PLVR post-trains by learning an inspectable program instead of updating weights

arXiv 2608.28421·medium signalXBlueskyLinkedInCopy link

Posted 2026-08-28, Program Learning with Verifiable Rewards argues that for tasks whose intermediate steps can be verified, reasoning belongs outside the weights as an explicit program of deterministic and neural primitives, because SFT and RL both bury the capability where it cannot be inspected, checked step by step, or transferred to another model. The mechanism is symbolic backpropagation: each program layer carries a typed ontology, loss is computed at the output, and required input ontologies propagate backward by type inference over primitive signatures, so credit assignment is a derivation rather than an estimate. Where RLVR verifies only a terminal outcome, PLVR's reward is a per-step contract verdict, evaluated on LiveCodeBench v6 and Tau2Bench.