Self-organization of feedforward structure and entrainment in excitatory neural networks with spike-timing-dependent plasticity

Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly toward synchrony is not entirely clear. We examine relations between STDP and synchronous firing in spontaneously firing neural populations. Using coupled heterogeneous phase oscillators placed on initial networks, we show numerically that STDP prunes some synapses and promotes formation of a feedforward network. Eventually a pacemaker, which is the neuron with the fastest inherent frequency in our numerical simulations, emerges at the root of the feedforward network. In each oscillatory cycle, a packet of neural activity is propagated from the pacemaker to downstream neurons along layers of the feedforward network. This event occurs above a clear-cut threshold value of the initial synaptic weight. Below the threshold, neurons are self-organized into separate clusters each of which is a feedforward network.

💡 Research Summary

The paper investigates how spike‑timing‑dependent plasticity (STDP) reshapes the topology of excitatory neural networks and promotes synchronous firing. Using a population of heterogeneous phase oscillators to represent neurons, the authors place them on initially random directed graphs and let synaptic weights evolve according to a classic pair‑based STDP rule. The key control parameter is the initial synaptic strength w₀. Numerical simulations reveal a sharp transition at a critical value w_c. When w₀ > w_c, the network self‑organizes into a single feed‑forward hierarchy. The neuron with the highest intrinsic frequency becomes a pacemaker at the root of this hierarchy. In each oscillation cycle a “packet” of spikes is emitted by the pacemaker, travels downstream through successive layers, and entrains all downstream neurons to fire in a precise temporal order. The resulting activity is globally synchronized to the pacemaker’s period.

Below the threshold (w₀ < w_c), the initial connectivity is insufficient to sustain widespread feed‑forward reinforcement. Instead, the network fragments into several independent feed‑forward clusters, each anchored by its own local pacemaker. Within each cluster, neurons synchronize, but inter‑cluster interactions remain weak, preventing global synchrony.

The authors analyze the weight dynamics in detail. STDP preferentially strengthens forward (pre‑to‑post) connections while weakening or eliminating backward links, thereby increasing network asymmetry and driving the emergence of directed pathways. This process reduces the prevalence of recurrent loops and creates an efficient, low‑dimensional conduit for information flow, reminiscent of biologically observed feed‑forward motifs in cortical circuits.

A systematic parameter sweep shows that the critical weight w_c depends on network size N, average degree k, and the STDP time constant τ. Larger k and shorter τ lower w_c, indicating that dense connectivity and rapid timing windows facilitate the formation of a unified feed‑forward structure. The findings suggest that STDP can act as a structural self‑organization mechanism that not only tunes synaptic efficacy but also sculpts the global wiring diagram toward configurations that support robust entrainment.

Overall, the study provides a mechanistic link between synaptic plasticity rules and the emergence of functional network architectures capable of generating coherent rhythmic activity. It offers testable predictions for experimental neuroscience—such as the existence of a dominant pacemaker neuron in spontaneously active excitatory cultures—and informs the design of artificial neural systems where directed, synchronizing pathways are desirable.