Determinants of Hyperparameter Invariance in Connectome Reservoir Computing
Biological neural circuits remain in functional computational ranges despite substantial variability in synaptic strengths, neuron leak, and inputs. In reservoir computing, performance and stability depend sensitively on hyperparameters such as spectral radius, input scaling, and leak rate; however, it is unclear which network properties govern invariance to these parameters. In this work, we investigate the determinants of hyperparameter invariance using the C. elegans connectome as a biologically
grounded reservoir model.
We quantify computational capability using task-agnostic metrics—Memory Capacity (MC), Information Processing Capacity (IPC), Kernel Rank (KR), and Generalization Rank (GR)—and measure invariance as the coefficient of variation of these metrics under hyperparameter sweeps. We construct controlled perturbations that independently alter connectivity topology, synaptic weight magnitude distributions, and excitatory/inhibitory sign structure while preserving other structural properties. This allows isolation of the causal contributions of topology, magnitude statistics, and global sign balance to computational invariance.
Preliminary results suggest that global sign balance and weight magnitude statistics account for a large fraction of the observed invariance.
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