|0.529 0.46|\n|pm2_5|**0.398 0.414**|0.427 0.428|0.417 0.426|0.421 0.426|0.425 0.428|\n|temp|**0.14 0.288**|0.235 0.365|0.152 0.3|0.207 0.341|0.201 0.339|\n\n---\n>**W4 Improve Figure 1**\n\nThank you for your insightful suggestion. We will add **'(d) Multi-Model Ensemble Forecasting'** to enhance the completeness of Figure 4. \n\n---\n>**W5 Minor concerns**\n\nThank you for your suggestions. We will revise Figures 5 and 6 accordingly.\n\n---\n>**Q1 Relation to Hierarchical Forecsating & Reconciliation Constraints** \n\nThank you for the insightful question. \n- **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.\n- **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.\n\n---\n>**Q2 Are Sub-task ever Changing?**\n\nThanks for your constructive question. \n* **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.\n* **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.\n\n|Source|Target|MAFS|MAFS_Dynamic|\n|-|:-:|:-:|:-:|\n|ETTh1|ETTh1|**0.433 0.437**|0.438 0.441|\n|ETTm2|ETTm2|**0.265 0.322**|0.275 0.341|\n|ETTh2|ETTh1|0.481 0.476|**0.473 0.472**|\n|ETTm1|ETTm2|0.274 0.329|**0.270 0.326**|\n\n---\n>**Q5 More Ablations**\n\nIn 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**:\n||Ensemble|w/AVA|w/Comm|w/STS|\n|:-:|:-:|:-:|:-:|:-:|\n|ETTh1|0.457 0.486|0.465 0.469|0.456 0.463|0.448 0.454|\n|ETTh2|0.364 0.402|0.385 0.411|0.377 0.408|0.366 0.405|\n|ETTm1|0.442 0.459|0.379 0.402|0.377 0.399|0.376 0.401|\n|ETTm2|0.369 0.404|0.292 0.339|0.282 0.336|0.281 0.337|\n|Weather|0.240 0.288|0.246 0.277|0.249 0.281|0.242 0.275|\n|AQShunyi|0.739 0.557|0.745 0.525|0.724 0.523|0.721 0.518|\n|AQWan|0.853 0.555|0.846 0.522|0.848 0.523|0.832 0.521|\n|CzeLan|0.275 0.355|0.247 0.291|0.251 0.295|0.229 0.280|\n|ZafNoo|0.539 0.474|0.552 0.479|0.547 0.481|0.533 0.464|\n|PM2.5|0.453 0.493|0.431 0.419|0.417 0.423|0.441 0.429|\n|Temp|0.283 0.414|0.182 0.326|0.175 0.302|0.170 0.312|\n|Mean Imp|-|4.85% 8.72%|6.20% 9.26%|7.47% 10.04%|\n\nThe 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**. \n\n---\n***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.***\n\nYours sincerely,\n\nAuthors of Paper 474"}, {"review_id": "RIhjCSxMce", "reviewer": "Reviewer_VZEb", "summary": "The paper proposes a novel Multi-Agent Forecasting System (MAFS) for time series forecasting, which abandons the traditional one-size-fits-all model paradigm. MAFS decomposes the forecasting task into multiple sub-tasks, each handled by a dedicated agent trained on specific temporal perspectives, such as different forecasting resolutions or signal characteristics. These agents then share and refine information through structured communication topologies, enabling cooperative reasoning across different temporal views. A lightweight voting aggregator integrates their outputs into consistent final predictions.", "questions": "1. Why multiple agents are needed for time series forecasting problem? Is it making the problem more complex in an unnecessary way, when many time series forecasting problems are domain-specific and can be well resolved with a single deep learning model?\n2. What about the benefit-cost tradeoff? While some improvements in the forecasting accuracy is achieved, what are the computational cost increment?\n3. While transfer learning can be well used for knowledge sharing among different time series datasets, why no consider this approach?\n4. How to valid the robustness of the proposed approach, e.g., when the number of unseen datasets increase?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strengths\n1. The authors propose principled task decomposition strategies, including multi-scale temporal forecasting and multi-aspect signal forecasting. These strategies enable agents to specialize in distinct aspects of the time series, capturing diverse temporal dynamics and improving overall accuracy.\n2. The paper introduces an explicit communication mechanism among agents, implemented via graph convolutional networks. This allows agents to share contextual information, enhancing their generalization capacity and overcoming the limitations of isolated modeling.