Integrating Annamalai Combinatorial Systems into the Foundations of Artificial Intelligence

This paper explores a transformative framework for Artificial Intelligence (AI) by integrating the Annamalai Combinatorial System into deep learning architectures. Standard AI models frequently encounter computational bottlenecks, such as numerical instability and memory errors, due to a reliance on traditional factorial-based counting methods. This study demonstrates how an optimized combinatorial approach, characterized by a stable product of ratios, provides a robust alternative for high-dimensional data processing. The paper maps this mathematical framework across the four functional pillars of AI—Perception, Learning, Reasoning, and Action—and details specific structural applications within the input, hidden, and output layers of neural networks. By utilizing recursive additive properties for feature extraction and a logarithmic probability mass function for optimization, AI systems achieve higher precision and reduced latency. Additionally, the system introduces a generating function as a closed-form solution for sequence modeling. This integration offers a path toward more efficient, energy-conscious AI capable of performance on low-power hardware without requiring changes to the fundamental logic of existing models