Hebbian-Oscillatory Co-Learning

2026-03-11 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

Hebbian-Oscillatory Co-Learning (HOC-L) is a novel, unified two-timescale dynamical framework for bio-inspired sparse neural architectures, integrating structural plasticity and phase synchronization. It combines Resonant Sparse Geometry Networks (RSGN) for hyperbolic sparse geometry and Hebbian-driven dynamic sparsity with Selective Synchronization Attention (SSA) for oscillator-based attention and Kuramoto-type phase-locking. The core mechanism is synchronization-gated plasticity, where the macroscopic order parameter $r(t)$ of the oscillator ensemble gates Hebbian structural updates, consolidating connectivity only when sufficient phase coherence signals a meaningful computational pattern. The framework achieves $O(n\cdot k)$ complexity, where $k\ll n$, preserving the sparsity of its parent frameworks. Theoretical analysis proves convergence to a stable equilibrium via a composite Lyapunov function, with explicit timescale separation bounds. Numerical simulations confirm emergent cluster-aligned connectivity and monotonic Lyapunov decrease.

Key takeaway

For AI Researchers developing biologically inspired neural networks, HOC-L offers a principled approach to integrate structural plasticity with dynamic coordination. Your models can achieve greater efficiency and adaptability by using synchronization-gated Hebbian learning, allowing network topology to evolve based on emergent oscillatory coherence. Consider implementing this two-timescale framework to build sparse, self-organizing architectures that mirror biological brain function more closely.

Key insights

HOC-L unifies structural plasticity and phase synchronization in sparse neural networks via synchronization-gated Hebbian learning.

Principles

• Oscillatory coherence modulates structural plasticity.
• Two-timescale dynamics enable efficient learning.
• Hyperbolic geometry supports hierarchical sparse connectivity.

Method

HOC-L uses a smooth sigmoid gate $G(r)=\sigma(\beta(r-r_{c}))$ to control Hebbian weight updates based on the global order parameter $r(t)$, ensuring plasticity only occurs during sufficient phase synchronization.

In practice

• Implement synchronization-gated plasticity for adaptive network structures.
• Utilize hyperbolic embeddings for hierarchical data representation.
• Restrict oscillatory coupling to sparse neighborhoods for efficiency.

Topics

• Hebbian-Oscillatory Co-Learning
• Phase Synchronization
• Structural Plasticity
• Sparse Neural Networks
• Hyperbolic Geometry

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.