Title: MoFo: Empowering Long-term Time Series Forecasting with Periodic Pattern Modeling
Venue: NeurIPS 2025
Accepted: yes
Keywords: Time Series; Deep Learning; Position Information Encoding
Abstract: The stable periodic patterns present in the time series data serve as the foundation for long-term forecasting. However, existing models suffer from limitations such as continuous and chaotic input partitioning, as well as weak inductive biases, which restrict their ability to capture such recurring structures. In this paper, we propose MoFo, which interprets periodicity as both the correlation of period-aligned time steps and the trend of period-offset time steps. We first design period-structured patches—2D tensors generated through discrete sampling—where each row contains only period-aligned time steps, enabling direct modeling of periodic correlations. Period-offset time steps within a period are aligned in columns. To capture trends across these offset time steps, we introduce a period-aware modulator. This modulator introduces an adaptive strong inductive bias through a regulated relaxation function, encouraging the model to generate attention coefficients that align with periodic trends. This function is end-to-end trainable, enabling the model to adaptively capture the distinct periodic patterns across diverse datasets. Extensive empirical results on widely used benchmark datasets demonstrate that MoFo achieves competitive performance while maintaining high memory efficiency and fast training speed.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes the MoFo framework for long-term time series forecasting, which models periodicity as the correlation of period-aligned time steps and the trend of period-offset time steps. By designing a periodic structural patch and a periodic-aware modulator, the framework captures periodic patterns effectively. Experiments demonstrate that it outperforms 17 baselines, achieving both a 14x improvement in memory efficiency and a 10x faster training speed.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. Modeling periodicity as the correlation of period-aligned time steps and the trend of period-offset time steps provides a novel modeling perspective for long-term time series forecasting.\n2. MoFo demonstrates competitive predictive performance compared to 17 state-of-the-art baselines on multiple popular benchmark datasets, validating the effectiveness of the proposed method.\n3. The model's computational complexity is related to the period length rather than the input sequence length, achieving up to a 14$\\times$ improvement in memory efficiency and a 10$\\times$ speedup in training.\n\n**Weaknesses**\n\n1. Presentation Issues \n   - Grammatical errors. For example, there is a subject-verb agreement issue on line 182 regarding singular and plural forms. \n   - The names of all designed modules should be in lowercase.\n2. Clarifications Needed \n   - The description of the patch-based structured input is unclear, especially the padding strategy. Using data from the last period for padding may introduce potential information redundancy —could this affect model generalization? \n   - How to determine the cycle length? What does formula H mean in Eq.10?\n3. Baselines \n   - How many layers of Transformer did the author use? Did the author perform a sensitivity analysis on this parameter?\n   - A hyperparameter study on the period length is suggested, for example, using double the default period length, to evaluate its impact on performance.\n\nQUESTIONS:\nThe authors can refer to the weakness listed above.\n\nLIMITATIONS:\nThe authors can refer to the weakness listed above.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-05"}

comments: SUMMARY:
This paper introduces MoFo, a Transformer-based approach for long-term sequence forecasting. The method employs a periodicity-structured patching strategy along with a periodicity-aware modulator, inspired by theoretical mathematical insights. Extensive experimental results demonstrate that MoFo achieves highly competitive performance and superior efficiency.

STRENGTHS AND WEAKNESSES:
### Strength:
S1. The paper has a strong and clearly articulated motivation. The authors have effectively identified and explained the gap in existing work on time series forecasting.

S2. The proposed method is novel, incorporating a periodicity-aware modulator and an input representation strategy that emphasize the modeling of temporal periodicity. And the approach is driven by theoretical mathematical insights.

S3. Extensive experiments validate the model’s effectiveness, showcasing significant performance improvements and approximately 15× efficiency gains. 

S4.  The paper is well-written and well-structured, and The mathematical formulas are presented in a clear and explicit manner.

### Weakness:
W1. Some time series forecasting benchmarks need to be supplemented. For example, how does the model compare to FITS and SparseTF models?

W2. Why does the time complexity of MoFo remain stable as the input time series becomes longer?

W3. What does MACs mean in Table 3?  What is the purpose of this indicator?

QUESTIONS:
Please kindly see the Weaknesses above.

