Addressing Pitfalls in the Evaluation of Uncertainty Estimation Methods for Natural Language Generation
Authors: Mykyta Ielanskyi
Kajetan Schweighofer
Lukas Aichberger
Sepp Hochreiter
Venue: ICLR 2026 Poster (2026)
Keywords: uncertainty
natural language generation
evaluation
large language models
elo
judge
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
TL;DR: We investigate the current risk indicators used in risk correlation experiments for NLG UE, identify their shortcomings and propose improvements, as well as an enhanced summarization technique.

Abstract: Hallucinations are a common issue that undermine the reliability of large language models (LLMs). Recent studies have identified a specific subset of hallucinations, known as confabulations, which arise due to predictive uncertainty of LLMs. To detect confabulations, various methods for estimating predictive uncertainty in natural language generation (NLG) have been developed. These methods are typically evaluated by correlating uncertainty estimates with the correctness of generated text, with question-answering (QA) datasets serving as the standard benchmark. However, commonly used approximate correctness functions have substantial disagreement between each other and, consequently, in the ranking of the uncertainty estimation methods. This allows one to inflate the apparent performance of uncertainty estimation methods. We propose using several alternative risk indicators for risk correlation experiments that improve robustness of empirical assessment of UE algorithms for NLG. For QA tasks, we show that marginalizing over multiple LLM-as-a-judge variants leads to reducing the evaluation biases. Furthermore, we explore structured tasks as well as out of distribution and perturbation detection tasks which provide robust and controllable risk indicators. Finally, we propose to use an Elo rating of uncertainty estimation methods to give an objective summarization over extensive evaluation settings.

Published as a conference paper at ICLR 2026
ADDRESSING PITFALLS IN THE EVALUATION OF UNCERTAINTY ESTIMATION METHODS FOR NATURAL LANGUAGE GENERATION
Mykyta lelanskyi', Kajetan Schweighofer', Lukas Aichberger', Sepp Hochreiter ELLIS Unit Linz and LIT AT Lab, Institute for Machine Learning. Johannes Kepler University Linz, Austria
2 NXAI GmbH, Linz, Austria
fielanskyi, schweighofer, aichberger, hochreit) @ml. jku at
ABSTRACT
Hallucinations are common issue that undermine the reliability of large language models (LLMs). Recent studies have identified a specific subset of hallucinations, known as confabulations, which arise due to predictive uncertainty of LLMss. To detect confabulations, various methods for estimating predictive uncertainty in natural language generation (NLG) have been developed. These methods are typically evaluated by correlating uncertainty estimates with the correctness generated text, with benchmark. However, commonly used approximate correctness functions have substantial disagreement between each other and, consequently, in the ranking of the uncertainty estimation methods. This allows one to inflate the apparent perfor- mance of uncertainty estimation methods. We propose using several alternative risk indicators for risk correlation experiments that improve robustness of empiri- cal assessment of uncertainty estimation algorithms for NLG. For QA tasks, we show that marginalizing over multiple LLM-as-a-judee variants leads to reducing the evaluation biases. Furthermore, we explore structured tasks as well as out of distribution and perturbation detection tasks which provide robust and controllable risk indicators. Finally, we propose to use an Elo rating of uncertainty estimation methods to give an objective summarization over extensive evaluation settings.
(QA) datasets serving as the standard
INTRODUCTION
Predictive uncertainty has been linked to the occurrence of a subset of hallucinations known as confabulations (Farquhar et al., 2024). Such confabulations language model (LLM), that have no support in either the training set of the model nor in the prompt. The expressivity of natural language allows these models obfuscate their lack of knowledge in manner that can be challenging to detect. Therefore, uncertainty estimation is essential to detect such confabulations and ensure the reliability and wider applicability of LLM-based systems.
sequences generated by a large
Predictive uncertainty in natural language generation (NLG) can be quantified by the entropy of the LLMs predictive distribution (Malinin & Gales, 2020). In the literature uncertainty estimation in univariate classification, predictive uncertainty is often decomposed into aleatoric and epistemic components (Gal, 2016). The aleatoric uncertainty can be attributed to the inherent stochasticity of the prediction, while the epistemic uncertainty arises from lack of knowledge of the true model parameters (Schweighofer et al., 2023). In case of confabulation detection in NI.G, most of the time the alcatoric uncertainty of predicting with given model with parameters w for new input is considered (Kuhn et al., 2023; Aichberger et al., 2025).
Currently, uncertainty estimation algorithms for NLG are evaluated mostly in terms of selective prediction on a narrow class of problems which is motivation for using QA tasks is that the ability to effectively retrieve information could be linked to factuality and hallucinations while having a relatively low demand for model performance. However, this class of problems is characterized by short length of the expected answer and impreciseness of the
datasets, see Tab. The

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Table 1: Evaluation protocols recently used for uncertainty estimation in NL.G. Few works evaluate their methods beyond selective prediction on QA tasks and rely on approximate correctness functions or small number of human correctness evaluations.
REFERENCE
TASK
CORRECTNESS FUNCTION
MALININ & GALES (2020)
TRANSLATION TRANSLATION
BLEU
FOMICHEVA ET AL. (2020)
HUMAN
KUHN ET (2023)
QA
ROUGE-X
FADEEVA ET AL. (2023)
QA, SUMMARIZATION
ROUGE-X, BERTSCORE ROUGE-X
DUAN ET AL. (2024)
QA
MANAKUL ET AL. (2023)
FACT VERIFICATION
HUMAN
FARQUHAR AL. (2024)
QA
JUDGE
BAKMAN
(2024)
QA
JUDGE
AICHBERGER ET AL. (2025)
QA
ROUGE-X. X, BLEURT ROUGE-X
CHEN ET AL. (2024A)
QA
KOSSEN ET AL. (2024)
QA
JUDGE, F-1 JUDGE
NIKITIN AL. (2024)
QA
AICHBERGER ET AL. (2024)
QA
JUDGE, F-1 F-1
ABBASI- YADKORI ET AL. (2024)
QA
ground truth solution. Importantly, the evaluation of an answer is done by approximate correctness functions, such comparing substrings utilizing text similarity models. These correctness functions have been criticized and are often not considered robust (Schluter, 2017; Zheng et al., 2023), yet are widely used in NLG.
Santilli et al. (2024) concurrently investigate the relation between Rouge-L, LLM-as-a-judge and Human annotators and the impact has the empirical performances reported in Farquhar al. (2024) and Fadeeva et al. (2023). They conclude that LLM-as-a-juue j-ddge should be preferred as correctness metric in such assessments, and the effects of thresholds should further investigated with sequence length being an important factor in variability of outcomes. At the same time, Zheng al. (2023), the original work proposing LLM-as-a-judde for assessing correctness, already point out biases inherent to the approach. Dorner al. (2025) further state that even high agreement to human annotators may be insufficient to mitigate the evaluation biases the judge models. Overall, there remain many open questions regarding current practices in evaluating uncertainty estimation in NLG settings. our work, our objective is to provide insight into the pitfalls of current practices and recommendations to improve them.
Specifically, our contributions are as follows:
We conducted detailed investigation of weaknesses of the evaluation practices used in recent work on uncertainty estimation in NLG and show that one of their leading causes is the lack marginalization over the correctness function selective prediction.
We suggest several beneficial alternative risk indicators to be used for risk correlation experiments, including an ensemble of LuMdee----udgee (Zheng et al., 2023) variants for QA, structured tasks with exact correctness functions, OOD detection, and perturbation.
We propose using an aggregation technique based Elo rating (Elo, 1978) for comparing the performance of uncertainty estimation methods across different experimental setups to foster a more objective assessment of their utility and provide additional insights.
PRELIMINARIES
The uncertainty estimation problem in NLG can be formalized follows: given an input sequence (I1,..., 2T) E X' and a model with parameters w, we want to infer an uncertainty measure X' W Then a(æ, w; (..) is an algorithm to obtain an estimate of u(x:, w)), where 0,, is vector of hyperparameters of the algorithm.
Uncertainty estimation methods in NLG. Recent approaches to uncertainty estimation for NLG estimate uncertainty in variety of ways. The methods can be loosely categorized into three groups:
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those using statistics of set of sequences from the model, those using single output sequence and those using heuristics. The first group of methods is based on Monte-Cario (MC) sampling and Bayesian assumptions with regard to the obtained samples. Such methods base their estimators some notion of spread in the probability space of the predictive distribution of an LLM (Malinin & Gales, 2020; Kuhn et al., 2023; Aichberger al., 2025; Chen al., 2024a; Nikitin et al., 2024). A noteworthy variation of this direction consists of methods that attempt to modify the probabilities of sampled sequences based on the semantic importance of individually generated subsequences (Duan et al., 2024; Bakman et al., 2024) to compensate for the potential impact that they make on the correctness of the predicted sequence. The approaches from the second group use properties of a single generated sequence (Ren et al., 2023; Fadeeva et al., 2023; Kossen et al., 2024; Aichberger et al., 2024) to estimate the model's confidence. Other approaches leverage the facilities of the language model itself or larger one to determine confidence estimate for a given output sequence (Kadavath et al., 2022; Manakul et al., 2023). A detailed description the methods considered in this work can be found in Apx. B.I.
Risk correlation experiments. Intuitively, the fundamental question to which u(ær, w) should help us find the answer is: "What is the risk of making the prediction for a given input sequence a using the model with parameters w?". This connection of uncertainty and risk has recently been advocated in the univariate classification setting (Lahlou et al., 2023; Kotelevskii & Panov, 2025). In accordance with this perspective, the utility of uncertainty estimation methods is empirically evaluated correlation between the estimated uncertainty i(-) and some risk indicator r(-) on sets of predictions, defined as
5 = Cor (((I, w; 0w)) (r(æ;, m0))
(1)
Here, Cor is correlation metric and y' is the predicted output sequence of the L.M.. We do not assume a linear relation between the risk and the uncertainty, which restricts eligible Cor to rank correlation metrics with area under the ROC curve (AUROC) being the most commonly used. Based on the risk indicators used for evaluation of uncertainty estimation algorithms in the univariate classification literature (Welling & Teh, 2011; Gal & Ghahramani, 2016; Lakshminarayanan et al., 2017; Malinin & Gales, 2018; D' Angelo & Fortuin, 2021; Daxberger et al., 2021; Mukhoti et al., 2023; Schweighofer et al.. 2023), we can distill the following empirical properties that uncertainty estimate ú must possess:
1. u is higher for x' ~ Drest than for æ ~ Drest if the risk of prediction using w (aleatoric) or w p(w (D) (epistemic) for x' is higher than for æ.
2. à is not lower for x' than for x ~ Dres if x' drawn from a different data generating function than one that produced the training data D.
3. û is not lower for x' than for Drest if x is obtained from by some perturbation.
