Abstract
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 h = 10, we retrospectively exclude 260 IDs present in pre-threshold artifacts and retain the chronologically first post-threshold pair for each remaining ID, yielding a 240-pair chronology-audit set. On this set, accuracy changes from 82/240 to 88/240 (+2.50 percentage points; 13 corrections, 7 regressions; exact McNemar p = 0.2632; paired bootstrap 95% interval [-1.25, +6.25]). A broader 467-pair historical-coverage set of seed-matched pairs changes accuracy from 146/467 to 167/467 (+4.50 points; McNemar p = 0.000753), but includes 200 seed-1 IDs available before or during threshold selection and is reported only as an exploratory estimate. All 316 no-alarm outputs in the 467-pair set are identical to vanilla, while the 151 alarmed trajectories contain 29 corrections and 8 regressions. Neither analysis is confirmatory, and the empirical factors are not established as a valid e-process or e-detector. The results support a selective monitoring-and-repair mechanism for the studied MATH-500 setting, rather than a general or theoretically certified reasoning improvement.
Blogger's Review: The MGT-B approach introduced in this paper provides an innovative dynamic adjustment mechanism for quantized small language models by monitoring uncertainty and degeneration features during inference. The effectiveness of this method is preliminarily validated through experiments, although further confirmatory analyses are needed to establish its theoretical foundation.