\n3. MAFS is designed to be scalable and flexible, allowing for different communication topologies (e.g., ring, star, chain, fully-connected) and varying numbers of agents. This flexibility enables the system to adapt to different forecasting scenarios and datasets.\nWeaknesses\n1. The paper mentions occasional instability during training, especially when the number of agents increases or when dealing with highly volatile datasets.\n2. The multi-agent framework introduces additional complexity and computational overhead compared to single-model approaches. While the authors demonstrate scalability, the increased computational requirements may be a barrier for real-time applications or resource-constrained environments.\n3. The performance of MAFS is sensitive to the choice of communication topology. While the star topology is shown to be effective, selecting the optimal topology for a given dataset or task may require additional tuning and experimentation.\n4. The paper does not provide a comprehensive theoretical analysis of the proposed framework, such as convergence guarantees or bounds on forecasting accuracy. This lack of theoretical grounding may make it difficult to fully understand the system's behavior and potential limitations.\n5. With multiple specialized agents, there is a risk of overfitting to the training data, especially if the agents focus on capturing noise rather than underlying patterns.", "was_revised": true, "final_justification": "The authors make a good rebuttal for the questions raised in my previous comments. I think they have improved their manuscript as suggested and I would increase my rating.", "rebuttal": "Dear Reviewer VZEb,\n\nThank you very much for your review and valuable insights. We will address your questions and concerns point by point.\n\n---\n>**W1. Instability in Volatile Datasets.**\n\nThank 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.\n\nThe 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.** \n\n|#Agent|Weather|ZafNoo|ETTm2|\n|:-:|:-:|:-:|:-:|\n|4|0.167|0.471|0.182|\n|8|0.167|0.471|0.179|\n|12|0.166|0.470|0.179|\n|16|0.166|0.469|0.178|\n|20|0.166|0.467|0.178|\n|24|0.166|0.467|0.178|\n|*std*|*0.00069*|*0.00182*|*0.00152*|\n\n---\n>**W2&Q2. Efficiency Analysis**\n\nThank 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:\n1. **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**.\n2. **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.\n\nAs 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**.\n\n||Time(ms)|GPU(MB)|Params(M)|MSE|MAE|\n|:-:|:-:|:-:|:-:|:-:|:-:|\n|MAFS|18.6|136.22|0.08|0.433|0.437|\n|Time-MOE|140.23|1169.83|113.35|0.452|0.449|\n|Ensemble|39.29|146.67|0.25|0.457|0.486|\n|iTransformer|10.85|130.85|0.06|0.467|0.466|\n|TimeMixer|25.25|894.68|0.2|0.447|0.440|\n|PatchTST|12.61|214.28|0.41|0.469|0.454|\n\n---\n>**W3. Optimal Topology**\n\nThank 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.**\n\n|Topology|Weather|ZafNoo|ETTm2|\n|:-:|:-:|:-:|:-:|\n|chain|0.167|0.470|0.183|\n|full graph|0.166|0.469|0.178|\n|ring|0.166|0.468|0.179|\n|star|0.166|0.467|0.177|\n|*std*|*0.00079*|*0.00124*|*0.00259*|\n---\n>**W4. Theoretical Analysis**\n\nThank 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**.\n\n**Definition 1 (Single-model)**\n\nLet X be the input space and Y the output space. A single predictive model is defined as:\n$$\nf_{mono}: X \\to Y, \\quad f_{mono} \\in F_{mono},\n$$\nwhere $F_{mono}$ is a high-complexity function class that captures the full modeling space.\n\n**Definition 2 (Multi-Agent Forecasting System)**\n\nThe MAFS model is defined as:\n$$\\hat{Y} = AVA( Comm(\\{Agent_1(X), \\dots, Agent_N(X)\\}; G) ),$$\nThe overall function class is:\n$$F_{MAFS} = AVA \\circ Comm ( F_1 \\times \\cdots \\times F_N ).$$\n**Definition 3 (Empirical risk and function class complexity)**\n\nGiven training data $(x_i, y_i)_{i=1}^n$, Empirical risk:\n\n$$\\hat{L}(f) = \\frac{1}{n} \\sum_{i=1}^n \\ell(f(x_i), y_i)$$\n\nRademacher complexity:\n$$R_n(F) = E_{\\sigma}[ \\sup_{f \\in F} \\frac{1}{n} \\sum_{i=1}^n \\sigma_i f(x_i)],$$\nwhere $\\sigma_i \\in \\{-1, +1\\}$ are Rademacher variables and $\\ell(f(x), y)$ is 1-Lipschitz and bounded.\n\n**Theorem 1 (Generalization bound)**\n\nFor any $\\delta \\in (0, 1)$, if the loss function is Lipschitz and bounded, then with probability at least $1 - \\delta$:\n$$E[\\ell(f(x), y)] \\leq \\hat{L}(f) + 2 R_n(F) + 3 \\sqrt{\\frac{\\log(2/\\delta)}{2n}}.