Location of intrinsic timescales shapes the temporal repertoire of recurrent networks

Neural systems comprise units with varying intrinsic timescales, but how this heterogeneity contributes to temporal computation, and its interaction with recurrent dynamics are not fully resolved. Intrinsic heterogeneity provides a richer temporal basis to a readout, but on our temporal tasks recurrence can largely compensate for its absence as diverse effective dynamics emerge. In recurrent systems, keeping fixed the graph structure, its weights, and the intrinsic timescale multiset, we vary which nodes receive which timescales and find the effective temporal repertoire changes systematically with this placement. Degree and strength alignment effects are stronger when degree is heterogeneous in the network, whereas alignment with a spectral slow mode coordinate displays a comparable effect across topology families. Placement relative to slow recurrent modes therefore determines how the temporal repertoire is expressed.