Local noise additions identify weight ratios beyond node gains in fully observed linear circuits with scalar filters
We tested what controlled evidence can separate changes in directed interaction patterns from node gains. In a stable, fully observed linear circuit, one independent noise addition per node gives rank-one output spectral differences. Their response columns can be inverted without known input powers or waveforms. A ratio of four off-diagonal inverse entries equals a ratio of four latent weights. Unknown scalar cell filters, unchanged correlated drive, source gains, target gains and decay terms cancel. The proof holds at each fixed frequency. In models on Cook worm, FlyWire region and Knox mouse parcel graphs, source and target gain changes left one selected ratio per graph fixed to numerical precision. A 50 percent increase in one tested edge multiplied it by 1.5. The supports permit 4,496, 5,356 and 91,505 independent positive log contrasts beyond source and target factors. A 2,160-draw sampling test was less favorable. With 8,192 ideal spectral samples per setting, median error in a true relative ratio change of 0.5 was 0.189 at the strongest input setting and 1.593 at the weakest. Coherent off-target input gave incorrect ratios while all spectral differences stayed rank one. Hidden recurrent nodes and unknown channel calibration also limit interpretation. These are proofs and model tests, not new animal measurements. Code, aggregate evidence and exact external-input hashes support reproduction; external graph records remain outside the publication.
References
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