$$\n**Theorem 2 (Model complexity)**\n\nLet $F_{mono}$ 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 $c_0 > 0$:\n$$R_n(F_{mono}) \\geq c_0 \\cdot \\dim(X) > \\sum_{i=1}^N R_n(F_i) + R_n(Comm) + R_n(AVA).$$\n**Theorem 3 (Tighter generalization bound for MAFS)**\n\nAs the monolithic model space $F_{mono}$ has significantly higher complexity than the modularized structure, the overall Rademacher complexity satisfies:\n$$R_n(F_{MAFS}) \\leq \\sum_{i=1}^N R_n(F_i) + R_n(C) + R_n(AVA) < R_n(F_{mono}),$$\nwhich implies that, under comparable empirical risk, **MAFS enjoys a tighter generalization bound and thus stronger generalization ability.**\n\n[1] Vapnik V. The nature of statistical learning theory. Springer science & business media, 2013\n\n[2] Bartlett, P. Rademacher and Gaussian Complexities: Risk Bounds and Structural Results. Journal of Machine Learning Research, 3, 463–482, 2002.\n\n---\n>**W5. Could multiple specialized agents lead to overfitting?**\n\nThank 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.**\n\nTo 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.**\n\n|Source|Target|MAFS|iTransformer|PatchTST|\n|-|:-:|:-:|:-:|:-:|\n|ETTh2|ETTh1|0.481 0.476|0.513 0.522|0.565 0.513|\n|ETTm1|ETTm2|0.274 0.329|0.330 0.396|0.439 0.438|\n|ETTh1|ETTh2|0.365 0.399|0.394 0.418|0.380 0.405|\n|ETTm2|ETTm1|0.411 0.435|0.470 0.476|0.568 0.492|\n\n---\n>**Q1. Why multiple agents are needed for TSF?**\n\n* **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.\n* **Theoretical grounding:** Theorem 3 (see W4) shows that model splitting **leads to a tighter generalization bound, reducing overfitting risk and improving learning stability.**\n* **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.**\n\n||MAFS|Single\n|:-:|:-:|:-:\n|SegRNN |**0.398**|0.417\n|TimeMixer|**0.400**|0.417\n|PatchTST|**0.399**|0.422\n\n---\n>**Q3. Why no consider transfer learning?**\n\nThank 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**.\n\nAs 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**.\n\n---\n>**Q4.Robustness of MAFS**\n\n**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.**\n\nTo more thoroughly address your concern, we conducted systematic experiments to empirically validate the robustness of our proposed method:\n\n- **Zero-shot Forecasting (see W5)**: MAFS significantly outperforms iTransformer and PatchTST on multiple unseen datasets, demonstrating strong out-of-distribution generalization.\n\n- **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.**\n\nDataset|SeenRatio|MAFS|iTransformer|PatchTST|TimeMixer\n:-:|:-:|:-:|:-:|:-:|:-:\nETTm1|100%|0.366|0.383|0.387|0.381\n||70%|0.374|0.402|0.398|0.390\n||30%|0.386|0.435|0.412|0.401\n||10%|0.398|0.450|0.428|0.416\n|Weather|100%|0.233|0.243|0.259|0.240\n||70%|0.240|0.263|0.259|0.248\n||30%|0.252|0.276|0.274|0.261\n||10%|0.265|0.290|0.290|0.275\n|CzeLan|100%|0.222|0.232|0.227|0.228\n||70%|0.228|0.252|0.247|0.237\n||30%|0.235|0.270|0.256|0.245\n||10%|0.244|0.260|0.267|0.255\n|ZafNoo|100%|0.520|0.541|0.511|0.538\n||70%|0.531|0.559|0.564|0.551\n||30%|0.545|0.577|0.573|0.566\n||10%|0.560|0.593|0.598|0.582\n\n---\n***Thank you again for your valuable feedback. We hope our responses have clarified your concerns and welcome any further questions you may have.***\n\nYours Sincerely,\n\nAuthors of Paper 474"}, {"review_id": "IexLHjYUEk", "reviewer": "Reviewer_PB78", "summary": "This paper proposes a novel and effective framework, the Multi-Agent Forecasting System (MAFS), to address the inherent diversity and complexity of time series forecasting tasks. Unlike traditional single-model approaches, MAFS decomposes the problem into multiple specialized agents, each focusing on different temporal patterns or signal characteristics. These agents collaborate through flexible communication topologies and their outputs are aggregated via a lightweight voting mechanism. The approach is well-motivated, intuitive, and supported by extensive experiments across 11 benchmark datasets, demonstrating its superior robustness and adaptability compared to conventional forecasting models.", "questions": "Q1. Why was iTransformer chosen as the backbone for the agents in MAFS? Have other backbone networks been tried?