recurrent neural networks

Probability and Statis... @probns... · 11h The Krylov-Bogolyubov theorem guarantees that dynamical systems on a compact space have at least one invariant probability measure. In machine learning, this is the theoretical bedrock for Reinforcement Learning and Recurrent Neural Networks (RNNs). It proves that despite noise and complexity, an agent's policy or a network's state will eventually settle into a stable statistical equilibrium. In real life, it explains why physical systems reach thermodynamic equilibrium. Image: share.google/YJ84OhN4ZAxZh5... [Two plots: (a) time series x(t) oscillating chaotically between roughly -4.0 and 4.0 over t=1010-1100; (b) phase portrait x vs ẋ showing a butterfly/figure-eight chaotic attractor pattern (resembling a Lorenz-type or double-scroll attractor)]