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

TL;DR

Schrödinger AI reframes perception and reasoning as energy-driven processes on a learned semantic landscape. By pairing a time-independent Hamiltonian for classification with time-dependent dynamics and a low-rank operator calculus for symbolic tasks, it achieves emergent semantic topology, adaptive re-planning, and exact algebraic generalization beyond training length. The framework supports zero-shot rule editing, dual-system reasoning, and robust navigation in changing environments, demonstrating strong theoretical and empirical promises for interpretable, physically grounded AI. This spectrum-dynamics-operator integration offers a foundational alternative to traditional cross-entropy and attention-based models with potential impact on robust decision making and symbolic computation. The results suggest a path toward interpretable, adaptable AI capable of joint perceptual, planning, and symbolic capabilities within a unified mathematical structure.

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.

Figures (18)

• Figure 1: Learned inherent relationship among classes of a learned Schrödinger classifier
• Figure 2: Visualization of the group connection learned by Schrödinger reasoning model on $O_{11}$. It shows node $0$ is isolated while node $i$ and $j$ are connected if either $11*i\equiv j \mod 13$ or $11*j\equiv i \mod 13$
• Figure 3: Distribution of the distance (traversed graph edges) from original label to the failed output target.
• Figure 4: Sampled output of the trained Schrödinger classifier. First column: Sampled input, Second column: Potential Well $V(x)$, Third column: Prediction $|\psi_{i,0}|^2$, Forth column: Tunneling direction (next possible guess).
• Figure 5: Visualization example of the planning of Our Schrödinger AI Energy Seeker outperforms the classical LSTM route planner (fast) and energy heat map showing slow model awareness of the final goal, and that helps the agent naturally flows to the goal, unlike habitual model.