Frozen Multistable Attractors in Hebbian Adaptive Vector Networks

This paper characterizes the long-time behavior of Hebbian adaptive vector networks — systems in which node state vectors and edge weights co-evolve under a threshold Hebbian plasticity rule. Through systematic numerical experiments, we identify four simultaneous properties of the system: structural freezing (edge weights converge to absorbing states), multiplicity of attractors (different initial graph topologies produce geometrically distinct frozen configurations), local basin stability (small perturbations around the same initial condition converge to nearby attractors), and irreversible hysteresis (a transient curiosity pulse leaves a permanent structural imprint that persists after the pulse ends).