Ten neurons sit in two groups, A and B. Every pulse, the stimulation pattern picks which neurons fire: in "Correlated" mode a whole group fires together, so neurons inside it are always co-active; in "Random" mode a random, uncorrelated subset fires each time. After every pulse, each synapse's weight updates by Hebb's rule — strengthening when both of its neurons fired together, and passively decaying otherwise (a simple stand-in for homeostatic synaptic scaling). This is the cellular logic behind Donald Hebb's principle "neurons that fire together, wire together," and the same push-pull between activity-dependent strengthening (LTP) and weakening (LTD) that BDNF-modulated NMDA/AMPA signalling implements in real synapses.
Δw(i,j) = η · pre(i) · post(j) · (1 − w) − decay · w
w(i,j) → clamp(w + Δw, 0, 1)
- Learning rate η — how much a single co-firing pulse strengthens a synapse; higher values reach saturation ("consolidated" wiring) in fewer repetitions.
- Decay / homeostasis — passive weakening applied to every synapse each pulse, modelling LTD and homeostatic scaling that keep total synaptic strength from growing without bound.
- Pulse rate — how often the network is stimulated; faster pulses accumulate LTP more quickly for a given η.
- Stimulation pattern — Correlated stimulation reliably co-activates neurons within a group, so within-group synapses climb toward 1 while cross-group synapses decay toward 0. Random stimulation offers no consistent co-activation, so no stable structure emerges — decay dominates and the weight matrix stays close to its noisy baseline.
Real-world relevance: this is the same associative learning rule (with modern refinements like spike-timing-dependent plasticity) believed to underlie memory formation, skill acquisition and post-injury rehabilitation — repeated, correlated activity physically rewires which neurons talk to each other most strongly.