arxiv: 2601.02179 · v2 · pith:7L2HV45Wnew · submitted 2026-01-05 · 💻 cs.CL

Confidence Estimation for LLMs in Multi-turn Interactions

Caiqi Zhang , Ruihan Yang , Xiaochen Zhu , Chengzu Li , Tiancheng Hu , Yijiang River Dong , Deqing Yang , Nigel Collier This is my paper

Pith reviewed 2026-05-16 17:53 UTC · model grok-4.3

classification 💻 cs.CL

keywords LLM confidence estimationmulti-turn conversationscalibrationmonotonicityP(Sufficient)hallucination mitigationHinter-GuesserInfoECE

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The pith

A new logit probe called P(Sufficient) tracks how LLMs accumulate evidence across conversation turns while staying calibrated.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets up an evaluation framework for confidence estimation specifically in multi-turn LLM dialogues. It defines success through two requirements: accurate confidence scores at each individual turn and steady growth in those scores as the model receives clarifying information that resolves ambiguity. Standard approaches based on token probabilities or similar signals fail to meet either requirement consistently. In their place the authors introduce P(Sufficient), a logit-derived measure that focuses on whether enough evidence has arrived to support a correct answer and that separates this signal from ordinary conversational filler. They also supply a length-adjusted calibration error called InfoECE and a controlled data-generation method called the Hinter-Guesser paradigm to produce test dialogues in which ambiguity clears turn by turn.

Core claim

In multi-turn interactions, LLM confidence must be calibrated at every turn and must increase monotonically as more information becomes available; a logit-based probe named P(Sufficient) satisfies both conditions more reliably than existing techniques by directly measuring whether accumulated evidence suffices for a correct response.

What carries the argument

The P(Sufficient) probe, a logit-derived quantity that assesses whether the model has received enough information to answer correctly rather than relying on raw token probabilities.

If this is right

Widely used confidence methods lose calibration and monotonicity once conversations extend beyond a single turn.
InfoECE supplies a calibration metric that normalizes for the growing length of dialogue context.
The Hinter-Guesser construction yields reproducible datasets in which each added hint reduces ambiguity in a controlled way.
Better per-turn confidence signals can be used to decide when an LLM should hedge or request clarification instead of producing an unsupported answer.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If P(Sufficient) generalizes beyond the synthetic datasets, it could trigger self-correction or clarification requests inside production chat systems.
The same evidence-accumulation logic might transfer to other interactive settings such as tool-using agents or multi-step reasoning chains.
Deployment would still need direct measurement on natural human conversations to confirm that the monotonicity property survives noisy user input.

Load-bearing premise

The two requirements of per-turn calibration and monotonic growth with added information are enough to evaluate and improve confidence estimation, and the Hinter-Guesser method produces dialogues representative of real ambiguity resolution.

What would settle it

A held-out collection of multi-turn dialogues in which P(Sufficient) scores fail to rise monotonically as hints are added or in which its length-normalized calibration error exceeds that of standard baselines.

read the original abstract

While confidence estimation is a promising direction for mitigating hallucinations in Large Language Models (LLMs), current research overwhelmingly focuses on single-turn settings. The dynamics of model confidence in multi-turn conversations, where context accumulates and ambiguity is progressively resolved, remain largely unexplored. This work presents the first systematic study of confidence estimation in multi-turn interactions, establishing a formal evaluation framework grounded in two key desiderata: per-turn calibration and monotonicity of confidence as more information becomes available. To facilitate this, we introduce novel metrics, including a length-normalized Expected Calibration Error (InfoECE), and a new "Hinter-Guesser" paradigm for generating controlled evaluation datasets. Our experiments reveal that widely-used confidence techniques struggle with calibration and monotonicity in multi-turn dialogues. In contrast, a novel logit-based probe we introduce, P(Sufficient), proves comparatively more effective, robustly tracking evidence accumulation and distinguishing it from conversational filler. Our work provides a foundational methodology for developing more reliable and trustworthy conversational agents.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

P(Sufficient) tracks evidence buildup better than baselines on their synthetic data, but the gains may not survive real multi-turn dialogue.

read the letter

The main takeaway is that this paper gives the first clear framework for evaluating confidence in multi-turn LLM chats, with a new probe that follows accumulating information more reliably than standard methods in their tests. They define two practical goals—per-turn calibration and monotonic confidence growth—and introduce InfoECE plus the Hinter-Guesser data generator to measure them. That setup is a solid step beyond single-turn work and makes the problem concrete enough to test. The probe itself is simple (logit-based) and appears to separate real evidence from filler in the controlled sequences they built. Those are real positives for anyone working on dialogue reliability. The soft spot is the data. Every result comes from Hinter-Guesser synthetic turns, which force a tidy, incremental resolution of ambiguity. Natural conversations mix in topic shifts, partial answers, and noise that could flatten or reverse the monotonicity the probe is praised for. No experiments on actual chat logs or existing multi-turn corpora are reported, so the claimed robustness is still untested outside the generator. This matters because the abstract positions the work as directly useful for deployed agents. The paper is aimed at people building calibration methods for conversational systems. Readers who want a starting point for multi-turn evaluation will get value from the desiderata and metrics even if they end up modifying the probe. It deserves peer review because the question is timely and the formalization is new, though any referee will likely ask for validation on messier, real-world data.

