LILAD: Learning In-context Lyapunov-stable Adaptive Dynamics Models

• URL: http://arxiv.org/abs/2511.21846v1
• Date: Wed, 26 Nov 2025 19:20:49 GMT
• Title: LILAD: Learning In-context Lyapunov-stable Adaptive Dynamics Models
• Authors: Amit Jena, Na Li, Le Xie,
• Abstract summary: LILAD is a novel framework for system identification that jointly guarantees stability and adaptability.<n>We evaluate LILAD on benchmark autonomous systems and demonstrate that it outperforms adaptive, robust, and non-adaptive baselines in predictive accuracy.
• Score: 4.66260462241022
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as stability and typically assume stationary dynamics, limiting their applicability under distribution shifts. Existing approaches generally address either stability or adaptability in isolation, lacking a unified framework that ensures both. We propose LILAD (Learning In-Context Lyapunov-stable Adaptive Dynamics), a novel framework for system identification that jointly guarantees adaptability and stability. LILAD simultaneously learns a dynamics model and a Lyapunov function through in-context learning (ICL), explicitly accounting for parametric uncertainty. Trained across a diverse set of tasks, LILAD produces a stability-aware, adaptive dynamics model alongside an adaptive Lyapunov certificate. At test time, both components adapt to a new system instance using a short trajectory prompt, which enables fast generalization. To rigorously ensure stability, LILAD also computes a state-dependent attenuator that enforces a sufficient decrease condition on the Lyapunov function for any state in the new system instance. This mechanism extends stability guarantees even under out-of-distribution and out-of-task scenarios. We evaluate LILAD on benchmark autonomous systems and demonstrate that it outperforms adaptive, robust, and non-adaptive baselines in predictive accuracy.

Related papers

• Not All Preferences Are Created Equal: Stability-Aware and Gradient-Efficient Alignment for Reasoning Models [52.48582333951919]
  We propose a dynamic framework designed to enhance alignment reliability by maximizing the Signal-to-Noise Ratio of policy updates.<n>SAGE (Stability-Aware Gradient Efficiency) integrates a coarse-grained curriculum mechanism that refreshes candidate pools based on model competence.<n> Experiments on multiple mathematical reasoning benchmarks demonstrate that SAGE significantly accelerates convergence and outperforms static baselines.
  arXiv  Detail & Related papers  (2026-02-01T12:56:10Z)
• Adaptive Dual-Weighting Framework for Federated Learning via Out-of-Distribution Detection [53.45696787935487]
  Federated Learning (FL) enables collaborative model training across large-scale distributed service nodes.<n>In real-world service-oriented deployments, data generated by heterogeneous users, devices, and application scenarios are inherently non-IID.<n>We propose FLood, a novel FL framework inspired by out-of-distribution (OOD) detection.
  arXiv  Detail & Related papers  (2026-02-01T05:54:59Z)
• Stability as a Liability:Systematic Breakdown of Linguistic Structure in LLMs [5.96875296117642]
  We show that stable parameter trajectories lead stationary solutions to minimize the forward KL divergence to the empirical distribution.<n>We empirically validate this effect using a controlled feedback-based training framework.<n>It indicates that optimization stability and generative expressivity are not inherently aligned, and that stability alone is an insufficient indicator of generative quality.
  arXiv  Detail & Related papers  (2026-01-26T15:34:50Z)
• Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification [6.5745172279769255]
  We propose a neural network-based state-space model that simultaneously learns latent states and internal scheduling variables.<n>The state-transition matrix is guaranteed to be stable through a Schur-based parameterization.<n>The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods.
  arXiv  Detail & Related papers  (2025-10-21T10:25:54Z)
• MaP: A Unified Framework for Reliable Evaluation of Pre-training Dynamics [72.00014675808228]
  Instability in Large Language Models evaluation process obscures true learning dynamics.<n>We introduce textbfMaP, a framework that integrates underlineMerging underlineand the underlinePass@k metric.<n>Experiments show that MaP yields significantly smoother performance curves, reduces inter-run variance, and ensures more consistent rankings.
  arXiv  Detail & Related papers  (2025-10-10T11:40:27Z)
• Zubov-Net: Adaptive Stability for Neural ODEs Reconciling Accuracy with Robustness [0.16355471507854133]
  We propose an adaptive stable learning framework named ZubovNet, which reformulates Zubov's equation into a consistency characterization.<n>We introduce a new paradigm for actively controlling the geometry of RoAs by directly optimizing PRoAs to reconcile accuracy and robustness.
  arXiv  Detail & Related papers  (2025-09-26T05:01:51Z)
• Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation [67.63756749551924]
  Learning-based neural network (NN) control policies have shown impressive empirical performance in a wide range of tasks in robotics and control. Lyapunov stability guarantees over the region-of-attraction (ROA) for NN controllers with nonlinear dynamical systems are challenging to obtain. We demonstrate a new framework for learning NN controllers together with Lyapunov certificates using fast empirical falsification and strategic regularizations.
  arXiv  Detail & Related papers  (2024-04-11T17:49:15Z)
• Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems (Extended Version) [1.2430809884830318]
  This paper presents a policy parameterization for learning-based control on nonlinear, partially-observed dynamical systems. We prove that the resulting Youla-REN parameterization automatically satisfies stability (contraction) and user-tunable robustness (Lipschitz) conditions. We find that the Youla-REN performs similarly to existing learning-based and optimal control methods while also ensuring stability and exhibiting improved robustness to adversarial disturbances.
  arXiv  Detail & Related papers  (2023-04-12T23:55:56Z)
• KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems [66.9461097311667]
  We propose a model-based reinforcement learning framework with formal stability guarantees. The proposed method learns the system dynamics up to a confidence interval using feature representation. We show that KCRL is guaranteed to learn a stabilizing policy in a finite number of interactions with the underlying unknown system.
  arXiv  Detail & Related papers  (2022-06-03T17:27:04Z)
• Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness [3.2872586139884623]
  This paper introduces recurrent equilibrium networks (RENs) for applications in machine learning, system identification and control. RENs are parameterized directly by quadratic vector in RN, i.e. stability and robustness are ensured without parameter constraints. The paper also presents applications in data-driven nonlinear observer design and control with stability guarantees.
  arXiv  Detail & Related papers  (2021-04-13T05:09:41Z)
• Stability and Identification of Random Asynchronous Linear Time-Invariant Systems [81.02274958043883]
  We show the additional benefits of randomization and asynchrony on the stability of linear dynamical systems. For unknown randomized LTI systems, we propose a systematic identification method to recover the underlying dynamics.
  arXiv  Detail & Related papers  (2020-12-08T02:00:04Z)
• Efficient Empowerment Estimation for Unsupervised Stabilization [75.32013242448151]
  empowerment principle enables unsupervised stabilization of dynamical systems at upright positions. We propose an alternative solution based on a trainable representation of a dynamical system as a Gaussian channel. We show that our method has a lower sample complexity, is more stable in training, possesses the essential properties of the empowerment function, and allows estimation of empowerment from images.
  arXiv  Detail & Related papers  (2020-07-14T21:10:16Z)

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.