\n\nQ2. The communication structures between agents are limited to graph/star/ring/chain. What is the rationale behind this selection? Are there other possible communication topologies worth exploring?\n\nQ3. For the distribution-focused agent, why was the design to predict six separate statistical values instead of directly modeling the future data distribution?", "limitations": "Yes, the authors have properly discussed the potential limitations of this research.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "**Strengths:**\n\nS1. Exploring a multi-agent system for time-series forecasting tasks is a novel and meaningful attempt, as forecasting inherently involves multiple factors and randomness. The proposed MAFS framework with multi-role agents improves the robustness of prediction process.\n\nS2. MAFS decomposes the forecasting task into trend, seasonality, frequency, and distribution agents, which intuitively makes sense and enhances interpretability.\n\nS3. The experimental results are comprehensive, which validate the consistent effectiveness of MAFS across 11 real-world datasets, and further verifies the robustness and adaptiveness of the multi-agent system across various datasets. The ablation studies confirm that the multi-agent system outperforms single-model baselines.\n\nS4. The paper is well-structured, with clear figures and strong readability.\n\n**Weaknesses:**\n\nW1. MAFS performs worse than Crossformer on the AQShunyi and AQWan datasets, and the authors have not provided a detailed analysis of the reasons behind this.\n\nW2. There are two typos in the paper: line 270 \"MAS forecasting system\" and line 194 \"H^{L} \\_i\", which should be corrected. In addition, the decimal places in Table 1 should be consistently kept to three digits.\n\nW3. In Section 5.7 (Case Study), the learned interaction weights among agents are visualized, but it appears that self-interaction weights are consistently dominant. The paper lacks an analysis of this phenomenon.", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer PB78,\n\nThank you very much for your valuable comments and positive support for our work. We will address your questions and concerns point by point.\n\n---\n>**W1. More Detailed Analysis of Results**\n\nThank 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.\n\n**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.\n\n---\n>**W2. Minor Typos**\n\nThank 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.\n\n---\n>**W3. More analysis of Figure 5**\n\nThank 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.\n\n---\n>**Q1. Why was iTransformer chosen as the backbone for the agents in MAFS? Have other backbone networks been tried?**\n\nWe 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.\n\nTo verify the generality of MAFS, we also integrated it with other representative backbones from different model families, including:\n\n* **PatchTST** (former-based)\n* **TimeMixer** (linear-based)\n* **SegRNN** (RNN-based)\n\nAcross all 11 datasets, MAFS consistently outperforms their single-model counterparts, as shown below:\n\n\n\n|  Dataset |  MAFS(PatchTST) | Single(PatchTST) |\n| :------: | :-------------: | :--------------: |\n|   ETTh1  | **0.437 0.439** |    0.469 0.455   |\n|   ETTh2  | **0.373 0.394** |    0.387 0.407   |\n|   ETTm1  | **0.371 0.390** |    0.387 0.400   |\n|   ETTm2  | **0.265 0.318** |    0.281 0.326   |\n|  weather | **0.231 0.272** |    0.259 0.280   |\n| AQShunyi | **0.678 0.496** |    0.705 0.509   |\n|   AQWan  | **0.774 0.483** |    0.812 0.499   |\n|  CzeLan  | **0.217 0.273** |    0.227 0.290   |\n|  ZafNoo  | **0.494 0.453** |    0.512 0.465   |\n|  pm2\\_5  | **0.407 0.420** |    0.460 0.479   |\n|   temp   | **0.142 0.289** |    0.147 0.306   |\n\n\n\n|  Dataset | MAFS(TimeMixer) | Single(TimeMixer) |\n| :------: | :-------------: | :---------------: |\n|   ETTh1  | **0.434 0.426** |     0.447 0.44    |\n|   ETTh2  | **0.353 0.382** |    0.365 0.395    |\n|   ETTm1  | **0.368 0.381** |    0.381 0.396    |\n|   ETTm2  | **0.264 0.314** |    0.275 0.323    |\n|  weather | **0.231 0.264** |     0.24 