Reobserve: Allocating a Fixed Budget Between Visual Readings and Reasoning Chains

A vision-language system answers a question about an image by encoding the image once and then sampling several reasoning chains over that single encoding, which are then combined by a majority vote. Under a fixed budget one can instead read the image over again. Chains built on one reading share whatever that reading got wrong, so they are not independent observations: with $r$ readings and $k$ chains on each, the variance of the vote mean is $\text{vsV}/r+\text{vsR}/(rk)$, whose first term, the between-reading variance, does not shrink however many chains are added. The decomposition and its cost-optimal split, $k^{\star }=\sqrt{\text{cV}\text{vsR}/(\text{cR}\text{vsV})}$, are classical results of two-stage sampling and we claim neither. What the paper adds is the object: a reading as the cluster, a definition of reading diversity under which the between-reading variance is a property of the system, and the measurement of the two components on nine multimodal benchmarks under three ways of reading again. Reobserve estimates the components by a nested calibration and enumerates the feasible integer schedules. On every measured $r\times k$ grid the accuracy falls with the vote-mean variance, so the variance-optimal schedule is also the accuracy-optimal one on every benchmark, and the oracle row is the same schedule. The size of the two components says where reallocation is possible: on seven of nine benchmarks the default single-reading schedule sits $2.4$ points below the best equal-cost schedule, and on the two with a between-reading variance below $10^{-5}$ there is nothing to reallocate. Most of the gain is reading again at all: one chain per reading is within $0.04$ points of the calibrated rule at the anchor cost, and the split matters only when a reading costs about twice a chain. Where a question's mean support is on the wrong side of one half, less variance lowers its accuracy.