{"ID":6537609,"CreatedAt":"2026-07-14T02:54:43.516908796Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.11317","arxiv_id":"2607.11317","title":"Calibrated e-CUSUM Decoding for Quantized Reasoning Models: Why Token Log-Probability Is the Wrong Observable for Decoding Monitors","abstract":"Low-bit quantization makes small reasoning models inexpensive to deploy but can degrade their chains of thought. This motivates decoder-side monitors that intervene when generation becomes unreliable. We show that a natural candidate, the centered token log-probability increment $\\log p(w_t)+H_t$, is the wrong observable for this purpose. Under the model's own sampling law it is a mean-zero martingale by construction, so it measures sampling self-consistency rather than trajectory health and is nearly silent during confident repetition, where both $\\log p(w_t)$ and entropy are close to zero. We introduce a training-free decoding controller that combines (i) a degeneration-aware alarm score fusing token uncertainty with explicit verbatim repetition and (ii) a calibrated e-process-inspired sequential detector. The raw product process is Ville-valid under a conditional-mean null, while the deployed CUSUM-floored statistic is treated as an empirical change detector because the score is history-dependent and autocorrelated. On GSM8K with DeepSeek-R1-Distill-Qwen-1.5B in FP16 and INT4, calibration turns a monitor that fires on 93--95% of generations into a selective detector of failing traces ($φ\\approx 0.3$, precision $\\approx 0.6$ against a 0.38 base rate). In this pilot, the controller reduces measured verbatim-degeneration signals and yields a positive but statistically inconclusive INT4 accuracy change from 63% to 69% (paired McNemar $p=0.18$, $n=100$), at a 28% token-budget cost. We also find that non-termination, rather than looping, is the dominant failure mode on GSM8K. The main contribution is methodological: an explanation of why centered token log-probability is inadequate for decoder monitoring and a calibrated, cautiously evaluated replacement.","short_abstract":"Low-bit quantization makes small reasoning models inexpensive to deploy but can degrade their chains of thought. This motivates decoder-side monitors that intervene when generation becomes unreliable. We show that a natural candidate, the centered token log-probability increment $\\log p(w_t)+H_t$, is the wrong observab...","url_abs":"https://arxiv.org/abs/2607.11317","url_pdf":"https://arxiv.org/pdf/2607.11317v1","authors":"[\"El Hassane Ettifouri\",\"Ayoub Belfatmi\",\"Mahaman Sanoussi Yahaya Alassan\",\"Walid Dahhane\"]","published":"2026-07-13T09:34:36Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"cs.IT\"]","methods":"[]","has_code":false}