Infinitely large, randomly wired sensors cannot predict their input unless they are close to deterministic

Building predictive sensors is of paramount importance in science. Can we make a randomly wired sensor “good enough” at predicting its input simply by making it larger? We show that infinitely large, randomly wired sensors are nonspecific for their input, and therefore nonpredictive of future input, unless they are close to deterministic. Nearly deterministic, randomly wired sensors can capture ∼ 10% of the predictive information of their inputs for “typical” environments.