Transformers as Implicit State Estimators: In-Context Learning in Dynamical Systems

ArXi:2410.16546v3 Announce Type: replace Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear minimum mean-square error estimator of the state trajectory -- is optimal in the Bayesian sense. For nonlinear systems, Bayesian filtering is typically approached using suboptimal heuristics such as the Extended Kalman Filter (EKF), or numerical methods such as particle filtering (PF.