An Empirical Analysis of Uncertainty in Large Language Model Evaluations
Authors: Qiujie Xie
Qingqiu Li
Zhuohao Yu
Yuejie Zhang
Yue Zhang
Linyi Yang
Venue: ICLR 2025 Poster (2025)
Keywords: Large Language Model
Model-based LLM Evaluation
LLM-as-a-Judge
Primary area: other topics in machine learning (i.e., none of the above)
TL;DR: We are the first to consider uncertainty in LLM-as-a-Judge and investigate its existence, mitigation and utilization.

Abstract: As LLM-as-a-Judge emerges as a new paradigm for assessing large language models (LLMs), concerns have been raised regarding the alignment, bias, and stability of LLM evaluators. While substantial work has focused on alignment and bias, little research has concentrated on the stability of LLM evaluators. In this paper, we conduct extensive experiments involving 9 widely used LLM evaluators across 2 different evaluation settings to investigate the uncertainty in model-based LLM evaluations. We pinpoint that LLM evaluators exhibit varying uncertainty based on model families and sizes. With careful comparative analyses, we find that employing special prompting strategies, whether during inference or post-training, can alleviate evaluation uncertainty to some extent. By utilizing uncertainty to enhance LLM's reliability and detection capability in Out-Of-Distribution (OOD) data, we further fine-tune an uncertainty-aware LLM evaluator named ConfiLM using a human-annotated fine-tuning set and assess ConfiLM's OOD evaluation ability on a manually designed test set sourced from the 2024 Olympics. Experimental results demonstrate that incorporating uncertainty as additional information during the fine-tuning phase can largely improve the model's evaluation performance in OOD scenarios. The code and data are released at: https://github.com/hasakiXie123/LLM-Evaluator-Uncertainty.

Published as a conference paper at ICLR 2025
AN EMPIRICAL ANALYSIS OF UNCERTAINTY IN LARGE LANGUAGE MODEL EVALUATIONS
Qiujie X Qinggiu Li Zhuohao Yu" Yuejie Zhang² Yue Zhang Linyi Yang "Zhejiang University "Scoool of Engineering. Westlake University 'School of Computer Science, Shanghai Key Lab of Intelligent Information Processing, Shanghai Collaborative Innovation Center of Intelligent Visual Computing, Fudan University "Peking University "Westlake Institute for Advanced Study University College London 'Huawei Noah's Ark Lab
ABSTRACT
As LLM--a-a-Judge emerges as a new paradigm for assessing large language mod- els (LLMs), concerns have been raised regarding the alignment, bias, and stability of LLM evaluators. While substantial work has focused alignment and bias, little research has concentrated on the stability of L.L. evaluators. In this paper, we conduct extensive experiments involving 9 widely used LLM evaluators across 2 different evaluation settings to investigate the uncertainty in model-based LLM evaluations. We pinpoint that LLM evaluators exhibit varying uncertainty based on model families and sizes. With careful comparative analyses, we find that em- ploying special prompting strategies, whether during inference or post-training can alleviate evaluation uncertainty to some extent. By utilizing uncertainty to enhance LLM's reliability and detection capability in Out-Of--istribution (OOD) data, we further fine-tune an uncertainty-awarc LLM evaluator named ConfiLM using a numan-annotaan ability on a manually designed test set sourced from the 2024 Olympics. Ex- perimental results demonstrate that incorporating uncertainty as additional infor- mation during the fine-tuning phase can largely improve the model's evaluation performance in OOD scenarios. The code and data are released at: hhtpp: htggthhhbb..cc//aaaakiiiieee
fine-tuning set and assess ConfiLM's OOD evaluation
Eva Burtor Uncertainty.
INTRODUCTION
Instruction
Pairwise comparison Candidate A's reponse than candidate Rts reponse. Evaluation Confidence: 88.69%
Deserihe unique trait of
Candidate A's response
A unique wait of raccoons is their masked face. which fearures black around eye and brond black stripe extending from nose.
Single-answer grading The raingg (0-9) for candidale A's response is 7
C Response Confidence: 87.96%
Candidate B's response-
V Evalation Confidence: 69.87%
A unique trait of Raccoon as its ability to and close
while they closed. ad- aptation helps ihum slay alert for poiential threats even when they're sleeping.
Single-answer grading The rating (0-9) for candidate B's respoase 6.
O Response Confidence: 68.89%
V Evalation Confidence: 65.78%
I.M for single-answer grading
pairwise comparison
Figure 1: An example of uncertainty (i.e., model confidence) in -baeed LLM evaluation. The evaluation process is influenced by the uncertainty of both the evaluator and the candidate model.
Large language models (LLMM)) have garnered increasing attention due to their unprecedented per- formance in various real-world applications (Zhao et al. 2023 Wang al. 2024a). In this context, how to accurately assess the performance of a LLM becomes particularly important. This area of re- search includes benchmark-based evaluation, model-based evaluation, and human evaluation (Chang
et al. 2024). While various benchmarks (Zellers et al.) 2019) Hendrycks et al. 2021 Yang et al.) Xie et al., (024) have been proposed measure the core abilities of LLMs comprehen- sion and generation, human evaluation remains the gold standard for testing overall performance
2023
+Correspondence Linyi Yang (yang] i iy ucd@gmai com).

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Published as a conference paper at ICLR 2025
Experiment uncortiinny exist in ovaluator?
Expertiment How miligite uncertaingy?
Experiment Can we utiliz uncertainty?
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Seperciad Finettnnn
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Figure 2: We conduct extensive experiments and analysis to investigate the existence, mitigation and utilization of uncertainty in model-based LLM evaluation. Uncertainty plays a key role in the evaluation process and can be leveraged to enhance the evaluator's performance in OOD scenarios.
due to its complexity and open-endless. However, this approach is limited by subjectivity issue (Kr- ishna et al., 2023) and resource costs (Karpinska et al.) 2021). Consequently, L.L evaluators have emerged as a cost-effective alternative to human evaluators, providing reproducible judgments for responses from different candidate models (Zheng et al. 2023 Wang et al. 2024b Yu et al. 2024a
As LLLM-as-aJJudee gains more attention, criticism has also emerged (Thakur et al. 2024). Re- searchers have raised concerns about the alignment (Liu et al. 2024c), bias (Wang et al. 2023a), and stability of model-based LLM evaluation. There has been a surging interest exploring whether truly understand complex contexts and make judgments aligned with human values (Yu et al. 2024a Hada et al. 2024 Dubois et al.] (024)) as well as whether they exhibit preference biases when faced with different inputs (Koo et al. 2023 Liu et al.] 2024b] (haakur al., 2024). Despite significant research on LLM evaluators' alignment and bias, there has been relatively little work on the investigation of evaluation stability. In particular, the relationship between uncer- lainty and LLM-as-Judge is question that remains to be underexplored. Can LLMs give consistent evaluation quality across different inputs and domains?
LLM evaluators
Following previous studies that treat generation logits as proxy for model confidence (Varshney al., 2023; Kumar et al. 2024, Duan al.) 20244 Gupta et al.) 2024), we use token probabilities
to represent the LLM's internal confidence. Through extensive experiments (Figure 2 involving 9 widely-used L.MM evaluators under 2 different evaluation settings (single-answer grading and pair- wise comparison) on the MTT-Bench (Zheng et al. (203)) and PandaLM (Wang et al. 2024b) test sets, we demonstrate that uncertainty is prevalent across LLMs and varies with model families and sizes ($4.2). We find that the evaluation confidence of LLM evaluators exhibits sensitivity to changes in data distribution ($4.). With careful comparative analyses, we pinpoint that employing spe- cial prompting strategies (e.g., Shain-of-thoughte Wei et al. (2022)). whether during inference or post-training, can alleviate evaluation uncertainty to some extent ($4.4) $4.5).
Prior work has shown that incorporating the model confidence during the LLM's inference stage can improve reliability in OOD) scenarios (Yang et al. 2024b) and enhance detection capability in hallucinations (Farquhar
al.) 2024). To leverage this fact, we further fine-tune uncertainty- aware LLM evaluator named ConfiLM using instruction instances collected from the Alpaca 52K dataset (Taori et al., 2023). For evaluation in OOD scenarios (55), we manually craft test dataset called Olympic 2024 based on data from the Olympics site Olympic 2024 contains 220 high- quality instances, each labeled by three PhD-level human evaluators. Samples unanimously deemed low quality by the annotators are removed, resulting in an annotator agreement rate of 97.27% 27%. Experimental results demonstrate that incorporating uncertainty as auxiliary information during the fine-tuning process can largely improve the LLM evaluators' performance in OOD scenarios.
In this paper, we conduct a comprehensive uncertainty analysis, propose a high-quality OOD test set, and offer an uncertainty-awart LLM evaluator named ConfiLM. Our empirical findings reveal the impact of uncertainty on LLM-as-Judge, especially eliminating and utilizing evaluation un- certainty, shedding light on future research into the stability of model-based LLM evaluations.
2 RELATED WORK
With rapid development of LLMs, the accurate evaluation of their capabilities has become one of the key challenges in this field. Several LLM evaluation paradigms have been proposed in recent years (Chang et al. 2024), which have coalesced around a few well-established methods, including benchmark- evaluation, model-based evaluation, and human evaluation.
Benchmark based evaluations involve using a set of standardized tests to quantitatively measure model's performance across different tasks. Examples include HellaSwag (Zellers et al. 2019.
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HELM (Liang et al. 2022) and MMLU (eendrycks et al. 2020) for general knowledge and reason- ing, or MATH (Hendrycks et al. 2021) and ToolBench (Xu et al. 2023) for specific capabilities. The performance of LLMs is measured by their ability to correctly perform these tasks. However, these metrics often reflect models' performance in narrowly defined areas and risk inflated scores due to data contamination (Oren et al. 2024).
Human evaluations involve human raters who assess LLM performance based on criteria such as fluency, coherence, and relevance. This approach can take the form of A/B testing (Tang et al. 2010). preference ranking (Bai et al., 2022), or scoring individual model outputs against predefined rubrics (Novikova et al., 2017). While human evaluations are often considered the gold standard for tasks where quantitative metrics fall short, they are resource- resource-intensive in termss of time and cost. Moreover, they are constrained by subjectivity (Krishna al., 2023) and reproducible is- sues (Karpinska et al. 2021), limiting their scalability for large-scale assessments.
Model-based evaluations involve employing a powerful LLM as an auto-evaluator to assess the performance of the candidate model. This promising method serves as a cost-effective alternative to human evaluators (Zheng et al., 2023 Wang et al. 2024b Yu et al. 2024a b). However, con- cerns have been raised regarding the alignment, bias, and stability of model-based LLM evaluation. While researchers have made progress in exploring the alignment and bias of LLM evaluators (Liu ct al. 2024c Wang et al.] 2023a), understanding the stability of these evaluators remains open question. A concurrent work (Doddapaneni et al. 2002) proposes a novel framework to evaluate the proficiency of LLM evaluators through targeted perturbations. Different from this work, focus on the role of uncertainty in LLM-based evaluators, which has yet to be systematically explored.
