TITLE: A Multi-Scale Novel Neural Networks Learning Algorithms Optimization Framework

ABSTRACTThis research operates on a singular, elegant identity axiom: a localized environment is fundamentally identical to its absolute matrix of latent information potential ((Equ,1)): (E ≡ I_Abs). By treating energy gradients and informational structures as the exact same physical property, we establish a universal framework for predicting structural failure modes before they occur. To execute this theory, we introduce the Neural Networks Learning Algorithms optimization framework, a continuous-time physics-informed mapping pipeline. Rather than treating raw streaming data as flat, isolated sequences, this architecture bridges the gap between machine learning and physical laws by binding a 50,433-parameter Neural Network directly to a 16-equation governing system matrix. Crucially, the 16 equations and the 50,433 parameters are parts of the exact same computational body. The physics equations do not run side-by-side with the network; they are baked directly into the hidden layers, forward-propagation equations, and output branches of the Multilayer Perceptron (MLP) engine. An Informational Topology Collapse is formally defined as a non-linear phase transition under acute phase-space volume constriction ((Equ,2)): (V_eff → 0). The failure occurs when local processing nodes completely uncouple from global tracking coordinates. Topologically, this mimics an elementary simplicial collapse where multi-scale structural loops—measured mathematically by independent network Betti numbers (beta_k(t))—instantly dissolve to zero ((Equ,3)): (beta_k(t) → 0), eliminating higher-dimensional systemic connectivity.