Hebbian-Oscillatory Co-Learning

• URL: http://arxiv.org/abs/2603.08731v1
• Date: Sat, 21 Feb 2026 06:25:51 GMT
• Title: Hebbian-Oscillatory Co-Learning
• Abstract summary: Hebbian-Oscillatory Co-Learning (HOC-L) is a unified two-timescale dynamical framework for joint structural plasticity and phase synchronization.<n>We introduce HOC-L in the hyperbolic sparse geometry of Resonant Sparse Geometry Networks (RSGN), which employs Poincaré ball embeddings with Hebbian-driven dynamic sparsity.<n>We prove convergence of the joint system to a stable equilibrium via a composite Lyapunov function and derive explicit timescale separation bounds.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce Hebbian-Oscillatory Co-Learning (HOC-L), a unified two-timescale dynamical framework for joint structural plasticity and phase synchronization in bio-inspired sparse neural architectures. HOC-L couples two recent frameworks: the hyperbolic sparse geometry of Resonant Sparse Geometry Networks (RSGN), which employs Poincaré ball embeddings with Hebbian-driven dynamic sparsity, and the oscillator-based attention of Selective Synchronization Attention (SSA), which replaces dot-product attention with Kuramoto-type phase-locking dynamics. The key mechanism is synchronization-gated plasticity: the macroscopic order parameter $r(t)$ of the oscillator ensemble gates Hebbian structural updates, so that connectivity consolidation occurs only when sufficient phase coherence signals a meaningful computational pattern. We prove convergence of the joint system to a stable equilibrium via a composite Lyapunov function and derive explicit timescale separation bounds. The resulting architecture achieves $O(n \cdot k)$ complexity with $k \ll n$, preserving the sparsity of both parent frameworks. Numerical simulations confirm the theoretical predictions, demonstrating emergent cluster-aligned connectivity and monotonic Lyapunov decrease.

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