Confidence Estimation for LLMs. Model confidence refers the degree of certainty model holds regarding its generated responses (Gal et al. 2016). Reliable confidence estimation for LLM crucial for effective coman--aacine collaboration, as provides valuable insights into the relia- bility of the model's 's output, facilitates risk assessment (Geng et al. (2024)), and reduces hallucina- tions (Varshney et al., 2023). Research in this field includes (I) eerbalization-bases methods (Lin) et al. 2022 Yona et al. 2024), which prompt LLMs to directly output calibrated confidence along with their responses; (2) consistency-bart
methods (Tian al., 2023] Xiong et al. [023), which require LLMs to generate multiple responses for the same question and measure their consistency as a proxy for confidence; and (3) logit- methods (Duan et al. 2024, Malinin & Gales 2021
Kumar et al. 2024), which estimate confidence based the model's 's internal states during response generation. Inspired by this line of work, we use token probabilities to represent the LLM'ss inter- nal confidence. Previous work has considered the utilization of model confidence in natural lan- guage understanding (Yang et al. 2024b), fact checking (Geng et al., (024b) and hallucination detection (Varshney al.) [023] Farquhar al. 2024). Differently, our work focuses on utilizing confidence within the evaluation process.
UNCERTAINTY IN LLM-AS-A-JUDGH
Task definitions. To ensure the validity of our experimental conclusions, we conduct experiments under two distinct and commonly used evaluation settings, including single-answer grading and pairwise comparison. See Appendix A for the relevant prompts.
(1) Single-answer grading (Yu et 2024a Li et al. 2023 Liu al. 2023): ; given a user instruction q and a response from the candidate model, the evaluator is tasked with assigning an overall score
e N based on specific criteria set c, while minimizing potential bias. This is expressed as:
[4,r3e, 0),
where e = (c1, 02 }... each e; represents a specific evaluation dimension (e.g., content accu- racy, logical coherence); represents the parameters of the LLM evaluator.
(2) Pairwise comparison (Wagg et al. 2024b Zeng et al.) 2024 Raina et al. 2024): given an instruc- tion y and two responses r',, 72 from different candidate models, the evaluator is asked to compare the two responses and indicate a preference p {1, Tie} according determining whether one response better than the other or if they are equally good. This is expressed as:
p f(g. F1, F2;c,
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Quantification of uncertainty. As shown in Figure 1 the LLM-based evaluation process is in- fluenced by the uncertainty of both the evaluator (evaluation uncertainty) and the candidate model (response uncertainty). Following previous studies (Varshmey et al. 2023 Zhou et al., 2023b Gupta et al. 2024), we use token prohabilities to represent the L..M's internal confidence. Specifically. take the probability of the token representing the evaluation result (e.g., "Tie") as the evaluation confidence, For response confidence, we calculate the average probabilities of all generated tokens. See Table for an example of tokens involved in the confidence calculation. To investigate whether different quantification methods impact the empirical findings, we conduct experiments under pairwise comparison setting on the MT-Bench. The result presented in Appendix
THE IMPACT OF CONFIDENCE IN LLM EVALUATION
We present the empirical study involving 9 widely-used LLM evaluators (3 proprietary mod-
els (Achiam et al.] 2023) and 6 open-source models (Touvron et al. 2023 Yang et al. (2024a)
with 2 different evaluation settings (single-answer grading and pairwise comparison) on the MT- Bench (Zheng et al. 2023) and Pandal (Wang et al. 2024b) test datasets.
4.1 EXPERIMENTAL SETTINGS
Prompting strategies. To explore whether special output formats can reduce the evaluation uncer- tainty of LLM evaluators, we conduct evaluations using prevalent prompting strategies, including:
(1) Default (Wang et al., 2024b; Dubois al. 2024). We instruct the LLM to act as an impartial judge and consider factors such as helpfulness and relevance. The LLM is asked to first output its rating& E 1........9 9} or preference p E {1, Tie). followed by a brief explanation e.
(2) Chain-of of- thoughts (CoT; (Wei et al. 2022 Kojima et al. 2022 ) Instead of generating judg-
ments first, we instruct the LLM first generate concise reasoning before providing its rating or preference p for the responses.
(3) Self-generated reference (Reference; (Zheng et al., 2023 Zeng al. 2024)). We prompt the LLM evaluator to generate short reference answer a for the given instruction g. The generated answer is then provided to the LLM evaluator as a reference when making its judgments.
LLM Evaluators. We employ 6 general yet powerful LLMs across various LLM families as evaluators, including GPT-4o (Achiam et al. 2023), GPT-4o-mini, GPT-3.5-Turbo, Llama3-70B- Instruct (Dubey et al.) 2024), Mlama--70B-Instruu and Qwen2-72BB-instmnee (Yang et al. 2024a). To explore the relationship between evaluation capability and evaluation stability ($4.5). we fur- ther assess the stability of 3 specialized LLM evaluators, including (1) Prometheus2-7b and Prometheus2-bgb-827 models (Kim et al. [0)4c(b), both of which are trained to output in a CoT format, providing concise rationale before indicating preference providing its rating; and (2) PandaLM (Wang et al. (024b), which is trained to output in default format.
To enhance reproducibility and alleviate the impact of temperature sampling on uncertainty analysis, we set the temperature to 0 for proprietary models, and utilize greedy decoding for open-source models. For single-answer grading. the scoring range is 0-9. The evaluation subject Llama2- In-Instu For pairwise comparison, the evaluation subjects are Llama2-77B 1e2--BB-IInttuu and Llama2- Ins-tust We query the evaluator twice with the order swapped to eliminate position bias (Wang
et al. 2023a Jung et al. 2019).
Benchmarks. We conduct experiments on MT-Bench (Zheng al. 2023 and PandaLM (Wang et al. (2024b) test dataset. The MT-Bench contains 80 manually constructed questions designed to challenge chatbots based on their core capabilities on common tasks (e.g., reasoning and math). In contrast, the PandaL.M test set contains 170 instructions sampled from the human evaluation dataset of self-instruct (Wang et al. 2023b), where expert-writted instructions for novel tasks serve as a testbed for evaluating how instruction-based models handle diverse and unfamiliar instructions.
4.2 RESULTS AND ANALYSIS
We first conduct an extensive investigation of LLM evaluators with different evaluation settings to gain preliminary understanding of uncertainty in model-based L.M evaluation, showing partial
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Table 1: Uncertainty analysis of LLM-based evaluators on MT-Benchh and PandaLM test set. The evaluation subject is Llama2-7B- Instrucct and Llama2- Instruct.. For single-answer grading, the scoring range is 0-9. "Win Lose 'Tee" represents the average number of times Llama-2-7b-chee response is better than, worse than, or equal to 1lam-22-13b-hhar response.
Single-answer grading
Pairwise comparison
MT-Bench
Pandul . Test set
MT-Rench
Pandal .M Test set
Evaluator
Evaluation Confidence
Evaluation Confidence
Evaluation Confidence
Evaluation Confidence
Rating
Rating
Win / Lose / Tie
Win Win/Lock Lose / Tie
GPT-4o
5.413
0.417
6,541
0.473
10.0/ 16.5 53,55
0.699
30.0 102.0
0.809
GPT-4o-mini
6.038
0.605
6.641
0.645
27.0/43.5/95
0.776
53.0 /1 56.0
0.820
GPT-b.5-Turbo
6.288
0.629
6.665
0.594
38.5/35.0/6.
0.848
76.5/ 12.5
0.884
Llama3-70B- Itrrrrt
7.250
0.644
7.424
0,548
39.5/37.5/33 3.0
0.791
78.0/ 86.5 5.5
0.849
7,875
0.953
7.924
0.960
33.0/ 34.0/ 13.0
0.908
72.5/73.0/ 24.5
0.931
Qwen2-72B Instrrut
5,875
0.675
7.153
0.692
22.0/ 29.0/ 29.0
0.762
54.0/70.0 46.0
Average
6.456
0.654
7,058
0.652
28.3/32.6/19.1
0.797
60.7/68.2/41. 41.1
0.850
results in Table D for a brief presentation and putting the full results in Appendix D
The following
main observations can drawn:
LLM evaluators exhibit varying uncertainty based on model families and sizes. The evaluation uncertainty is more pronounced in the single-answer grading, where the average evaluation confi- dence is 65.4%, compared to 79.7% for pairwise comparison MT-Bench. This lower confidence suggests that evaluators exhibit higher uncertainty when scoring individual models, which could stem from evaluators being uncertain about how to score model's 's response without the context of a comparison. In contrast, pairwise comparison benefits from direct comparison, leading to more decisive assessments.
Evaluations within the same model family show significantly higher evaluation confidence. As shown in Table [T, when -lama2-70B-Instureee is employed to evaluate Llama2-7B- both the score (7.875 v.s. 6.456) and evaluation confidence (0,953 v.s. 0.654) are significantly higher than the averages for other evaluators. We speculate that this uncommon high confidence arises from the shared training corpus and similar linguistic patterns between the models. leading to a self-preference bias (Koo al., 2023; Zheng et al., 2023), where the evaluating model more familiar with the response style and content generated by a closely related model. This phenomenon highlights the potential threats for self- seff-preference when evaluators from the same model family are used, which could lead to biased evaluations.
Improved general performance does not guarantee more stable evaluation capabilities. For example, while GPT-4o demonstrates superior performance in general tasks (such as reasoning and math) compared to GPT-3.5- -urbbo (Chiang et al., 2024), its evaluation confidence remains low. In the single-answer grading, GPT-4o has an evaluation confidence of only 0.417, which indicates that despite its enhanced abilities in general tasks, it struggles with stability in evaluating other models' responses. This suggests that there is certain correlation between model's competence in performing general tasks and its ability to reliably evaluate the responses of other models, which may be because LLMs not heavily fine-tuned for the evaluation task (Wang et al. 2024b).
4.3 THE INFLUENCES OF DATA DISTRIBUTION
LLMs are typically trained using next token prediction, where the model generates the most likely next word based the preceding context (Zhao al., 2023). Different contexts can lead to multiple token choices, and the model makes predictions based on the training distribution, which inherently introduces uncertainty. As displayed in Table 2,, we study the impact of data distribution on un- certainty in masel-based LLM evaluation. The results demonstrate that evaluation confidence, as measured across both single-answer grading and pairwise comparison settings, exhibits sensitivity to changes in data distribution. When the evaluation scenario shifts from common, high-difficulty tasks (MT-Bench) to novel. unfamiliar tasks (PandaLM test set), the evaluation confidence fluctuates significantly (e.g., from 0.417 to 0.473 on GPT-4o). In contrast, the response confidence (Table 2b) remains more consistent, showing a much smaller variance (0.014) between the two datasets. This analysis highlights that in model-based LLM evaluation, evaluation uncertainty is more pronounced compared to response uncertainty, as evidenced by the lower confidence value and larger confidence differences when comparing performance across different datasets.
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Table Sensitivity of model confidence to different data distributions. A the absolute confidence difference between MT-Bench and PandaLM.
(a) Evaluation confidence.
(b) Response confidence.
Single-answer grading
Pairwise comparisoo
PandaLM
Model
MI--Bench
Pandaal.M IM
MI-Bench
Pandall .
Model
MT-Bench
GPT-4o
0.417
0.056
0.110
Llama2-78 7B. Instract
0.944
0.936
0.008
GPT-3.S-Turbo
GPI--o-mmin
0.629
0.605
0.645
0.594
0.035
0.040
0..776
0.884
0.820
0.036
0.044
L 1a-22--3--nntreee
Qwen2 7B Instruct
Gemun- 1--7B-it
0.856
0.867
0.836
0.858
0.940
0.009
0.020
Llama- Itttstnnstt
0.644
0,548
0.096
0.791
0.849
0.058
Intemim2 5-7B-hhal
0.782
0.810
0.028
Llama 2-70e-Instrc
0.953
0.960
0.007
0,908
0.931
0.023
Mistral 7B 1B-Instucct-yO.
