While search-augmented large language models (LLMs) exhibit impressive capabilities, their reliability in complex multi-hop reasoning remains limited. This limitation arises from three fundamental challenges: decomposition errors, where tasks are incorrectly broken down; retrieval missing, where key evidence fails to be retrieved; and reasoning errors, where flawed logic propagates through the reasoning chain. A single failure in any of these stages can derail the final answer. We propose Erasable Reinforcement Learning (ERL), a novel framework that transforms fragile reasoning into a robust process. ERL explicitly identifies faulty steps, erases them, and regenerates reasoning in place, preventing defective logic from propagating through the reasoning chain. This targeted correction mechanism turns brittle reasoning into a more resilient process. Models trained with ERL, termed ESearch, achieve substantial improvements on HotpotQA, MuSiQue, 2Wiki, and Bamboogle, with the 3B model achieving +8.48% EM and +11.56% F1, and the 7B model achieving +5.38% EM and +7.22% F1 over previous state-of-the-art(SOTA) results. These findings suggest that erasable reinforcement learning provides a powerful paradigm shift for robust multi-step reasoning in LLMs.

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