Solomonoff's uncomputable universal prediction scheme $ξ$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $μ$. This scheme will be generalized to arbitrary environmental classes, which, among others, allows the construction of computable universal prediction schemes $ξ$. Convergence of $ξ$ to $μ$ in a conditional mean squared sense and with $μ$ probability 1 is proven. It is shown that the average number of prediction errors made by the universal $ξ$ scheme rapidly converges to those made by the best possible informed $μ$ scheme. The schemes, theorems and proofs are given for general finite alphabet, which results in additional complications as compared to the binary case. Several extensions of the presented theory and results are outlined. They include general loss functions and bounds, games of chance, infinite alphabet, partial and delayed prediction, classification, and more active systems.
Broad stochastic configuration residual learning system for norm-convergent universal approximation
School of Control and Computer Engineering, North China Electric Power University（控制与计算机工程学院，华北电力大学）；School of Mathematics and Physics, North China Electric Power University（数学与物理学院，华北电力大学）；School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University（智能系统工程学院，中山大学深圳校区）
IDInit: A Universal and Stable Initialization Method for Neural Network Training
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Polytechnic University（香港理工大学）；MetaAI（元宇宙人工智能实验室）；Fudan University（复旦大学）；Shanghai Academy of AI for Science（上海人工智能科学研究院）
