A simple spontaneously active Hebbian learning model: homeostasis of activity and connectivity, and consequences for learning and epileptogenesis

A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that connectivity is maintained at a state that is optimal for information transmission and storage. This state is referred to as the critical state. We present a simple stochastic computational Hebbian learning model that incorporates both firing rate and critical homeostasis, and we explore its stability and connectivity properties. We also examine the behavior of our model with a simulated seizure and with simulated acute deafferentation. We argue that a neural system that is more highly connected than the critical state (i.e., one that is “supercritical”) is epileptogenic. Based on our simulations, we predict that the post-seizural and post-deafferentation states should be supercritical and epileptogenic. Furthermore, interventions that boost spontaneous activity should be protective against epileptogenesis.

💡 Research Summary

The authors address a fundamental problem in neuroscience: how a spontaneously active neural network can continuously learn while keeping both firing rates and synaptic connectivity within stable bounds. To this end they construct a stochastic Hebbian learning model that incorporates two homeostatic mechanisms. The first mechanism regulates the average firing rate by applying a negative feedback term whenever the network’s mean activity deviates from a predefined target. The second mechanism enforces “critical connectivity” by adjusting the total synaptic weight toward a value that theoretical work predicts maximizes information transmission and storage. Mathematically, the weight update rule combines the classic Hebbian term (proportional to the product of pre‑ and postsynaptic activities) with two corrective terms weighted by parameters α (firing‑rate homeostasis) and β (connectivity homeostasis).

Simulation experiments reveal that only the simultaneous operation of both homeostatic terms yields a stable critical state. If only firing‑rate homeostasis is active, synaptic weights drift upward, pushing the network into a super‑critical regime where activity can spread explosively. Conversely, if only connectivity homeostasis is present, the network’s firing rate becomes unstable, leading to runaway excitation. Thus the two mechanisms are mutually necessary, mirroring biological observations that neurons regulate both excitability and structural connectivity.

The authors then probe two pathological perturbations. In a simulated seizure, a brief, strong excitatory input drives the system into a super‑critical state; after the input ceases, the elevated synaptic strength persists, making the network prone to recurrent seizures. In a simulated acute deafferentation (loss of sensory input), the homeostatic drive to compensate for reduced drive paradoxically strengthens connections, again producing a super‑critical configuration. Both scenarios support the hypothesis that a network more connected than the critical point is epileptogenic.

Finally, the model predicts that enhancing spontaneous activity—through low‑intensity electrical stimulation, optogenetic activation, or pharmacological means—can restore the balance. By modestly raising the mean firing rate toward its target, the firing‑rate homeostatic term engages more quickly, and the connectivity term can more effectively pull the system back to the critical regime, thereby reducing seizure susceptibility.

In summary, the paper provides a concise yet rigorous computational framework that unifies firing‑rate and connectivity homeostasis, demonstrates how their breakdown leads to super‑critical, seizure‑prone states, and suggests that modest augmentation of spontaneous activity may serve as a protective, non‑invasive strategy against epileptogenesis.