What question did this study set out to answer?

The research aims to address catastrophic forgetting in continual learning using biologically-inspired mechanisms.

March 25, 2026Open Access

Geometric Modulation of Synaptic Plasticity via MGD Metrics Enables Continual Learning in Spiking Neural Networks

Key Points

The research aims to address catastrophic forgetting in continual learning using biologically-inspired mechanisms.
Developed BioMGDBrain architecture based on MGD framework.
Implemented local, geometrically-modulated synaptic updates.
Optimized task routing using Ryu-Takayanagi entropy proxy.
Introduced sleep phase for prioritizing experience replay.
Achieved 3x acceleration in forward transfer over standard STDP methods.
Delivered 47x speedup in computation using local MGD processes.
Simulated a temporal cascade reminiscent of biological brain's memory consolidation.

Abstract

This paper presents BioMGDBrain, a novel, biologically-inspired Spiking Neural Network (SNN) architecture designed to solve the catastrophic forgetting problem in continual learning. The system's mechanisms are strictly grounded in the Generative Mathematics of Dimensions (MGD) framework and validated against neuroscientific principles. Unlike traditional approaches that rely on artificial constraints or global error backpropagation, BioMGDBrain achieves continual learning through local, geometrically-modulated synaptic updates. Core Contributions & Mechanisms: Geometrically Modulated Learning Rate (₌₆₃): Plasticity is dynamically scaled using the Forman-Ricci curvature (F) and the effective dimension (D₀ₕ₆) of the network. This acts as a mathematical analogue to dopaminergic novelty signaling, accelerating forward transfer by 3 compared to standard STDP. Low-Variance Gating & Sₑₓ Routing: Task-dedicated neurons are selected by identifying geometrically unspecialised cells (low-variance criterion). New tasks are automatically routed to the cortical area with the maximal residual capacity, measured by the Ryu-Takayanagi entropy proxy (Sₑₓ). Priority Sleep Consolidation: An offline sleep phase replays stored experiences ordered by descending Sₑₓ priority, mimicking the role of noradrenaline in slow-wave sleep. Local MGD (O (n) Complexity): Global matrix operations (like SVD) are replaced by a per-synapse Forman-Ricci curvature computation based only on immediate neural neighbors, delivering a 47 speedup and making the system neuromorphic-ready. Biologically Grounded Overlap & Readout: The architecture features a three-modulator system (Dopamine, Acetylcholine, Noradrenaline) to allow task overlap without dedicated hardware. Furthermore, the system is entirely independent of Adam/backpropagation: it utilizes a "BioReadout" module combining the Oja rule, BCM metaplasticity, and a dopamine-gated perceptron for purely online, label-free updates during sleep. Three-Level Temporal Hierarchy: The final architecture (System K) simulates the biological brain's temporal cascade (Hippocampus Sensory Cortex Deep Neocortex) using two distinct sleep phases for memory crystallization. Hyperparameters for this temporal hierarchy were strictly validated using the OpenEvolve evolutionary coding agent.

Geometric Modulation of Synaptic Plasticity via MGD Metrics Enables Continual Learning in Spiking Neural Networks

Key Points

Abstract

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