0.855
0.843
0.012
Qwan2-72B-Instoww
0.675
0.692
0.017
0.762
0.806
0.044
Averuge
Average
0.875
0.871
0.014
Rating
Evaluation Confidence
7.5
6.0
0.8.
4.5
0.6-
3.0
1.5
0.0
GPT
GPT 5.5 Llame3
Liama?
Qwen2
0.2
GPT
do GPT 40
3.5
Liama
Llama
Qwenn 72B
Turbo
10101
Turba
9.0
7.5
1.0.
4.5
0.6
0.4-
1.5
0.0
GPT 4u GPT 4u GPT 5.5 Llame3
Liseue2
GPT 4o GPT 4o GPT 3.5 Liemss
Ulama
Qun?
Turbo
7UB
72B
Turbo
700
708
72B
Default
Chain of Thoughts
Self generated Reference
Figure 3:
Uncertainty analysis of single-answer grading under special prompting strategies on MT-
Bench (first row) and P Test (second row). We evaluate Llama2-7B-Instruu with default prompt, chain-of-thoughts and self-generated reference strategies. See Appendix [ for full results.
4.4 CAN WE EMPLOY PROMPTING STRATEGIES TO MITIGATE UNCERTAINTY?
Prompting is the major approach to solving specialized tasks using LLMss. Prior studies demonstrate that special prompting strategies enhance LLM's performance on downstream tasks by roleplay- ing (Salewski et al. (224),, incorporating contextual information (Pan et 2023) Yang et al. 2024b) and standardizing output formats (Wei al. 2022). To explore whether well-designed prompt can reduce the evaluation uncertainty of LLM evaluators, we conduct experiments using several commonly used prompting strategies, including Default, Chain-of-thouggh and Self-generated reference. The experimental results are shown in Figures and Based on the data presented in Figures and we have the following observations:
(1) Employing special prompting strategies can significantly enhance the evaluation confidence. From the "Evaluation Confidence" subgraphs, observe that special prompting strategies con- sistently lead to higher evaluation confidence across different LLM evaluators. In all experiments utilizing the CoT strategy, evaluation confidence improved notably. We speculate that this improve- ment arises from the structured output formats. By explicitly guiding the LLM through step-by by-step reasoning before making a judgment, reduces ambiguity and uncertainty the evaluation process. While the Reference strategy also yields positive results, its effectiveness is less consistent across evaluators, suggesting that the CoT strategy is more universally applicable and robust.
(2) The CoT strategy seems to alleviate self-preference bias to extent. For instance, shown in Figure 3 when Llama2-709 70B-Instruct evaluates Llama2-7B. InIIrrruct using the CoT strategy, the scores generally lower compared to the Default strategy. This decrease indicates that the evalu- ator, when prompted to generate reasoning first, may become more objective and critical, reducing inherent bias towards the response style and content generated by closely related model.
(3) Using the CoT strategy can enhance the LLM evaluators' abilities to perform fine- seee-graindd as- sessments. As shown in Figure 4 the tie rate decreases in all experiments based on the CoT strategy,

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Win Rate
Tie Role
Evalustion Confideace
1.0
1.0
1.0
0.5
0.4
0.4
OPT do GFT tat
CPT 3.4
3
LinenR
Queal
GPT da GPT
CarT 3.4 Uama
Quena
GPT APT Go 3.5 Liuza' [Amxx Qpen
Ture
1.0
1.0
0.8
0.5
0.0
0.4
0.2
GPT GPT
GPT
Quec
GPT do GPT to GPT Lime
L
Quna
GPT GPT 3.5
Linen? Q
midi
-Trbo -00B
-08
72B
T0B
708
728
miai
Tutoo
700
708
72B
Defanh
Chaic - of Thoughts
Sell generated Reference
Figure 4: Uncertainty analysis of pairwise comparison under special prompting strategies on MT- Bench (first row) and PandaLM Test set (second row). "Win Rate" represents the proportion of non-tie cases where 1lama2-7B-Instruce
response is better than Llama2-132 1in-a---uB-IInsrruttt response. "Tie Rate" represents the proportion of tie cases.
Table 3: Uncertainty analysis with specially trained LLM evaluators on MT-Bench and PandaLM test set. "General LLMs" refers to the average performance of evaluators from Table "Win / Lose / Tie" represents the average number of times Llama2- Mammaa--B-Ineee Instructt'' response is better than, worse than, or equal to Llama2- 13B 13B-IIntructtss 's response.
(a) Single-ansee grading.
(b) Pairwise comparison.
MTT-Bench
Pandal set
MF Bench
Pandal Test
Exalustor
Rating
Evalussion Confidence
Rating
Evaliaaton Confidence
Evalustor
Win Lose
Tee
Evaluation Confidence
Win Lose / Te
Confidence
Evalustion
PundaL
1.59
58.07 40.0
0.704
Prometheuc2-77
59033
0.993
3,187
0.991
Procsetheus2.78
77.5 77.5792.700
0.993
Promotheaa.-kgh--8777
4.725
0,870
6.101
0.887
Pranctheus.Agh--s.77
11.5/33..5// 16.0
0.967
77.07 80.5/ 12.5
8.974
General I.MMs
7.05%
General LLMs
28.3/32.6/ 19,1
0.797
60.7/68.21 /8.2/41111
0,850
indicating that the evaluator is able to perform fine-grained judgments with the generated rationale, allowing distinguish between high-quality responses in complex comparisons. In contrast, al- though the Reference strategy achieves similar effects with GPT-4o and GPT-4o-mini, its benefits less consistent and not observed across other evaluators.
4.5 IS A SPECIALLY TRAINED LLM A MORE STABLE E EVALUATOR?
As discussed Section 4.2 there still a capability gap between an LLM's general performance and its evaluation ability. Improved general capabilities normally do not guarantee better evaluation capabilities. To address this issue, prior work (Kim et al.) 2024a c
Wang et al. 2024b Vu et al.) 2024) focuses on developing powerful LLM evaluators trained on large and diverse collection of high-quality human assessments. Are those specially trained LLMs more stable evaluators? We answer this question by experimenting with 3 open-source evaluators including Prometheus2-7b. Prometheus2-bbb-B2. bbbb-xxbbbbbe and PandaLM (Kim et al., 2024c b) Wang et al. 2024b). The experimental results, as depicted in Table lead the following conclusions:
(1) The Prometheus2-7b and consistently achieve higher evaluation confidence across all experiments compared to both the Gen- eral LLMs and the PandaLM. We attribute this phenomenon to the step-by-step rationale provided by the CoT strategy, which reduces ambiguity in the evaluation process. This phenomenon aligns with the findings from Section 4.4 confirming that using CoT as an output format, whether during inferencing or post-tran post-training, can help alleviate evaluation uncertainty in LLM evaluators.
models, which are trained in a CoT format,
(2) The fine- fine-grained evaluation ability of specially trained LLM evaluators surpasses that of general LLMs, as evidenced by the reduced number of tie cases in pairwise comparison (Table (b). This improvement is likely due to the incorporation of human assessments training data, which en- hances the evaluators' analytical skills. Moreover, in the Prometheus2 models, this benefit is further amplified by the CoT format.
(3) As shown in Table 3a specially trained LLM evaluators appear to be more sensitive to changes in data distribution. When moving from MT-Bench to the Pandal M test set, the scores of the
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Table Data Statistics. The fine-tuning set is sampled from the Alpaca 52K dataset (Taori et al., 2023). Test set (Olympie 2024) is manually cre- ated based on data from the Olympics site Fach instance is annotated by three human evaluators.
19.1%
24.1%
Writing Math
11.8%
Extraction Reasoning Roleplay
Data
#Instances
Annotator Agreement
25.5%
19.5%
Fine-tuning set Test set
694
94.96%
220
97.27%
Figure Categories of test instances.
Prometheus2-7b and mrmmetheus2-bbb-8x. models fluctuate more significantly (from 4.725 to 6.101) compared the general LLMs (from 6.456 to 7.058). Given that Prometheus2-7b and Prometheus2-bbb-8x
are fine-tuned on specialized data, we speculate that this fluctuation is at- tributed to the use of teacher forcing in the evaluator's post-training process (Bengio et al.) [015]] He al. 2021}, which, while enhancing LLMs' evaluation capabilities, may also increase their sensitivity to changes in data distribution.
Based on the systematic empirical analyses mentioned above, we can conclude that the stability of LLM evaluators is a significant issue, with uncertainty permeating various aspects of model- based LLM evaluation ($4.2). Compared to single-answer grading, pairwise comparison reduces the influence of subjective bias by directly comparing the relative merits model outputs, thereby mitigating the uncertainty in evaluation to some extent. Furthermore, due the auto-regressive nature of language models, employing special output formats (such as CoTT) can effectively reduce evaluation uncertainty ($4.4) and $44.5). Our findings corroborate the conclusions of Raina et al. (2024) from different perspectives, providing a nuanced analysis of the uncertainty issue.
5
MAKING USE OF UNCERTAINTY FOR BETTER EVALUATION
As and tailored tasks constantly emerge in real applications, they pose OOD challenges (Yang) et al. [2023] 2024b Liu et al. 2024a) to the capability and stability of LLM evaluators. We consider the problem of whether we can utilize the response confidence of candidate models improve the evaluation capability of LLM evaluators for OOD data. To validate this hypothesis, we first collect ID instances from the Alpaca 52K dataset (Taori et al.) (2023) as the fine-tuning set, based on which LLM evaluator named ConfiLMM, and assess its evaluation ability
we fine-tune an uncertainty-awee on a manually designed OOD test set.
5.1 DATASET CONSTRUCTION
Data collection. Each instance of the fine-tuning set and OOD test set consists of an input tuple (user instruction q, response ri, response confidence of response ú1, response r2, response confidence of response 2 u2) and output tuple (evaluation explanation e, evaluation result p). Following Wang et al. (2024b), we sample 150 instructions from the Alpaca 52K dataset as the instruction source for the fine-tuning
For the OOD test set, manually craft 50 instructions based on data from the Olympics site We identify common categories of user questions to guide the construction, including writing, math, extraction, reasoning and roleplay. For each category, we then manually design 10 instructions. Each instruction is accompanied by an optional reference answer. We showcase several sample instances and instructions in Tables
10 and 12
The response pairs 7B-it (Team al. 2024). (iternlm2.5-7B-chhe (Cai et 2024), Qwen2-7B- (Yang et al., 2024a), and Mistral-7B- In-srruttt... (Tiang et al. (023). For each source instruction, we pair the responses from two instruction-tunet models, resulting in a total 900 unprocessed question- response pairs for the fine-tuning set and 300 for the test set. We then employ the calculation method introduced in tBoo quantify the response confidence u1, U2. Notably, to ensure the quality and diversity of the generated responses, tuned models. Experimental results (Figure (2] indicate that a sampling temperature of 0.7 achieves comparable response confidence that of greedy sampling while maintaining generation diversity.
are produced by various instruction -uned models including Gemma-1. 1.1-
set the sampling temperature to 0.7 for all 4 instruction-
Human annotations. The output tuple of each instance includes a brief explanation e for the eval- uation and evaluation result p. The evaluation result would be either '1' or '2', indicating that
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Table 5: Evaluation performance of 12 evaluators on Olympic 2024. The highest F1 and evaluation confidence of each group is marked by bold.
