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However, this approach becomes challenging for reasoning capabilities, which exhibit emergent behavior that only appear reliably at larger model sizes, often exceeding 7B parameters. To address this, we introduce rBridge, showing that small proxies ($\\leq$1B) can effectively predict large-model reasoning by aligning more closely with (1) the pre-training objective and (2) the target task. rBridge achieves this by weighting negative log-likelihood with task alignment, using reasoning traces from frontier models as gold labels. 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To address this, we introduce rBridge, showing that small proxies ($\\leq$1B) can effectively predict large-model reasoning by aligning more closely with (1) the pre-training objective and (2) the target task. rBridge achieves this by weighting negative log-likelihood with task alignment, using reasoning traces from frontier models as gold labels. 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