# Adaptive Oscillatory-State Alignment for Time Series Forecasting

arXiv: https://arxiv.org/abs/2606.06010 · HTML: https://mlsanity.com/paper/2606.06010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 4 Jun 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [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)
- [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)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [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)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2304.05206/) (2023)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [SAMformer: Unlocking the Potential of Transformers in Time Series Forecasting with Sharpness-Aware Minimization and Channel-Wise Attention](https://mlsanity.com/paper/2402.10198/) (2024)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting](https://mlsanity.com/paper/2410.04442/) (2024)
- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Amplifier: Bringing Attention to Neglected Low-Energy Components in Time Series Forecasting](https://mlsanity.com/paper/2501.17216/) (2025)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [Multi-period Learning for Financial Time Series Forecasting](https://mlsanity.com/paper/2511.08622/) (2025)
- [Channel, Trend and Periodic-Wise Representation Learning for Multivariate Long-term Time Series Forecasting](https://mlsanity.com/paper/2509.23583/) (2025)

## Abstract (arXiv)

Long-term time series forecasting benefits from inductive biases that expose recurring temporal structure. Existing periodic forecasting methods typically model recurrence through predefined periods, global spectral components, or fixed learnable templates. However, real-world temporal dynamics are rarely rigidly periodic: around a nominal cycle, oscillatory behavior often exhibits non-rigid periodicity (NRP), where cycle magnitude, cycle alignment, and local cycle duration vary over time. Under these conditions, fixed-template periodic modeling can become fundamentally mismatched to the underlying temporal states. We propose AOSNet, a Hilbert-guided forecasting framework that reformulates periodic forecasting from fixed template matching to adaptive oscillatory-state alignment. AOSNet extracts analytic-signal descriptors from both the observed sequence and a learnable global oscillatory prior, then adaptively aligns local states through a descriptor-conditioned gate that selectively preserves reliable observations while softly correcting mismatched regions. The learned prior serves not as a rigid repeated template but as a flexible oscillatory reference interpreted through local state dynamics. Experiments on eight public benchmarks and two cloud workload traces demonstrate leading or highly competitive accuracy with a compact model size and low inference latency, supporting repeated forecasting settings such as capacity planning and autoscaling. Controlled synthetic studies that isolate cycle-magnitude and cycle-alignment variation and combine them with cycle-duration changes show that the advantage of oscillatory-state alignment increases as NRP intensifies.