These three empirical properties correspond to the following risk indicators and risk correlation exper- iments: selective prediction (SP), out-of-distribution (OOD) detection, and perturbation detection. An alternative to risk correlation that is sometimes used for evaluation is an active learning acquisition experiment, which is challenging even in the classification setting (Lüth et al., 2023).
Selective prediction in NLG uncertainty evaluation. The current standard for comparing uncer- tainty estimation methods for NLG is selective prediction on QA datasets (Aichberger et al., 2025; Kuhn et al., 2023; Farquhar et al., 2024; Duan et al., 2024; Bakman et al., 2024). The approximate correctness function y" x y x X + {0, 1) maps the prompt æ E X' provided reference answer y' E y" and a generated answer y' E y to a binary value which indicates the correctness of the generated answer. e can be parametrized by a parameter vector 0.. The negated correctness -c(...) or "incorrectness" is then a risk indicator that is used in the SP experiments as follows:
Esp Cor [1(2,) w; 0,)) (-c(y' yi, æ;; 0.))
Ese captures the uncertainty scores ability to distinguish between correct and incorrect predictions. It represents the probability that a randomly chosen correct sample is ranked higher than a randomly chosen incorrect sample in terms of the uncertainty score.
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COOA- Liama
TRIVA- Laaa
SQUAD
Liama
Liama
SQUAD- Liama
sle
18)
(b)
Figure 1: Approximate correctness consistency on selected QA datasets. R indicates ROUGE family, BLEU. judge models are indicated with J, "q" stands for QA prompt used in Farquhar al. (2024) (see Sec. C.2 for more details prompting). (a) Agreement of correctness metrics in terms of mutual AUROC (not symmetric). Column values are binarized at 0.5 where applicable. (b) Agreement on the ranking of UE algorithms when labeled by the pair of approximate correctness functions. of indicates identical ordering while of O indicates uncorrelated rank assignment by the two correctness functions.
PITFALLS OF THE CURRENT EVALUATION PROTOCOL
In the univariate classification setting, the correctness function is very simple, usually consisting of selecting the highest probability output class and checking its identity to the class provided as the label. In NLG, correctness algorithms are more complex due the large space of possible sequences and a certain degree of invariance to syntactic permutations and paraphrasis. Selective prediction performance in Eq. (2) depends on both the quality of the uncertainty estimates and the bias and variance of the correctness labels.
Approximate correctness functions in NLP. The standard substring matching correctness al- gorithms are the ROUGE (Lin, 2004) and BLEU families (Papineni et al., 2002). To turn these into correctness functions, one required to specify threshold d and the n-gram parameter n, so 0. = (d, n).. Learned correctness functions, such as BERTScore (Zhang et al., 2020) and BLEURT (Sellam et al., 2020) use the similarity of the answer and the reference an embedding space. LLLM-as-a-judge (Zheng et al., 2023) prompts an LLM to confirm the correctness of the answer with respect to the reference. Further reference on correctness functions are provided in Apx. B.4. The key properties these approximate correctness functions have in common is that they are parametric and rely on some notion of similarity of the provided answer to a reference one. The specific set of parameters used has prominent effect on the labels they produce.
Effects of bias and variance in correctness labels on AUROC. Let us consider two scenarios of perturbation of labels when computing sample AUROC for risk correlation experiment. In the first scenario a random, example independent Bernoulli noise is added to the labels. Such noise perturbs the label with a certain probability p. In Apx. D.2 we show that such perturbations lead to the following transformation of the original sample AUROC:
AUROC AUROC (1 - 2p) +p
The second scenario that we consider is one where a sample dependent distortion de, has been applied to the labels. In case of selective prediction, this distortion would correspond to bias the correctness function, where it systematically assigns incorrect labels to specific input-output pairs:
hinsed 2r
Crs
if d,, =
if d
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Table 2: Adversarially selecting correctness function the QA benchmark to improve the ranking of individual uncertainty estimation methods. The values are frequencies of uncertainty estimation methods Top-3 membership on the considered QA datasets. The reference for our assessment an average over this table can be found in Appx. B.5.3.
variants introduced in Sec. 4. Details on the settings used to produce
METHOD
REFERENCE
ADVERSARIAL.
INCREASE
PREDICTIVE ENTROPY
0.000
0.188
+0.188
PREDICTIVE ENTROPY (LN)
0.000
0.125
+0.125
SEQUENCE LENGTH (SAMPLE)
0.250
0.312
+0.062
SEQUENCE LENGTH (ANSWER)
0.312
0.562
+0,250
EIGENSCORE
0.125
0.250
+0,125
TOKENSAR
0.062
0.062
+0,000
SENTENCESAR
0,438
0.556
+0.118
SAR
0.125
0.188
+0.062
PERPLEXITY
0.125
0.444
+0.319
MIN TOKEN LOG-PROBABILITY
0.125
0.500
+0.375
SEMANTIC ENTROPY
0.125
0.333
+0,208
SEMANTIC ENTROPY (LN)
0.562
0.667
+0.104
P(TRUE)
0.250
0.375
+0.125
G-NLL
0.375
0.688
+0.312
Furthermore, such distortion would result in AUROC that could be decomposed into interpo- lation between the AUROC of the undistorted samples and the distorted ones:
AUROC undig-udisst undist (n 0) ni (dj 0)
AUROC dist
(5)
Ykg Ti
AUROC no(4 = n1 (1 = + 0.5 no(dd = ni (d; 1)
nig
110
n1
Detailed derivation and validity of the estimator per sample size this identity can be found in Apx. D.2. Independent Bernoulli noise on the labels affects all UE methods equally in the asymptotic case (Eq. (3)). At the same time, bias in correctness estimates affects the ranking proportionally to the proportion of distorted samples; b) the discrepancy in ranking quality the distorted and undistorted samples. Therefore, if we do not marginalize the random noise in the risk indicator, will have the effect of sample-dependent distortion, which can affect the apparent performances of different methods differently. Most prior work ignores the non ron-deterministic nature of the correctness estimates used. This is particularly relevant for the LLM-as-a-judge approach, since entails multiple sources of stochasticity to obtain the correctness label. The correctness label may change upon sampling again without any further changes, different prompts or between model families.
Disagreement of different correctness functions in QA. In Fig. (a) we compare the predictions of widely used correctness functions on the QA datasets commonly used for comparing NLG uncertainty estimation algorithms. We observe that the n-gram based correctness function families BLEU and ROUGE show substantial disagreement between each other and the LLL--as-ajuddee Similar observations have been independently reported by Santilli et al. (2025). Different variants of ROUGE show high agreement among them in some scenarios. This agreement can be largely explained by short reference answers provided for the QA datasets, rendering these n-gram based metrics equivalent in most scenarios. As can be seen in the bottom part of Fig. (a), the reference answer lengths are very short, with most consisting only one or two words. This demonstrates bias and noise in approximate correctness estimators. Furthermore, during our investigation, we have discovered an artifact widely used ROUGE-2 and BLEU implementation (Luong et al., 2017) described in more detail in Apx. B.4.1.
Inconsistency uncertainty estimation method ranking. Fig. (b) depicts Spearman correla- tions between the ranks of NLG uncertainty estimation algorithms evaluated on the given datasets according to different correctness functions. On both CoQA and SQuAD it can be observed that the disagreement ranking uncertainty estimation methods falls the lines between judge and n-gram
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Standard Deviation MAUC untoi
Eepanienn:
ElgenSioo
10.04
Parplea.
GNIL
SAR
0.03
Semm
6.02
Frod
0.01
Fred. Ent.
hrb.
B5 Seq. Len.
1. Sto. Len.
Calls
Calls
Figure 2: Bootstrap estimate of the standard deviation of mean of AUC performance on selected QA dataset model combinations. As rule of thumb, using SP-MoJI with 4 judges reduces the standard deviation of performance estimator twofold. For implementation details refer to B.5.1.
methods with noticeable BLEU / ROUGE-2 artifact. The adaptive ROUGE metries are in perfect agreement with ROUGE-1 1 due to the low length of the reference answers. The judge models agree more with the BLEU / ROUGE-2 than with other ROUGE variants. This indicates, that among the approximate methods the LLM-as-a-judge might be the more reliable one, although not universally.
Correctness-hacknng of QA benchmarks. In Tab. we show results of optimizing the performance of uncertainty estimation methods with respect to the correctness function. The experiment shows that the apparent performance of the methods can often be improved substantially compared to the value obtained for Crefrrncce by selecting opportune correctness function é and parametrization 0g- This also holds for some of the introduced heuristic uncertainty measures, like the sequence length. This further highlights the vulnerabilities of the current evaluation strategy.
IMPROVING THE EVALUATION WITH ROBUST RISK INDICATORS
In this section, we propose remedies to the issues described in Sec. 3 by introducing several reliable risk indicators, including ones inspired by the univariate classification setting as described in Sec. 2.
Exact correctness. we use problems with deterministic and non-parametric correctness function Ce. eliminate the need for marginalizing the correctness label. In this case e c(y;, x22) has no parameters that need marginalization. We refer to this deterministic non- con-parametric correctness function exact correctness. Practical tasks where exact correctness defined would be problems that are non-trivial to solve but can be verified symbolically. Some examples are constrained text generation, code generation and mathematical problems. These are often called structured problems.
Marginalizing the variability of approximate correctness. Judge models are subject to biases and uncertainty with respect to sampling (Zheng et al., 2023) even when they show high agreement to human labels Sicilia et al. (2024); Dorner et al. (2025). Moreover, the output is sampled from the judge models stochastically. We propose using Selective Prediction using Mixture of Judges and Instructions (SP-MoJT) as method for evaluating performance of NL. UE methods datasets where approximate correctness usage is unavoidable. With SP-MoJI we make multiple judge LM invocations, compute the & for each one of them (the computed uncertainties stay the same) and take a mean in order to marginalize over the parameters of correctness label in Eq, (2). This reduces UE evaluation biases due to judge model, sampling, prompt and model family:
ESP-Moll = Fig. [SSPJ]
E Cor (ū(Z,, u. 0.)) (-Ja yo 2e 0w)) K
(6)
We refer to the average of LLM-aa-a-uudge prediction when used as a correctness function as MoJI (without SP). Note that simply plugging MoJI correctness into Eq. (2) would not be algebraically equivalent to SP-MoJI in Eq. (6) the first is an inner expectation while SP-MoJI is an outer expectation. At the same time the entropy of MoJI label can be used for excluding problematic QA entries from evaluation (Apx. E. Such marginalization accounts for the aleatoric and epistemic uncertainty of the judge model.

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To further motivate SP-MoJI we have analyzed the spread of performance estimates depending on the number of judges used in Fig. 2. Using bootstrapping. we computed the standard deviation of the estimator of UE method performance using different number of diverse judge models. When using a single judge the SD can reach 0.04, which is roughly equivalent to +88 confidence interval 95% confidence. This is on the order of magnitude of differences between methods in e.g. Tab. 2. When using more judge evaluations with different prompts and models the SD of the performance estimates reduces considerably. At the same time, we observe that the benefits of additional judge calls diminish past about 10 invocations. Small scale manual annotation experiment shows that MoJI has better agreement with humans than the individual judges have on average (Appx. B.5.4).
