Horizon-Constrained Rashomon Sets for Chaotic Forecasting

TL;DR

This paper introduces horizon-constrained Rashomon sets to analyze model multiplicity in chaotic systems, revealing exponential contraction with prediction horizon and improving decision-making in safety-critical applications.

Contribution

It provides a theoretical framework linking chaos theory and predictive multiplicity, including Lyapunov-weighted metrics and decision algorithms for chaotic forecasting.

Findings

Rashomon set contracts exponentially with lead time based on Lyapunov exponent

Lyapunov-weighted metrics offer tighter bounds on predictive disagreement

Decision-aligned algorithms improve decision quality by 18-34% in chaotic systems

Abstract

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.