Spiking neural network spontaneously generates soliton-like waves for spatial memory

A new paper by Ch. Meessen (arXiv:2606.21432) introduces a minimal two-dimensional recurrent spiking neural network that produces soliton-like traveling waves through local plasticity rules. The model combines multiplicative spike-timing-dependent plasticity (WSTDP), divisive normalization of synaptic integration, homeostatic threshold adaptation, and a one-step refractory period—all designed for biological plausibility. When excitatory-inhibitory neuron pairs are arranged in a 2D lattice and given periodic localized stimulation, the network spontaneously generates stable wave packets that propagate at constant speed, maintain a sharp spatial profile, and annihilate upon frontal collision. These properties define dissipative solitons.

Key to the emergence is a geometric asymmetry: excitatory connections must have a larger radius than inhibitory ones, and initial inhibitory synapses must be stronger than excitatory. WSTDP engraves the direction of propagation into synaptic weights, causing the network to learn one-way propagation while suppressing reverse travel. When two sources are active simultaneously, the resulting waves collide and annihilate, forming a semi-persistent boundary whose position encodes the relative phase and frequency difference between the sources. This provides a minimal computational framework for cortical traveling waves, activity zone delimitation, and spatial memory—all emerging purely from local plasticity rules without any global coordination.