Sequential statistical inference for Large Language Models: Representation, validity, and monitoring

Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs are just unsupervised clustering algorithms. We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.

Model cards quote trust-benchmark scores without recording when they were measured, and the same number is routinely carried across successive checkpoints of one release line as if the model behind it had not shifted. We test whether it has shifted by auditing four open-source release lines, Yi, Qwen, Mistral, and Gemma, at three successive generations each, on a fixed basket of trust benchmarks under multiple prompt templates. Mean absolute adjacent-generation drift lands well above an independence-based no-drift reference null, and the gap persists when we drop a benchmark, drop a release line, or switch to strict scoring. We therefore conclude that a trust score attached to a release line should not be carried forward to the next checkpoint without remeasurement; it should instead be reported as a checkpoint-bound, dated artefact, which we package as a longitudinal model card. Closed APIs, larger models, canonical benchmark protocols, and fixed month-cadence rules lie outside the audited scope and require their own evaluation.

Reliability assessment of large language models (LLMs) seeks to estimate the probability that a model produces correct responses under a specified operational profile. Conventional benchmark-based evaluation, often summarized by aggregate accuracy, provides a point estimate of performance but does not characterize the uncertainty associated with reliability claims. Currently, statistical inference methods for LLM reliability assessment are emerging. However, a key assumption underlying these models is that test outcomes can be treated as independent repeated trials. This assumption may be inappropriate in sequential settings, where later responses depend on earlier interactions through retained context, error propagation, or an evolving interaction state. We extend a hierarchical Bayesian framework for LLM reliability assessment by relaxing the assumption of independent task outcomes and introducing a Hidden Markov Model to capture sequential dependence in benchmark-constructed interaction sessions. In this formulation, outcomes are generated from a latent interaction state evolving according to a first-order Markov process, capturing changes in interaction context. Through experiments using Anthropic Claude and OpenAI on four datasets, we demonstrate the potential impact of sequential dependence on reliability assessment. The results suggest that ignoring sequential dependence may lead to overconfident reliability estimates.