MCFEIA: A Cognitive Memory Engine with Graph-based Computation and Physics-Inspired Reasoning

Abstract

This paper presents MCFEIA, a graph-based cognitive memory engine designed for associative recall, reasoning, and generation through bidirectional energy propagation. Knowledge is stored as nodes with six-dimensional probability vectors, and edges are implicitly defined via an RBF kernel, eliminating explicit adjacency storage. A sparse linear solver, derived from the Hamiltonian of the system, computes global energy distributions in a single step, achieving over 3,800x speedup compared to iterative propagation. The architecture supports O(1) role-indexed queries, zero catastrophic forgetting, and full interpretability of connections. A front-end locality-sensitive hashing forest enables real-time intuitive responses with sub-millisecond latency, while a back-end hierarchical matrix solver provides high-precision global reasoning. Empirical results demonstrate sub-millisecond query latency, zero forgetting under incremental learning, and robust retention under 90% noise. The system natively supports multi-modal perception through a unified Fourier spectral encoder, eliminating the need for external pre-trained models. MCFEIA provides a physically grounded framework for building interpretable, efficient, and continuously learning cognitive systems.

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