Backpropagation is not biologically plausible because it the error signals to update the weights of the hidden layers need to be propagated back from the top layer.

Feedback alignment side-steps this problem by replacing the weights in the backpropagation rule with random ones:

\begin{equation} \delta_{i}^{(l)}=\sigma^{\prime}\left(a_{i}^{(l)}\right) \sum_{k} \delta_{k}^{(l+1)} G_{k i}^{(l)} \end{equation}

where \(G^{(l)}\) is a fixed, random matrix with the same dimensions as \(W\). The replacement of \(W^{T,(l)}\) with \(G^{(l)}\) breaks the dependency of the backward phase on \(W\), enabling the rule to be more local. Another variation is to replace the backpropagation of the errors in each layer with a random propagation of errors to each layer:

\begin{equation} \delta_{i}^{(l)}=\sigma^{\prime}\left(a_{i}^{(l)}\right) \sum_{k} \delta_{k}^{(L)} H_{k i}^{(l)} \end{equation}

Random BP applied to SNNs do not account for the temporal dynamics of neurons and synapses. SuperSpike solves this problem.