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

• URL: http://arxiv.org/abs/2607.20129v1
• Date: Wed, 22 Jul 2026 13:34:17 GMT
• Title: CUSUM-Shaped Inference-Time Monitoring and Targeted Re-Decoding for Quantized Small Language Model Reasoning
• Abstract summary: MGT-B maps overlapping windows of pre-sampling uncertainty and degeneration features to position-conditional empirical tail probabilities.<n>We audit whether the effect persists on problem identities first observed after the manual choice of log threshold h = 10.<n>Neither analysis is confirmatory, and the empirical factors are not established as a valid e-process or e-detector.
• Score: 0.6999740786886536
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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