This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret modern architectures like Transformers, revealing fundamental limitations in scalability, efficiency, and interpretability. Building on these insights, we propose the Universal State Machine (USM), a novel computational paradigm designed from first principles. The USM employs a dynamic, queryable computation graph that evolves in real time, enabling modular, interpretable, and resource-efficient computation. This framework not only overcomes the inefficiencies and rigidity of current models but also lays the groundwork for scalable, generalizable artificial intelligence systems.