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Program Learning with Verifiable Rewards: Symbolic Backpropagation for Post-Training LLMs

arXiv · AI, language, vision and robotics · article · Aug 28, 2026 · UTC

Post training a language model to reason means updating its weights. Supervised finetuning and reinforcement learning both place the acquired capability inside the model where it cannot be inspected cannot be checked step by step and cannot be moved to another model. We argue that for tasks whose intermediate steps admit verification, reasoning is better placed outside the base models weights as an explicit program composed from deterministic and neural primitives. We introduce PLVR (Program Learning with Verifiable Rewards): a post training method that learns such programs directly from input

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