(A) Schematic of a “vanilla” RNN cell or neuron. An RNN neuron maintains a hidden state $r(t)$ that is computed at each timestep by linearly weighting the input signal and the previous output of itself and neighboring neurons through a recurrent connection. The output $S(t)$ is computed by applying a nonlinear transformation (e.g., ReLU, tanh, or sigmoid) to $r(t)$⁠. (B, C) Schematics of a GLIFR neuron. Each neuron maintains a synaptic current $Isyn$ that is computed at each timestep by linearly weighting the input signal by $Win$⁠, as well as the previous output of its neuron layer through a lateral or recurrent connection by $Wlat$⁠. The neuron's voltage $V$ decays over time according to membrane decay factor $km$ and integrates synaptic currents and after-spike currents $Ij$ over time based on membrane resistance $Rm$ and the membrane decay factor. Additionally, the voltage tends toward $Vreset$ through a continuous reset mechanism based on the firing rate at a given time. An exponential transformation of the difference between the voltage and the threshold voltage yields a continuous-valued normalized firing rate, which varies between 0 and 1. The normalized firing rate, along with terms $aj$ and $rj$⁠, is used to modulate the after-spike currents that decay according to decay factor $kj$⁠. The dynamics present in a GLIFR neuron give rise to its key differences from RNN neurons; GLIFR neurons can express heterogeneous dynamics, in contrast to the fixed static transformations utilized in RNN neurons.