Schrodinger AI: A Unified Spectral-Dynamical Framework for Classification, Reasoning, and Operator-Based Generalization

• URL: http://arxiv.org/abs/2512.22774v1
• Date: Sun, 28 Dec 2025 04:33:18 GMT
• Title: Schrodinger AI: A Unified Spectral-Dynamical Framework for Classification, Reasoning, and Operator-Based Generalization
• Abstract summary: We introduce textbfSchrdinger AI, a unified machine learning framework inspired by quantum mechanics.<n>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
• Score: 1.2691047660244335
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce \textbf{Schrödinger 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, Schrödinger 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.

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