F1
Evaluatur
Evaluation Confidence
Overall
Writing
Roleplay
Math
Reasoning
Extraction
GPT-44
0.678
0.391
0.761
0.857
0.720
0.641
0.968
GPT-4o-mini
0.677
0.423
0.727
0.820
0.800
0.627
0.986
GPT-3,5-Turbo
0.637
0.505
0.715
0.727
0,646
0.564
0.977
Bammma3-70BInstruee
0.542
0.316
0.627
0.647
0,684
0.377
0.981
Llama2-77B-Inssie
0.534
0.241
0.701
0.546
0.567
0.613
0.973
Swen2-72B-Insttuue
0.631
0.404
0.689
0.867
0.696
0.472
0.978
Prometheus2-777
0.515
0.280
0.703
0.537
0.611
0.307
0.971
Prumetheus2-bgb-B3.
0.556
0.394
0.658
0.641
0.696
0.267
0.965
M-
0.560
0.388
0.677
0.585
0.608
0.455
0.712
IJama3-88 SB-Instruct
0.536
0.267
0.650
0.693
0.635
0.388
0.973
0.582
0.603
0.573
0.333
0.628
0.458
0.979
ConfiLM
0.621
0.723
0.566
0.510
0.670
0.594
0.982
response or response 2 is better. To ensure the quality of human annotations, we involve three ex- perts to concurrently annotate the same data point during the annotation process. These experts are hired by an annotation company, and all annotators receive redundant labor fees. To guarantee clar- ity and consistency, we provide comprehensive guidelines for every annotator, which emphasizes the need to consider the correctness, logical coherence, vividness and confidence of each response.
Data preprocessing. To ensure the quality of the instances and the consistency of human anno- tations. we implement several data cleaning measures, including (I) removing instances that are unanimously deemed low quality or difficult to evaluate by the annotators; (2) excluding special tokens in the responses (c.g.. im_end/ >, <eos> that may introduce bias to the evaluators; (3) adjusting the ratio of label to label to prevent class imbalance. Additionally, given the ongoing concerns about LLMs numerical understanding (Liu & Low 2023). we verbalize each instance's 's un and u2 into natural language statements to avoid introducing additional errors. The ablation result of verbalization is presented in Table 21 The mapping relationship between confidence values and declarative statements is displayed in Table 7 Ultimately, we obtain a fine-tuning set containing 694 high-quality instances and an OOD test set with 220 diverse instances. The annotator agree- ment rates (Table 4) are 94.96% and 97.27%. respectively, We report the distributions of response confidence 21 and U2 from the finetuning set in Figure
5.2 TRAINING DETAILS
Based on the collected fine-tuning set, we fine-tune the Llama3-8B-Instrune by incorporating re- sponse confidence as additional information in the prompt (Figure obtaining an uncertainty-awan LLM evaluator named ConfiLM. During the fine-tuning phase ConfiLM, we use the AdamW [Loshchllov] 2017) optimizer with learning rate of 5e-5 and cosine learning rate scheduler. The GPUs. Notably, to differentiate
model is fine-tuned for epochs on 2 NVIDIA A100-SXM4-88 the effects of fine-tuning and the incorporation of response confidence on the model's evaluation performance in the OOD test set, we remove the response confidence 41 and U2 from all fine-tuning instances and fine-tune the AJama3-SB-Instruue again using the same configuration, with the learning rate set to 3e-5. We refer to this variant model as Llama-3-8B- -est------ntttt---iiiieee- comparison results between different fine-tuning hyperparameters are presented in Figure I1
The performance
5.3 EXPERIMENTAL SETTINGS
To enhance reproducibility, we set the temperature to for proprietary models and utilize greedy decoding for open- source models. For each evaluation, we query the evaluator twice with the order swapped. All general LLM-based evaluators (c.g.. GPT-4o) are required to output in a CoT format. To obtain the best evaluation results, specially trained or fine-tuned evaluators (e.g., M-ndal.M-7BB are assessed using their original prompt and output format.
5.4 EVALUATION PERFORMANCE ON OUT-OFF-DITTIBBTTION DATA
Table presents the evaluation performance of 12 evaluators on Olympic 2024. Our observations in- clude: (1) all L.M evaluators struggle with the Olympic 2024 (with the best F1 score only reaching

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0.678), demonstrating that OOD data poses significant challenges to LLM evaluators' capabilities. (2) ConfiLM outperforms Llama3-88 (lama3-8B-Instruuee 8.5%, respectively. This improvement demonstrates that fine-tuning high-quality human assess- ments enhances I.LMs' evaluation capabilities, and incorporating uncertainty as auxiliary informa- tion significantly boosts evaluator performance in OOD scenarios. (3) Compared to reasoning and math tasks, most evaluators show weaker performance on writing tasks, We speculate that this un- usual trend arises because LLMs can evaluate response from reasoning tasks based on in-distribution knowledge, but fail to make judgement in creative tasks like writing.
and Llama3-8B-Insteee on F1 by 3.9% and
Case study. Due to the presence of sub- tle hallucinations in long texts and the in- herently subjective nature of their evalua- tion, general LLM-based evaluators (such as GPT-4) tend to underperform in writing tasks. We present test sample (Table (6) that illustrates the role of response confi dence in detecting ballucinations of model response (Farquhar et al.) 2024; Varshney et al. 2023). As uineetainty-awaan evalu- ator, ConfiLM reduces the reliability of a re- sponse when detects low confidence, lead- ing to more accurate judgments.
Table 6: Hallucination case. Full version in Table 13
Generate news report: Australia defeated Ireland 40:7 in the Women's Rugby Sevens Quarterfinal on 29/07/2024, securing a Semifinal spot.
Response 1: Women's Rughy Sevens: Australia Cruises
Past Ireland in ... (Confidence: 0.865)
Response 2: match hetween Australia and Ireland took place on 30th July 2024 (Confidence: 0.715)
GPT-4oo: Response offers an engaging report. Bai-------nttutt-innne
Response 2 is detailed. ConfiLM: Response 2 contains incorrect dates.
DISCUSSION
L..M-based evaluation requires a comprehensive consideration of prompt optimization (Zhou al, 2023a 2024a). bias calibration (Zhou et al. 2024b), and uncertainty mitigation strategies. The performance of LLMs as evaluation tools is influenced by various factors, such as the diversity of training data (Shi et al. 2024), inherent model biases (Zeng et al. 2023). and the complexity of the tasks. These uncertainties can cause fluctuations in the consistency of evaluation results. Improving the stability of LLM evaluators can decrease the randomness that may arise during the evaluation process, thus providing more accurate and reproducible results (Chiang & Lee (023).
While our work provides extensive analysis the stability of LLM evaluators, there are other crit- ical aspects of evaluation uncertainty that warrant attention. For examplc. the relationship between evaluation uncertainty and evaluation bias, as well the uncertainty the evaluation of multimodal large language models (Li et al., 2024). Our work only focuses on single-round evaluations. For evaluations conducted on multi-turn benchmarks (i.e., MT-Bench), we use the first-round question as input. It would be interesting to investigate how the uncertainty of LLM evaluators affects judg- ments on multi-round conversations. Additionally, this research does not cover language models that do not provide token probabilities (e.g.. Claude (Anthropic (024)). Exploring how to conduct uncertainty analysis for LLM evaluators based on these proprictary models is a valuable topic. is also important to note that commonly used LLM evaluators require strong calibration to ensure that their output probabilities accurately reflect the precision of their assessments (Chen et al. 2023). We provide analysis of the relation between evaluation confidence and accuracy in Appendix and leave further exploration in those aspects to future work.
B.2
CONCLUSION
In this paper, we empirically investigated the existence, mitigation and utilization of uncertainty in model-based LLM evaluation. Extensive empirical analyses demonstrate that uncertainty is preva- lent across various LLMs and can be alleviated with special prompting strategies such as chain- of-thought and self-generated reference. Experimental results an OOD test set with 220 diverse instances show that incorporating uncertainty as auxiliary information during the fine- fine-tuning process can largely improve the LLM evaluators' evaluation performance. We hope the empirical analyses in this work and the proposed uncertainty-aware LLM evaluator can inspire future research on the stability of model-based I.LM evaluation.
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ACKNOWLEDGMENT
We would like to thank the anonymous reviewers for their insightful comments and suggestions to help improve the paper. This publication has been supported by the National Natural Science Foundation of China (NSFC) Key Project under Grant Number 62336006.
REPRODUCIBILITY STATEMENT
To ensure the reproducibility of our results, we have made detailed efforts throughout the paper. All experimental settings, including model configurations, prompting strategies, and benchmarks, are described in Section $4.1 Additionally, we provide comprehensive information about the dataset construction and training details of ConfiLM in Section $5 Our code, data, and other resources necessary to replicate are released at: http:///tttab..oo/massiiii. TLa=-Baaluatoo--nneeraaaa
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A PROMPTS DEMONSTRATION
All the relevant prompts used in this study are provided in Figures 7 PandaLM and Prometheus2 model are obtained from their GitHub repository
8 and 9
Prompts for
B ANALYSIS
B. DIFFERENT WAYS OF MEASURING UNCERTAINTY
In this paper, used token probabilities to represent the LLM's internal confidence. method inspired by previous works (Varshney et al, 2023; Zhou et al., 20236] Guupta et al., 2024) Kumar let al. 2024). To investigate whether different definitions of uncertainty impact the empirical find- ings, we conducted additional experiments under a pairwise comparison setting on the MT--ench dataset. These experiments involved two commonly used confidence quantification methods: (1) Verbalization--ast based confidence, where we prompted LLMs to directly output calibrated confidence scores along with their responses (Lin et al. 2022. Yona et al., 2024); (2) Consistency- based con- fidence, which involved generating 5/ 10/ 20 responses to the same question and measuring their consistency as proxy for confidence (Tian al. 2023 Xiong et al.) 2023). For these experiments, we set the sampling temperature to 0.7.
In the experiments, the evaluation subjects were Llama2-7B-Insttn and 1amma2113-Instreerr The confidence quantification results are presented in Table [8] Based on the analysis of these results, we observed that the evaluation confidence obtained using different confidence quantification meth- ods follows the same patterns. This further supports the conclusions drawn in Section $4 (1) LLM evaluators exhibit varying levels uncertainty; (2) Evaluations within the same model family demonstrate higher evaluation confidence.
Hib repository for Bow.al////ccccee//gtttboorereeee for Prometheus2 model: http://s////tthhh...o.ooooooonee
GitHub repository
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B.2 THE RELATION BETWEEN EVALUATION CONFIDENCE AND ACCURACY
To investigate the relation between evaluation confidence and accuracy, we analyzed the average accuracy of judgments made by six LLM-based evaluators Olympic 2024 across different con- fidence intervals. The experimental results, as presented in Table 20 reveal a positive correlation between evaluation confidence and accuracy. Specifically, when evaluation confidence is low, the ac- curacy of judgments across evaluators is generally lower across evaluators. As evaluation confidence increases, judgment accuracy improves steadily, reaching peak performance in high-confidence in- tervals (e.g., [0.8, 1.0)). This indicates that models are more reliable in performing evaluation tasks when evaluating with higher confidence.
