# OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain

arXiv: https://arxiv.org/abs/2505.08550 · HTML: https://mlsanity.com/paper/2505.08550/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 52 references that are in the map.
- First posted on arXiv 12 May 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [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)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FLatten Transformer: Vision Transformer using Focused Linear Attention](https://mlsanity.com/paper/2308.00442/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Flowformer: Linearizing Transformers with Conservation Flows](https://mlsanity.com/paper/2202.06258/) (2022)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)

## Built on by (most cited first, 26 of 26)

- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)
- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models](https://mlsanity.com/paper/2511.00053/) (2025)
- [Unlocking the Value of Text: Event-Driven Reasoning and Multi-Level Alignment for Time Series Forecasting](https://mlsanity.com/paper/2603.15452/) (2026)
- [PHAT: Modeling Period Heterogeneity for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.00654/) (2026)
- [Deep Time-series Forecasting Needs Kernelized Moment Balancing](https://mlsanity.com/paper/2602.00717/) (2026)
- [Position: The Inevitable End of One-Architecture-Fits-All-Domains in Time Series Forecasting](https://mlsanity.com/paper/2602.01736/) (2026)
- [vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2601.13768/) (2026)
- [CAPS: Unifying Attention, Recurrence, and Alignment in Transformer-based Time Series Forecasting](https://mlsanity.com/paper/2602.02729/) (2026)
- [StretchTime: Adaptive Time Series Forecasting via Symplectic Attention](https://mlsanity.com/paper/2602.08983/) (2026)
- [CSRA: Controlled Spectral Residual Augmentation for Robust Sepsis Prediction](https://mlsanity.com/paper/2604.14532/) (2026)
- [Existence Precedes Value: Joint Modeling of Observational Existence and Evolving States in Time Series Forecasting](https://mlsanity.com/paper/2606.13571/) (2026)
- [When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series](https://mlsanity.com/paper/2608.07333/) (2026)
- [ReNF: Rethinking the Design of Neural Long-Term Time Series Forecasters](https://mlsanity.com/paper/2509.25914/) (2025)
- [CATS-Linear: Classification Auxiliary Linear Model for Time Series Forecasting](https://mlsanity.com/paper/2510.08661/) (2025)
- [AltTS: A Dual-Path Framework with Alternating Optimization for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.11533/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [DAD4TS: Data-Augmentation-Oriented Diffusion Model for Time-Series Forecasting with Small-Scale Data](https://mlsanity.com/paper/2605.17866/) (2026)
- [Beyond Holistic Models: Systematic Component-level Benchmarking of Deep Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2605.26562/) (2026)
- [OrEdge: Efficient Multi-Modal Anomaly Detection in Distributed Software Systems via Orthogonal-Domain Learning](https://mlsanity.com/paper/2608.00309/) (2026)
- [MixBench-TS: A Multivariate Time Series Forecasting Benchmark Where Channel Mixing Pays Off](https://mlsanity.com/paper/2609.32656/) (2026)
- [SFlexRCA: Lightweight, Scalable, and Flexible Root Cause Analysis for IIoT Edge Systems](https://mlsanity.com/paper/2610.04893/) (2026)

## Abstract (arXiv)

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear