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However, the reward sparsity and the long reasoning horizon make effective exploration challenging. In practice, this challenge manifests as the \\emph{entropy collapse} phenomenon, where RLVR improves single-rollout accuracy but fails to expand coverage on successful reasoning trajectories. Passive exploration techniques like entropy regularization tend to dismiss generation quality, resulting in noisy rollouts. In response to this issue, we propose an Information-Maximizing Augmented eXploration (IMAX) framework to train a pool of soft prefixes that reshapes the base model's prior over reasoning trajectories. Rather than relying on RL to incentivize exploration on top of the base model, each prefix acts as a trainable control knob that induces a distinct rollout distribution from the same backbone model. 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Rather than relying on RL to incentivize exploration on top of the base model, each prefix acts as a trainable control knob that induces a distinct rollout distribution from the same backbone model. 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