Allostatic Update Rule

The Allostatic Update Rule is a spiking neuron model that adjusts its internal target activation level over time, supporting dynamic homeostasis. Based on Falandays et al. (2021), it captures regulatory processes that balance activation around a moving set point.

Each neuron maintains:

  • An activation level \(x_n\).
  • A target activation level \(T_n\).
  • A spiking threshold \(T'_n = 2T_n\).

The neuron updates as follows:

  1. Activation decay with input
    \(x_n \leftarrow \max(0,\; x_n \cdot \text{leakRate} + \sum_j w_j \cdot \text{spike}_j)\)

  2. Spike condition and reset
    \(\text{if } x_n > T'_n \Rightarrow \text{spike}, \quad x_n \leftarrow x_n - T'_n\)

  3. Synaptic weight adaptation (only from spiking sources) \(w_j \leftarrow w_j - \frac{x_n - T_n}{N}\)

  4. Target adaptation and threshold update \(T_n \leftarrow \max(1,\; T_n + \eta \cdot (x_n - T_n)), \quad T'_n \leftarrow 2T_n\)

This rule causes a neuron to maintain activity around its evolving target, modifying both its incoming weights and threshold accordingly.

Parameters

  • Leak Rate: Proportion of activation retained after each time step. A value of 0.75 implies a 25% decay in the absence of input.
  • Learning Rate: How quickly the target activation level adapts to current activity.

For all other parameters, see common neuron properties