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Efficient Reasoning at Fixed Test-Time Cost via Length-Aware Attention Priors and Gain-Aware Training

We study efficient reasoning under tight compute. We ask how to make structured, correct decisions without increasing test time cost. We add two training only components to small and medium Transformers that also transfer to broader differentiable optimizers. First, a length aware attention prior built via fuzzy regime position alignment, RPA, yields a normalized pre softmax bias that guides attention like a structured regularizer while adding no new inference parameters. Second, a minimal gain aware controller, Guardian, nudges attention sharpness only when validation improvements warrant it, following a two timescale policy gradient view of nonconvex optimization. It is disabled at inference. A KL perspective shows softmax of z plus log pi as MAP with KL regularization, grounding the prior in a principled objective. Under strict compute parity on WikiText 2, we reduce validation cross entropy while matching baseline latency and memory. At inference, we add a precomputed, cached prior B of T as a single additive bias per head. The controller does not run. In practice, this incurs negligible overhead, a cached bias add per head, with no measurable p50 latency shift. Our results suggest that length aware priors and late phase gain control preserve scarce improvements, especially in long span, noisy logit regimes, while keeping test time costs effectively unchanged.

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