STDP-Driven Rewiring in Spiking Neural Networks under Stimulus-Induced and Spontaneous Activity

Abstract

Mathematical and computer simulation of learning in living neural networks have typically focused on changes in the efficiency of synaptic connections represented by synaptic weights in the models. Synaptic plasticity is believed to be the cellular basis for learning and memory. In spiking neural networks composed of dynamical spiking units, a biologically relevant learning rule is based on the so-called spike-timing-dependent plasticity or STDP. However, experimental data suggest that synaptic plasticity is only a part of brain circuit plasticity, which also includes homeostatic and structural plasticity. A model of structural plasticity proposed in this study is based on the activity-dependent appearance and disappearance of synaptic connections. The results of the research indicate that such adaptive rewiring enables the consolidation of the effects of STDP in response to a local external stimulation of a neural network. Subsequently, a vector field approach is used to demonstrate the successive "recording" of spike paths in both functional connectome and synaptic connectome, and finally in the anatomical connectome of the network. Moreover, the findings suggest that the adaptive rewiring could stabilize network dynamics over time in the context of activity patterns' reproducibility. A universal measure of such reproducibility introduced in this article is based on similarity between time-consequent patterns of the special vector fields characterizing both functional and anatomical connectomes.

Keywords: STDP; activity vector field; learning; rewiring; spiking neural network; structural plasticity; synaptic plasticity; weight vector field; wiring vector field.

Figure 1

Example of rewiring in the model.

Figure 2

Vector fields of a small neural circuit: (A) the wiring vector field, (B) the weight vector field, and (C) the activity vector field after 20 s stimulation of a neuron (marked in green).

Figure 3

Stimulus-induced changes in a neural line circuit mediated by STDP and structural plasticity: (A) the initial condition, (B) the activity vector field reflects stimulus-induced activity, (C) STDP-driven weight rearrangement, and (D) rewiring mediated by STDP and structural plasticity. As in Figure 2, the red/black/blue arrows represent the activity/weights/wiring vector field. The rewiring parameters were as follows: $w_{min}$ = 0.05, $t_w$ = 5 s, and $w_{new}$ = 0.1.

Figure 4

Stimulus-induced changes in a 2D neural circuit. (A) the wiring vector field, (B) the weight vector field, and (C) the activity vector field after 20 s stimulation of a neuron, (D) rewiring captures these functional rearrangements into structural changes in the SNN. The rewiring parameters were set as follows: $w_{min}$ = 0.2, $t_w$ = 5 s, and $w_{new}$ = 0.05.

Figure 5

Stimulus-induced changes in a neural network mediated by STDP and structural plasticity: (A) general view of the neural network and propagating spike activity at different time points after the start of the stimulation, (B) the activity vector field, (C) the weight vector field, and (D) the wiring vector field. Rewiring parameters were set as follows: $w_{min}$ = 0.05, $t_w$ = 100 s, and $w_{new}$ = 0.1.

Figure 6

The effect of SNN stabilization under structural plasticity: (A) example of weight vector fields at different time points after the introduction of rewiring and the similarities of vector fields S; (B) dynamics of the vector fields’ similarity in the case of structural plasticity (STDP + rewiring) and without it (STDP only).

Figure 7

Influence of rewiring parameters on the stabilization of the neural network: (A) network similarity vs. weight of newborn connections ($w_{min}$ = 0.05, $t_w$ = 5 s); (B) network similarity vs. lifetime of weak connections ($w_{min}$ = 0.05, $w_{new}$ = 0.06). *, ●—statistically significant differences between the current network with rewiring and the network without rewiring (*—p < 10⁻⁷, ●—p < 0.01, Mann–Whitney U test).