Generally the way to do this in Nengo currently is to create a custom neuron model that will handle everything from the “+” node, onwards, as in:
There are a couple examples on how to use random samples to generate a spike train, here: https://github.com/nengo/nengo/issues/1487. There is also a short tutorial on adding new objects to Nengo here: https://www.nengo.ai/nengo/examples/usage/rectified_linear.html.
For the rest of the drawing: The $\gamma_i$ term is supplied automatically by the ensemble, through its bias term. Likewise, the $\alpha$ terms are computed and supplied automatically by Nengo on the connection to the ensemble, through the product of the ensemble’s encoders, the presynaptic decoders (trained by Nengo), and the ensemble’s gain. You can also customize these terms by providing them to nengo.Ensemble. All of the resulting weights are generated automatically and solved for by connecting into the ensemble and specifying the function and transform.