5 Supplementary Material

Dendritic updates Complete versions of the dendritic update rules (summarised in Eqns (2) & (3)) are given below. This is valid in our regime where the environmental latent updates slowly compared to neural timescales. The notation we're using admits the possible presence of biases as well as the weights (though biases typically aren't used) by assuming a row of constant 1's could be added to the synaptic inputs effectively absorbing a bias into the weight matrix without loss of generality, for example wgB p(t) wgB p(t)+ bgB . Somatic updates Somatic updates rules (Eqns (4) & (5)) and are repeated here for completeness: p(t)= (t)pB(t)+(1 (t))pA(t) g(t)= (t)gB(t)+(1 (t))gA(t). Update ordering For this hierarchical network of multicompartmental neurons we must specify the order in which we perform these discrete updates to the different layers and the different compartments within these layers.