Neurons with firing adaptation

[jlubo]

So far, neurons with firing adaptation have not yet been added to the Lava library (although according neurons have been implemented in Lava-DL, see the links below). But such neurons are needed for applications that require sophisticated neuron-intrinsic plasticity as well for realistic neuroscience models.

[jlubo]

One possible such model is given by a Leaky Integrate-and-Fire neuron with adaptive threshold and adaptive refractoriness (which I'd therefore call ATRLIF neuron).

The dynamics of the model are described by the following formulation, originating from Lava-DL (see here and here):

• Current: $i[t] = (1-\delta_i) \cdot i[t-1] + x[t]$

• Voltage: $v[t] = (1-\delta_v) \cdot v[t-1] + i[t] + \mathrm{bias}$

• Threshold: $\theta[t] = (1-\delta_{\theta}),(\theta[t-1] - \theta_0) + \theta_0$

• Refractory state: $r[t] = (1-\delta_r),r[t-1]$

• Spike event: $s[t] = (x[t] - r[t]) \geq \theta[t]$

• Refractory post-spike event: $r[t] = r[t] + 2,\theta[t]$

• Threshold post-spike event: $\theta[t] = \theta[t] + \theta_{\text{step}}$

With the following parameters (cf. the PR here):

• $\delta_i$: Decay constant for current $i$.

• $\delta_v$: Decay constant for voltage $v$.

• $\delta_\theta$: Decay constant for threshold $\theta$.

• $\delta_r$: Decay constant for refractory state $r$.

• $\theta_0$: Initial/baseline value of threshold $\theta$.

• $\theta_\text{step}$: Increase of threshold theta upon the occurrence of a spike.

• $\mathrm{bias}$: Neuron's bias.

[PhilippPlank]

Thanks for adding this. I will take a look at the PR.