Title: DBLoss: Decomposition-based Loss Function for Time Series Forecasting
Venue: NeurIPS 2025
Accepted: yes
Keywords: Time Series Forecasting

Loss Function
Abstract: Time series forecasting holds significant value in various domains such as economics, traffic, energy, and AIOps, as accurate predictions facilitate informed decision-making. However, the existing Mean Squared Error (MSE) loss function sometimes fails to accurately capture the seasonality or trend within the forecasting horizon, even when decomposition modules are used in the forward propagation to model the trend and seasonality separately. To address these challenges, we propose a simple yet effective Decomposition-Based Loss function called DBLoss. This method uses exponential moving averages to decompose the time series into seasonal and trend components within the forecasting horizon, and then calculates the loss for each of these components separately, followed by weighting them. As a general loss function, DBLoss can be combined with any deep learning forecasting model. Extensive experiments demonstrate that DBLoss significantly improves the performance of state-of-the-art models across diverse real-world datasets and provides a new perspective on the design of time series loss functions.


Peer reviews:
comments: SUMMARY:
The paper introduces DBLoss, decomposition-based loss function designed to improve time series forecasting performance by modeling seasonality and trend components within the forecasting horizon.  DBLoss employs EMA, exponential moving average, to seperate into each components. Experiments demonstrate that the DBLoss consistently outperforms traditional MSE loss by comparing SOTA models trained by each loss.

STRENGTHS AND WEAKNESSES:
Strengths:
Identifies a limitation of MSE loss function for TSF, making the problem clearly. Proposed DBLoss is easily integrable into various forecasting models without significant increasing computational costs, which can lead to high potential for practical adoption. Experiments are comprehensive, covering diverse datasets and various type of SOTA models. Several robustness experiments are shown, too.

Weaknesses:
1. Contrasting to strong empirical results, theoretical justification or analysis of why DBLoss improves forecasting performance is lacking. A clear theoretical explanation or analysis of empirical results is needed.
2. There should be a empirical or theoretical justification of why 2-norm is used for seasonality loss and 1-norm is used for trend loss.
3. The method relies on existing, well-known exponential moving average decomposition. Novelty of the methodological contribution is quite limited.
4. Computational cost analysis must be shown for adapting this loss. Empirical timing experiments would make it clearer.

QUESTIONS:
As weaknesses.

LIMITATIONS:
As weaknesses.
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-06-24

