Heteroskedastic Signals in Budgeted LLM Verification: Structural Heterogeneity Limits Optimization Gains (opens in new tab)

Large language model (LLM) systems increasingly use uncertainty signals to allocate limited computation across verification, test-time scaling, tool execution, and other selective-compute decisions. Such policies rely on a \emph{global signal comparability assumption}: equal scores should carry comparable decision value across inputs. Using budgeted verification as a controlled diagnostic setting, we identify a failure mode of this assumption: u...