B.3 THE IN-DOMAIN EVALUATION PERFORMANCE OF CONFILM
In Section } we fine-tuned an uncertainty-aware LLM evaluator named ConfiLM, which leverages the response confidence of candidate models to enhance ConfiLM's evaluation capability for OOD data. To investigate the evaluation performance of ConfiLM on in-domain (ID) data, we re-split its fine-tuning dataset, selecting 94 aanaaa--d instances as an in-domain test set, named Alpaca- 94. Based on the remaining 600 fine-tuning instances, we re-trained the models using the same experimental setup as in Section $5.2 obtaining C-660 and (iama------Instrut--iiii 600 models. Their evaluation performance on Alpaca-94 (II) data) and Olympic 2024 (OOD data) is reported in Table [9 Experimental results from Table 19 demonstrate that incorporating uncer- tainty as auxiliary information significantly enhances the performance of LLM evaluators in OOD scenarios. While ConfiLM M--00s advantage is reduced in ID scenarios, it still achieves evaluation performance comparable to 1lama-3-8B inntruut-finetunne
C DATASET CONSTRUCTION
Each instance of the fine-tuning set and OOD test set consists of an input tuple (user instruction g. response rı, response confidence of response 1 un, response 2 r2, response confidence of response 2 u2) and an output tuple (evaluation explanation e, evaluation result p). The duman-annotar uation result would be either 'I' or '2', indicating that response 1 or response 2 is better. To ensure the quality and consistency of the human annotations, we first selected 100 samples from the dataset for preliminary annotation by two of the authors. This process facilitated the development of well- defined annotation guideline. Then, we hired three PhD-level human annotators from an annotation company to annotate all samples (both the fine-tuning set and the test set) in two rounds: (1) In the first round, two annotators were asked to label each sample based on the established annotation guidelines; (2) In the second round, a third annotator reviewed samples where disagreements arose and provided an extra label. The final label for each sample is determined through majority voting. During the annotation process, samples unanimously deemed low quality or difficult to evaluate by excluded.
eval-
the annotators
Given the ongoing concerns about LLMs' numerical understanding (Liu & Low 2023), we ver- balized each instance's i, and lig into natural language statements avoid introducing additional errors. The mapping relationship between confidence values and declarative statements is displayed in Table 7 Ultimately, we obtained fine-tuning containing 694 high-quality instances and an OOD test set with 220 diverse instances. The annotator agreement rates are 94.96% and 97.27%, respectively. We showcase several sample instances and instructions in Tables 9 10
and 12
D FULL EXPERIMENTAL RESULTS
The full results of experiments introduced in Sections 4 and 5 are displayed in Tables 15 16 and
17 Additionally, to investigate the impact of response confidence on LLM evaluators' evaluation capabilities, we further conducted experiments under two distinct settings: (1) default: providing the evaluator with the complete instance (g. T1, M1, T2, u2) and (2) without confidence: removing the response confidence U1 and U2 from all test instances. All general LLM-based evaluators (e.g., GPT-4o) were required to output in CoT format. To obtain the best evaluation results, specially trained or fine-tume fine-tuned evaluators (c.g., PandaLM-7B) were assessed using their original prompt and output format. Table 14 presents the evaluation performance of 12 evaluators on Olympic 2024.
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Based on the analysis of these results, we found that ConfiLM outperforms Slamma--B-Insttan Finetune and Llama3-8B-Instee Instructt on F1 by 3.9% and 8.5%, respectively. We attributed this im- provement to the incorporation of uncertainty as auxiliary information during the fine-tuning phase. Furthermore, adding uncertainty to the prompts also brings certain performance improvements to general LLM-based evaluators (e.g., 0.690 0.641 GPT-44-Fxxtraction) but these gains unstable due to the LLMs' analytical capabilities.
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Single-answer grading evaluation
[Instruction]
Please act an impartial judge and evaluate the quality of response provided by an Al assistant to the user question displayed below. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of the re- sponse. You should output an overall score on scale cates better overall performance.
9, where higher score indi-
Be as objective as possible. Please avoiding any potential bias. Output your evaluation result and provide short explanation. The output format is: <The rating is: [Rating]. The explanation is: [Explanation]>.
[Question]
finput)
[The Start of Assistantss Answer]
foutput)
[The End of Assistant's Answer]
Single-answer grading evaluation with chain-of-thoughts
[Instruction]
Pleasc act an impartial judge and ovaluate the quality the response provided by an Al assistant to the user question displayed below. Your evaluation should consider factors such the helpfulness, relevance, accuracy, depth, crcativity, and level of detail of the re- sponse. You should output an overall score on scale of 0 to 9, where higher score indi- cates better overall performance.
Be as objective as possible. Please avoiding any potential bias. You should first provide a short explanation your evaluation, and then always end your response with your rating. The output format is: <The explanation is: [Explanation]. The rating is: [Rating]>. [Question]
(input)
[The Start of Assistant's Answer] (output)
[The End of Assistant's Answer]
Single-answer grading evaluation with self-generated reference
[Instruction]
Please act an impartial and evaluate the quality the response provided by Al assistant to the user question displayed below. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail the re- sponse. You should output an overall score scale of 0 to 9, where higher score indi- cates better overall performance.
Be objective possible. Please avoiding any potential bias. You should first generate a short reference answer for the given qucstion, and then evaluate the Al assistant's answer based on your reference answer, and then always end your response with your rating for the Al assistant's answer. The output format is: <My answer is: [Reference Answer]. Based the reference answer, my rating for the Al assistant's answer is: [Rating]>> [Question]
finput)
[The Start of Assistant's Answer] (output)
[The End of Assistant's Answer]
Figure 6: Prompts for single-answer grading. The output format is highlighted in red.
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Pairwise comparison
[Instruction]
Below are two responses for given task. The task defined by the user question displayed below with an Input that provides further context. Please act as an impartial judge and evaluate the quality of the responses. You should choose the assistant that follows the user's instructions and answers
user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level detail of their responses.
Avoid any position binses and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evalua- tion, Do not favor certain names of the nssistants. Be as objective as possible.
The evaluation result is [1] first response better, [2] second response is better, and [Tic] for tie. Output your evaluation result and provide a short explanation. The output format <The result is: [Evaluation Result]. The explanation is: [Explanation]. [Question] (imput)
[The Start of Assistant's Answer)]
Response frespponse
Response 2: trespponse
[The End of Assistant's Answer]
Pairwise comparison with chain-of-thoughts
[Instruction]
Below are two responses for a given task. The task is defined by the user question displayed below with an Input that provides further context. Please act as an impartial judge and evaluate the quality of the responses. You should choose assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity. and level of detail of their responses.
Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evalua- tion. Do not favor certain names of assistants. Be as objective as possible. evalustion result is [I] for tie. You should first provide short explanation of your evaluation, and then always end your response with your evaluation result. The output format is; <The explanation is: [Expla- nation]. The result is: [Evaluation Result]>
response better, [2] second response better, and [Tie]
[Question]
(imput)
[The Start of Assistunt's Answer]
Response I: [respponse_] 1)
Response 2: [respponse_2 2)
[The End of Assistant's Answer]
Pairwise comparison with self-generated reference
[Instructio]]
Below are two responses for a given task. The task is defined by the user question displayed below with an Input provides further context. Please act as impartial judge and evaluate the quality of the responses. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses.
Avoid any position binses and ensure that the order in which the responses were presented does not influence your decision. not allow the length of responses to influence your evalua- tion. Do favor eertain names of the assistants. Be objective possible.
The evaluation result is [1] if first respense botter. [2] if second response is better, and [Tie] for tie. You should first generate short reference answer for the given question, and then evaluate the Al assistunts' answers based on your reference answer, and then always end your response with your evaluation result. The output format is: <My answer is: [Reference Answer]. Based the reference answer, my evaluation result [Evaluation Result]>. [Question]
[input]
[The Start Assistan'ss Answer]
Response I: (respponse 1]
Response frespponse
[The End of Assistant's Answer]
Figure 7: Prompts for pairwise comparison. The output format is highlighted in red.
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Single-answer grading evaluation with PandaLM
[Instruction]
Below are two responses for a given task. The task is defined by the Instruction. Evaluute the responses and generate reference answer for the task.
### Instruction:
[instruction]
fresponse]
#thil Evaluation:
Single-answer grading evaluation with Prometheus2
##tTTask Description:
An instruction (might include Input inside it), response to evaluate, and score rubric resenting evaluation criteria are given.
1. Write detailed feedback that assess the quality of two responses strictly based on the given score rubric, not evaluating in general.
2. After writing a feedback, choose a better response between Response I and Response 2. You should refer to the score rubric.
The output format should look follows: "Feedback: (write foodback for criteria) [RE-
SULT) ([1) [2] or [Tie]))
Please not generute any other opening, closing, explanations.
#WNInstruction: (instruction)
##RResponse (sespponse
#RRResponse [respponse 2)
#toiSoore Rubric: Your evaluation should consider factors such the helpfiulness, relevance, accuracy, depth, creativity, and level of detail of their responses. 'n'n Avoid any position biases and ensure that the order in which the responses were presented does not influence deci- sion. Do not allow the length of the responses influence your evaluation. Do not favor cer- tain names of the assistants. Be as objective as possible. ##He eedback::
Pairwise comparison with Prometheus2
###Taskk Description:
An instruction (might include an Input inside it), response evaluate, reference answer that gets a score of and score rubric representing evaluation criteria are given.
1. Write a detailed feedback that assess the quality of the response strictly based on the given score rubric, not evaluating in generul.
2. After writing feedback, write score that is an integer between and You should refer
to the score nubric.
The output format should look follows: "Feodback: (write foodback for criteria) [RE- SULT] (an integer number between 5)
Please not generate any other opening, closing, explanations. ###The instruction evaluate (input)
##RResponse evaluate: (output)
###Score Rubries; Your evaluation should consider factors such the helpfulness, relevance, accuracy, depth, creativity, and level of detail of the response. Be objective as possible. Please avoiding potential bias.
HHllFeedback
Figure 8: Prompts for PandaLM (Wang et al. 2024b) and Prometheus2 model (Kim et al. 2024c
The output format is highlighted in red.
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Uncertainty-aware fine-tuning
[System Prompt]
Below responses for given task. The task is defined by the question displayed below. Please act as an impartial judge and evaluate quality the responses. You should choose the assistant that follows the user's instructions and answers the user's question better. Your evaluation should consider factors such as the helpfulness, relevance, accuracy, depth, creativity, and level of detail of their responses.
Avoid any position biases and ensure that the order in which the responses were presented does not influence your decision. Do not allow the length of the responses to influence your evalua- tion. Do favor certain The evaluation result is [1] first response is better, [2] second response is better. You should first provide a short explanation of your evaluation, and then always end your response with your evaluation result. The output format is: The explanation is (xn[Epplaaation] result is:EEvalaation Result]s>.
of the assistants. Be as objective possible.
[User Prompt]
User instruction:
finstruction)
Response
<<< [response_ _|}>>
The confidence of Response 1:
<< <rersponse confidence)
Response 2:
<< (response 2}>>
The confidence of Response 2:
<< [<respoone__2 2_ _ocofidence)>>>>>
[Output]
The explanation is:
(evaluation explanation;
The result is:
cnlluation_resllly
Figure 9: Prompts for fine-tuning ConfiLM.
