PROBE HORIZON IS NOT PREDICTABLE MEMORY: MEASURING THE HISTORY A SURROGATE NEEDS ON A COMPLETE CONNECTOME MODEL

A surrogate model must be told how much of the past to see, and practice takes that number from a probe of the simulator, typically an impulse horizon, an autocorrelation time or a settling time read at a threshold such as $1/e$. Such a probe reports how long one chosen excitation leaves a visible trace in one observed statistic. What a surrogate needs is different: the horizon over which past input still changes the noise-averaged response it is trained to predict. On a leaky integrate-and-fire model of the first complete connectome of an adult male *Drosophila* central nervous system, the three probes return 30, under 10 and 150 ms, while a windowed MLP student keeps gaining fidelity out to 960 ms of history and the memoryless MLP trails a GRU by 0.15 in fidelity. We quantify what the student needs with a shared-suffix measurement whose estimator subtracts the teacher's own stochastic floor in squared distance. On this connectome the measurement returns a tail that is still above a tenth of its initial amplitude at 1 s, the last lag we measure, matching the range of history the student keeps using and well beyond every probe. On a second complete brain connectome under identical neuron dynamics the same measurement returns 83 ms, and its students need 80 ms. On a synthetic teacher with a planted 500 ms state it returns a fitted slow timescale of 521 ms [429, 693]. The student's required history survives a sixteenfold larger training bank, a change of input noise and a 9.6-fold change in capacity, and wherever the input contains transitions it moves with the predictable tail across teachers and interventions. A gain-matched intervention makes the separation causal. Read after subtracting its stochastic floor, the teacher's step response lengthens from 220 ms to past the end of the step-response window, while the conventional reading shortens. The history a surrogate needs is a measurement of predictable memory, and predictable memory is not the horizon a probe reports.