arXiv:2605.05218cs.LGcs.AI2026-05

用混沌预测的时域约束,解决模型多样性难题。

Horizon-Constrained Rashomon Sets for Chaotic Forecasting

论文配图:Horizon-Constrained Rashomon Sets for Chaotic Forecasting
图 1 · 摘自论文原文
  • 提出时域约束的Rashomon集,刻画模型多样性随时间演化
  • 预测误差随时间指数增长,速率由最大李雅普诺夫指数决定
  • 选模型不只看精度,更看下游决策效果,适合高风险场景

预测多重性与混沌动力学是机器学习中两个根本性挑战,虽概念相关却长期独立发展。本文提出时域约束的Rashomon集理论框架,刻画混沌系统中模型多重性随预测时长的变化规律。不同于静态任务中固定不变的Rashomon集,混沌导致初始相近模型指数发散,彻底改变预测等价性本质。我们证明有效Rashomon集随领先时间呈指数收缩,速率由最大李雅普诺夫指数决定,并引入李雅普诺夫加权度量,获得更紧的预测分歧上界。基于此,设计出决策对齐的选择算法,在近优模型中依据下游效用而非仅预报精度进行筛选。在合成混沌系统(Lorenz-96、Kuramoto-Sivashinsky)及真实场景(风电、交通、天气)的广泛实验表明,该框架将决策质量提升18%-34%,同时保持竞争力预测性能。本工作首次建立混沌理论与预测多重性间的严格联系,为安全关键型混沌领域部署机器学习提供原则性指导。

原文摘要 · Abstract (English)

Predictive multiplicity and chaotic dynamics represent two fundamental challenges in machine learning that have evolved independently despite their conceptual connections. We bridge this gap by introducing horizon-constrained Rashomon sets, a theoretical framework that characterizes how model multiplicity evolves with prediction horizon in chaotic systems. Unlike static prediction tasks where the Rashomon set remains fixed, chaos induces exponential divergence among initially similar models, fundamentally transforming the nature of predictive equivalence. We prove that the effective Rashomon set contracts exponentially with lead time at a rate determined by the maximum Lyapunov exponent and introduce Lyapunov-weighted metrics that provide tighter bounds on predictive disagreement. Leveraging these insights, we develop decision-aligned selection algorithms that choose among near-optimal models based on downstream utility rather than forecast accuracy alone. Extensive experiments on synthetic chaotic systems (Lorenz-96, Kuramoto-Sivashinsky) and real-world applications (wind power, traffic, weather) demonstrate that our framework improves decision quality by 18-34\% while maintaining competitive predictive performance. This work establishes the first rigorous connection between chaos theory and predictive multiplicity, providing principled guidance for deploying machine learning in safety-critical chaotic domains.

混沌预测模型选择决策优化

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