Crystalline Resonance Learning (CRL): Topological Node Grouping and Geometric Resonance for Stable Class-Incremental Learning

Abstract:Backpropagation underpins modern deep learning but faces fundamental limitations, including high memory overhead, catastrophic forgetting in continual learning, and biological implausibility. This paper introduces Crystalline Resonance Learning (CRL), a novel machine learning paradigm that bypasses backpropagation entirely through topological node grouping, geometric lattice structures, and a hybrid resonance metric combining cosine similarity and Gaussian dispersion. CRL enables stable class-incremental learning, one-shot adaptation, and lightweight inference without gradient descent. Extensive empirical evaluation on standard classification benchmarks demonstrates that CRL achieves superior or competitive accuracy compared to conventional batch and online learning baselines while requiring significantly lower storage and computational overhead.