# Invariant Representation Learning for Source-Free Time Series Forecasting with LLM-Centric Proxy Denoising

arXiv: https://arxiv.org/abs/2510.05589 · HTML: https://mlsanity.com/paper/2510.05589/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 83 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 30 of 47)

- [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)
- [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)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [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)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Universal Source-Free Domain Adaptation](https://mlsanity.com/paper/2004.04393/) (2020)
- [Exploiting the Intrinsic Neighborhood Structure for Source-free Domain Adaptation](https://mlsanity.com/paper/2110.04202/) (2021)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [Learning explanations that are hard to vary](https://mlsanity.com/paper/2009.00329/) (2020)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [CALF: Aligning LLMs for Time Series Forecasting via Cross-modal Fine-Tuning](https://mlsanity.com/paper/2403.07300/) (2024)
- [A Comprehensive Survey on Source-free Domain Adaptation](https://mlsanity.com/paper/2302.11803/) (2023)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [UniTS: A Unified Multi-Task Time Series Model](https://mlsanity.com/paper/2403.00131/) (2024)
- [Domain Adaptation without Source Data](https://mlsanity.com/paper/2007.01524/) (2020)
- [Multi-Source Deep Domain Adaptation with Weak Supervision for Time-Series Sensor Data](https://mlsanity.com/paper/2005.10996/) (2020)
- [Source-Free Unsupervised Domain Adaptation: A Survey](https://mlsanity.com/paper/2301.00265/) (2022)
- [Towards Spatio-Temporal Aware Traffic Time Series Forecasting--Full Version](https://mlsanity.com/paper/2203.15737/) (2022)
- [Time Series Domain Adaptation via Sparse Associative Structure Alignment](https://mlsanity.com/paper/2012.11797/) (2020)
- [LightPath: Lightweight and Scalable Path Representation Learning](https://mlsanity.com/paper/2307.10171/) (2023)

## Abstract (arXiv)

Effective time series forecasting enables various real-world applications, benefiting from the proliferation of mobile devices. However, the volume of time series data may vary significantly across domains due to high data acquisition costs and data regulations. To maximally create value from sparse data, this study focuses on a new problem of source-free time series forecasting, aiming to adapt a pretrained model from sufficient source time series to the sparse target time series without access to the source data, enabling data protection. To achieve this, we propose TimeID, a novel source-free time series forecasting framework with a large language model (LLM) centric proxy denoising inspired by the powerful generalization capabilities of LLMs. Specifically, TimeID consists of three key components: (1) dual-branch invariant disentangled feature learning that enforces representation- and gradient-wise invariance by means of season-trend decomposition; (2) lightweight, parameter-free proxy denoising that dynamically calibrates systematic biases of LLMs; and (3) knowledge distillation that bidirectionally aligns the denoised prediction and the original target prediction. Extensive experiments on real-world datasets demonstrate that TimeID outperforms state-of-the-art baselines, improving MSE and MAE by 10.7% and 9.3% on average. The code is available at https://github.com/decisionintelligence/TimeID.