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper identifies a key limitation of the commonly used MSE loss in time-series forecasting. To address this limation, the authors propose DBLoss, a decomposition-based loss function. DBLoss works by applying EMA decomposition to both the model's prediction and the ground truth, extracting their seasonal and trend components. It then computes the losses for each component separately, L2 loss for seasonal component and L1 loss for trend component, and combined via a weighted sum, controlled by a tunable hyperparameter $\\beta$. The method is model-agnostic and can be seamlessly applied to various time series forecasting models.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths : \n1. The paper address a timely and important issue in time-series forecasting: the limitations of MSE loss in modeling trend and seasonality. The motivation is clearly articulated and well-grounded.\n2. DBLoss is model-agnostic and can be easily incorporated into various deep learning forecasting models without requiring architectural changes.\n3. Extensive experiments on diverse datasets and models demonstrate consistent performance improvements, including in zero-shot and few-shot scenarios.\n\nWeakness : \n1. In Figure 4, the sensitivity analysis of the score weight $\\beta$ shows relatively small performance difference across a wide range of values. Although the authors acknowledge in Appendix D that the score weight $\\beta$ has limited impact within a certain range, I believe this observation points to a more fundamental  issue: DBLoss may lack explicitly control over which component dominates the learning process. For instance, if a dataset has dominant seasonal pattern, the model may still overly focus on that, similar to implicit bias in MSE training. \n2. While DBLoss decomposes the prediction and ground truth into seasonal and trend components, it ultimately sums the two losses and backpropagates through both. This raises the question: does it truly overcome the limitations of MSE, or is it just a reweighted version of the same distance based loss concept? \n3. The method applies EMA for decomposition, which is a smoothing technique. However, it does not explicitly account for residuals or noise components after decomposition. It remains unclear how well DBLoss handles unpredictable or irregular patterns that are not capturd by trend or seasonality.\n\nQUESTIONS:\n1. Time series data inherently follows certain statistical principles and often comes with well-estabilished decomposition theories. However,  the authors do not discuss which theoretical assumptions or statistical interpretations justify the use of DBLoss. While the empirical results are strong, I believe that a theoretical foundation is essential --- especially when introducing a new loss function --- so that we can better understand when and why DBLoss should work. The paper would be strengthened by a deeper discussion of such theoretical grounding. \n2. Follow question from Weakness 3 : Could the limited impact of the score weight $\\beta$ be due to  the residual noise component remaining in both the trend and seasonal parts after decomposition?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis study proposes a simple yet effective Decomposition-Based Loss function called DBLoss. This method uses exponential moving averages to decompose the time series into seasonal and trend components within the forecasting horizon, and then calculates the loss for each of these components separately, followed by weighting them.\n\nSTRENGTHS AND WEAKNESSES:\nS1. Multivariate time series forecasting is important to time-series analysis.\n\nS2. This work focuses on an important problem that could have real-world applications.\n\nS3. The tables and figures used in this work are clear and easy to read.\n\nS4. Experimental results demonstrate that DBLoss consistently outperforms state-of-the-art baselines across multiple real-world datasets.\n\n---\n\nW1. Why was EMA (Exponential Moving Average) decomposition chosen over other similar decomposition mechanisms? Providing corresponding explanations would make the paper more comprehensive.\n\nW2. This infamous \"ETT long term forecasting benchmark\" is often criticized for its flaws such as limited domain coverage and the practice of forecasting at unreasonable horizons (e.g., 720 days into the future for exchange rate or oil temperature of a transformer at a specific hour months into the future). Every new model somehow beats this benchmark; however, there is still barely any absolute progress, only an illusion of it. Please refer to the talk (and paper) from Christoph Bergmeir [1, 2] where he discusses the limitation of this benchmark and current evaluation practices. A very recent position paper [3] also conducted a comprehensive evaluation of models on this benchmark showing that there's no obvious winner.\n\nOne (not so difficult) way to improve the quality of evaluation is to include results on better benchmarks.\n\n---\n\nMinor. Some citations are nonstandard by referencing arXiv preprints. Please ensure all citations point to formally published versions.\n\n[1] https://neurips.cc/virtual/2024/workshop/84712#collapse108471\n\n[2] Hewamalage, Hansika, Klaus Ackermann, and Christoph Bergmeir. \"Forecast evaluation for data scientists: common pitfalls and best practices.\" Data Mining and Knowledge Discovery 37.2 (2023): 788-832.\n\n[3] Brigato, Lorenzo, et al. \"Position: There are no Champions in Long-Term Time Series Forecasting.\" arXiv preprint arXiv:2502.14045 (2025).\n\nQUESTIONS:\nno.\n\nLIMITATIONS:\nYES", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis study proposes a simple yet effective loss function for time series forecasting, called DBLoss, which can refine the characterization and representation of time series through decomposition within the forecasting horizon. By decomposing the future sequence into different trend and seasonal components, DBLoss enhances the loss function's ability to improve prediction performance for different items.\n\nSTRENGTHS AND WEAKNESSES:\nS1. This paper is well motivated as it faces the challenge of effectively capturing the seasonality or trend within the forecasting horizon.. The notations are clear, the experimental results show that the proposed method is effective.\n\nS2. This paper points out that the traditional MSE Loss sometimes fails to accurately capture the seasonality or trend within the forecasting horizon and designs a new Loss Function accordingly, providing a new perspective.\n\n\nW1. The end-to-end model in the paper was comprehensively evaluated on 8 benchmark datasets, while the foundation model was only validated on 4 datasets. Could you please explain the rationale behind this inconsistency in experimental design?\n\nW2. The paper employs EMA (Exponential Moving Average) decomposition. Why was STL (Seasonal-Trend decomposition using Loess) not adopted to decompose the series into trend, seasonal, and residual components, with separate loss calculations and weighted aggregation?\n\nW3. In Algorithm 1, the range of the EMA smoothing coefficient α is defined as (0, 1), suggesting that 0 and 1 are excluded. However, Figure 4 appears to include these boundary values. Could you clarify this discrepancy?\n\nW4. The proposed method is intuitively feasible, but a more fundamental theoretical explanation would help enhance the significance of the study. The study relies too heavily on empirical experimental analysis and lacks in-depth experimental justification.\n\nQUESTIONS:\nQ1: The end-to-end model in the paper was comprehensively evaluated on 8 benchmark datasets, while the foundation model was only validated on 4 datasets. Could you please explain the rationale behind this inconsistency in experimental design?\n\nQ2: In Algorithm 1, the range of the EMA smoothing coefficient α is defined as (0, 1), suggesting that 0 and 1 are excluded. However, Figure 4 appears to include these boundary values. Could you clarify this discrepancy?\n\nLIMITATIONS:\nThe paper includes a dedicated section addressing the inherent limitations of the proposed approach.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}