Reaction-Diffusion AI: An Emergent Language Model Inspired by Bhartrhari's Sphoṭa Theory and Turing's Computational Principles

This paper presents an interdisciplinary framework that reinterprets the ancient Indic concepts of sphoṭa , apoha, and śabda advaita in light of modern reaction-diffusion dynamics, neural heterogeneities, and probabilistic inference. Drawing upon seminal works such as Bhartrhari's Vākyapadīya, Panini's linguistic theories, and Buddhist Apoha, as well as Western philosophical and computational foundations from Wittgenstein and Turing, we propose a novel reaction-diffusion embedding (RD Sphoṭa model) for LLM-based architectures. Our model incorporates a learnable diffusion process that captures the "bursting forth" of meaning and the holistic emergence of linguistic content. We provide a detailed mathematical framework-including reaction-diffusion PDE approximations and probabilistic cue integration akin to the category adjustment model and compare our model experimentally against a standard GPT-2 baseline. Our experiments indicate that the RD Sphoṭa model achieves competitive perplexity while exhibiting emergent linguistic structuring. These findings suggest a novel paradigm for integrating self organising principles into LLM-driven AI systems, offering a fresh perspective on the evolution of large-scale neural language models.