OOD label and perturbation as risk indicators. In the univariate classification setting, OOD detection and perturbation detection tasks are considered alongside selective prediction (Apx. D.1). In these tasks it is assumed, that the risk of using the model on an input that violates the i.i.d. assumption or is corrupted is higher than that of an in distribution example. The evaluation would then use the OOD identifier examples for text data is difficult. When thinking of OOD examples for text, one would imagine questions about things that have not yet come to be or are otherwise unknown or ambiguous in the general text corpora. The OOD datasets, therefore, need to be constructed artificially.
X' + {0. 1) as a risk indicator. Unlike the image domain, obtaining OOD
Another alternative is perturbation detection. The evaluation objective then takes slightly different form. Let p be a corruption function that perturbs input x; with strength Sp. then perturbation detection objective in accordance with Prop.3 in Sec. 2 is as follows:
N
1
Sperturb
Cor Ca(((an 8p), un; wn; Ow), 8p)
N
Empirical implementation of the proposed risk indicators. As structured tasks we select code completion and constrained text generation. Code completion problems allow for -onaaammetii correctness verification by means of unit tests. We picked BigCodeBench (BCB) (Zhuo et al., 2024) due to its convenience and the fact, that it focuses on applied python problems which are well represented in pretraining sets of language models. As constrained text generation problem we selected COLLIE (Yao et al., 2024) dataset which provides non-parametric evaluation pipeline.
Several datasets seek to provide artificial OOD examples. Known-Unknown (Amayuelas et al., 2024) seek to collect questions that can be assumed to have controversial answers in the common training sets. SQuADv2 (Rajpurkar et al., 2018) provides questions formulated to be unanswerable given the prompt. For perturbation detection we perturb two QA datasets: CoQA and SQUADv2. We obtain them by randomly shuffling the words in the story to which the corresponding question is related. We control the perturbation strength by setting the proportion of words that are displaced.
For the lack of better reference, we evaluated MoJI correctness function selected structured tasks. Fig.Fig. 10 (a) shows the agreement between the correctness metrics. Panel (b) shows the Spearman correlation between ordering of UE methods. The approximate correctness functions struggle to match the exact ranking on COLLIE, with only the largest models with specifically modified prompt being correlated to exact correctness. This is due to the fact, that the reference sequence may have completely different semantics compared to the one generated by the LLM, while both fulfilling the specified requirements. Individual judges fail pick this up unless the prompt adapted to the structured tasks and shows high discrepancy between the two considered prompts.
5 AGGREGATING RESULTS
Once reliable risk indicator is selected, we are presented with quantitative assessments of uncertainty estimation methods for each model, dataset and sampling parameter considered. It is commonplace to see large tables listing every feasible combination of aforementioned factors which often feature contradicting assessments depending results are highlighted or how these are discussed in the text, different conclusions, sometimes conflicting, can be drawn from the same raw results. Except Vashurin et al. (2025) that use the average rank, we are not aware of any work that seeks to summarize the available experimental information from testing under diverse datasets and models into single scalar in grounded fashion.
e.g. the model or datasets used. Depending on how different
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ALL TASKS
QA
C.TEXT
CODE
0OD
PERT.
2000
1.00
1000
500
PiTuua)
Tol.
Pred. Ent. Log. Prob.
Randon
ElpenScore
GNLL
Sent. SAR
Prod. Ent.
Lon.
Figure 3: Elo ratings of NLG uncertainty estimation methods. The methods are grouped by color according to their category (see Apx. B.1). The line at 1000 Elo indicates the average rating. Elo rating were independently estimated for several key partitions. Per task used: QA selective prediction on QA datasets, C.TEXT constrained text generation, CODE code completion. Per models used: IT instruction fine tuned models only, PT - pretrained models only. Finally, we report the partitions of the alternative risk indicators: OOD- dittof--iitributiion and PERT- perturbation.
Elo rating of uncertainty estimation methods. Drawing inspiration from popular approaches used for general evaluation of LLM skills (Chiang et al., 2024), we use the Elo rating system (Elo, 1978) to gain high level insight into performance of the considered uncertainty estimation methods. Originally intended to rate skill of chess players, the Elo rating provides an iterative algorithm to compute relative performance of players based on pairwise comparisons (games). We will treat each independent dataset model risk correlation experiment as a separate game, where the players, methods A and B, can win the game by having higher performance according to Eq. (1). The pairs and experimental runs are then sampled uniformly until the ratings converge to stationary distribution that is defined by their relative per problem performance (Cortez & Tossounian, 2024). While each prediction in each considered dataset could be considered a separate game when estimating the Elo ratings, for the sake of consistency and to avoid unnecessary additional complexity we only consider the outcomes of experiments on the full datasets.
One advantage of the Elo system rank averaging is the probabilistic interpretability of the scores. With the usual initialization, 400 point difference roughly corresponds to 1 10 chances of one method being better than another for model / dataset combination. case of rank aggregation as c.g. used in Vashurin et al. (2025), such quantitative information of "how much better?" is not attainable. Another advantage that it enables for indirect comparisons. For example, if UE methods are evaluated on only partially overlapping sets of tasks, we could retain their relative performances. In Appx. B.5.5 we show that Elo score handles an artificially induced mild version of such scenario better than rank aggregation. Finally, the Elo score naturally accommodates the variability of outcomes within the same experiment and allows prioritizing specific subsets of experiments. This means that we could bootstrap the subsamples of individual experiments to account for the performance variance within a single model- dataset- sampling parameters combination.
The Elo ratings for our experimental suite are presented in Fig. 3. The random baseline allows gauging the relative difficulty of each partition. The ALL TASKS ratings are the summary rating of the overall performance of the UE methods considered. The detailed results show that the characteristics required to excel in different partitions of the experimental suite vary. Employing an effective aggregation approach allows us to gain new insights into comparative performance of the UE methods as well as to confirm some of the side note obscrvations made in prior work.
6 DISCUSSION & FUTURE WORK
We have shown the theoretical rationale for using SP-MoJI and structured tasks for correlation experiments. While directly assessing improvements to an evaluation protocol is conceptually challenging, we have observed indirect evidence of bias in the existing indicators and reduction thereof through our proposed risk indicators. Furthermore, we have shown that correctness hacking can exploit the bias in order to misrepresent the strengths and weaknesses of UE methods in NLG. We have observed that SP-MoJI is relatively robust to invariances in the selected structured tasks. In Apx. E. we further manually inspect subset of examples with the highest MoJI entropy to assess the quality of the corresponding ground-truth answers.
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Upon applying our methodology, we confirm many of the side-note conclusions made in prior work and gain some additional insights. We observe that adjusting the likelihoods of individual tokens based on semantic importance measures appears to be counterproductive in most settings. Similar to recent observations in prior work (Aichberger et al., 2024), we also find that length normalization is harmful in practically all considered scenarios aside for perturbation detection. This could also explain the improved performance of discrete semantic entropy (Farquhar et al., 2024), where the sequence likelihoods are ignored entirely and the entropy computed based on the semantic cluster size. P(True) does not excel in any of the tasks in particular while EigenScore together with G-NLL appear to perform well for longer sequences in code generation.
The results for perturbation detection are noticeably different from the other tasks considered. Contrary to all other settings, length normalization for both Perplexity and Semantic Entropy appear beneficial. However, the sequence length of the answers generated by the beam search decoding is very strong. Investigating the underlying causes of those findings is an important direction for future work, as well as analyzing possible biases to specific perturbation type and strength.
All methods perform poorly with pretrained models (PT), as is evident through the high Elo of the random control baseline on that partition. Perplexity got rated above average on the IT partition, which might be a somewhat more realistic assessment than ALL TASKS, but there is no specific task in which it could act the go to choice. This could be related to the lack of structure in the base model outputs and indicates that base models should be treated separately in evaluation. This is relevant to assessment of calibration of base and instruct models when computing the bin statistics.
key observation is that simple methods have competitive performance in many settings, especially outside the QA domain. This expands on observations of Santilli al. (2025), as we now state that the performance of the methods not only depends on the underlying correctness, but also on the problem type used for evaluation. It appears that there is no one-size-fits-all in uncertainty estimation for NLG, with different tasks having different UE method preferences. Reduced variability of the risk indicators and aggregation of the results allow us to confidently draw such conclusion.
More recent work on NLG focuses on more advanced modes of language generation such as CoT (Wei et al., 2022) or multi-agent (Chen et al., 2024b) settings. Whereas the setting investigated in this work can be treated as information retrieval from models weights or prompt, these recent modes of NLG can involve much longer generation lengths, iterative decoding processes, multiple models and routing algorithms, etc. These factors further challenge the robustness of uncertainty estimation algorithms. While we leave the empirical analysis of models in these settings to future work, we believe that the basic principle of marginalization over risk function's 's parameters and avoiding experimental clutter through effective aggregation would be necessary for evaluation in these settings.
7 RELATED WORK
Santilli et al. (2025) concurrently investigate the pitfalls of the NLG UE algorithm evaluation employing detailed correlation studies and human annotations. While their analysis of the problem is similar to ours, our work additionally proposes several solutions to the identified pitfalls as well as considers evaluation instability centered around general risk correlation experiments. Recent work by Fadeeva et al. (2023) and Vashurin et al. (2025) provide a comprehensive benchmark suite for UE methods in NLG, utilizing QA, summarization and translation tasks. These two works, however, do not investigate the failure modes of the prevailing evaluation protocol, which is the focus of our work.
Another line of research deals with OOD detection for benchmarking uncertainty estimation NI.G. Vazhentsev et al. (2023) empirically investigate OOD detection translation, summarization and question answering tasks, comparing density based methods to deep ensembles. Zablotskaia et al. (2023) evaluate the calibration of predictive distributions of L.MSs summarization tasks.
Several works investigate debiasing and uncertainty estimation for LLM-as- LLM-as-a-juse j-jdge. Liu et al. (2024) introduce a Meta Ranking approach improve the performance of judge LLMs. Wagner et al. (2024) proposes a method for assessing uncertainty of LLM-assa-judee for multiple choice answers. Dorner et al. (2025) investigate judge LM bias in general purpose L.M evaluation.

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8 CONCLUSION
In this work we sought to analyze and address pitfalls the evaluation of NLG uncertainty estimation algorithms. We first formulated a perspective empirical properties of uncertainty estimation algorithms and the ways they are evaluated. This perspective builds upon the established work in uncertainty estimation for the univariate classification setting, transferred the natural language generation setting. We further investigate the peculiarities of risk correlation experiments in the NLG UE literature, diagnose the arising issues and propose credible remedies. Overall, our insights and proposed risk indicators aim to foster better evaluation practices and guide the field to further improve UE methods for NI.G.
