Title: Towards Accurate Time Series Forecasting via Implicit Decoding
Venue: NeurIPS 2025
Accepted: yes
Keywords: Time Series Forecasting

Frequency-domain
Abstract: Recent booming time series models have demonstrated remarkable forecasting performance. However, these methods often place greater focus on more effectively modelling the historical series, largely neglecting the forecasting phase, which generates long-term forecasts by separately predicting multiple time points. Given that real-world time series typically consist of various long short-term dynamics, independent predictions over individual time points may fail to express complex underlying patterns and can lead to a lack of global views. To address these issues, this work explores new perspectives from the forecasting phase and proposes a novel Implicit Forecaster (IF) as an additional decoding module. Inspired by decomposition forecasting, IF adopts a more nuanced approach by implicitly predicting constituent waves represented by their frequency, amplitude, and phase, thereby accurately forming the time series. Extensive experimental results from multiple real-world datasets show that IF can consistently boost mainstream time series models, achieving state-of-the-art forecasting performance. Code is available at this repository: [https://github.com/rakuyorain/Implicit-Forecaster](https://github.com/rakuyorain/Implicit-Forecaster).


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses a limitation in current time series forecasting (TSF) models: while existing methods mainly focus on effectively encoding historical data, they often overlook the decoding (forecasting) phase, which translates learned information into future predictions. To tackle this, the authors propose the Implicit Forecaster (IF) — a novel decoding module that improves the forecasting phase by predicting the future series as a combination of implicit frequency-based components. Instead of forecasting each future time point independently, IF models the time series globally by predicting the amplitude and phase of multiple constituent waves, leveraging Fourier analysis for signal reconstruction. Extensive experiments show that integrating IF into mainstream TSF models consistently improves their forecasting accuracy across diverse real-world datasets, setting new state-of-the-art results. Overall, the work highlights the importance of refining the forecasting stage in TSF pipelines and demonstrates the effectiveness of a frequency-domain approach to better capture global trends and periodic dynamics.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The Implicit Forecaster is well motivated, combining frequency-domain analysis with implicit decomposition, and the design choices (e.g., amplitude and phase heads, skip-connections) are thoughtfully justified.\n\n2. The authors conduct extensive experiments on 13 diverse, real-world datasets, demonstrating consistent performance gains over strong baselines, which shows the method’s generality and practical relevance.\n\n3. The paper is well written, well structured, and easy to follow. The figures and tables effectively illustrate key points and results.\n\nWeaknesses: \n\n1. The choice of a fixed-size frequency pool might not be optimal across all domains. Some discussion on adaptive or learnable frequency selection could make the approach more flexible.\n\n2. The authors should add more visualization results to demonstrate the effectiveness of the model design. For example, I suggest the authors to provide the visualization results for both Frequency prediction and Amplitude prediction.\n\nQUESTIONS:\n1. I am quite curious about the scalability of this method. Could it be applied in some time series foundation models (e.g., \\[1\\]\\[2\\])? \n\n[1] Timer: Generative Pre-trained Transformers Are Large Time Series Models\n\n[2] Unified Training of Universal Time Series Forecasting Transformers\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a model-agnostic framework for time series forecasting that identifies prediction failure cases through uncertainty estimation and corrects them from local and global perspectives. The method aims to enhance predictive performance while maintaining extensibility, with experimental validation across multiple scenarios.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths and Weaknesses: Strengths:\n- As a flexible decoding model, the method can adapt to various time\nseries forecasting models, exhibiting model-agnostic\n   characteristics;\n- Experimental results demonstrate effectiveness in forecasting tasks.