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

Technical Summary: Sequential Statistical Inference for Large Language Models

Problem Statement
Current statistical frameworks for Large Language Models (LLMs) often rely on a "next-token prediction" lens, treating model outputs as isolated, independent events. However, in practical deployment, LLMs operate within dynamic environments where they are queried repeatedly, conditioned on evolving contexts, interact with users and tools, and incorporate feedback loops. This operational reality creates dependent stochastic processes rather than sequences of independent prompt–response pairs. Consequently, standard statistical assumptions, such as exchangeability required for classical conformal prediction, are frequently violated. The paper argues that treating LLMs as static predictors fails to address critical deployment challenges: the need for validity guarantees under dependence, the management of adaptive interactions, and the detection of behavioral shifts (e.g., in calibration, safety, or hallucination rates) after model updates or distribution changes.

Methodology and Framework
The paper proposes a unified framework for trustworthy LLM deployment centered on sequential statistical inference, organized around three interconnected components:

1. Representation (The Unit of Analysis):
   The authors advocate shifting the statistical unit of analysis from isolated prompt–response pairs to dependent interaction trajectories. An LLM-driven workflow is modeled as a stochastic process where each interaction $t$ is a tuple $X_t = (P_t, R_t, U_t)$, representing the prompt/context, the model response, and subsequent user/tool/environmental feedback. The history $H_t$ and filtration $\mathcal{F}_t$ capture the adaptive nature of the system, where future prompts are chosen based on past interactions. This representation acknowledges that the conditional law of the response $R_t$ depends on the entire history $(P_t, \mathcal{F}_{t-1})$, rendering standard exchangeability assumptions invalid.

2. Validity (Uncertainty under Dependence):
   The paper reframes uncertainty quantification from a static "confidence" metric to online validity. It distinguishes between confidence (a model-facing quantity derived from token probabilities) and validity (a procedure-facing guarantee that an uncertainty statement holds under specific deployment conditions).

   • Conformal Inference: While classical conformal prediction relies on exchangeability, the paper suggests utilizing extensions such as online conformal inference, conformal inference under distribution shift, and methods for dependent time-series data.
   • Sequential Scores: Validity is assessed over a stream of task-specific scores $S_t = \phi_t(X_t, \mathcal{F}_{t-1})$, which summarize properties like reliability, safety, or alignment. This approach addresses "optional stopping" issues inherent in repeated prompting and ensures guarantees remain meaningful under adaptive interaction.

3. Monitoring (Change-Point Detection):
   The framework treats post-deployment monitoring as a sequential change-point detection problem. The goal is to detect shifts in the system's regime (e.g., changes in calibration, refusal behavior, or fairness) rather than isolated errors.

   • Mechanism: A monitored score sequence $\{Z_t\}$ is generated from the interaction stream. An alarm time $\tau$ is defined as a stopping time where a detection statistic $W_t$ exceeds a threshold $b$.
   • Scope of Drift: Unlike traditional concept drift which focuses on input-output distribution changes, LLM monitoring must account for shifts in the prompt distribution, model updates, retrieval system changes, tool environments, and user feedback loops.
   • Integration: Monitoring is tightly coupled with validity; when a change-point is detected, previous calibration guarantees may be suspended, necessitating recalibration or human review.

Key Contributions

• Conceptual Shift: The paper establishes that the "sequential inference layer" is a distinct and necessary statistical component for LLMs, complementing existing agendas on uncertainty quantification, fairness, and interpretability.
• Reframing the Unit of Analysis: It explicitly moves the focus from token-level probabilities to trajectory-level reliability, providing a natural interface with stochastic process theory, filtrations, and state evolution.
• Unifying Structure: It identifies a common operational structure across diverse LLM challenges (uncertainty, conformal prediction, model adaptation, fairness), unifying them under the paradigm of Statistical Process Control (SPC) for adaptive systems.
• Methodological Bridge: It connects LLM deployment to established statistical literature on dependent data, including sequential generalized linear models, time-series analysis, and online change-point detection, offering a rigorous language for addressing dependence and non-stationarity.

Results and Claims
As a discussion paper, the work does not present new experimental results or empirical benchmarks. Instead, its "results" are theoretical and structural:

• It demonstrates that viewing LLMs as dependent stochastic processes resolves the mismatch between standard statistical assumptions (exchangeability) and deployment realities (adaptation and feedback).
• It argues that validity guarantees must be "anytime-valid" to accommodate repeated use and optional stopping.
• It posits that monitoring via sequential alarms is essential for maintaining trustworthiness, as static pre-deployment evaluations cannot account for regime shifts caused by model updates or evolving user behavior.

Significance
The paper claims that the era of LLMs makes classical statistical questions regarding dependence, validity, and change detection newly urgent. By framing trustworthy LLM deployment as a problem of online validity and statistical process control, the authors provide a natural language for statisticians to contribute to LLM research. This perspective does not replace existing agendas (such as those by Ji et al., 2026) but complements them by making explicit the sequential structure underlying uncertainty quantification, conformal prediction, and human–AI collaboration. The ultimate implication is that robust LLM systems require trajectory-level modeling, validity procedures that hold under dependence, and continuous monitoring mechanisms linked to human-in-the-loop workflows for recalibration and auditing.