Reasoning-conditioned embeddings can improve retrieval by progressively refining semantic constraints. However, additional reasoning may introduce over-generalized or semantically noisy abstractions that weaken retrieval specificity. Existing methods largely supervise reasoning through final retrieval outcomes, providing limited guidance over the refinement process itself. We propose AURA, a framework that directly supervises intermediate reasoning states according to how well they separate relevant documents from hard distractors. AURA further trains a lightweight utility estimator over prefix-conditioned embeddings to adapt reasoning depth at inference time. On the reasoning-intensive BRIGHT benchmark, AURA-4B achieves 34.7 average nDCG@10 while using 2.8 reasoning steps and 96 generated tokens per query. Under matched deployment conditions, adaptive stopping reduces latency from 4.6 to 0.76 seconds relative to full-trajectory reasoning. Results on MS MARCO further suggest that this specialization need not substantially degrade conventional in-domain retrieval.

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