Characterizing a Configuration Where Inference-Time PRM-Pruned Fragment Grafting Is Inert: Evidence from Three Reasoning LMs
Abstract: Diversity collapse in parallel chain-of-thought has motivated inference-time interventions built on a natural design: when a process reward model (PRM) prunes a chain, its high-PRM prefix is extracted and grafted verbatim as an in-context demonstration into a still-decoding sibling. We isolate this mechanism, PRM-Pruned Fragment Grafting (PPFG), as the most cost-minimal operationalization of cross-trajectory step-level transfer, and test it at the operating point where prior fragment-grafting work reports gains only under additional compensating ingredients. On Qwen2.5-7B-Instruct with Math-Shepherd on full MATH500 (n=500, three seeds), PPFG in both stagnation- and random-targeting variants is statistically indistinguishable from an independent parallel-CoT baseline on every measured axis. We characterize why: a four-bucket classification of 322 stagnation-rule injection events shows only 14% targeted a genuinely struggling chain; the rest landed on chains that had already succeeded, were near completion, or sat on a flat PRM plateau, states a rescue graft cannot change. No compound-gate refinement jointly achieves well-targeted firing and adequate density, and a random control matches the same parity at 2.4x the firing rate, so the inertness is not heuristic-specific. The finding replicates across three base LMs, six benchmarks, a second PRM, and a compatibility-gate sweep; two-one-sided-tests analysis promotes the parity to positive equivalence on all twelve Qwen/LLaMA cells. A per-event spot-check finds injected chains prune at 2.75x the matched-step rate, but a surviving-sibling counterfactual finds no population-level compensation. A hindsight oracle bounds any per-problem gain from choosing PPFG over independent at +0.13 pp. We contribute an equivalence-testing template for establishing inference-time mechanism nulls, with every claim scoped to its tested operating point.
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