FineCE: Fine-Grained Confidence Estimation for LLMs

• FineCE is a confidence estimation method that produces fine-grained, continuous scores throughout the text generation process to mitigate overconfidence in LLMs.
• It leverages a supervised data construction pipeline combined with instruction fine-tuning and Backward Confidence Integration to dynamically refine prediction confidence.
• Empirical evaluations show FineCE improves AUROC by up to 15% and reduces Expected Calibration Error by up to 60% compared to baseline approaches.

Searching arXiv for the FineCE paper and closely related confidence-estimation work. FineCE is a confidence estimation method for LLMs that is designed to provide fine-grained, continuous confidence estimates throughout the generation process rather than only a coarse score at the end of an answer. It is introduced to address the observation that LLMs frequently exhibit overconfidence, assigning high confidence scores to incorrect predictions, and it combines a supervised training-data construction pipeline, instruction-fine-tuning for scalar confidence prediction, a Backward Confidence Integration (BCI) inference strategy, and three position-selection strategies for deciding when confidence should be estimated during generation (Han et al., 16 Aug 2025).

1. Problem setting and conceptual scope

FineCE is motivated by a calibration problem specific to autoregressive generation: existing approaches are described as suffering from coarse-grained scoring mechanisms that fail to provide fine-grained, continuous confidence estimates throughout the generation process. The method therefore targets confidence for arbitrary text sequences $s$, where $s$ may be only the question $x$ or $x$ plus a partial answer, and it seeks to approximate the probability that the gold answer $\bar{Y}$ is correct under the LLM conditioned on that sequence (Han et al., 16 Aug 2025).

In this formulation, the central quantity is the confidence label associated with a sequence. FineCE constructs supervised pairs $\langle s, Conf_s\rangle$ intended to faithfully approximate the true probability $p(y=\bar{Y}\mid s)$ under the LLM $M$. This places the method between outcome-oriented confidence estimation, which focuses on end-of-answer correctness, and process-oriented confidence estimation, which evaluates confidence at intermediate points such as early or penultimate segments of a generated response. A common misconception is that confidence estimation for LLMs is necessarily an end-of-answer problem; FineCE is explicitly framed against that assumption by estimating confidence during generation as well as at completion (Han et al., 16 Aug 2025).

The paper’s design suggests a distinction between two calibration targets. One target is the confidence of a completed output, where correctness can be judged directly. The other is the confidence of an incomplete generation prefix, where the relevant object is the probability that continuation from the current sequence will ultimately yield the gold answer. This suggests that FineCE treats confidence as a dynamic property of the generation trajectory rather than a static post hoc attribute.

2. Supervised data construction for text–confidence pairs

The first component of FineCE is a training-data construction pipeline for building a large supervised dataset of text-confidence pairs $\langle s, Conf_s\rangle$. For any input sequence $s$, FineCE draws $s$0 independent samples at high temperature from the model:

$s$1

If $s$2 is the gold answer, the empirical confidence label is defined as

$s$3

By the law of large numbers, as $s$4, $s$5 (Han et al., 16 Aug 2025).

The method is not restricted to question-only inputs. FineCE also labels prefixes of the model’s answer through a progressive partial-answer pipeline. A naive procedure would truncate every sample and then re-sample all $s$6 continuations at each truncation depth, which is stated to cost $s$7. FineCE instead proceeds by first sampling $s$8 complete answers $s$9 for a question $x$0, truncating each to its first fragment $x$1, clustering the resulting fragments into $x$2 semantic clusters, and selecting the centroid fragment of each cluster. For each centroid $x$3, it forms $x$4, samples $x$5 completions, computes $x$6 with the same Monte Carlo formula, truncates those completions again, reclusters, and repeats for $x$7 truncations. The total number of inferences is thereby reduced from $x$8 to roughly $x$9 (Han et al., 16 Aug 2025).

Completed answers receive explicit terminal labels. Each sampled full answer $x$0 is assigned

$x$1

so a completed answer is labeled $x$2 if exactly correct and $x$3 otherwise. This creates a dataset that contains question-only inputs, partial-answer states, and full-answer states within a single supervised framework (Han et al., 16 Aug 2025).

