CUSUM-Shaped Inference-Time Monitoring and Targeted Re-Decoding for Quantized Small Language Model Reasoning

Abstract

Quantized small reasoning models can enter repetitive or otherwise unproductive trajectories, yet standard decoding does not adapt to the trajectory as it unfolds. We study MGT-B, a fixed, weight-preserving controller that converts overlapping windows of uncertainty, repetition, and local-change features into position-conditional empirical tail probabilities. It accumulates mixture betting factors with a CUSUM-shaped reset, and, after an alarm, restores a coherent earlier token and key-value-cache state before constrained re-decoding. On MATH-500, a paired three-seed evaluation over 1,500 generations per method raises exact-normalized accuracy from 54.73% for vanilla decoding to 56.40% (+1.67 percentage points; problem-clustered bootstrap 95% CI [+0.47, +2.80]), while a prospectively profiled random-intervention control reaches 54.60%. The gain is positive in all three seeds and costs 5.14% more sampled tokens. Seed-0 ablations show that rollback alone does not explain the result and that an isolated repetition penalty is harmful. Five-sample self-consistency reaches 70.0% but uses about 4.84x as many tokens as MGT-B. On the harder, non-overlapping Omni-MATH evaluation, however, MGT-B obtains 16.60% versus 16.67% for vanilla (-0.07 points; clustered 95% CI [-0.33, +0.20]) with 2.10% more sampled tokens. Thus, MGT-B provides a modest, reproducible local improvement on MATH-500 in the studied configuration, but the effect does not transfer to Omni-MATH and should not be interpreted as a general improvement in mathematical reasoning.