# Patch-wise Structural Loss for Time Series Forecasting

arXiv: https://arxiv.org/abs/2503.00877 · HTML: https://mlsanity.com/paper/2503.00877/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 2 Mar 2025.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Channel-wise Knowledge Distillation for Dense Prediction](https://mlsanity.com/paper/2011.13256/) (2020)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [DSformer: A Double Sampling Transformer for Multivariate Time Series Long-term Prediction](https://mlsanity.com/paper/2308.03274/) (2023)
- [A Comprehensive Survey of Deep Learning for Time Series Forecasting: Architectural Diversity and Open Challenges](https://mlsanity.com/paper/2411.05793/) (2024)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [From Similarity to Superiority: Channel Clustering for Time Series Forecasting](https://mlsanity.com/paper/2404.01340/) (2024)
- [Hierarchical Classification Auxiliary Network for Time Series Forecasting](https://mlsanity.com/paper/2405.18975/) (2024)
- [Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift](https://mlsanity.com/paper/2410.09836/) (2024)
- [PETformer: Long-term Time Series Forecasting via Placeholder-enhanced Transformer](https://mlsanity.com/paper/2308.04791/) (2023)

## Built on by (most cited first, 30 of 35)

- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [Accurate Parameter-Efficient Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2506.23424/) (2025)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)
- [Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models](https://mlsanity.com/paper/2511.00053/) (2025)
- [Selective Learning for Deep Time Series Forecasting](https://mlsanity.com/paper/2510.25207/) (2025)
- [From Observations to States: Latent Time Series Forecasting](https://mlsanity.com/paper/2602.00297/) (2026)
- [Diffusion-Based Image Editing: An Unforeseen Adversary to Robust Invisible Watermarks](https://mlsanity.com/paper/2511.05598/) (2025)
- [Deep Time-series Forecasting Needs Kernelized Moment Balancing](https://mlsanity.com/paper/2602.00717/) (2026)
- [Vanishing Watermarks: Diffusion-Based Image Editing Undermines Robust Invisible Watermarking](https://mlsanity.com/paper/2602.20680/) (2026)
- [TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series](https://mlsanity.com/paper/2602.22520/) (2026)
- [To See Far, Look Close: Evolutionary Forecasting for Long-term Time Series](https://mlsanity.com/paper/2601.23114/) (2026)
- [Editing on the Generative Manifold: A Theoretical and Empirical Study of General Diffusion-Based Image Editing Trade-offs](https://mlsanity.com/paper/2603.29736/) (2026)
- [Multivariate Time Series Forecasting needs Cross Variable Loss](https://mlsanity.com/paper/2608.05742/) (2026)
- [FADE: Adversarial Concept Erasure in Flow Models](https://mlsanity.com/paper/2507.12283/) (2025)
- [Robust Concept Erasure in Diffusion Models: A Theoretical Perspective on Security and Robustness](https://mlsanity.com/paper/2509.12024/) (2025)
- [An Improved Time Series Anomaly Detection by Applying Structural Similarity](https://mlsanity.com/paper/2509.20184/) (2025)
- [ReNF: Rethinking the Design of Neural Long-Term Time Series Forecasters](https://mlsanity.com/paper/2509.25914/) (2025)
- [MoE-Enhanced Multi-Domain Feature Selection and Fusion for Fast Map-Free Trajectory Prediction](https://mlsanity.com/paper/2512.02368/) (2025)
- [Dual-Prototype Disentanglement: A Context-Aware Enhancement Framework for Time Series Forecasting](https://mlsanity.com/paper/2601.16632/) (2026)
- [CP Loss: Channel-wise Perceptual Loss for Time Series Forecasting](https://mlsanity.com/paper/2601.18829/) (2026)
- [Breaking the Correlation Plateau: On the Optimization and Capacity Limits of Attention-Based Regressors](https://mlsanity.com/paper/2602.17898/) (2026)
- [When Denoising Becomes Unsigning: Theoretical and Empirical Analysis of Watermark Fragility Under Diffusion-Based Image Editing](https://mlsanity.com/paper/2603.04696/) (2026)
- [Editing Away the Evidence: Diffusion-Based Image Manipulation and the Failure Modes of Robust Watermarking](https://mlsanity.com/paper/2603.12949/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Beyond Extrapolation: Knowledge Utilization Paradigm with Bidirectional Inspiration for Time Series Forecasting](https://mlsanity.com/paper/2605.19249/) (2026)
- [Beyond Holistic Models: Systematic Component-level Benchmarking of Deep Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2605.26562/) (2026)
- [VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting](https://mlsanity.com/paper/2606.02138/) (2026)
- [Adaptive Patching Is Harder Than It Looks For Time-Series Forecasting](https://mlsanity.com/paper/2606.04074/) (2026)
- [On the Controllability-Fidelity Frontier in Diffusion Editing](https://mlsanity.com/paper/2606.09901/) (2026)

## Abstract (arXiv)

Time-series forecasting has gained significant attention in machine learning due to its crucial role in various domains. However, most existing forecasting models rely heavily on point-wise loss functions like Mean Square Error, which treat each time step independently and neglect the structural dependencies inherent in time series data, making it challenging to capture complex temporal patterns accurately. To address these challenges, we propose a novel Patch-wise Structural (PS) loss, designed to enhance structural alignment by comparing time series at the patch level. Through leveraging local statistical properties, such as correlation, variance, and mean, PS loss captures nuanced structural discrepancies overlooked by traditional point-wise losses. Furthermore, it integrates seamlessly with point-wise loss, simultaneously addressing local structural inconsistencies and individual time-step errors. PS loss establishes a novel benchmark for accurately modeling complex time series data and provides a new perspective on time series loss function design. Extensive experiments demonstrate that PS loss significantly improves the performance of state-of-the-art models across diverse real-world datasets.