EXACT: OPTIMIZING ADAPTIVE INFERENCE UTILITY VIA EXECUTION COMPILATION

Adaptive inference trades terminal answer quality against the cost of acquiring responses. We introduce EXACT, a method for optimizing the expected utility of a specified adaptive inference procedure. Given IID response banks and controllers with finite sufficient state, it compiles shared continuation states to average subset selection, reveal order, and stopping conditional on each bank. With the controller fixed, the resulting credits weight generator sequence-score updates (EXACT-G); with the generator fixed, differentiating the compiled value trains the stopping controller (EXACT-C). The generator estimator is the conditional expectation of its causal trajectory counterpart, eliminating conditional execution variance while retaining response sampling. Across three paired Qwen3-4B seeds under a 200-update budget, development-selected EXACT-G checkpoints improve mean six-benchmark deployment utility by 0.0140 and adaptive accuracy by 1.19 percentage points over correctness GRPO, with 1.54% fewer expected rollouts. A separate Qwen3-1.7B rank-eight LoRA diagnostic attributes 51% of sampled-gradient energy to execution variation under aggressive stopping. On frozen Qwen3-4B banks, EXACT-C computes exact conditional controller gradients and reaches comparable observed held-out utility to Order-MC-64 with 19.5% less controller-training CPU.