The paper also provides Algorithm 1 in plain-text form. For each question $x$4 in a question set $x$5, the algorithm generates $x$6 full answers, computes $x$7, truncates answers to fragments, clusters those fragments into $x$8 clusters, iteratively samples and labels centroid-conditioned continuations for truncation steps $x$9, and finally labels each sampled full answer as correct or incorrect. The output is the aggregate dataset $\bar{Y}$0 of sequence-confidence pairs (Han et al., 16 Aug 2025).

3. Confidence prediction model and training objective

FineCE uses instruction-fine-tuning (IFT) of the base LLM so that, given any text sequence $\bar{Y}$1, the model emits a continuous confidence estimate. The input representation is specified as:

<Instruction> Given sequence: ‹s›. What is your confidence p(correct) in [0,1]? Answer:

The fine-tuned LLM is then trained to generate a numeric string such as 0.73 (Han et al., 16 Aug 2025).

The supervised dataset is $\bar{Y}$2 from the data-construction stage. Training maximizes the likelihood of the correct tokenization of the target confidence string under a standard cross-entropy loss over output tokens. The paper notes an equivalent scalar interpretation: if $\bar{Y}$3 is the scalar parsed from the model’s output, one may also view the objective as minimizing squared error,

$\bar{Y}$4

In practice, FineCE uses token-level cross-entropy with teacher forcing on the 0.xxx tokens (Han et al., 16 Aug 2025).

An alternative value-head variant is described but not used in the final FineCE system. That variant adds a small regression head on top of the model’s last hidden state and trains it with a multi-class or regression loss to predict $\bar{Y}$5. Appendix comparisons indicate that IFT is preferred. This distinction is methodologically important: the final system treats confidence prediction as an instruction-following generation task rather than as a separate scalar head attached to the model (Han et al., 16 Aug 2025).

This training choice suggests that FineCE aligns confidence estimation with the model’s native autoregressive interface. A plausible implication is that the confidence estimator can be deployed with the same generation mechanisms used for ordinary instruction following, although implementation details beyond the provided summary are not specified.

4. Backward Confidence Integration during inference

FineCE augments local confidence prediction with a Backward Confidence Integration strategy. BCI is an inference-time procedure rather than a retraining method. When confidence estimates are produced at a sequence of calibration positions $\bar{Y}$6, the estimate at position $\bar{Y}$7 can be refined by looking $\bar{Y}$8 steps ahead. The relevant quantities are the initial estimate $\bar{Y}$9, the integration depth $\langle s, Conf_s\rangle$0, the integration width $\langle s, Conf_s\rangle$1 corresponding to the number of future sampling paths, and a trade-off coefficient $\langle s, Conf_s\rangle$2 (Han et al., 16 Aug 2025).

For each branch $\langle s, Conf_s\rangle$3, generation continues from $\langle s, Conf_s\rangle$4 to obtain the next calibration position $\langle s, Conf_s\rangle$5, after which the confidence is recursively adjusted. The update rule is

$\langle s, Conf_s\rangle$6

with base recursion at depth $\langle s, Conf_s\rangle$7 given by

$\langle s, Conf_s\rangle$8

The stated intuition is that if the model’s future path shows low confidence, the current estimate should be down-weighted (Han et al., 16 Aug 2025).

Empirically, BCI is reported to reduce Expected Calibration Error by up to approximately $\langle s, Conf_s\rangle$9 with $p(y=\bar{Y}\mid s)$0 and $p(y=\bar{Y}\mid s)$1, and more generally by up to $p(y=\bar{Y}\mid s)$2 when $p(y=\bar{Y}\mid s)$3 and $p(y=\bar{Y}\mid s)$4. This is significant because it indicates that confidence at a current prefix can be improved by conditioning on plausible downstream continuations rather than relying only on the local prefix representation (Han et al., 16 Aug 2025).

A possible misunderstanding is that BCI estimates a different target than the base FineCE model. The formulation given in the paper instead presents BCI as a refinement of the same confidence quantity through recursive integration of subsequent confidence estimates.

5. Calibration positions and query scheduling

Because confidence estimation after every token would be inefficient, FineCE introduces three strategies for identifying optimal positions at which confidence should be estimated during generation. These strategies are paragraph-end calibration, periodic fixed-token calibration, and entropy-based calibration (Han et al., 16 Aug 2025).

