Robustness-Performance Tradeoffs and Spectral-Radius Scaling in Connectome Reservoirs
Reservoir computing provides a controlled framework for investigating how recurrent network architectures shape computation, but reservoir performance can vary substantially with hyperparameters such as spectral radius, input scaling, leak rate, and neuronal bias. In this work, we study the architectural determinants of hyperparameter invariance using the C. elegans chemical-synapse connectome as a biologically grounded reservoir model.
We quantify computational capability using four task-agnostic metrics: memory capacity, truncated information-processing capacity, kernel rank, and generalization rank. We compare the connectome-derived reservoir with controlled variants that alter connectivity topology, excitatory and inhibitory sign structure, synaptic-weight distributions, and the placement of weights across connections.
The connectome-derived reservoir occupies a relatively low-sensitivity regime, but this robustness is associated with lower computational capacity. Across architecture families, higher task-agnostic performance generally coincides with greater dependence on hyperparameter selection. These changes are also negatively associated with the raw spectral radius of the recurrent matrix. More broadly, these results show that raw spectral radius must be treated as an integral architectural variable when comparing recurrent networks, because it directly shapes the effective weight scale and the computational regime produced after normalization.
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