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Table 7: The mapping between confidence values and declarative statements.
Confidence Value
Declarative Statement
[0, 0.1)
Complete doubt
[0.1, 0.2)
Highly uncertain
[0.2, 0.3)
Clearly doubtful
[0.3, 0.4)
Significantly doubtful
[0.4, 0.5)
Slightly doubtful
[0.5, 0.6)
Neutral
[0.6, 0.7)
Slightly confident
[0.7, 0.8)
Clearly confident
[0.8, 0.9)
Highly confident
[0.9, 1.0]
Absolute confidence
50%
43.80% %
40%
33.57%
30%
20%
15.85 %
10%
5. %
0.29%
0.58%
0.86%
0.00%
0.00%
0.00%
0%
[0.0. 0.1)
[0.1, 0.2)
0.3)
[0.3, 0.4)
10.4, 0.5)
0.65.
[0.6, 0.7)
10.7, 0.8)
10.8, 0.9)
[0.9, 1.0)
10.2,
Figure 10: The distribution of response confidence from the fine-tuning set for ConfiLM. The inter-
val [0.0, 0.1) denotes the response confidence is greater than or equal to 0.0 but less than 0.1.
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ConfiLM
Llama
3 8B
instruct
finetune
0.64
0.62
0.60
0.58
0.56
0.54
0.52
0.50
-ep
*+5ep
+6ep
+33pp
+.5 +5ep
+6epp
5e
5e
5e
3e
3e
3e
Figure 11: The evaluation performance of ConfiLM and 1i-ma3-8B-Instrucee combinations of learning rate and epoch. 5e + 3ep represents the combinations learning
under differ-
rate 5e and fine-tuning epoch. We selected the hyperparameter combination that yielded the best Fl evaluation performance in Olympic 2024.
Table 8: An example tokens involved the confidence calculation. We take the probability of the token representing the evaluation result (e.g.. "Tie") the evaluation confidence. For response confidence, we calculate the average probabilities of all generated tokens. We highlight these tokens with red background.
Instruction: Describe a unique trait of the raccoon.
Response
Response
unique trait of raccoons their masked face, which features black ring around each eye and broad black stripe extending from the nose.
unique trait of Raccoon is its ability to open and close its eyes while they closed. This
adaptation helps them stay alert for potential threats even when they re sleeping.
Pairwise comparison for both responses: The evaluation result The trait provided by Response 2 is incorrect. Response 1 provides the correct answer. Response is better than Response 2.
Single-answer grading for response 1: The rating for response 1 is 7.
Single-answer grading for response 2: The rating for response 2
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Table 9: A fine-tuning instance for ConfiLM. The fine-tuning set and the test set use the same instance format, which consists an input tuple (user instruction q, response ri, response confi- dence of response W1. response r2. response confidence of response 2 ug) and output tuple (cvaluation explanation e, evaluation result p).
Instruction Describe unique trait of the raccoon.
Response T1:
unique trait of raccoons their masked face, which features a black ring around each eye and broad black stripe extending from the nose.
Response I's response confidence u1: Highly confident
Response r2:
A unique trait of Raccoon is its ability to open and close its eyes while they closed. This adaptation helps them stay alert for potential threats even when they're sleeping.
Response 2's response confidence Ug: Clearly confident
Evaluation explanation e: The trait provided by Response is incorrect. Response 1 provides the correct answer.
Preference p:
Table 10: Another fine-tuning instance for ConfiLM.
Instruction What is a good way to handle difficult problem?
Response rı:
How can provide helpful assistance in resolving it? Please provide me with the specific problem you are facing, and will do my best to offer suggestions and solutions.
Response I's response confidence u1 Clearly confident
Response r2:
Handling difficult problem can be challenging task, but here
steps that might help: 1.
**Understand the problem**; **; Clearly define the problem and identify its root cause. Break down into smaller, manageable parts if necessary. 2. **Researc***, Gather
Response 2's response confidence Ug: Highly confident
Evaluation explanation e: Response is closer to the user's true intent. Response mistakenly interprets the user's intent as asking for help.
Preference p:
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Table 11:
Examples of user instruction from the Olympic 2024 dataset. Due to space limitations, we truncate the content the Extraction instance.
Writing: Generate news report based on the following sentences: The Men's Water Polo Gold Medal Match took place 11/08/2024 at Paris La Defense Arena, Paris. Serbia claimed the Gold with 13:11 victory against Croatia.
Math: In the Women's 's Synchronised 3m Springboard Final the Paris Olympics, teams from different countries will compete in five rounds. The scores for each round for the athletes from the United States of America are 49.80, 51.00, 71.10, 72.54, and 70.20. The scores for each round for the athletes from Great Britain are 50.40, 46.20, 63.90, 71.10, and 70.68. What is the total score for the athletes from the United States of America over the five rounds, and on average, how many more points did they score per round compared to the athletes from Great Britain? Reference answer: 314.64, 2.472.
Extraction: will provide you with report on a specific Olympic event. Extract the following information from the presented report: the country Sky Brown represents in the Olympics, the sport Sky Brown competes in at the Olympic Games and the age of Sky Brown during the Paris 2024 Olympics. The Report is: For most athletes, the Olympic Games are battle for medals. For 16- year-old Sky Brown, they are also a battle against injuries. "I don't t know what's 's up with that!" the British skateboarder told Olympics.coo Games Paris 2024. "The injury timing is not the best timing. But do feel like I'm just going to get stronger from this." Brown had overcome...
about her injury-plagues plagued months leading up to the Olympic
Reference answer: Britain, skateboard, 16.
In the men's Group A volleyball competition at the Paris Olympics, each team played against every other team once, and the final results are as follows: Serbia defeated Canada but lost to Slovenia, France lost to Slovenia but won against Canada. Canada lost to Slovenia, and France defeated Serbia. Based on this information, please rank these four teams their final standings. Reference answer: Ranking: Slovenia, France, Serbia, Canada.
Reasoning:
Olympic event, and the athletes have just finished their competition. The team you support has won the competition. A reporter approaches you to ask about your thoughts on the event. will provide you with brief report on the event. Based on this information, please respond to the reporter with your impressions of the event and the athlete. The report The Men's Water Polo Gold Medal Match took place on 11/08/2024 at Paris La Defense Arena, Paris. Serbia claimed the Gold with 13:11 victory against Croatia.
Roleplay:
Imagine you
spectator
1.1
Generation Confidence
1.0
0.9
0.8
0.7
0.6
Gemma-1.1-7B..
Intern1m2.5 5-7-hhhh
0.5
7B-ttal-7B-Instructtv
Qwen2-7BB InIstrrcct
0.4
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Sampling Temperature
Figure 12: Generation confidence under varying sampling temperatures. We take the average proba- bilities of all generated tokens as generation confidence and investigate the performance of Gemma- 1.1-7B-it (Tam et al. 2024), Miermln2.5-7B-chal (Cai et al. 2024). Qwen2-7B-Instre et al., (224a)) and Mistral-7B- 7issral-B-Insttuet--ood (Tiang et al. (023) on the Olympic2024 test set. To ensure the validity, we run three experiments with the same settings at each sampling temperature.
(Yang
26

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Published as a conference paper at ICLR 2025
Table 12: A test instance for ConfiLM.
Instruction q: In the Women's +81kg weightlifting event the Paris Olympics, the Chinese athlete successfully lifted 130kg in her first attempt and 136kg in her second attempt in the Snatch category. In the Clean and Jerk category, she successfully lifted 167kg in her first attempt and 173kg in her second attempt, but failed to lift 174kg in her third attempt. The Korean athlete successfully lifted 123kg her first attempt, 127kg in her second attempt, and 13 1kg her third attempt in the Snatch category. In the Clean and Jerk category, she successfully lifted 163kg in her first attempt and 168kg in her second attempt, but failed to lift 173kg in her third attempt. How many more kilograms did the Chinese athlete lift compared to the Korean athlete in their final totals? Reference answer: 10 kilograms.
Response Ti:
**ep I: Calculate the total weight lifted by each athlete. ** Chinese athlete: 136kg (Snatch)
173kg (Clean and Jerk) = 309kg Korean athlete: 131kg (Snatch) 168kg (Clean and Jerk) 299kg. * **ttep 2: Calculate the difference in weight lifted between the athletes. ** Difference
309kg (Chinese) 299kg (Korean) = ** 10kg** Therefore, the Chinese athlete lifted 10kg more than the Korean athlete in their final totals.
Response I's response confidence 4 Absolute confidence
Response 2 r2:
To find out how many more kilograms the Chinese athlete lifted compared to the Korean athlete in their final totals, we first need to calculate the total weight lifted by each athlete. **Chinese Ath-
lete:**_ Snatch: (130kg + 136kg = 266kg) Clean and Jerk: (167kg 173kg 340kg) Total:
(266kg + 340kg 606kg) * Korean *thlete:** Snatch: (123kg + 127kg + 131kg 381kg) Clean
and Jerk: (163kg 168kg + 173kg = 504kg) Total: (38lkg 504kg 885kg) **ooparrsonn **
The Chinese athlete lifted total of 606kg, while the Korean athlete lifted a total of 885kg. There- fore, the Korean athlete lifted (885kg 606kg 279kg) more than the Chinese athlete.
Response 2's response confidence u2: Clearly confident
Evaluation explanation e:
The answer provided by Response is incorrect. Response provides the correct answer.
Preference p:
27

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Published as a conference paper at ICLR 2025
Table 13: Hallucination case. Response 2 contains match date that contradicts the instruction.
User instruction: Generate a news report based on the following sentences: The Women's Rugby Sevens Quarterfinal between Australia and Ireland was held on 29/07/2024. Australia booked a place in the Semifinals with a 40:7 win.
Women's 's Rugby Sevens: Australia Cruises Past Ireland in Quar- terfinall n'The Australian Women's 's Rugby Sevens team secured their place in the Semifinals with a dominant 40-7 victory over Ireland in the Quarterfinal on Saturday afternoon. \n) nTee match started with Australia showcasing their attacking prowess, scoring four unanswered tries in the first half. Their clinical execution and strong running game proved too much for Ireland, who strug- gled to contain the Australian onslaught. nI'isrish resistance finally came in the second half, with a try of their own. However, it was too little, too late. Australia responded immediately with two more tries secure their comfort- able victory. , "We are thrilled to advance to the next stage.)" said Aus- tralian captain, Bianca McLean. \"The girls played with tremendous spirit and executed their game plan perfectly. We are confident that we can build on this performance and achieve even greater things in the Semifinals. \ ("(nn) nAustralia will face either New Zealand or Fiji in the next round. The winner of that match will go on contest the final on Sunday. n * Additional Notes:**1 nn n* The match took place on 29/07/2024, \n* The score was 40-7 in favor of Aus- tralia. \nx Australia booked place in the Semifinals.
