Schrodinger AI: A Unified Spectral-Dynamical Framework for Classification, Reasoning, and Operator-Based Generalization
Abstract
We introduce \textbf{Schr\"{o}dinger AI}, a unified machine learning framework inspired by quantum mechanics. The system is defined by three tightly coupled components: (1) a {time-independent wave-energy solver} that treats perception and classification as spectral decomposition under a learned Hamiltonian; (2) a {time-dependent dynamical solver} governing the evolution of semantic wavefunctions over time, enabling context-aware decision revision, re-routing, and reasoning under environmental changes; and (3) a {low-rank operator calculus} that learns symbolic transformations such as modular arithmetic through learned quantum-like transition operators. Together, these components form a coherent physics-driven alternative to conventional cross-entropy training and transformer attention, providing robust generalization, interpretable semantics, and emergent topology. Empirically, Schr\"{o}dinger AI demonstrates: (a) emergent semantic manifolds that reflect human-conceived class relations without explicit supervision; (b) dynamic reasoning that adapts to changing environments, including maze navigation with real-time potential-field perturbations; and (c) exact operator generalization on modular arithmetic tasks, where the system learns group actions and composes them across sequences far beyond training length. These results suggest a new foundational direction for machine learning, where learning is cast as discovering and navigating an underlying semantic energy landscape.
Cite
@article{arxiv.2512.22774,
title = {Schrodinger AI: A Unified Spectral-Dynamical Framework for Classification, Reasoning, and Operator-Based Generalization},
author = {Truong Son Nguyen},
journal= {arXiv preprint arXiv:2512.22774},
year = {2025}
}