Prediction Limits and Koopman Closure of Geometry-Induced Soft State Abstractions

תקציר מקורי באנגליתarXiv:2609.32652v2 Announce Type: replace Abstract: A soft state representation assigns each state a vector of nonnegative class weights that sum to one. We study how the construction of these weights and the state dynamics jointly determine the accuracy of linear prediction. For any fixed measurable representation, we derive a finite-sample lower confidence bound on the smallest population root-mean-square prediction error among matrices with a specified spectral-norm limit. The bound compares variation in successor coordinates within each reference class with the improvement that soft inputs could provide. It is computed from independent evaluation pairs without fitting a prediction matrix. A bound above a chosen tolerance rules out that tolerance for the entire matrix class; a zero boun