0.272    |\n| AQShunyi | **0.695 0.502** |     0.719 0.53    |\n|   AQWan  | **0.781 0.478** |    0.828 0.499    |\n|  CzeLan  |  **0.22 0.273** |     0.228 0.28    |\n|  ZafNoo  | **0.518 0.425** |    0.538 0.441    |\n|  pm2\\_5  | **0.401 0.416** |    0.415 0.436    |\n|   temp   | **0.139 0.291** |    0.146 0.305    |\n\n\n\n|  Dataset |   MAFS(SegRNN)  | Single(SegRNN) |\n| :------: | :-------------: | :------------: |\n|   ETTh1  |  **0.43 0.438** |   0.442 0.45   |\n|   ETTh2  | **0.368 0.399** |   0.389 0.42   |\n|   ETTm1  |  **0.369 0.39** |   0.38 0.405   |\n|   ETTm2  |  **0.262 0.32** |   0.27 0.327   |\n|  weather | **0.227 0.272** |   0.237 0.275  |\n| AQShunyi | **0.686 0.498** |   0.701 0.504  |\n|   AQWan  | **0.774 0.481** |    0.8 0.496   |\n|  CzeLan  | **0.218 0.268** |   0.23 0.284   |\n|  ZafNoo  | **0.504 0.446** |   0.512 0.451  |\n|  pm2\\_5  |  **0.397 0.41** |   0.421 0.426  |\n|   temp   | **0.146 0.295** |   0.207 0.341  |\n\n\nThese results further demonstrate that MAFS acts as a general plug-and-play framework that consistently improves forecasting accuracy across diverse backbone models.\n\n---\n>**Q2. What is the rationale behind this selection?**\n\nThank you for the insightful question.\n\nWe select the four communication structures,**graph**, **star**, **ring**, and **chain** as representative topologies due to their diverse communication patterns and their interpretability:\n* **Graph**: Fully connected communication offers an upper bound on information sharing.\n* **Star**: Emphasizes centralized coordination, where a core agent integrates and disseminates information.\n* **Ring** and **chain**: Represent decentralized topologies, with local or sequential message passing, mimicking diffusion-like processes.\n\nWhile 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.**\n\n|Topology|Weather|ZafNoo|ETTm2|\n|:-:|:-:|:-:|:-:|\n|chain|0.167|0.470|0.183|\n|full graph|0.166|0.469|0.178|\n|ring|0.166|0.468|0.179|\n|star|0.166|0.467|0.177|\n|*std*|*0.00079*|*0.00124*|*0.00259*|\n\n\n---\n>**Q3. Explanation of the Distribution-focused Agent Design**\n\nThank you for this thoughtful question.\n\nMAFS 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:\n\n1. **Interpretability**: Each predicted statistic corresponds to a distinct distributional property, making the agent's learning outcome transparent and easier to analyze.\n2. **Supervision efficiency**: These statistics can be **directly computed** from ground-truth sequences, enabling effective supervised learning.\n3. **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.\n\nWhile end-to-end distribution modeling (e.g., via normalizing flows or quantile regression) is an interesting alternative, o**ur 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.\n\n\n---\n\n***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.***\n\n\nYours sincerely,\n\nAuthors of Paper 474"}]

Author rebuttal:

Meta-review: This work proposes a multi-agent forecasting system that tackles several issues pertaining to the single-model forecasters, particularly under non-stationary conditions. The proposed system splits the overall task into several subtasks such that every agent can specialize with respect to a certain subtask. Agents share information through structured message-passing graph and their outputs are combined by a global voter weighted by per-agent confidence scores with iTransformer serving as the encoder. 

The paper received 3 reviews with the initial ratings being borderline and several issues were raised by the reviewers. The major points of contention were:

* Empirical analysis was on the weaker side with several baselines missing and well as focusing on a very specific encoder architecture.
* Communication structures were also limited.

The authors provided a detailed rebuttal and the overall motivation and the story became clearer to the reviewers. During the reviewer discussion phase, I read the paper and found myself agreeing with the reviewer's concerns of the empirical evidence not being enough. That being said we all were in unison that the new presented results have significantly strengthened the paper. Overall, I propose acceptance.
Decision: Accept (poster)