Paragraph-end calibration triggers confidence estimation only when the LLM emits a paragraph-break token such as \n\n. The motivation given is that each estimate then aligns with a semantically coherent block. Periodic calibration instead requests a confidence estimate after every $p(y=\bar{Y}\mid s)$5 tokens, with examples given as $p(y=\bar{Y}\mid s)$6 or $p(y=\bar{Y}\mid s)$7, yielding a deterministic and easily implemented schedule. Entropy-based calibration uses the model’s next-token distribution $p(y=\bar{Y}\mid s)$8 at step $p(y=\bar{Y}\mid s)$9 and its entropy

$M$0

If $M$1, with an example threshold $M$2, a confidence query is triggered. This strategy reacts when the model is uncertain under its own token distribution (Han et al., 16 Aug 2025).

The ablation results identify different trade-offs. Paragraph-end calibration gave the best ECE/token-ratio tradeoffs, whereas entropy-based calibration was the most lightweight at approximately $M$3 of tokens. Representative values are reported for Llama2-13B. On GSM8K, paragraph-end achieved $M$4, $M$5, and a token ratio of $M$6; entropy achieved $M$7, $M$8, and $M$9; fixed-token achieved $\langle s, Conf_s\rangle$0, $\langle s, Conf_s\rangle$1, and $\langle s, Conf_s\rangle$2. On CSQA, paragraph-end achieved $\langle s, Conf_s\rangle$3, $\langle s, Conf_s\rangle$4, and $\langle s, Conf_s\rangle$5; entropy achieved $\langle s, Conf_s\rangle$6, $\langle s, Conf_s\rangle$7, and $\langle s, Conf_s\rangle$8; fixed-token achieved $\langle s, Conf_s\rangle$9, $s$0, and $s$1 (Han et al., 16 Aug 2025).

These results indicate that FineCE is not tied to a single calibration schedule. Instead, the method separates the problem of estimating confidence from the problem of deciding when confidence should be queried, allowing a practitioner to favor semantic coherence, deterministic spacing, or minimal overhead depending on the deployment constraint.

6. Experimental evaluation, benchmarks, and implications

FineCE is evaluated on GSM8K, CommonsenseQA (CSQA), TriviaQA, AIME24, MMLU, and NQ-Open. The reported metrics are Expected Calibration Error (ECE), AUROC for predicting correct versus incorrect, and ACC for final answer accuracy, with ACC included to show no drop in task performance (Han et al., 16 Aug 2025).

For process-oriented confidence estimation with Llama2-13B, the paper reports that baselines Multi-Step and LECO achieve AUROC of approximately $s$2–$s$3 and ECE of approximately $s$4–$s$5, whereas FineCE achieves AUROC of approximately $s$6 and ECE of approximately $s$7. The improvement holds at both the first paragraph position $s$8 and the penultimate position $s$9. In the representative GSM8K table, Multi-Step records $s$00 at $s$01, $s$02 at $s$03, and an average of $s$04; LECO records $s$05, $s$06, and $s$07; FineCE records $s$08, $s$09, and $s$10, where each pair is $s$11 (Han et al., 16 Aug 2025).

For question- or outcome-oriented evaluation with Llama3.1-8B on GSM8K, the best baseline P(IK) records $s$12 and $s$13, while FineCE records $s$14 and $s$15. The other listed baselines are First-Prob with $s$16, SuC with $s$17, Verb with $s$18, and SE with $s$19. Across six datasets and three models, FineCE yields $s$20–$s$21 absolute AUROC gains and $s$22–$s$23 relative ECE reductions (Han et al., 16 Aug 2025).

The paper also reports a downstream early-stop setting. With a confidence threshold $s$24, FineCE filters out low-confidence outputs and raises end-to-end answer accuracy by $s$25–$s$26. Together with the statement that the method improves calibration without harming final answer quality, this positions FineCE as a practical mechanism for selective prediction and abstention in LLM pipelines (Han et al., 16 Aug 2025).

The broader significance of these results lies in the coupling of supervised fine-grained training, inference-time backward integration, and selective query heuristics. The reported evidence indicates that the method improves both process-oriented and end-of-answer calibration, and that these gains translate into operational benefits when confidence is used to accept, reject, or defer generated outputs.