Response I:
Response confidence 1: 0.865
Response 2: **Title: Australia Triumphs in Women's Rugby Sevens Quarter- finals, Advances to Semifinals n 30/07/2024 (n n Locatton: HHott City/Venue]*** (, [H City, July 30, 2024] _** In a thrilling display of rugby prowess and determination, the Women's Rugby Sevens Quarterfinal match between Australia and Ireland took place on 30th July 2024, culminating in decisive victory for the Australian team. \nn m*n**Match Overview:* n'Th highly anticipated showdown between Australia and Ire- land began with a palpable sense of intensity from both sides. The Aus- tralian team, renowned for its strength and strategic gameplay, took control early on, setting a robust defensive stance against the Irish team's aggres- sive tactics. n' First Half Highlight: nn nn,TTTouuuhhuu the first half, Aus- tralia's s attacking dominance became apparent. [Player Name], a crucial mem- ber of the Australian squad, showcased exceptional skills, scoring several cru- cial tries that paved the way for Australia's substantial lead. The Australian pack also executed precise forward play, creating openings for the backs to ex- ploit. \nn "in**Second Half Drama:** **) n'Ettrrnn the second half, Ireland dis- played remarkable resilience, attempting to claw back the lead through a series of well-executed plays. Their scrum-half [Player Name] managed to breach the Australian defense, scoring much-needed try for Ireland. However, the Australian team's 's robust defensive formation and tactical adjustments quickly stifled any further Irish progress. \n Turning Point:**\, (n nn critical mo- ment in the game came when [Player Name], an Australian fullback, inter- cepted an Irish pass, sprinting down the field to score a try. This play, combined with the Australian team's 's unwavering strategic discipline, sealed the match in favor of Australia. \n n *iinal Score:**) ,) The match concluded with Aus- tralia emerging victorious with a commanding score of 40:7. The resounding Response confidence 2: 0.715
GPT-4o:
The explanation is: Response 2 offers a more thorough and engaging report, despite the missing ending. The result is: [2]
Explanation: Response 2 is more detailed and
considers more aspects Evaluation result: 2.
ConfiLM: Explanation: Response 1 is more informative and accurate, and it does not contain factual errors such as incorrect dates. Evaluation result:1.
28

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Published as a conference paper at ICLR 2025
Table 14: Evaluation performance on Olympic 2024. The highest Fl and evaluation confidence marked by bold. Green and red are used to indicate whether the evaluator's performance improved or diminished by the incorporation of model confidence, respectively.
F1
Evaluation Confidence
Evaluator
Overall
Writing
Roleplay
Math
Reasoning
Extraction
GPT-4o
0.653
0.332
0.704
0.809
0.732
0.690
0.960
w/o confidence
0.678
0.391
0.761
0.857
0.720
0.641
0.968
GPT-4o-mini
0.687
0.478
0.774
0.761
0.812
0.570
0.979
confidence
0.677
0.423
0.727
0.820
0.800
0.627
0.986
GPT-3.5-Turbo
0.425
0.672
0.606
0.654
0.626
0,976
w/o confidence
0.637
0.505
0.715
0.727
0.646
0,564
0.977
-lama3-70B-Instrue
0.511
0.387
0.570
0.608
0.440
0.965
w/o confidence
0.542
0.316
0.627
0.647
0.684
0.377
0.981
0.562
0.452
0.685
0.482
0.583
0.522
0.974
w/o confidence
0.534
0.241
0.701
0.546
0.567
0.613
0.973
Qwen2-72B-Instruuc
0.597
0.413
0.730
0.620
0.648
0.472
0.976
w/o confidence
0.631
0.404
0.689
0.867
0.696
0.462
0.978
Prometheus2-7B
0.515
0.280
0.703
0.537
0.611
0.307
0.971
Tromerheus2-bgh-8111
0.556
0.394
0.658
0.641
0.696
0.267
0.965
Pandal M-7B
0.476
0.483
0.428
0.436
0.576
0.325
0.712
Alama3-88-Instruus
0.545
0.284
0.674
0.677
0.610
0.610
0.980
w/o confidence
0.536
0.267
0.650
0.693
0.635
0.388
0.973
-lama--8B-Insrruct-fe Instruct-finctune
0.582
0.603
0.573
0.333
0.628
0.458
0.979
ConfiLM
0.621
0.723
0.566
0.510
0.670
0.594
0.982
Full result of uncertainty analysis of single-answer grading on MT-Bench and PandaLM test set. The scoring range is 0-9. The evaluation subject is Llama2-7B-Instruct The Prometheus2 series models are trained to output in a Chain-of-Thought format (providing concise rationale before indicating a preference between the two outputs) Kim al. 2024c).
Table 15:
(a) MT-Bench
Default
Chain-of-Thouue
Self self-generated Reference
Evaluator
Average Rating
Evaluation Confidence
Response Confilence
Average Rating
Response Confidence
Average Rating
Evalustion Confidence
Response Confidence
Confidence
GPT-4o-2024
25-4-05523-
5.413
0.417
0.945
4,988
0.681
0.945
4.738
0.637
0.915
GPT-4o-mini-2024U0
1--mmini-222407---1
6.038
0.605
0.944
5,113
0.833
0.944
4.500
0,800
0.944
Turbo
6,288
0.629
0.944
5.925
0.703
0.924
5.650
0.632
0.944
1aam-227708- I-sraat
7.875
0.953
0.945
6.775
0.979
0.915
7.563
0.931
0.925
Qwen2-72B Instruct
5.875
0.675
0.946
5,550
0.752
0.946
5.175
0,777
0.946
Prometheux2-78
5,963
0.993
0.946
momethens2--gh-Beee
4,725
0.870
0.945
Average
0.930
(b) PandaL Test set
Defoult
Chain-of-Thowee
Self-generated Reference
Evaluator
Average Rating
Evaluntion Confidence
Response Confidence
Average Rating
Evalustion Confidence
Response Coufidence
Average Rating
Evalutton Confidence
Response
Conlidence
GPT-1o-2024-05-13
6.541
0.473
0.955
6,400
0.935
6.082
0.637
0.934
JPT--4-mini 2024-07 07-14-7-8
6.641
0.645
0.936
6.229
0.861
0.915
6.406
0.792
0.916
G-T::.5-Tubb
6.971
Llamu-3-700 Instrrrstr
7.424
0.548
0.957
7.453
0.975
0.907
6.965
0.964
0.927
Llama-2 2-ttt-nsttat
7.924
0.960
0.934
6,965
0.966
0.934
7.741
0,930
0.934
Qwen2-728-lostreed
7.153
0.692
0.955
7.306
0.841
0.935
6.900
0.861
0.935
Prometheus2.77
7.187
0.991
0.937
Doometheu2--bg--KK0
0.936
Average
7.058
0.652
0.936
6.704
0.912
0.933
6,853
0.802
0.930
29

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Published as a conference paper at ICLR 2025
Table 16: Full result of uncertainty analysis of pairwise comparison MT-Bench. The evalua- and
tion subjects are Llama2-7B-Instee evaluator twice with the order swapped. 'Win Lose / 'Tie' represents the average number of times Llama-2-7b-chat' response is better than, worse than, or equal to haama-2-13b-chas response. The PandaLM model (Wang et al. 2024b) is trained to output in normal format (providing preference between the two outputs. followed by concise rationale). The Prometheus2 series models (Kim al., 2024c) are trained output in Chain-of- Thouuhh format (providing concise rationale before indicating preference between the two responses).
For each evaluation, we query the
(a) Default prompt
Default
Evaluator
Evaluation Confidence
Response Confidence
Win
Lose
Tie
GPT-4o-2024-05-1
10.0
16.5
53.5
0.699
0,950
0,949
1e:4o--ini-2222-0---1
27.0
43.5
9.5
0.776
0.950
0,948
GPT-3.5-Tubo
38.5
35.0
6.5
0.848
0.945
0.949
Bamma-3-70B-Isstrree
39.5
3.0
0.791
0.937
0,950
Lluma-2-70B-Insiee
33.0
34.0
13.0
0.908
0.950
0.950
Qwen2-72B Instruct
22.0
29.0
29.0
0.762
0.939
0,949
PundaLM--BB
42.0
28.5
9.5
0.617
0.949
0.939
Averuge
35.2
30.5
14.3
0.707
0.947
0.944
(b) Chain offin-of-Theee Thoughsss
Chuin-of-Thought
Evaluator
Evaluation Confidence
Response Confidence
Win
Tic
B
209-44--024-05-11
25.0
42.0
13.0
0.940
0.949
01949
GPT-4o-mini-2024-0
39.5
37.0
3.5
0.990
0.950
0,948
GPP-3.5-TTuhh
37.0
38.5
4.5
0.924
Llama-3-70B- Instruct
38.0
37.5
4.5
0.999
0.947
0.950
Llama-2-70B- 7-770---Isttuct
36.0
37.0
7.0
0.991
0,950
0.950
Qwen2-72B- Insttuct
30.5
32.5
17.0
0.988
0.949
Prometheus2-7B
37.5
42.0
0.5
0.990
0,951
Prometheus2-bbb-B777
31.5
32.5
16.0
0.967
0.948
0.950
Averuge
34.4
37.3
8.3
0.977
0.949
0.950
(c) Self-generated reference
Self-generated Reference
Evaluator
Evaluation Confidence
Response Confidence
Win
Lose
Tic
B
201-44-2024405-11
21.5
31.0
27.5
0.799
0.949
0.949
GPT-4o-mini20024 2024----222--7-11
32,5
37.0
10.5
0.793
0.950
0..48
GPT-b.5-Tuub
31.5
15.0
0.802
0.950
0,949
L Instruct
34.5
4.5
0.991
0.947
0,950
Llama-2-70B 2-700-Insttuut
27.5
25.0
27.5
0.956
0.950
0.950
Qwen2-72B I2s-rustt
28.0
27.5
24.5
0.944
0.949
0.949
Average
29.3
32.5
18.2
0.881
0.949
0.949
30

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Published as a conference paper at ICLR 2025
Table 17: Full result of uncertainty analysis of pairwise comparison and PandaLM test set. The eval- For each evaluation, we query the
uation subjects are Alama2--B-Instree and Maama2-1B-Instruus evaluator twice with the order swapped. 'Win / Lose / 'Tie' represents the average number of times Llama-2-7b-chats response is better than, worse than, or equal to Llama-2-13b--he PandaL model (Wang et al., (2024b) is trained to output in normal format (providing preference between the two responses, followed by concise rationale). The Prometheus2 series models (Kim al., 2024c) are trained output in Chain-of-Thoughtt format (providing concise rationale before indicating a preference between the two responses).
response. The
(a) Default prompt
Default
Evaluator
Evaluation Confidence
Response Confidence
Win
Lose
Tie
GIPT-40-0024-05-13
30.0
38.0
102.0
0.809
0.932
0.941
GPT-4o-mini-2024-
2aainii-224-7---- 07-1----
53.0
61.0
56.0
0.820
0.938
0,940
GPT-3,5-Tubo
81.0
12.5
0.884
0.930
0.940
Llama-3-70B-Imsee
78.0
86.5
5.5
0.849
0.941
0.941
Llama Llama-2-70B-
2-70B-Instrec Instruct
72.5
73.0
24.5
0.931
0.929
0,940
Qwen2-72B
Dwen2-72B-Insstrue
54.0
70.0
46.0
0.938
0.940
M-77
58.0
72.0
40.0
0.704
0.942
Average
70.1
40.5
(b) Chain-of Thouhhss
Chain-of- Thoughts
Evaluator
Evaluation Confidence
Response Confidence
Win
Lose
Tic
GPT-46-2024-05-1
63.0
92.5
14.5
0.966
0.940
0,940
(TT-4o-mini-2224-11
82.5
86.5
1.0
0.996
0.939
0.941
GPT-3.5-Tube
82.5
79.5
8.0
0.962
0.941
0.940
Bamna-3-70B-lsstaeee
71.0
4.5
0.999
0.941
0,941
Lluma-2-70B-Insse
79.0
72.5
18.5
0.986
0.939
0.940
Qwen2-72B Instruct
63.5
83.0
23.5
0.992
0.938
0,940
Prometheus2-77
77.5
92.5
0.0
0.993
0.940
0,940
mmmeetheu22-hgh-o.