\nWeaknesses:\n- The frequency-domain approach introduces additional computational overhead, which may be more pronounced in multi-variable datasets, but the paper lacks analysis on how variable counts affect computational costs;\n- The proposed new perspective essentially aligns with the conventional decomposition-based approach (e.g., decomposing time series into periodic components), a methodology already prevalent in works like TimesNet and TimeMixer[1]. The frequency-based MLP method (FIST[2]) is also not novel. The paper provides insufficient comparative analysis or case studies to justify its novelty;\n- No comparison with the strong baseline TimeMixer, which also employs decomposition-based methods.\n[1] Timemixer: Decomposable multiscale mixing for time series forecasting\n[2] FITS: Modeling Time Series with Parameters\n\nQUESTIONS:\n- The paper does not use the widely adopted traffic dataset in this\nfield. Is this omission due to the dataset's large number of variables? Could the authors further analyze how the number of variables impacts the computational overhead of the frequency- domain method (e.g., the relationship between variable count and computation time/resource consumption)?\n- Some models (e.g., TimesNet) exhibit poor performance on certain datasets. Could the authors investigate the root causes of these performance differences? Are they driven by dataset characteristics, model architectural design, or other factors?\n- Further justification is needed to clarify how the proposed method differs from and improves upon prior scale-based decomposition approaches (e.g., TimesNet, TimeMixer). Could the authors supplement experiments on TimeMixer to validate the method's competitiveness?\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel decoding module, Implicit Forecaster (IF), which decomposes time series into frequency components (amplitude, phase, frequency) for implicit prediction and reconstructs future series via inverse DFT. Experiments show IF consistently boosts mainstream models (e.g., 23.9% MSE reduction on PEMS) and achieves SOTA on 13 real-world datasets, especially for long-term and mixed-frequency patterns.\n\nSTRENGTHS AND WEAKNESSES:\nstrong\n(1) It introduces a novel innovative decoding: Implicit Forecaster (IF) replaces point-wise prediction with frequency-based implicit modeling, addressing the lack of global views. And it could seamlessly integrates with Transformers, RNNs, CNNs, etc., with significant improvements (e.g., 16.2% avg. MSE drop on Crossformer).\n(2) By setting P≥L, IF directly models ultra-low-frequency waves, enhancing long-term forecasting. It also gives the interpretability analysis to reveal key frequencies learned by the model.\n(3) It covers 13 datasets and 7 baselines, validating generality (e.g., 10.9% MAE improvement on SegRNN). And rigorous ablations (decoder replacements, skip-connection, window length) isolate each design choice.\n(4) The O(P) time and less memory than a Transformer decoder while improving accuracy.\n\nweak:\n(1) Lacks theoretical comparison between frequency vs. point-wise prediction.\n(2) Theoretical analysis is shallow, the convergence or approximation error of implicit reconstruction is not explored. \n(3) There is no adaptive frequency selection because it needs to predict all frequencies, which may be inefficient. And manual P setting may not match optimal data specific frequencies. While sin/cos decomposition stabilises phase prediction, it fails to model abrupt phase shifts (e.g., traffic congestion spikes in PEMS), causing residual errors in high frequency components (Figure 4).\n(4) Channel-independent forecasting overlooks inter-variable frequency correlations (e.g., synchronized power grid fluctuations), potentially losing multivariate dynamics.\n\nQUESTIONS:\nSeen in the weak part\n\nLIMITATIONS:\nSeen in the weak part", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper studies the problem of time series forecasting, and proposes an implicit forecaster to predict decomposed constituent waves. The proposed method addresses the overlooked forecasting phase, and the empirical performance is demonstrated on various real-world datasets.

STRENGTHS AND WEAKNESSES:
The paper is generally well-written and easy to follow. The idea is intuitive and focuses on the decoding phase of time series forecasting, which is less explored than the encoder. 

While the method is intuitive and demonstrated empirically, the paper lack of theoretical justification, which limits the applicability of this method. More discussion would enhance the significance of this work, and guide the application more broadly.

The proposed implicit forecaster is plug-and-play, and leads to an inherent dependence and potential sensitivity to the quality of the encoder. It would be better to have a thorough investigation on the robustness with mediocre encoders.

QUESTIONS:
Is there any other intuition why the proposed decoding strategy is better beyond DFT properties?

Maybe I missed it, how is the frequency pool determined? Is the performance sensitive to the its size?

Minor: It would be better to repeat the experiments with different runs to exam the robustness of the results and report "error bars".

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