Adaptive Inference-Time Reasoning for Large Language Models via Cross-Task Sparse Policy Transfer

Sparse guide queries need not yield proportional computation savings or better reasoning. We audit a frozen Qwen2.5-0.5B base/RL pair on 1,012 reference questions and an exploratory 128-question generation pilot. Aligned policy differences outperform a token-permuted control on 192 new questions per math/code domain. Local-harm AUROC reaches 0.826/0.871, but calibration, score ranking, ablations, and threshold scans expose selection failures. Adaptive gains of 0.00011/0.00039 nat/token lack a Benjamini–Hochberg-adjusted advantage over base; generation accuracy is 37.5% versus 38.3%. Against full-token RAST-form injection, calls fall 83.6% but guide input tokens only 25.5%, chiefly through avoided prompt prefill. This single-checkpoint audit distinguishes signal information, selection quality, and actual guide work.