A Universal Balance–Feedback Loss Framework for Artificial General Intelligence Training: A Unified, Stable, and Generalizable Objective

Abstract We present a rigorous mathematical formulation of the Universal Balance–Feedback Loss (UBFL) framework for Artificial General Intelligence (AGI) training, grounded in the Universal Balance–Feedback Framework (UBFF) and its Four Universal Laws: System Integrity, Universal Balance, Universal Feedback Loop Mechanism, and Universal Interconnected Nodes. The framework unifies alignment, safety, adaptive learning, and dynamical stability into a single principled objective function. We formalize internal and external cognitive states within a separable Hilbert space, derive a composite loss function integrating balance residuals, structured error signals, and long-horizon risk, and establish global asymptotic stability via Lyapunov’s direct method extended to nonlinear perturbations. We formally prove that Reinforcement Learning from Human Feedback (RLHF), the Free Energy Principle (FEP), and Safe Reinforcement Learning are proper special cases of UBFL under explicit parameter reductions. The framework is further extended to multi-agent consensus systems, stochastic environments with sublinear regret bounds, and Bayesian KL-divergence formulations. Simulation experiments on standard benchmarks (CartPole, MuJoCo HalfCheetah) demonstrate statistically significant improvements in convergence rate and alignment fidelity over RLHF and PPO baselines. Implementation strategies for modern deep learning architectures are provided, including a contraction-theoretic training algorithm with formal convergence guarantees. This work provides a mathematically grounded, empirically validated, and practically implementable foundation for building stable, aligned, and adaptive AGI systems.