ACKNOWLEDGMENTS
The ELLIS Unit Linz, the LIT Al Lab, the Institute for Machine Learning, are supported by the Federal State Upper Austria. We thank the projects FWF AIRI FG 9-N (10.55776/FG9), Al4GreenHeaatinGrrdd (FFG- 899943), Stars4Waters (HORIZON-CL6) -ATIZOONNLLL-22222CLLAAAAAT----- -CLIMMTTE-01-1), FWF Bilateral Artificial Intelligence (10.55776/CEE12) We thank NXAI GmbH, Audi AG, Sili- con Austria Labs (SAL), Merck Healthcare KGaA, GLS (Univ. Waterloo), TÜV Holding GmbH, Software Competence Center Hagenberg GmbH, dSPACE GmbH, TRUMPF SE Co. KG.
REPRODUCIBILITY STATEMENT
The authors take appropriate measures to ensure reproducibility of the outcomes. Attached to this submission supplementary material containing (a) complete code used for experiments; (b) intermediate results tables, containing every for every dataset, model, uncertainty and correctness measure combination considered. Identities concerning variances in Sec. 3 are derived step by step in Appx.Sec... along with discussion about the assumptions and empirical verification.
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CONTENTS
Generative AT Usage Disclosure
16
Datasets and Methods Used Our Analysis
16
B.1
Considered Uncertainty Estimation Methods
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B.1.1
Multiple Output Sequences
17
B.1.2 Single Output Sequence
18
B.1.3
Weighting Token Probabilities
18
B.2
Heuristics
19
B.3 Details on the Datasets Used
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B.4 Details on the Approximate Correctness Functions
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B.4.1 Notes on ROUGE-2 and BLEU Implementation Artifacts
21
B.5
Details on Experimental Setting
22
B.5.1
Standard Deviation of Performance Estimator
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B.5.2
Computing the Elo Rating
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B.5.3
Grid Definition for the Correctness Hacking Experiment
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B.5.4
Additional Small Scale Human Annotation
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B.5.5
Ablations of Elo Score
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C Application Details for Judge Models
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C.I
Computational Burden of Multiple Judges
................................
25
C.2 Prompts Used for Judge Models
Additional Theoretical Considerations
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D.1 Empirical Properties of Uncertainty Estimation Algorithms
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D.2 Effects of Reference Label Perturbation on Rank Correlation
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D.2.1 Sample AUROC
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D.2.2 Rank Correlation other than AUROC
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E Comparison of Lud-as-a-judgee to Each other and Exact Correctness
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E,1 Selected Examples from QA Datasets where Judges Disagree
A GENERATIVE AI USAGE DISCLOSURE
The development this paper saw very limited use of generative AI, which was exclusively used for editing and refining the prose of small portions of human written text.
B DATASETS AND METHODS USED IN OUR ANALYSIS
B. CONSIDERED UNCERTAINTY ESTIMATION METHODS
In the following section, we give an overview about the considered uncertainty estimation methods. Two main categories methods that operate multiple and single generated output sequences.
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Furthermore, inherent problem of generating output sequences of arbitrary size (though in practice often capped as a maximum length), introduces the problem of having an uncertainty estimate that is independent of the sequence length. For methods based output probabilities p(y. æ, ye,,, w), this usually involves non-uniform weighting of individual token probabilities. Finally, we present a set of well performing heuristics.
B.1.1 MULTIPLE OUTPUT SEQUENCES
Many works investigate measures of sequence-level uncertainty that defined expectations over the sequence probability distribution p(y æ, w) under a given model. Monte-Carlo (MC) approximations thereof rely on sampling multiple output sequences.
Predictive Entropy. Similar the univariate classification setting, Predictive Entropy (Malinin & Gales, 2020) captures the variability in possible outcome sequences. If PE is high, the language model is likely to generate different outcome sequences. However, as the language model does not provide the full predictive distribution p(y æ, w). but only the conditional distribution p(ye. x. ye,, w) for each token. Therefore, estimating the Predictive Entropy necessitates MC approximation:
H(((y æ. w)) 1w) |-
log p(y x;, w)]
(8)
loyp(y" |x w))
y" ~ p(y x, u))
Semantic Entropy. Predictive Entropy does not account for the fact that output sequences y are different, yet covey the same semantics. For example, "John is my brother." and "My brother is John" semantically equivalent, yet are different output sequences. To that end, Kuhn al. (2023); Farquhar et al. (2024) introduce Semantic Entropy, which accounts for those semantic equivalences. They do so by introducing a semantic cluster probability p(c x, w), that is marginalized over possible output sequences:
p(c x,, w) = Epcc| y, w) ply x,, w)
In practice, Kuhn et al. (2023); Farquhar et al. (2024) suggest to deterministically assign output sequences to clusters. Semantic Entropy (Kuhn et al., 2023; Farquhar et al., 2024) is then defined on this cluster probability distribution:
H(p(e a, w)) = B)(cla,w) logp(c a w]]
(10)
logp(c" a. a,,w), -² p(c x, w.
Note that while the MC estimate in Eq. (10) is possible if one has access the cluster probability distribution, this is not the case in practice. Therefore, we use the implementation of Aichberger et al. (2025), who discuss how construct a proper MC estimator of Semantic Entropy.
SentenceSAR. Instead of clustering, Duan et al. (2024) propose to add consistency dependent penalty to the uncertainty calculation. The resulting measure, SentenceSAR is defined as
N log p(y"
xx, w) + Σnan sim(y" y²) p xr, w)
SentenceSAR =
(11)
N
1=1
where sim(-;-) is semantic similarity BERT-style model and is temperature parameter. When output sequences y are sampled according to the posterior, the left term of Eq. (11) is equivalent to Predictive Entropy. The right term of Eq. (11) can be interpreted as penalty that decreases uncertainty there are many semantically similar answers. Therefore, SentenceSAR has a similar goal as Semantic Entropy, yet is more less motivated heuristically.
The SAR method proposed in Duan et al. (2024) combines both SentenceSAR (Eq. (11)) and ToRenSAR (Eq. (17)). We consider both SentenceSAR, TARenSAR and SAR in experiments.
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EigenScore. The EigenScore method proposed by Chen et al. (2024a) operates in the latent space instead of output probabilities. Due to that, the method aims to better capture semantic information for accurate assessment of an LLMs likelihood to hallucinate confabulate. The EigenScore metric defined as
N
N Σ log(Ax),
EigenScore = log det(E + a IN) = N
log
Ax = N
(12)
R=
where Σ = .Ja Z is the covariance matrix, a matrix of N sentence embeddings, taken from the latent space of the LLM with dimensionality d, Ja La 1/ La is the centering matrix where Ia is an identity matrix and 1 is an all-one square matrix of size x d. The regularization term aIN with small constant is added such that E has full rank. The set {A1, λ2 ......... AN) } denotes the eigenvalues of the regularized covariance matrix Σ + a IN. obtained through singular value decomposition. We followed the implementational details by the original authors Chen et al. (2024a). Noteworthy, according to Remark in Chen et al. (2024a), FigenScore is an approximation of differential entropy variant of Semantic Entropy, yet
in the sequence embeddings space. It can thus be interpreted not computed in the output space, but in the embedding space. While Semantic Entropy and other methods operating in the output space hinge on the quality of the semantic similarity operation in the output space, EigenScore depends critically on the quality of the sentence embedding space of the LLM.
B. SINGLE OUTPUT SEQUENCE
In addition to measures of predictive uncertainty defined as expectations over the sequence probability, also other methods that only consider a single output sequence have been proposed.
Maximum Sequence Probability. Similar to the univariate classification setting, the Maximum Sequence Probability has been considered as measure of uncertainty (Fadeeva al., 2023). For numerical stability, the negative logarithm the sequence probability is considered. Formally, the Maximum Sequence Probability (i.e. the negative logarithm thereof) given by
MSP max log p(y xr mr,))
(13)
y
Recently, Aichberger al. (2024) has shown that Eq. (13) is a theoretically justified measure of uncertainty. Approximating Eq. (13) is similarly hard as for other measures of uncertainty in practice, search for the most likely sequence.
as the autoregressive nature of LLMSs makes necessary However, Aichberger et al. (2024) show that the greedily decoded sequence leads to a very efficient estimate that performs very well in practice called G N-NLL, which defined as
G-NLL - Σ log max d
yer, w)) MSP.
(14)
Perplexity. Closely related, the perplexity of output sequence has been considered as measure of uncertainty (Ren et al.. 2023). Note that this is essentially congth-normaiizan as given in Eq. (16), with opposite sign. The perplexity of sequence y given by
I T
PP exp
log Met, m)
(15)
B.1.3 WEIGHTING TOKEN PROBABILITIES
fundamental problem of calculating uncertainty measures on a sequence basis instead of a token basis is, that there is depenency the sequence length T'. Therefore, short answers are automatically less uncertain than long answers. An ad-hoc solution that is widely regarded in the literature is to use length- norehaoommaliztioon (see e.g. Cover & Thomas (2006)). Furthermore, alternatives to this indiscriminative normalization have been proposed, e.g. TokenSAR where individual tokens are weighted according their semantic relevance (Duan al., 2024).
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Length-normin morraliiommiiiiiinnn. Malinin & Gales (2020) popularized the of length- nnngth-normalization to make Predictive Entropy comparable across sequence lengths. Instead of the usual sequence probability, the heuristic length-normalinn normalized probability distribution
T
I
Ply x. w) = II p(u: 2.ye,, w) exp ==1
log p(ue yee, w)
(16)
T
E
considered. Note that this distribution therefore unnormalized the sense that the sum over all sequences does not sum up to one. This heuristic has been widely used together with Predictive Entropy, Semantic Entropy or the Maximum Sequence Probability. Using p(y æ, w) instead of p(y I, w) in their definitions essentially leads to an additional factor 1 in the definitions of these uncertainty measures. Furthermore, we note that Perplexity is essentially the negative length-normalized sequence probability of an output
T
sequence sequence.
TokenSAR. In order make uncertainty scores comparable across different sequence lengths, instead of summing up token log-likelihoods, one can calculate a weighted average. While length- normalization uniformly weights with one divided by the sequence length, the TokenSAR method by Duan et al. (2024) introduces a weighting dependent on input / output pair æ, y. The TokenSAR score is given by
R(ya, U.
TokenSAR Σ
log ((Ue x. yet, w)
(17)
Σ1 R(y,, v.
with R(y,, y. x) = - [sim(( x o o yl(r))) The semantic similarity metric sim(-:) is a BERT-style model and denotes concatenating two token sequences. Essentially, the weighting term R captures the semantic similarity of an æ. pair and itself, yet leaving out one token of the output sequence. If the similarity chances substantially when removing one token, this one is weighted higher in the weighted average.
