Closing the Loop: A Control-Theoretic Framework for Provably Stable Time Series Forecasting with LLMs

• URL: http://arxiv.org/abs/2602.12756v1
• Date: Fri, 13 Feb 2026 09:35:12 GMT
• Title: Closing the Loop: A Control-Theoretic Framework for Provably Stable Time Series Forecasting with LLMs
• Authors: Xingyu Zhang, Hanyun Du, Zeen Song, Jianqi Zhang, Changwen Zheng, Wenwen Qiang,
• Abstract summary: Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting.<n>Existing approaches typically employ a naive autoregressive generation strategy.<n>We propose textbfF-LLM, a novel closed-loop framework.
• Score: 22.486083545585984
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting, leveraging their inherent sequential reasoning capabilities to model complex temporal dynamics. However, existing approaches typically employ a naive autoregressive generation strategy. We identify a critical theoretical flaw in this paradigm: during inference, the model operates in an open-loop manner, consuming its own generated outputs recursively. This leads to inevitable error accumulation (exposure bias), where minor early deviations cascade into significant trajectory drift over long horizons. In this paper, we reformulate autoregressive forecasting through the lens of control theory, proposing \textbf{F-LLM} (Feedback-driven LLM), a novel closed-loop framework. Unlike standard methods that passively propagate errors, F-LLM actively stabilizes the trajectory via a learnable residual estimator (Observer) and a feedback controller. Furthermore, we provide a theoretical guarantee that our closed-loop mechanism ensures uniformly bounded error, provided the base model satisfies a local Lipschitz constraint. Extensive experiments demonstrate that F-LLM significantly mitigates error propagation, achieving good performance on time series benchmarks.

Related papers

• On Multi-Step Theorem Prediction via Non-Parametric Structural Priors [50.16583672681106]
  In this work, we explore training-free theorem prediction through the lens of in-context learning (ICL)<n>We propose Theorem Precedence Graphs, which encode temporal dependencies from historical solution traces as directed graphs, and impose explicit topological constraints that effectively prune the search space during inference.<n>Experiments on the FormalGeo7k benchmark show that our method achieves 89.29% accuracy, substantially outperforming ICL baselines and matching state-of-the-art supervised models.
  arXiv  Detail & Related papers  (2026-03-05T06:08:50Z)
• GTS: Inference-Time Scaling of Latent Reasoning with a Learnable Gaussian Thought Sampler [54.10960908347221]
  We model latent thought exploration as conditional sampling from learnable densities and instantiate this idea as a Gaussian Thought Sampler (GTS)<n>GTS predicts context-dependent perturbation distributions over continuous reasoning states and is trained with GRPO-style policy optimization while keeping the backbone frozen.
  arXiv  Detail & Related papers  (2026-02-15T09:57:47Z)
• From Observations to States: Latent Time Series Forecasting [65.98504021691666]
  We propose Latent Time Series Forecasting (LatentTSF), a novel paradigm that shifts TSF from observation regression to latent state prediction.<n>Specifically, LatentTSF employs an AutoEncoder to project observations at each time step into a higher-dimensional latent state space.<n>Our proposed latent objectives implicitly maximize mutual information between predicted latent states and ground-truth states and observations.
  arXiv  Detail & Related papers  (2026-01-30T20:39:44Z)
• To See Far, Look Close: Evolutionary Forecasting for Long-term Time Series [27.499122225390092]
  The prevailing Direct Forecasting (DF) paradigm dominates Long-term Time Series Forecasting (LTSF) by forcing models to predict the entire future horizon in a single forward pass.<n>In this work, we uncover a counter-intuitive optimization anomaly: models trained on short horizons-when coupled with our proposed Evolutionary Forecasting (EF) paradigm-significantly outperform those trained directly on long horizons.
  arXiv  Detail & Related papers  (2026-01-30T16:02:27Z)
• Closed-Loop Transformers: Autoregressive Modeling as Iterative Latent Equilibrium [0.6820746164515952]
  We introduce the closed-loop prediction principle, which requires that models iteratively refine latent representations until reaching a self-consistent equilibrium.<n>We instantiate this principle as Equilibrium Transformers, which augment standard transformer layers with an Equilibrium Refinement Module.<n>Preliminary experiments on the binary parity task demonstrate +3.28% average improvement on challenging sequences, with gains reaching +8.07% where standard transformers approach random performance.
  arXiv  Detail & Related papers  (2025-11-26T20:02:59Z)
• Drift No More? Context Equilibria in Multi-Turn LLM Interactions [58.69551510148673]
  contexts drift is the gradual divergence of a model's outputs from goal-consistent behavior across turns.<n>Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics.<n>We show that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay.
  arXiv  Detail & Related papers  (2025-10-09T04:48:49Z)
• ReNF: Rethinking the Design Space of Neural Long-Term Time Series Forecasters [48.79331759671512]
  We introduce a Multiple Neural Forecasting Theorem that provides a theoretical basis for our approach.<n>We propose Boosted Direct Output (BDO), a novel forecasting strategy that combines the advantages of both Auto-Regressive (AR) and Direct Output (DO)
  arXiv  Detail & Related papers  (2025-09-30T08:05:59Z)
• Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence [19.484676783876306]
  Diffusion models have emerged as powerful tools for generative modeling.<n>We propose a control framework for fine-tuning diffusion models.<n>We show that PI-FT achieves global convergence at a linear rate.
  arXiv  Detail & Related papers  (2024-12-24T04:55:46Z)
• Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior [51.60683890503293]
  We propose a theoretical framework for studying behavior cloning of complex expert demonstrations using generative modeling. We show that pure supervised cloning can generate trajectories matching the per-time step distribution of arbitrary expert trajectories.
  arXiv  Detail & Related papers  (2023-07-27T04:27:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.