Supplementary Material.

Additional derivations and results omitted from main manuscript. Derivations include the computation of the large population limit for Fisher information and the relation between the memory fidelity and the Fisher information. We report the stimuli separation analysis for the hierarchical code, analogous to the analysis of Fig. 16 in the manuscript. Following the comments of a reviewer, we studied the relationship between the conjunctivity ratio and the population size in a mixed population code, as our parametrisation creates a dependence between them. Finally, we show how increasing the number of features affects the ratio of conjunctivity for a fixed population size.
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