Simplicity Bias and Algorithmic Probability in the Random Logistic Map
Simplicity bias, where simple patterns have exponentially higher probability than complex patterns, is observed in the digitized trajectories of the random logistic map for specific parameter regimes. This bias persists even with the introduction of small measurement noise, but diminishes as noise levels increase. The study also reveals insights into noise-induced chaos in the logistic map and the counterintuitive implications of algorithmic probability-based induction.
Constructing a Minimal Linear Realization to Analyze Observability of Nonlinear Dynamical Systems over Finite Fields
This paper develops a linear approach for analyzing the observability of nonlinear dynamical systems over finite fields using the Koopman operator framework. It constructs a minimal linear realization (LOR) that can reproduce all the output sequences of the original nonlinear system, and provides necessary and sufficient conditions for the observability of the nonlinear system through the LOR. The paper also establishes an upper bound on the number of outputs required for the unique reconstruction of the initial condition.