LIMITATIONS:
YES
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-29

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes MoFo, a Transformer-based forecasting method that models time series in a two-dimensional structure by leveraging their periodic patterns. The authors conduct correlation-based experiments in an attempt to validate the effectiveness of the proposed approach.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nS1: The method for handling periodicity in the paper is reasonable and demonstrates a certain degree of novelty.\n\nS2: The figures and tables throughout the paper are clear, and the presentation is well-structured.\n\nWeaknesses:\n\nW1: The paper lacks comparisons with important baseline methods, especially since the proposed method also relies on 2D modeling. Therefore, it should be compared with previous classic SOTA methods that also use 2D modeling, such as TimesNet[1] (CNN-based), WITRAN[2] (RNN-based), and TPGN[3] (PGN-based, where PGN is a new paradigm based on RNN). Moreover, in the related work section, these key methods are not addressed, and other emerging approaches, such as TimeKAN[4] (KAN-based, where KAN is a new paradigm based on Linear), are also omitted.\n\n[1] Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., & Long, M. (2023). Timesnet: Temporal 2d-variation modeling for general time series analysis. In The Eleventh International Conference on Learning Representations.\n\n[2] Jia, Y., Lin, Y., Hao, X., Lin, Y., Guo, S., & Wan, H. (2023). WITRAN: Water-wave Information Transmission and Recurrent Acceleration Network for Long-range Time Series Forecasting. In Thirty-seventh Annual Conference on Neural Information Processing Systems.\n\n[3] Jia, Y., Lin, Y., Yu, J., Wang, S., Liu, T., & Wan, H. (2024). PGN: The RNN's New Successor is Effective for Long-Range Time Series Forecasting. In The Thirty-eighth Annual Conference on Neural Information Processing Systems.\n\n[4] Huang, S., Zhao, Z., Li, C., & Bai, L. (2025). TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting. In The Thirteenth International Conference on Learning Representations.\n\nW2: The experimental setup contains clear flaws. Although the authors claim to follow configurations from previous studies, the actual design lacks fairness and rigor.\n\n(1) Improper handling of historical look-back length\n\n(1.1) Different look-back lengths may alter the data splitting process, thereby affecting model training. This represents a lack of control over experimental variables.\n\n(1.2) Different models exhibit varying sensitivity to look-back lengths, so treating it uniformly as a hyperparameter is clearly inappropriate. A more fair and rigorous approach would be to predefine several common look-back lengths and treat them as separate experimental groups, enabling a more systematic comparison of how each method performs under different historical horizons.\n\n(2) Limited hyperparameter search space\nThe TFB paper cited by the authors only expands to 8 parameter configurations. Taking Transformers as an example, even commonly used parameters like d_model, e_layer, and d_layer are barely covered—let alone other hyperparameters. Such a narrow search space makes it difficult to draw convincing conclusions.\n\n(3) Why an extensive hyperparameter search is necessary\n\n(3.1) Even with identical random seeds and hyperparameter values, experimental results may still vary across hardware platforms.\n\n(3.2) Different models have different levels of sensitivity to hyperparameters. When the experimental platform changes, directly reusing published settings cannot guarantee that baseline models operate at their optimal capacity, nor that results are consistent with those reported originally.\n\nTherefore, to ensure a fair comparison, it is essential to perform a fresh hyperparameter search for all models within a unified and sufficiently broad search space by selecting optimal configurations on the validation set and then evaluating and reporting results on the test set. While models with more hyperparameters may lead to a larger search space, this process is critical for ensuring fairness and rigor. Only after eliminating platform differences and hyperparameter biases, and ensuring that all models perform at their best, can a trustworthy and meaningful comparison be made.\n\nFurthermore, the authors do not compare their approach with the baselines mentioned in W1. Consequently, the current experiments are insufficient to convincingly establish the effectiveness of the proposed method.\n\nW3: The efficiency experiments likewise omit comparisons with the baselines listed in W1, as well as with FITS and DLinear. In addition, the paper does not specify how the hyperparameters were chosen for these tests. It must be emphasized that efficiency studies are intended to measure the resource consumption inherent to each model architecture; hence, all experimental variables should be controlled to ensure a fair comparison. In particular, shared hyperparameters should be kept identical so as to eliminate confounding effects, such as one method being run with very small settings while another is evaluated with much larger ones.\n\nQUESTIONS:\nIs MoFo still effective on time series data without clear periodicity? Has the method been explored on such datasets, for example, the Human Connectome Project (HCP), which involves non-periodic time series? I would like to see more discussion on the applicability and performance of the proposed method in non-periodic scenarios.\n\nLIMITATIONS:\nThe authors mentioned limitations regarding computational complexity.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

comments: SUMMARY:
The paper introduces MoFo, a Transformer-based long-term time-series forecasting model comprising
1. Period-Structured Patching (PSP): reshapes an input length-$T$ series into $P$ rows of phase-aligned "patches", reducing the number of tokens processed;
2. Period-Aware Modulator (PAM): multiplies attention logits by a learnable sigmoid mask of phase distances, theoretically shown to approximate a hard phase gate.
The authors claim significant memory and runtime savings, as well as competitive accuracy, on eight periodic benchmarks, and provide a theoretical bound on the mask approximation error.

STRENGTHS AND WEAKNESSES:
Strengths
S1) PSP and PAM are easy to implement and interpret; the paper is mostly well written.
S2) On datasets with a single, stable period, MoFo yields substantial token reduction and lower memory/FLOPs.
S3) The paper provides a concise proof that the sigmoid mask converges to a binary phase filter.

Weaknesses
W1) The proposed method relies on the assumption of a period length $P$. However, real-world time series often exhibit complex, time-varying periodic patterns. For example, in Figure 1(a), the "Successive Patching" clearly shows multiple peaks representing mixed periodicities. Why is it reasonable to treat these as belonging to the same period? When dealing with multiple samples from different time periods, how can we ensure accurate and meaningful period selection? When data faces mixed periodicities and time-varying periods (e.g., summer vs. winter electricity consumption patterns), can MoFo effectively handle such complex periodic variations?

QUESTIONS:
How does accuracy change if the supplied $P$ is perturbed by ±5–15 % or if multiple periods (e.g., 24 h & 7 d) coexist?

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-03