Researchers have explored how increasing representation size impacts dynamics learning in deep learning models, specifically through autoregressive prediction. They analyzed learned time evolution using the eigenstructure of Koopman operators, identifying spurious eigenpairs by examining relative residuals. The study demonstrated that minimal residuals over learned dictionary spaces converge to their full-space counterparts as these spaces approximate the observable space in L2. Experiments across six chaotic systems showed that a spectral-residual model consistently outperformed a latent-prediction model in reducing rollout error and increasing valid prediction times with increasing dimension. AI
IMPACT Provides theoretical insights into scaling laws for dynamics learning, potentially guiding future model architectures.
RANK_REASON This is a research paper published on arXiv detailing a new methodology for understanding latent-dimension scaling in dynamical-system learning. [lever_c_demoted from research: ic=1 ai=1.0]
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