CUSUM-Shaped Inference-Time Monitoring and Targeted Re-Decoding for Quantized Small Language Model Reasoning· CUSUM 形状推理时监控与目标重解码

Quantized small autoregressive reasoning models can enter long, repetitive, or unproductive trajectories, yet inference-time compute is usually allocated without observing how a trajectory develops. Building on an earlier token-level e-CUSUM controller, we develop MGT-B (Monitoring-Guided Test-time Backtracking), a revised external controller that maps overlapping windows of pre-sampling uncertainty and degeneration features to position-conditional empirical tail probabilities, accumulates mixture betting factors with a CUSUM-shaped reset, and responds to an alarm by estimating a rollback point, restoring token and key-value-cache state, and performing constrained re-decoding. To audit whether the effect persists on problem identities first observed after the manual choice of log threshold