How Much Does Correctness Cost? Budgeted Placement of Strong Correctors in a Weak Multi-Agent Swarm

What the math gives to ML

The paper turns sparse intervention placement into a spectral design problem: adding diagonal rank-one pins to a positive-definite consensus operator reduces the trace of its inverse, and the reduction has diminishing returns. This yields a cost-aware greedy strategy with a principled budget-versus-correctness interpretation rather than choosing interventions by local confidence alone. A direct neural-network transfer is a modular inference system in which many cheap predictors exchange information over a similarity graph while a limited number of expensive verifiers are selectively attached as strong anchors. The useful asset is the explicit rank-one marginal-gain formula, which makes placement measurable, adaptive, and testable under a fixed verifier-call budget.