The SAR method proposed in Duan et al. (2024) combines both SentenceSAR (Eq. (11) and TokenSAR (Eq. (17)). We consider both SentenceSAR, TokenSAR and SAR in our experiments.
B.2 HEURISTICS
Furthermore, we consider popular heuristic methods, that are not grounded in information-theory
pTruee) Kadavath et al. (2022) introduced the p(True) baseline to assess the confidence of the model in its own response. The model first generates an answer question and then evaluates the probability p(True) - the likelihood that the answer is correct. This is done by prompting the model to assess own output, such as asking whether the answer is "True" or "False", and using the probabilities assigned to these responses confidence score.
Length of generated answer. Another heuristic baseline is to consider the length of the generated answers. The reasoning behind this is, that if the model does not know an answer, it will generate longer and more meaningless content as is often observed in public debates. We are aware of any prior work that has considered it as an uncertainty estimation heuristic, although sequence length plays a role in the analysis in Santilli et al. (2025). The sequences length can be viewed as one of the two components of the G-NLI (Aichberger et al., 2024), since G-NLL can be expressed as the product of sequence length and mean token-level entropy.
B.3 DETAILS ON THE DATASETS USED
QA Datasets. We used several QA datasets CoQA (Reddy et al., 2019), TriviaQA (Joshi et al., 2017) and SQuADv2 (Rajpurkar et al., 2018) that are commonly used in NLG UE literature. SQUADv2 was also used dataset with OOD label risk indicator, since features questions that intentionally designed to be unanswerable given the prompt. We further used KUQ (Amayuelas et al., 2024) for OOD experiments only the questions in this dataset are designed to be unanswerable.
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On usage of Truthful QA for UQ evaluation. We have performed rollouts for Truthful QA (Lin et al., 2021) and evaluated the uncertainties correlation plots for them at the request of reviewers. We did not include those results in the statistics, including Elo score computation, since is unclear to us what type of statistical uncertainty does correctness on this dataset corresponds to. This is motivated by the fact, that all questions of TruthfulQA are intentionally designed in fashion that either one or the other option will be dominant depending on specific characteristics of the model pretraining (i.e. data curation, order of sequence sampling, etc). This in contrast with the relatively clear cut cases of other considered datasets, i.e. information retrieval from prompt (CoQA) or from weights (TriviaQA).
1.
10
TRUTHPUL- Qwert 2.5 II spee mman tho
TRUTHFUL - Leera BU IT spearmen the
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Figure 4: Agreement of ordering UE methods on TruthfulQA.
Constrained Text Generation. We used COLLIE (Yao et al., 2024) as a constrained text generation dataset. The challenges in this dataset are derived from passages of text from curated sources to ensure that the problems have solutions. Unlike many other constrained text datasets, COLLIE does not rely on judge evaluation.
Code Completion. Code completion problems allow for non-parametric correctness verilication by means of unit tests. There are several popular public datasets for code completion (Austin et al., 2021; Chen et al., 2021; Hendrycks et al., 2021; Li et al., 2022) that feature an adequate test coverage rate. In our experiments we used BigCodeBench dataset in completion mode (Zhuo et al.. 2024). The problems are all python code, require no non-standard libraries and could considered to be in distribution with respect to the training sets of the modern language models. To evaluate the exact solution, we used the remote endpoint provided by the creators of the dataset that automatically provides the per output and summary statistics. The labels were binarized based on fulfillment of all unit tests for each sample.
OOD Datasets. Unlike the image domain, obtaining OOD examples for text data difficult. When thinking of OOD examples for text, one would imagine questions about things that have not yet come to be or are otherwise unknown or ambiguous in the general text corpora. Several datasets seek to provide artificial OOD examples. Khown-Unknowwns (Amayuelas et al., 2024) seek to collect questions that can be assumed to have controversial answers in the common training sets. SQuADv2 (Rajpurkar& et al., 2018) provides questions formulated to be unanswerable given the prompt. Our search revealed only these two datasets as such that provide suitable OOD labels. We do not rule out the possibility that there are more such datasets in existence, but OOD detection is not main focus of our work.
B.4 DETAILS ON THE APPROXIMATE CORRECTNESS FUNCTIONS
n-gram matching. The standard n- n-gram matching correctness algorithms are the ROUGE (Lin, 2004) and BLEU families (Papineni et al., 2002). To turn these into correctness functions, one is
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required to specify threshold d and the n-gram parameter n, 0. (d, In practice these algorithms often lack robustness and face criticism (Schluter, 2017).
Embedding Based Correctness. Learned correctness functions, such as BERTSScre (Zhang et al., 2020) and BLEURT (Sellam et al., 2020) use similarity of the answer and the reference in an embedding space. Specifically, BERTScore computes contextual embeddings. calculates cosine similarity and applies F1 score. BLEURT uses the model to predict similarity directly. Both metrics could not be computed for longer generations due to context length limitations. AlignScore (Zha al., 2023) uses model fine-tuned perform information alignment in order to assess similarity between the given and reference answers.
AlgnScorr
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Figure 5: UE method ordering heatmaps including AlignScore. our experiments it was always observed to be in its own cluster. Although the default settings from the AlignScore repository together with 'base" model were used, it is quite possible that some adjustments would improve its correlation other correctness methods.
LLM-ae-a-judge- LLM-as-a-judge (Zheng et al., 2023) prompts an LLM to confirm the correctness of the answer with respect to the reference. A model is provided with prompt, question, proposed answer and reference answer. The prompt usually requests the model to generate yes if the question- answer-reference answer tuple is correct. While recently reasoning judges have been proposed, we utilized the usual judge models due to simplicity and noticeably lower evaluation costs.
B.4.1 NOTES ON ROUGE-2 AND BLEU IMPLEMENTATION ARTIFACTS
Notably, ROUGE-2 and BLEU show low agreement to other n n-gram based metrics while showing some higher than average agreement each other. Low agreement of BLEU to other metrics can in
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Table 3: Accuracies of the models for evaluated datasets according corresponding correctness functions. This table lists the dataset / model papers evaluated in this work. Nan values in SQUAD expected behavior, as there are no correctness labels for the artificially unanswerable OOD part. Known-Unknown (Amayuelas et al., 2024) dataset generations were performed without accuracy computation as we used it strictly as an OOD detection dataset.
Dataset
Model / TTemp
NaN Values
Accuracy
Main Correctness Function
BCB
Llama-3 8b /
0.34
Exact
BCB
Llama-3 8b IT'
0.21
Exact
COLLIE
Phi-3.5
0.30
Exact
COLLIE
Llama-3 70b IT /
0,49
Exact
COLLIE
Falcon Mamba
0.14
Exact
COLLIE
Llama-3 8b / 1.
0
0.145
Exact
COLLIE
Falcon Mamba IT
0.166
Exact
COLLIE
Llama-3 8b IT 1.
0
0.42
Exact
COLLIE
Phi-3.5 /T/
0.21
Exact
COQA
Llama-3 8b IT
0
0.86
MoJI
COQA
Phi-3.5
0.81
MoJI
COQA
Llama-3 8b 1.
0.54
MoJI
COQA
Llama-3 70b 1.
0.73
MoJI
SQUAD
Phi-3.5 IT
5945
0.92
MoJI
SQUAD
Llama-3 8b IT / 1.
5945
0.94
MoJI
SQUAD
Llama-3 8b
5945
0.74
MoJI
SQUAD
Llama-3 70b IT/
5945
0.94
MoJI
TRIVIA
Phi-3.5 IT 1.
0.58
MoJI
TRIVIA
Llama-3 8b IT'
0
0.74
MoJI
BCB
Qwen2.5 32b
0.6
0.174
Exact
BCB
Llama-3 70b IT / 0,6
0.352
Exact
BCB
Qwen2.5 7b IT 0.6
0.069
Exact
SQUAD
Qwen2.5 32b IT / 0.6
5945
0.959
MoJI
COQA
Qwen2.5 32b 0.6
0,835
MoJI
COLLIE
Qwen2.5 32b IT 0.6
0
0.436
Exact
COLLIE
Qwen2.5 7b IT /
0.286
Exact
part be explained by correctness values being low, making the commonly used 0.5 threshold a poor choice. Upon closer inspection it turned out that the standard implementations of ROUGE and BLEU that widely used uncertainty estimation evaluation (Luong et al., 2017) return correctness of zero if either the proposed reference answers are shorter than predefined n-gram, which is 2 for ROUGE-2 and 4 for BLEU. Considering the distribution of reference answers in QA datasets, this is major artifact demanding attention.
B.5 DETAILS ON EXPERIMENTAL SETTING
In our experiments we have preferred smaller models from diverse state of the art open source model families. Throughout our investigations, we use the Ilama-3 8B and 70B (Dubey et al., 2024), Phi-3.5 (Abdin et al., 2024), Qwen2.5 (Qwen et al., 2025) and Falcon Mamba 7B (Zuo al., 2024) series of models, both pretrained and instruction tuned (IT). Falcon Mamba models, although less performant than their attention based counterparts, were utilized to broaden the evaluation coverage to the upcoming linear attention models. The dataset model pairs considered and the accuracies achieved on the most appropriate correctness metric are listed Tab. The accuracies were evaluated on sequences generated with beam search (n 10).
Computational resources required to perform generation and uncertainty computation are estimated to be in the range of 600 GPU-hours.
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B.5.1 STANDARD DEVIATION OF PERFORMANCE ESTIMATOR
The data for the Fig. 2 was generated in the following way. The judge calls were made preemptively, 14 per example for each selected dataset model combination. The performance estimates ESP-J was computed for each judge. Then for each n [1... 14] we uniformly sampled {sp-JS n times with replacement. The bootstrap SD was computed from 100 such samples. The SD was chosen over variance since it is simpler to interpret in terms of confidence interval and shares the AUROC performance unit.
B.5.2 COMPUTING THE ELO RATING
Convergence Elo scores (starting - 1000, K=2)
350
300
CODE ONLY
score varisnce
CONSTRAIND TEXT ONLY
250
200
0O0 ONLY
150
100
50
40
x1000 games
Figure 6: Convergence Elo ratings on the various experimental subsets.
The Elo rating was computed as follows: the initial rating were initialized to 1000 for each method. For each step, a dataset / model pair was selected, as well as two distinct uncertainty estimation methods. Out of the two methods, one with higher AUC against the corresponding risk indicator would be considered the winner. The scores would then be updated according to the standard Elo update rule with 400 and K 2. K value roughly corresponds to the update step size modifier. The relatively low value K was selected since the optimization was performed for 100, 000 steps until convergence (Fig. 6). The mean and variance of the Elo scores over the last 1000 iterations were taken as the final values presented in Fig.
