Calibration Is Not Enough: An Anytime Monitor for Trustworthy Abstention

Version 2 (9 September 2026) — erratum. An independent audit found several statements in v1 that the paper's own logs and results did not support — stale prose from an earlier run of the same experiment, not a change to the method. Corrected: the batch baseline's overall answered risk in Section 6.4 (was misstated as 0.164; the artifact says 0.112); a false claim that k-NN was worst on two conditions in Section 6.3 (it is never worst); an overclaim that TRIBUNAL was "the only method" beating two baselines in Section 6.2; Figure 3's theory sweep, which had been scored partly on the calibration half — re-scored on held-out data only, TRIBUNAL is worse than MSP at p=0 and overtakes it around p=0.2-0.3, not p=0.15; Section 6.5 and Figure 6, which described an earlier LLM run (kappa=0) rather than the one actually behind the published results (kappa=4, where TRIBUNAL is worse than plain sequence probability); the LLM accuracy figure, corrected from a held-out-half value (0.152) to the true full-500 figure (0.138); and an unconditional claim in Section 5 / Appendix A.3 that the anytime monitor "cannot stay silent forever" once risk rises, corrected to state the threshold below which it has no detection power — the LLM experiment is shown to be a live example of exactly that limit, not a success case as v1 described it. The two central results are unchanged and were independently re-verified: Theorem 4.1's separation bound and the anytime monitor's false-alarm guarantee both check out, and the core CIFAR-10 numbers reproduce bit-for-bit from the released checkpoint. Full erratum detail is in the paper's own preface. A predictor that abstains when it is likely wrong is far more useful than one that is merely accurate on average, but abstention is only as good as the confidence signal it runs on. We show that the signal almost everyone uses is structurally inadequate. For any selector that abstains by thresholding a single calibrated confidence score, there is an irreducible floor on the area under its risk–coverage curve: on inputs that are confident and wrong because the model has never seen anything like them, no amount of calibration helps. A selector that also reads an epistemic signal escapes this floor. The catch is that the calibration the floor survives is the only kind a post-hoc method can actually obtain: a score can be calibrated on the reference data it is given and still be badly miscalibrated on the off-support inputs it was never shown, and no amount of post-hoc recalibration repairs that. That impossibility is our first result. Our second is a tool for deployment. The standard distribution-free fix, calibrating a fixed abstention threshold on held-out data, quietly stops working under distribution shift: the system keeps certifying a risk bound it no longer meets. We give an anytime-valid, false-alarm-controlled monitor for selective risk — a betting process whose false-alarm probability is provably at most δ and which raises an alarm once the risk it is tracking creeps up. Over 300 stationary streams its empirical false-alarm rate is 0.000, and on a shifting stream where a calibrated baseline silently runs at 1.5× its promised risk, the monitor fires. Third, we give a concrete post-hoc score, TRIBUNAL, that studentizes a frozen model's confidence by the worst-case doubt its own evidence cannot rule out. It improves selective risk where the theory says it should, on overconfident models facing out-of-distribution and corrupted inputs, and it collapses to plain confidence where the model is already well separated. We report that null result rather than hide it. Everything runs on a frozen model with one extra forward pass. Working paper, self-archived. Code, checkpoints and full results are described in the paper; the frozen-model experiments use CIFAR-10/100 ResNet-18 and a Qwen2.5-1.5B-Instruct LLM run.