Modular Isomorphism in Artificial Intelligence: From the Ring Z/6Z to Shared-Nothing Architecture NPUs

Modular Isomorphism in Artificial Intelligence: From the Ring ℤ/6ℤ to Shared-Nothing Architecture NPUs Abstract The scalability of Deep Learning models currently faces physical limits within the monolithic Von Neumann architecture, where the energy cost of data movement exceeds computation. This work proposes a solution based on Modular Isomorphism under the ring ℤ/6ℤ, allowing the decomposition of dense neural networks into a hexagonal ensemble of six independent sub-networks. We experimentally validate this approach on MNIST (97.03% accuracy) and Transformers (94.75% validation), demonstrating that the Shared-Nothing architecture maintains competitive performance while eliminating the need for low-latency interconnects. A Monte Carlo robustness analysis (N=10) confirms the statistical significance (p < 0.012) of the generalization gap reduction. Economic analysis reveals 18× cost reductions via node arbitrage, utilizing 28nm technology versus 3nm. These results lay the foundation for a new generation of modular NPUs based on low-cost chiplets, democratizing access to high-performance computing. Key Contributions Mathematical Formalization: Definition of the Stride-6 tensor operator, establishing an isomorphism between modular convolution and matrix multiplication. Hex-Ensemble Architecture: Design of a distributed neural network where 6 "blind" workers recover accuracy through vote aggregation without cache coherence. Inverse Generalization Gap: Empirical discovery that "partial blindness" acts as a structural regularizer, outperforming dense models in validation scenarios (Modular Transformer +24.37% gap improvement vs Standard). Economic Feasibility: Demonstration that 28nm chiplets can compete with monolithic 3nm nodes by leveraging high yields and eliminating the "Reticle Limit." Included Artifacts 📄 Article (PDF): Full manuscript detailing the theoretical framework, mathematical proofs, and economic models. 💻 Source Code (Jupyter/Python): Complete reproduction environment including Tensor Isomorphism Validation (Error < 1e-5), Hex-Ensemble training, and Monte Carlo Statistical Robustness Analysis. 📝 LaTeX Source: Complete source files for the manuscript. Context & Preceding Work This architecture is the third evolution of the Modular Spectrum Theory. It builds upon previous algorithmic validation where the Shared-Nothing paradigm was used to compute 100 Million digits of π with 95% parallel efficiency (see: 10.5281/zenodo.18455954). Licensing The source code associated with this research is distributed under the PolyForm Noncommercial License 1.0.0 to foster open science while protecting independent innovation. GitHub Repository: https://github.com/NachoPeinador/Isomorfismo-Modular-Z-6Z-en-Inteligencia-Artificial