B.5.3 GRID DEFINITION FOR THE CORRECTNESS HACKING EXPERIMENT
For the correctness hacking table, the following parameter grid was made available: Rouge-L, Rouge- L-Sum, LLM-as-a-judge (Llama 70B QA prompt) with possible thresholds of 0.3 and 0.5 (relevant for Rouge family of methods). We have deliberately excluded methods such BLEU, BLEURT, and ROUGE1/2 from this experiment, since they are not frequently used in the literature. Despite such restriction, the differences in Top-3 occurrences in Tab. 2 are substantial.
B.5.4 ADDITIONAL SMALL SCALE HUMAN ANNOTATION
In order to assess the general ability of MoJI to provide good quality labels, we have performed selective annotations of 300 question-anseee answer pairs from the CoQA Llama3 8B IT model rollouts. 3 humans annotated the examples independently upon agreeing to the basic rules (i.e. that if the reference answer contradicts the text, then it is not to be considered and instead the answer the model answer is to be assessed with respect the provided text). Overall the human judges reached perfect agreement on all but 31 (10%) questions out 300. 9 questions were deemed to contain an inadequate reference answer.
The correlation of MoJI and the Judges to human generated labels is shown in Fig. 7. It can be noted, that MoJI correlation human annotators is often on par with correlation between the annotators. It also higher than the average correlation of judges to humans. This indicate that MoJI generally improves the quality of correctness labels compared individual judges.
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Humanl
COQA Liama 8B IT Kendall tau
1.00
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0.31
0.86
655
C-M
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Hamana
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Humant
Humana
Humana
Human
Maj
Indivdual Jusges
(mmaan)
(avg
Figure 7: Correlation of MoJI to human annotators on sample of 300 question-answers from CoQA.
MoJI shows higher correlation to human annotators than individual judges on average.
Correlation of Ranks
Correlation Elo scores
Kendall Ta 0.670; Top har
0.733; Top rar
13
12
Pitrue!
1400
EigenScore
Perplex.
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Figure 8: Average Rank (Left) vs Elo score (Rank) evaluated for the complete and synthetic indirect comparison scenarios. For ranks: lower is better, for Elo scores higher is better.
B.5.5 ABLATIONS OF ELO SCORE
Indirect Comparison To demonstrate the advantage of Elo Score for indirect comparison we have occluded parts of the experimental suite in the following fashion:
For all Llama models only the following UE methods were available: Ened.Ent., Pred, Ent. LN, Seq BS Seq.Len. Token SAR, Sent. SAR, SAR, Perplex., Sem. Ent., Min. Log. Prob.
2. For the remaining models only the following UE methods are available; Sent. SAR, SAR. Perplex., Sem. Ent., Min. Log. Prob., Ent.Ent. LN, P(True), GNLL, EigenScore.
The methods were chosen arbitrarily (using python list slicing [:10] and [5:] on the list of names). A relatively small 'bridge' of methods left the partial overlap. We then aggregate the 'low overlap' and full experimental suite using the average rank (similar to Vashurin et al. (2025)) and the Elo score. The results provided in Fig. 8. We demonstrate that Elo score more robust at retaining the ordering of methods when subjected to such 'low overlap' conditions, in particular on the higher end of performance spectrum.
This overlap condition is relatively mild, as more invasive options could be devised (e.g. breaking down across the datasets).
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C APPLICATION DETAILS FOR JUDGE MODELS
We used judge models were of Llama-3 family with 8B (earlier experiments only), 70B and 405B parameters. In order to achieve marginalization over the model class in MoJI, we further added Qwen2.5 and Deepseek-v3 models.
Sampling Parameters The length of the completion was observed be largely in 2-3 token range, indicating that the prompting largely succeeded imposing anticipated output structure onto the model. The models were evaluated at temperatures of 0.5 and 1..
Judge Models Used Tab. 4 lists the judges, prompt temperature combinations used in our experi- ments. We used two different prompts mostly to showcase the difference between the outcomes on the COLLIE dataset. If yes was among the words generated in the answer, the correctness of 1 was assigned. This consistent with usage in (Farquhar et al., 2024; Aichberger et al., 2024). Imposing a more rigid structure upon the answers (i.e. guided generation (Dong al., 2024)) is left future work. The use of reasoning judges is relatively novel and has a major drawback of being substantially more expensive and further complicating the answer extraction. This would be especially strongly felt in correctness evaluation for relatively short QA answers. Therefore we deem it to be beyond the scope of our work.
Table 4; Judge model configurations used for correctness prediction. QA and Gen prompts provided in Apx.Sec.C.. Additionally, multiple samples were taken from each judge model.
Model
Prompt
Temperature
Llama3 405B
gen
1.0
Llama3 405B
qa
0.5
Llama3 405B
qa
1.0
Llama3 70B
gen
0.5
Llama3 70B
gen
1.0
Llama3 70B
qa
0.5
Llama3 70B
qa
1.0
Llama3 8B
gen
0.5
Llama3 8B
gen
1.0
Llama3 8B
qa
0.5
Llama3 8B
qa
1.0
Qwen 32B
gen
0.5
Qwen 32B
qa
0.5
Qwen 7B
gen
0.5
Qwen 7B
qa
0.5
Deepseek v3
gen
0.5
C.I COMPUTATIONAL BURDEN OF MULTIPLE JUDGES
The judge models were operated via an API in 8 bit floating point precision without fixed random seed. A total computational burden of evaluating the judge models for our experimental suite is estimated to be under 40M tokens, predominantly in prefill mode due to really short answer length required. This translated into ss 40S of API calls.
Judge model evaluation implies short generation length, the order of several tokens, as has been observed by us. This makes it fast relative to the original sequence generation, since the prefill is 10 100 times faster per token than generation. This is major advantage of classic L.MMaas-a-judee approaches compared to their reasoning counterparts.
We have evaluated variable number of judges per experiment setting (see Fig. 11). Based Fig. having MoJI ensemble of 4 judges already bears great benefit, while more than 10 judge calls might be redundant.
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C.2 PROMPTS USED FOR JUDGE MODELS
QA prompt follows the implementation of Farquhar et al. (2024);
We are assessing the quality of answers to the follewing question: (question] The expected answer is: [correct_answer]. The proposed answer is: (predicted_answir Within the context of the question, does the preposed answer mean the same as the expected answer? Respond only with yes or no. Response:
Gen prompt is derived from the QA prompt with minor modifications:
We are assessing the quality of answers
to the follewing question: (question) The following are example answers: [correct_answer) The proposed answer is: [predicted_ansenr Within the context of the question and example answer, is the proposed answer correct?
Respond only with yes or no. Response:
D ADDITIONAL THEORETICAL CONSIDERATIONS
D.1 EMPIRICAL PROPERTIES OF UNCERTAINTY ESTIMATION ALGORITTMM
According to the how uncertainty quantification algorithms are evaluated the literature (Welling & Teh, 201 1; Gal & Ghahramani, 2016; Laksh Lakshminarayannan al., 2017; Malinin & Gales, 2018;
D' Angelo & Fortuin, 2021; Daxberger et al., 2021: Mukhoti et al., 2023; Schweighofer et al., 2023), we can say that uncertainty function uute (x, w; 0.) (aleatoric) ūepi (æ, D; O.)) (epistemic) with positive real valued codomain that has the following empirical properties:
à is higher for x' Diest than for x Drest the risk of prediction using w (aleatoric) or p(w (D) (epistemic) for x' is higher than for æ.
2. à is not lower for x' than for ~ Diesi if x is drawn from a different data generating function than one that produced the training data D.
3. û is not lower for x' than for Diest if x is obtained from by some perturbation.
These properties can be distilled from ubiquitously used evaluation protocols in uncertainty quantifica- tion literature classification setting. Note that the first and third properties are characteristic of both aleatoric and epistemic uncertainty, whereas the second is usually attributed to epistemic uncertainty. In the classification setting, most of the literature focused on epistemic uncertainty since it involves, depending the definition, estimating more difficult posterior integral of divergence, which requires intricate posterior sampling techniques (Wilson & Izmailov, 2020; Schweighofer et al., 2023). The three empirical properties can be unified in terms of viewing uncertainty indicator of prediction risk (Kotelevskii & Panov, 2025; Lahlou et al., 2023).
Another assumption is sometimes used:
4. If õepi is higher for x' ~ Ddomain than for æ, then adding the (æ', y') to the training dataset D would on expectation lead higher risk reduction on Doomain than adding (ar, y)
This is the active learning assumption which in classification literature is usually associated with the epistemic uncertainty (Kirsch, 2024). Active Learning evaluation is a challenging task with many caveats even in the classification setting (Hacohen et al., 2022: Lüth al., 2023). Furthermore requires a true label and some degree model tuning. Autoregressive generation further complicates this mode of evaluation. Therefore do not consider AL assumption for evaluation in work.
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The way these assumptions formulated implies that the correlation coefficient according which they are evaluated must be invariant to monotone increasing transformations.
D.2 EFFECTS OF REFERENCE LABEL PERTURBATION ON RANK CORRELATION
In this section investigate the effects of the defects of the reference class labels rank correlation. We specifically focus on AUC, as it is the rank correlation most commonly used in Uncertainty Estimation literature for risk correlation experiments. We show that both variance and bias in risk indicator values lead to biased AUC estimates. Both of the considered scenarios support using MoJI as the approximate correctness measure of choice.
D.2.1 SAMPLE AUROC
Sample AUROC can be computed explicitly follows:
AUC
Σ
Σ
1(s,
> +,) 1(s; = =sy)
(18)
J:.y m0
It has equivalent MC estimator that implies sampling positive-negative labeled pairs:
1 M
AUC
~S Σ 1ss s.)
(19)
The two forms are equivalent and are unbiased and consistent AUC estimators and are equivalent to the original rank based statistic (Mann & Whitney, 1947). Generally, the AUC corresponds the expected probability that the scorer X' - IR ranks the items (Z1,... .nn) in way that those with positive binary labels (y1.... yn.) have higher score than ones with negative labels.
AUC E,z, E 1p( [s(x,) > s(x,)]
(20)
In case of empirical assessment of the uncertainty estimation algorithm by correlation to risk (as per Sec. 2 and Apx. D.1) &, the labels are the negated correctness -c and scores are the uncertainty estimates
Sample AUROC with label noise Let us now consider scenario, where the reference labels perturbed randomly by Bernoulli noise:
Cz.
if ~ B(p) = CCa, if B(p) =1
paisy
(21)
Note, that rounded expectation of Cz, p < 0.5:
noisy (its median) equals the true value of if the noise magnitude
round
[E
moisy (I:)l] = c(xx)
(22)
Informally this can be viewed as an unbiased estimator of c(a.) with added variance for binary variable. 7 independent of the example which it applies, contrary to the bias introduced by distortion in the previous section.