Referee Report

2 major / 1 minor

Summary. The manuscript presents the first systematic study of confidence estimation for LLMs in multi-turn interactions. It introduces an evaluation framework based on two desiderata (per-turn calibration and monotonicity of confidence as information accumulates), a length-normalized Expected Calibration Error metric (InfoECE), the Hinter-Guesser paradigm for generating controlled multi-turn datasets, and a novel logit-based probe P(Sufficient) that is reported to outperform standard confidence techniques by better tracking evidence accumulation and distinguishing it from conversational filler.

Significance. If the central results hold, the work supplies a foundational methodology and concrete desiderata for confidence estimation in conversational settings, which is relevant for reducing hallucinations in multi-turn agents. The P(Sufficient) probe and InfoECE metric represent concrete technical contributions that could be adopted or extended by others, though the exclusive use of synthetic data limits the immediate strength of the claims.

major comments (2)

Abstract and experimental results: the reported superiority of P(Sufficient) over standard methods is demonstrated exclusively on datasets produced by the Hinter-Guesser paradigm; without any results on non-synthetic multi-turn corpora, it remains possible that the probe's advantages are an artifact of the controlled, monotonic evidence buildup engineered by the data generator rather than a general property of the probe.
Abstract: the two desiderata (per-turn calibration and monotonicity) are treated as sufficient to evaluate confidence estimation, yet the manuscript provides no analysis of how these metrics behave under topic shifts, partial answers, or filler that are typical in natural multi-turn ambiguity resolution and that the Hinter-Guesser construction may systematically exclude.

minor comments (1)

The abstract refers to 'widely-used confidence techniques' without naming the specific baselines compared in the experiments; adding this list would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important limitations regarding the scope of our evaluation, which we address below by clarifying our design choices and committing to revisions that strengthen the framing without overstating generalizability.

read point-by-point responses

Referee: Abstract and experimental results: the reported superiority of P(Sufficient) over standard methods is demonstrated exclusively on datasets produced by the Hinter-Guesser paradigm; without any results on non-synthetic multi-turn corpora, it remains possible that the probe's advantages are an artifact of the controlled, monotonic evidence buildup engineered by the data generator rather than a general property of the probe.

Authors: We agree that all reported results use synthetic data from the Hinter-Guesser paradigm. This paradigm was introduced precisely to create controlled conditions where evidence accumulation can be precisely quantified and monotonicity can be measured against ground-truth sufficiency labels, which are difficult to obtain reliably in natural corpora. We will revise the abstract, introduction, and discussion to explicitly state that the superiority of P(Sufficient) is demonstrated under these controlled conditions and to frame the work as establishing a methodology and desiderata rather than claiming broad superiority on all multi-turn data. We will also add a dedicated limitations paragraph discussing the synthetic nature of the evaluation. revision: partial
Referee: Abstract: the two desiderata (per-turn calibration and monotonicity) are treated as sufficient to evaluate confidence estimation, yet the manuscript provides no analysis of how these metrics behave under topic shifts, partial answers, or filler that are typical in natural multi-turn ambiguity resolution and that the Hinter-Guesser construction may systematically exclude.

Authors: The two desiderata were chosen as minimal, testable properties that any multi-turn confidence estimator should satisfy when information accumulates monotonically. The Hinter-Guesser construction deliberately excludes topic shifts, partial answers, and filler to isolate these properties. We acknowledge that the manuscript does not analyze behavior under those additional phenomena. We will revise the abstract and add a new subsection in the discussion that explicitly notes these exclusions, explains why the controlled setting was used to establish baseline desiderata, and outlines how the framework could be extended to handle topic shifts and filler in future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines P(Sufficient) as a novel logit-based probe and introduces InfoECE and the Hinter-Guesser paradigm as independent methodological contributions. No equations or derivations are shown that reduce fitted parameters to predictions by construction, nor do any load-bearing steps rely on self-citations whose content collapses into the current claims. The two desiderata (per-turn calibration and monotonicity) are stated as evaluation criteria rather than derived from the probe itself, and experimental comparisons are presented as external tests rather than tautological outputs. This is the normal case of an empirical methods paper whose central results do not reduce to their inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical derivations, free parameters, or new physical entities are described in the abstract; the work is empirical and metric-driven.

pith-pipeline@v0.9.0 · 5483 in / 975 out tokens · 48542 ms · 2026-05-16T17:53:50.551350+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

a reliable confidence signal should satisfy two desiderata: (1) Calibration... (2) Monotonicity, where confidence consistently increases as more useful information becomes available... InfoECE... Kendall’s τ
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_strictMono_of_one_lt unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

P(SUFFICIENT)... probes the confidence by asking model if the current information is sufficient... distinguishes meaningful information gains from conversational filler

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