# CTRL: Control-Based Time Series Forecasting with LLM-Guided Residual Learning

arXiv: https://arxiv.org/abs/2609.23257 · HTML: https://mlsanity.com/paper/2609.23257/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [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)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [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)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [TEST: Text Prototype Aligned Embedding to Activate LLM's Ability for Time Series](https://mlsanity.com/paper/2308.08241/) (2023)
- [Active Learning on a Budget: Opposite Strategies Suit High and Low Budgets](https://mlsanity.com/paper/2202.02794/) (2022)
- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [CALF: Aligning LLMs for Time Series Forecasting via Cross-modal Fine-Tuning](https://mlsanity.com/paper/2403.07300/) (2024)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [Spatial-Temporal Large Language Model for Traffic Prediction](https://mlsanity.com/paper/2401.10134/) (2024)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [TimeXL: Explainable Multi-modal Time Series Prediction with LLM-in-the-Loop](https://mlsanity.com/paper/2503.01013/) (2025)
- [Residual Correction in Real-Time Traffic Forecasting](https://mlsanity.com/paper/2209.05406/) (2022)
- [Revisiting LLMs as Zero-Shot Time-Series Forecasters: Small Noise Can Break Large Models](https://mlsanity.com/paper/2506.00457/) (2025)

## Built on by (most cited first, 1 of 1)

- [JudgeCast: Time Series Forecasting with Experience-Informed Covariate Judgements](https://mlsanity.com/paper/2609.36966/) (2026)

## Abstract (arXiv)

Time series forecasting underpins critical decision-making across diverse domains. While large language models (LLMs) offer promising reasoning capabilities, existing LLM-based time series forecasting approaches either reduce them to numerical predictors that bypass their strengths, or allow direct forecast generation that destabilizes predictions in non-stationary settings. We introduce CTRL, a framework that decouples semantic reasoning from quantitative prediction. A frozen backbone generates base forecasts, while specialized LLM agents function as controllers that analyze backbone prediction errors through decomposed trend, seasonal, and irregular components, grounding reasoning in interpretable temporal structure. Each agent outputs compact control signals that a lightweight residual decoder translates into forecast corrections. CTRL incorporates label-free test-time adaptation that detects distribution shift from input statistics alone and readapts control signals with only 3-24 LLM calls via caching. CTRL is explicitly designed to improve robustness under non-stationary temporal dynamics and distribution shift, while remaining competitive on highly stationary time series where adaptive correction provides limited additional benefit.