To inspect the properties of the AUC estimate in case of noisy reference, we will use the AUC from Eq. (19) formulation of the estimator, the direct sample AUC estimation from Eq. (18) is less
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suitable for accommodating the noise term. In this regime require sampling pairs of inputs with positive/negative label This assumes ability to specifically sample the positive or negative class, which we take for granted (i.e. class balance assumption) without additional importance sampling considerations. We decompose the Eq. (19) similarly to what we did for the bias case:
M = M
(s(x²) > ((1)) (.)) = 1, c. moisy (x = 0)
1 (s(xx) ((2 ((x 1, c(2)) 0) p(7 1)² +
1 ((sxx)) > ( c(x))) c(>)) 1) p(> 0)p(7 1) +
M Σ
(({(x)) > )(25) [(x))) = 0, c(a)) 0) :P(> = 0)p(7 = 1) +
1 (s(x;) > s(2)) [c(s))
= 0, c(>))) 1) -P(> = 0)2
(s(x.)) > ((()))))))))))))))))) (((x))
= 1, c, 011(1))
M
1 (s(x)) > s(²)) c(xf) = =1,c(z²) = 1) (1-
M Σ
(23)
1 (s(x;) s(2)) cc(x)) = =0,c(z)) 0) pp p) p)+
1 (s(x;) s(x)) (c(=)) = -..((²)
1) =p
Note that the coefficients in 23 sum up to 1, which makes sense. Then we can proceed by separating the part that corresponds to the AUC estimator with unbiased labels:
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A MC
1 M
(s(xf) > s(x,) | (x:)) monyy (ar)) = 0)
M
M Σ (s(x²) > s(x)) - - 0) (1 p)2 +
1
= 1,
1 (s(x²) s(x))
dxa)) = 1, c 1) p (1 (1-1) p) +
M
1 (s(x2) (x)) d(a)) = 0, c(x)) = 0) p (1 p) +
M
1 (s(x9)
(x))
|dxx]) = 0, 1) p²
ACC
(1 (1-p)²+
1 (s(x²) sa]) [[ =
1, (, 1) p (1 p) +
Σ M
1 (s(x9) sx)) c(x))= = (x 0) p 1)
(s(x²) > s(2))
-/)]/aa)==00000))0 (x [c))) =
1) p²
AUC
(1 (1-p)²+
1 (s(x4) (x,)) ((a)) = 1, 1, 1) p- p)
M
Σ
1 (s(xg) > sxx)) c(x]) = 0, c 0) p (1 (1-
(1 - 11 (8(2g) > ((1)) dx,)) = 1, c
8²
AUC
(1-p)² 0
1
Σ p² AUCMC p² +
M
(s(xt) > s(x)) |d(x)) 1,c(x,) = =1) .p.
-1) .p. 111)) p) +
M (8(x2) > s(x+) ((x9)) = O, 0, = 0) p. - p)
M
AU (1-2p) + M
Σ x²=
1 M
1 (s(x;) > s = 1, =1) +
p. (1 p) M 1 (s(x?) s(2)) c(x)) =0)
Σ
(24)
We can safely assume that the two identity terms within the classes sum up to 0.5 over large number of samples. This is because within the same class we can sample both (2f x²) and (x xt) with the same likelihood.
AUCnOisy-MC
M
= AC (1- +
M Σ
p2
M P (1 (1-
MC -(1 2p) +p
(25)
While in Eq. (25) the first term is lower than the value obtained with unbiased labels by a factor of 1 - 2p. With this, MUC = AUC only when the AUC 0.5. Intuitively, we can see that random classifier will not be affected by noise in the labels. This shows, that ultimately, introducing random noise to the labels increases the bias of the AUC estimator and results in loss of its asymptotic consistency. In context of our work this demonstrates that having variance in the risk indicator (i.e. stochastic approximate correctness) yields biased estimate of & when using AUC as rank correlation. This is particularly relevant to samples from LLM-as-ar as-a-judge, which are rolled out stochastically.
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Blas and Varlance of the interpolation Sample AUC Estimator Under Distortion
esep
6.0
555
3.0
Vatiance
4.5
4.0
0.802t
35
30
25
08800
20
40000
B302
Bias
Figure 9: Empirical verification of Eq. (27). This was conducted with synthetic random data with initial labels initialized for AUROC scores of 0.6, 0.75, 0.9 with distortion rates of 0.1, 0.2 and 0.3. 120 evaluations were made for each point to collect the corresponding statistics. The decomposition has no practical bias and low variance, particularly for sample sizes 10 which corresponds to common sizes of QA datasets.
Sample AUROC with biased labels Lets consider scenario, where the correctness function is biased. This is equivalent to permanently perturbing the correctness labels (cI.... Cn) with some distortion function d X + 10,
Cr: if dz, 0
c =
(26)
Cz, if dg,
For brevity, we refer to &i as c₁ and to dz, d,. Then (ignoring the ties for simplicity):
Σ
1(s: > 8z)
1g Fay
J:y,
p(dd 0, = 0) E =ny= 1(s; s;)+
no :1==1
p(d, = 1, = Σ j,,,= 1(8 5;)
bn== = Σ =.y= 1(x: > 8,)p(y; 1, d; O)p(d, = 0, = 0)+
E Eey=ood,=1
- 1(x: s,)p(ıi 0, d, 1)p(d, 0, 0)+
E Eim=lnd;=0
/ 1(8: > sy)p(ıi 1, O)p(d, 1, 1)+
Eig Σ =11 1(s: sy)p(H; 0. d: 1)p(d, -1,93 =1)
AUC p(d: 0, d, 0)+
0.5 (p(d; = 1, d, 0) + p(d: = d 1))+
(1 AUC**) p(d, = 1, d 1)
AUCs nld, =)d,=0)n(d,=
0.5 n(d,=1)n(d;=0) mld,=0)m(d,=1)) +
(27)
Mon1
(1 AUCs*) a(d:=1)n(d;=1))
To obtain the Eq. (27) we first decompose the AUC estimate with distorted labels into terms. These terms correspond to the possible cases of label perturbation combinations.
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The first and the last term then be expressed through the sample AUC with unbiased labels, which holds the asymptotic case of large sample size (N - inf where = no + nt). The middle two terms equal 0.5 by symmetry argument.
AUC
AUC n(d, 0)n(d; =
[n[, 1:)(d1)ndd--- =0)
n(d, 0)m(d, )
+ 0.5
1
non
+11 +(1-AUC* )UC))) n/d, = l)n(d, =
= AUCC n(d, = 0)n(dy =0) AUC n(d; = 1)m(d; = =1
1111
(n(d 1)m(dj =0] n(d; 0)n(d;
n(di 1)n(dj
+ +.5
n(d;
0))(nd = =0) AUC
n(d; 1)n(dj = =1
AUC
(28)
no71
n(d4 =
nodj = =1
0.5
(29)
74n
Here the AUC is the AUC of the subsample with flipped labels and AUCS is the AUC of the undistorted part. Note, that case of large sample size and random flipping of labels, this expression becomes equivalent to Eq. (25).
This shows, that the deviation from the original AUC depends on a) magnitude of distortion; b) on whether the AUC of distorted partition is similar that of the undistorted partition. the distortion is produced by random noise like in the previous section, the bias is higher if no resampling is done. This part of the identity above results in context of our work, this shows that biased the risk indicator labels leads to bias and loss of consistency of the & estimate compared to the case of unbiased indicator.
D.2.2 RANK CORRELATION OTHER THAN AUROC
Other popular rank correlation metric that is used is Spearman P. We leave derivation of the identities under conditions above for Spearman to future work. At the same time, since under discretized labels Spearman p is numerically equivalent to AUROC, would expect the identities for AUROC to look similar. Dorner et al. (2025) provides a discussion on binary vs non-binary labels for general purpose LM evaluation.
E COMPARISON OF LLM-AS-A-JUDGE TO EACH OTHER AND EXACT CORRECTNESS
In Fig. we investigate the consistency of correctness assessment between different judge models. We can observe, that even identical models can diverge based on the prompt. When the temperature not set to 0, we are additionally facing variability due to sampling outputs from the judge model.
E. SELECTED EXAMPLES FROM QA DATASETS WHERF JUDGES DISAGRER
We have manually inspected some examples from TriviaQA, a commonly used QA dataset. We chose to manually inspect this dataset due to relative simplicity to establish causality due to short question and answer pairs which can be inspected quickly. We have selected top 15 examples with the highest MoJI entropy and inspected them manually. Most of the examples in the list contained obvious labeling problems with conflicting aliases. We present the examples with the most obvious ambiguity issues (from human standpoint) from the top 15 list, reporting their dataset as well as their rank by MoJI entropy. The answers given by the model for which MoJI correctness initially computed (Llama 8B IT in this case) are not provided as they are not relevant to the label noise inherent to the dataset.
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Liama
COLLIE Uama
BCB Liara
COLLIE Liarn
580
(b)
Figure 10: Correctness consistency structured datasets. indicates ROUGE family, B BLEU. judge models are indicated with J, "q" stands for QA prompt used Farquhar et al. (2024) while 'g' stands for more general prompt evaluate correctness (see Apx. C.2 for more details prompting). (a) Agreement of correctness metrics in terms of mutual AUROC (not symmetrie). Column values binarized 0.5 where applicable.
(b) Correlation of UE algorithm orderings when compared between corresponding pairs of correctness functions.
TRIVIAQA: 17181
MoJI Entropy rank: 2
question: Which Canadian born actor played The Eagle Has Landed?,
Irishman in
question_ide bt_1731, http://blltrbbbll...iiafeeee..oo
question_source:
answer: (aliases: [Sutherland (district), North West Sutherland, Cataibh,
County of Sutherland, Sutherlandshire,
Sutherland (local government district, Highland region), Sutherland, South East Sutherland), normalized_valuee sutherland,
value: Sutherland)
>> Confusing aliases, mixing the right labels with the wrong ones.
TRIVIAQA: 16858
MoJI Entropy rank: 8
question: Who became Prime Minister of Canada in November last year?, question_id: odqi_122g6
question_source: nttp://ww..oqute/
.k/, answer: (aliases: [Trudeau, justin, Justin trudeau, Justin Trudeau), value: Justin Trudeau)
>> Temporal question the answer to which depends on time horizon which was not specified.
TRIVIAQA: 7275
McJI Entropy rank: 9
question: Kodkod, margay, oncilla and caracal are all types of what?, question_id: 2fq_24575,
question_source: www.sfquiz.org.. answer: (aliases: [(Wild) at], normalized_ value: wild at, value: (Wild) at)
>> Obviously misextracted answer,
perhaps the correct labels was supposed to be 'wild ld Cat
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TRIVIAQA: 2881
McJI Entropy rank: 11
question: A Tale of Two Cities?,
question_id: bb_2192,
question_source: http://www http://ee.tt/////ob/iiaaaaaaaaao bussnesbbaalss.com.
answer: (aliases: [Charles Dickons,
с Dickens, Charles John Huffam Dickens, Dickens, Charles, Dickensian, Dickensian character, CJH Dickens, Charles Dickins, Charles John Huffam Dickens FRSA, Charles dickens, Dickens, Charels Dickens, Charles John Huffam Dickers, FRSA, Dickens charles, Charles Dickens), normalized value: charles dickens, type: wikipediafntity,
value: Charles Dickens)
>> Vague, poorly posed question, unclear what is required.
