Readout noise set an exact information-growth threshold in two adult worm circuit models

We tested when transient signal growth improves input detection in positive linear models from two partial adult C. elegans wiring maps. For stationary Gaussian process noise and a full-state readout, Fisher information about a brief input cannot increase without readout noise. With unit isotropic process noise and independent isotropic readout variance r, information can grow in some direction exactly when r exceeds 1/lambda_max(A+A transpose), if that eigenvalue is positive. We checked this boundary in eight binary and synapse-count models on 180 common cells. At binary coupling 0.95, signal norm peaks were 1.5401 and 1.4350. The readout variance thresholds were 1.9769 and 2.3128. At twice these thresholds, sampled peak information ratios were only 1.0297 and 1.0302. Code, a proof, aggregate results and checks are supplied. The threshold is an application of established linear Gaussian methods. Positive couplings, equal leaks, stationary noise, full observation, two partial maps and no matched activity limit biological inference.

connectome · C. elegans · transient amplification · Fisher information · readout noise · stationary covariance