Eqn. 3 represents the solution for a stationary energy with respect to the prospective voltage ŭ Here we consider a generalization of the energy function from the main manuscript that includes arbitrary "connectivity functions" f with parameters θ: E(ŭ Pseudo-code for our vanilla implementation can be found in Algorithm 1. Algorithm 1 Pseudo-code for the multi-layer implementation of Latent Equilibrium (LE) Figure 5: Learning to mimic a teacher microcircuit with LE. For the interneurons, the somatic membrane potentials of the pyramidal neurons in the layer above serve as targets. First, the output rate of the neurons must depend on the prospective voltage: ϕ (u) ϕ (ŭ). Note that this includes also the rates in the calculation of dendritic membrane potentials (Eqns. Learning is split into two stages: first, the learning of the so-called self-predicting state and afterwards the learning of the actual task.

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We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal.

Eqn. 3 represents the solution for a stationary energy with respect to the prospective voltage To include synaptic filtering in our theory, we introduce an additional LPF as in Eqn. 10 with time The target signal for the top-layer pyramidal is determined by the training set. We include LE in the dendritic microcircuit by two simple modifications. Learning is split into two stages: first, the learning of the so-called self-predicting state and afterwards the learning of the actual task. The full set of parameters used in Figure 1 and Figure 1 can be found in Section 15.2 . Table 1 lists all the parameters we used for the experiments shown in Figure 1 .

Because the true underlying structure of the data is rarely accessible, this "representation learning" must be