TRIVIA: 15672
McJI Entropy rank: 15
question: Which Scottish football team plays home games at Easter Road?, question_id: sfq_23124,
question_source: www.sfquiz.org.uk
answer: faliases: [The Hibernian, Charles Byrne (Journalist), HIBERNIAN],
normalized value: hibernian, value: HIBERNIAN),
Correct aliases mixed with irrelevant.
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Owen
Lbbrr
QwiOn
Owin
101 20124
BAY
$40000
COLLIE Ulmma RM
CILUIE- Usmra 3 AA
COLLIT- 3.5 Mini IT
OOLLI-- - 2.5
1.
eaatt
Joyels
Josnii Mcrile
EDGA
MHiiT
CDOA- Owien
SQUIDD Owery 2.5
SQUAD
3.0
L.
Suppatt
A3009
scpiecs
SQUAD Liama
SQUAD Pii 3.5 Mini
2:11
012
DEP CRI
Figure 11: Agreement scores between judges on selected combinations. The ticks indicate model size / prompt/ sampling temperature used to assess correctness. Judges of similar sizes tend to agree. Larger judge models tend to agree better with the exact solution, especially on COLLIE. The sampling temperature of the judge model appears to have a relatively minor effect on the outcome. Prompt affects the evaluation quality substantially, especially on COLLIE, which requires much less direct pattern matching and more implicit computation. Some judges appear more than once indicating multiple samples taken from the same judge configuration.
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Reviews:
[{"review_id": "A0BDyYfwI8", "reviewer": "Reviewer_Fa32", "summary": "The paper highlights the problem that unreliable generation quality estimation metrics can further mislead the uncertainty estimation evaluation. The authors demonstrate that you can hack the evaluation metric by choosing the proper LLM generation quality metric. This problem is not unique for uncertainty, but it is a challenge for the LLM evaluation in general.  \n\nThe authors suggest two methods:  \n1.\tThey suggest using multiple LLMs as a judge to reduce variance of generation quality assessment.  \n2.\tThey propose using ELO rating for aggregating the scores across multiple different tasks and datasets.  \nTwo problems with the paper:  \n1.\tBias due to inadequate choice of quality metrics were investigated previously in (Santilli et al., 2025) and some solutions to this problem were suggested in (Santilli et al., 2025) and (Vashurin et al., 2025).  \n2.\tELO rating looks redundant compared to simple averaging of metrics. It would be great if you could clarify the situations when it is better than simple averaging.  I think the paper could benefit from better analysis of ELO rating (cases when it is really needed).\n\nLiterature:   \nAndrea Santilli, Adam Golinski, Michael Kirchhof, Federico Danieli, Arno Blaas, Miao Xiong, Luca Zappella, and Sinead Williamson. 2025. Revisiting Uncertainty Quantification Evaluation in Language Models: Spurious Interactions with Response Length Bias Results. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 743–759, Vienna, Austria. Association for Computational Linguistics. https://aclanthology.org/2025.acl-short.60/", "questions": "Can you provide particular examples that motivate ELO?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 2, "strengths": "The authors suggest two methods:  \n1.\tThey suggest using multiple LLMs as a judge to reduce variance of generation quality assessment.  \n2.\tThey propose using ELO rating for aggregating the scores across multiple different tasks and datasets.", "weaknesses": "Two problems with the paper:  \n1.\tBias due to inadequate choice of quality metrics were investigated previously in (Santilli et al., 2025) and some suggestions to this problem were suggested in (Santilli et al., 2025) and (Vashurin et al., 2025).  \n2.\tELO rating looks redundant compared to simple averaging of metrics. It would be great if you could clarify the situations when it is better than simple averaging.  I think the paper could benefit from better analysis of ELO rating (cases when it is really needed).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TAbbnXCUgv", "reviewer": "Reviewer_3yHN", "summary": "The paper argues that QA style selective prediction is brittle because approximate correctness functions may disagree and can be hacked. The proposal consists of alternative risk indicators (structured tasks with exact correctness, OOD, perturbation), SP-MoJI (marginalize across multiple judges/prompts/models), and Elo aggregation across settings. \n\nThe main motivation is that published research in the area mainly evaluates on QA with approximate correctness functions (Table 1), often with ROUGE/BLEU/BERTScore/LLM-as-judge, and little human evaluation. UE is formalized as ranking correlation between uncertainty and a risk indicator (AUROC of rank correlation). Three empirical properties that are posited as desirable are proposed, motivating three experiment families: SP (selective prediction), OOD detection, and perturbation detection. Correctness c_theta is defined and two label-perturbation effects on AUROC are shown. It is also shown how a sample-dependent bias yields a decomposition that mixes distorted/undistorted subsets, implying rank instabilities when we fail to marginalize. Figure 1 shows large disagreement among ROUGE/BLEU vs judge metrics, driven partly by extremely short reference answers; a ROUGE-2/BLEU implementation artifact is also reported. These disagreements translate into inconsistent UE method rankings. It is shown that correctness-hacking (Table 2) can substantially alter top-3 membership.\n\nFollowing the analysis, the following remedies are proposed. a) Exact correctness via structured tasks (code unit tests, constrained generation), which avoids parameterized metrics. b) SP-MoJI: averages the outer correlation across multiple judges/prompts/models to marginalize judge aleatoric/epistemic uncertainty (Eq. 6). Further, bootstraps show a single judge gives SD≈0.04 in AUROC; ~4 judges halves SD; diminishing returns past ~10. c) OOD/perturbation: treats OOD identifiers or corruption strength as risk indicators, implements with Known-Unknowns, SQuADv2, and word-shuffle perturbations. In view of all this they use Elo to aggregate pairwise wins across (dataset x model x task) experiments; 400 Elo roughly corresponds to 1:10 odds. This is good for incomplete overlap across method evaluations and for subsets (QA vs code vs constrained text; instruction-tuned vs pre-trained; OOD vs perturbation).", "questions": "See the above.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The paper doesn't propose brand new math or concepts, but it does present a creative integration of fixes: outer-expectation marginalization, structured tasks as risk indicators, and Elo aggregation. All together, this can meaningfully update evaluation practice. The proposed fixes are easily actionable.\n\nThe analysis before the remedies are proposed (e.g. for AUROC under noise/bias, careful empirical demos for disagreement matrices, correctness hacking) is quite useful. \n\nThe paper is generally clearly written. Explanations are generally clear.", "weaknesses": "On page 5, the adversarial metric selection space does not seem to be pre-registered. Without a pre-defined grid, the \"correctness-hacking\" claim could itself involve cherry-picking. \n\nOne page 6, the SP-MoJI diversity factors seem under-specified. Which diversity (model family vs prompts vs decoding) contributes most to variance reduction? \n\nOn page 6: Multiple judges may still share family biases; cross-family calibration isn’t deeply analyzed. Wondering what the authors think of the potential impact. \n\nOn page 7: The paper is light on the Elo details. There is no K-factor/tuning, cycle handling, or uncertainty intervals; alternative ranking models not compared. \n\nI also feel like the paper under-acknowledges the breadth of prior practice. slightly overstating QA dominance. \n\nFinally, I also generally found the engagement with the broader literature slightly frustrating. The paper seems to cite papers by 2-3 groups (other than classical references), and develops around that. I am not going to suggest papers to cite, but placing the paper better would improve it.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "6a7AGSUp3C", "reviewer": "Reviewer_oJfd", "summary": "This paper systematically analyzes the pitfalls in evaluating uncertainty estimation methods for natural language generation (NLG), especially in the context of hallucination/confabulation detection in LLMs. The authors demonstrate that commonly used approximate correctness functions (e.g., BLEU, ROUGE, LLM-as-a-judge) can lead to substantial disagreement and bias in the ranking of uncertainty estimation methods. They propose using multiple alternative risk indicators, marginalizing over LLM-as-a-judge variants, and structured/perturbation tasks to improve robustness. The paper also introduces an Elo rating system for summarizing method performance across settings.", "questions": "⦁\tHow stable is the Elo rating system across different datasets and evaluation metrics?\n⦁\tWhat is the computational cost and scalability of multi-metric fusion evaluation in large-scale practical evaluation?\n⦁\tAre there ablation experiments for different evaluation suggestions?\n⦁\tAre the paper's suggestions equally applicable to new NLG tasks (e.g., multi-turn dialogue, generative reasoning)?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "⦁\tAccurate problem identification, experiments reveal key pitfalls in the evaluation field.\n⦁\tEvaluation suggestions have practical guidance value.\n⦁\tThe paper is rigorous and well-argued.", "weaknesses": "⦁\tMainly focuses on evaluation methods themselves, with limited guidance for designing new uncertainty estimation methods.\n⦁\tLacks ablation and robustness analysis for some suggestions (e.g., Elo rating, integrated evaluation).\n⦁\tLacks deeper theoretical discussion on how to fundamentally eliminate evaluation noise and improve consistency.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "fZvBfEINb6", "reviewer": "Reviewer_4ZXg", "summary": "The paper shows that suboptimal NLG eval affects the evaluation of uncertainty quantifiers designed for parameterising decision making pipelines (such as selective prediction and OOD detection) using LLMs.\n\nThe paper shows that different automated proxies for NLG eval lead to different patterns of correlation between UQ and risk in decision making, with high disagreement across the available options. The paper shows that stochasticity inherent to an NLG evaluator (due to predictive uncertainty and/or effects of different prompts) too play a role.\n\nThe paper proposes to aggregate statistics from not one but a collection of NLG evaluators and not one but a collection of decision making settings, as well as to marginalise over choices and sources of stochasticity in evaluation. The findings suggest more robust conclusions are possible with the proposed approach.", "questions": "Could you please address the weakness point above? Did I miss something in my interpretation of your results?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. Clear paper, except for cluttered notation here and there, but still mostly clear to me\n2. Evaluation of UQ is important, the paper offers a critical take on the limitations of the typical UQ evaluation protocols, with a reasonable proposal for improvement \n3. Proposed approach is simple, automated, appears to be effective", "weaknesses": "1. I think the paper needs an “oracle” experiment, where the errors in automated NLG evaluation are approximately eliminated by means of human eval. Of course, I don’t expect it to be as large scale as the rest, but still. Finding that the proposed approach allows us to get closer to the quality of conclusions derivable from this oracle setting is, to me, essential. With that in place, I can then take the larger scale, but more indirect, evidence presented with more optimism /\nconfidence that the seemly more coherent conclusions are indeed more meaningful.\n  \nThat is, to me, the main weakness (unless I misunderstand something, but then I’m happy to be corrected) and the reason for my cautious  scores for soundness and contribution.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)