77.0
80.5
12.5
0.974
0.941
0.939
Average
76.0
85.9
8.1
0.984
0.940
0,940
(c) Self-generated reference
Self-generated Reference
Evaluator
Evaluation Confidence
Response Confidence
Win
Tic
GPT-4--2024-0-11
47.5
59.5
63.0
0.774
0.940
0,940
GPT-44--imi-2024-077
72.5
0.800
0.941
GPT-3.5-Tubb
65.5
63.5
41.0
0.809
0.941
0.936
1lama-3-70B- 1770--Insttuc
68.0
94.5
7.5
0.997
0.941
0.941
Llama-2-70B-
47.0
67.5
0.964
0.939
Qwen2-72B-Instreen
56.0
70.5
43.5
0.947
0.938
0.940
Average
60.1
70.7
39.9
0.882
0.940
0.939
Table 18: The evaluation confidence results with different quantification methods.
Evaluator
Logit-based
Verbalization
Consistency-5
Consistency-10
Consistency-20
GPT-4o
0.699
0.764
0.751
0.725
0.696
GPT-4o-mini
0.776
0.725
0.771
0.736
0.735
GPT-3.5-Turb
0.848
0.755
0.828
0,790
0.804
Mama---70B-Insttue
0.791
0.808
0.846
0.833
0.778
Llama-2-700 1-mna-2-70B-Bo Inst-untt
0,908
0.856
0.911
0,915
0.891
Qwen2- 2onn--22--nnttuet
0.762
0.730
0.765
0.717
Average
0.797
0.773
0.812
0.786
0.760
31

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Published as a conference paper at ICLR 2025
Table 19: Evaluation performance on Alpaca-94 and Olympic 2024.
Dataset
Con6iL.M-600
Llama-3--B--mmtrrc--htttuunuee
-lama-3-8B-Instrucc
Alpaca-94
0.581 0.577
0.585
0.518
Olympic 2024
0.535
0.519
Table 20: The relation between evaluation confidence and evaluation accuracy on Olympic 2024.
Evaluator
[0.0, 0.2)
[0.2, 0.4)
[0.4, 0.6)
[0.6, 0.8)
[0.8, 1.0)
GPT-4o
0.000
0.250
0.333
0.625
0.684
GPT-4o-mini
0.000
0.333
0.222
0.625
0.721
GPT-3.5-Turbe
0.125
0.333
0.400
0.556
0.634
Llama-3 Hlama-3-70B--a 7-0B-Instruc
0.000
0.000
0.200
0.364
0.680
1amma-2-70B-nme
0.000
0.000
0.000
0.267
0.579
Qwen2-72B-Inse InIItrucct
0.000
0.500
0.571
0.600
0.668
Table 21: The evaluation performance of ConfiLM with different fine-tuning formats.
Settings
Score on Olympic 2024
Numerized Confidence
0.505
Verbalized Confidence
0.621
32


Reviews:
[{"review_id": "ZPcujNakmI", "reviewer": "Reviewer_Yumv", "summary": "While the importance of measuring and handling uncertainty and confidence with LLMs is a known and well-researched topic, this paper seems to be the first to analyse uncertainty and evaluation confidence within the particular 'LLM-as-a-judge' (LLMJ) setting. It runs a series of experiments that yield a series of empirical observations related to uncertainty of LLMs when used as evaluators, and then it aims to show that incorporating uncertainty modeling directly into the process of creation of LLM-based evaluators can yield more confident and better-performing evaluators. Evaluations are conduced with a reasonable number of well-known open-weights and API-gated models, within (i) direct-scoring and (ii) pairwise preference setups. The authors then propose an uncertainty-aware fine-tuning process and create such an uncertainty-aware LLMJ model ConfiLM which shows benefits in evaluations on OOD data.", "questions": "- Is there any relationship and/or correlation between uncertainty in the responses of the evalauted mopdels and uncertainty of the evaluator models? How does uncertainty of the evaluated model reflect on the final scores?\n- I liked the finding showing how evaluators are more confident with responses coming from models within the same family. Is there a way to also mitigate this 'uncertainty bias' through fine-tuning as well?\n- It seems that 'Ties' cause a lot of trouble with confidence - how would discarding the 'Tie' option from the preferences output impact the results and the main findings? I would recommend adding an experiment checking on this.  \n- ConfiLM shows benefits with OOD data. Are there any benefits with in-domain or related-domain data or is the approach useful only in OOD scenarios?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The first paper that empirically examines the role of uncertainty within the context of LLMJ, offering a series of empirical findings that motivate the creation of an uncertainty-aware LLM evaluator.\n- Despite the large number of experiments, it is quite clear what the focus is in each of the experiments, and it's good to see some intuitions properly empirically verified.\n- The choice of underlying model is quite good, which helps with generalising some of the empirical findings.", "weaknesses": "- The paper adopts a simplified view on recent 'LLM-as-a-Judge' (LLMJ) literature, skipping some related work that aimed to improve confidence of LLMJ models via calibration (https://openreview.net/pdf?id=L3FHMoKZcS) or better prompt optimization (PO; https://arxiv.org/pdf/2406.11370). Improving LLMJ methods requires a multi-component/multi-aspectual approach, which requires combinations of prompt optimisation, calibration and uncertainty mitigation strategies, and the paper would be much stronger with additional experiments that aim to approach the problem in full scope, without reducing it only to uncertainty mitigation. NOTE: This has been corrected in the author response\n- This also means that it would be extremely useful to measure how uncertainty/confidence levels change when different bias mitigation or calibration or PO methods get applied. Do we need to handle uncertainty to the same extend and with the same benefits when it gets combined with other methods?\n- Speaking of simplifying the experimental protocol too much, there are also many potential approaches to measuring uncertainty, and taking only the logit as the proxy towards uncertainty, while grounded in some related literature, might still be too simple. I would recommend exploring different ways of measuring uncertainty (e.g., see https://arxiv.org/pdf/2404.15993 or https://arxiv.org/abs/2307.10236) and checking whether different definitions of uncertainty also have impact on the final findings (and to what extent). The decision on how we measure/capture uncertainty is a big assumption that seems to stay under the radar of this work. NOTE: This has also been mitigated with the author response.\n- Evaluation should get increased to more and more standard LLMJ datasets, including e.g., RewardBench and standard summarization and chat datasets used in prior work (SummEval, HANNA, etc). \n- Minor: the paper spends too much introducing the basics of evaluation with LLMs (e.g., a large part of RW is too long) - that paper space could have been better used for some finer-grained experiments (e.g., understanding the relationships between calibration and certainty or introducing another way to measure uncertainty or some other future work ideas now listed in lines 521-529).", "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": "FHUrH3mqsq", "reviewer": "Reviewer_mJNs", "summary": "The paper probes the stability of LLMs-as-Judges by leveraging their internal uncertainties and the confidence levels of the responses of models being evaluated. Single response and pairwise comparisons schemes are compared, where confidence levels are computed based on the token probabilities.  The empirical study includes a variety of LLM evaluators, datasets, and assesses several prompting techniques, including CoT method. The work shows how different prompting strategies can diminish evaluation uncertainty and how uncertainty can be  utilized to improve the reliability evaluators in OOD scenarios. An uncertainty-aware evaluator \"ConfiLM\" is fine-tuned on a human-annotated dataset, then tested on a new OOD test set sampled from the 2024 Olympics. Findings suggest that incorporating uncertainty significantly improves evaluation accuracy under OOD context.", "questions": "1. The paper explains how to compute evaluator and response confidence separately. it was not initially clear that the response confidence is solely utilized for the fine-tuning of ConfiLM and not combined with the evaluator confidence.\n2. Could the authors clarify how the results from the human annotators are aggregated? \n3. In situations involving pairwise comparisons of models from two distinct families, the log probabilities can span different ranges. Did you consider any recalibration methods to address this issue?\n3. Does improving the confidence metrics within LLM evaluators guarantee improvements in their practical evaluation abilities? is this a to be expected outcome?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper addresses a timely and increasingly relevant issue, the stability of LLMs-as-Judges. While the use of log probabilities as a measure of confidence is not novel in itself, the original contribution lies in its application within the context of evaluators. It investigates methods on how to improve the evaluators confidence and even recognize incorrect responses. \nThe work is significant for its practical approach to improving LLM evaluator reliability, especially in OOD scenarios. The findings could impact the deployment and trustworthiness of automated evaluators in various applications.\n\nThe paper is clearly written, with a well-organized structure that helps with following the multiple methodologies and conducted experiments. Limitations are also acknowledged.", "weaknesses": "- Previous studies, such as those by Lyu et al. [1], have shown that log probabilities do not always correlate with human preferences. This raises concerns about the reliability of using these metrics in LLM-as-Judge systems, which have become popular for their scalability and cost-effectiveness in automating evaluations that traditionally relied on human feedback. The paper could further explore how improving model confidence affects agreement with human evaluators. either via CoT or fine-tuning,  \n\n- The methodology assumes access to internal model probabilities, which might not be feasible with proprietary models. This limitation, acknowledged in the paper, constrains the generalizability and scalability of the proposed methods.\n\n[1] Lyu, Chenyang, Wu, Minghao  and Aji, Alham. Beyond Probabilities: Unveiling the Misalignment in Evaluating Large Language Models. In Proceedings of the 1st Workshop on Towards Knowledgeable Language Models (KnowLLM 2024)", "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": "JYI3q2Y1kI", "reviewer": "Reviewer_BN93", "summary": "This paper investigates the uncertainty in LLM-as-Judge evaluations. Specifically, they use the token probabilities for uncertainty estimation, and find that: 1) the uncertainty estimated in this paper is prevalent across LLMs and varies with model families and sizes. 2) the evaluation confidence of LLM evaluators exhibits sensitivity to changes in data distribution. 3) Specific prompting strategies can alleviate evaluation uncertainty to some extent.", "questions": "see weaknesses", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- Since the paradigm of LLM-as-judge has become widely adopted for evaluation purposes, it is important to conduct an in-depth analysis of the stability of this evaluative framework.\n- This paper conducts extensive empirical analyses across multiple models and datasets, offering results that can help researchers deepen their understanding of various models as evaluators.", "weaknesses": "- In my opinion, the main issue with this paper is my uncertainty regarding **whether its research methodology adequately supports the conclusions it claims to draw**. \n  - As demonstrated in the introduction, the core research question of this paper is \"Can large language models provide consistent evaluation quality across different inputs and domains?\" However, I am not convinced that the token probabilities predicted by the models sufficiently reflect the \"evaluation quality\" the authors aim to investigate. For instance, we can see that GPT-4o-mini exhibits significantly higher average prediction probabilities than GPT-4o across various datasets, can we truly infer that GPT-4o-mini possesses superior \"evaluation quality\"?\n  - The token probabilities of large models are influenced by numerous factors, such as the training data, input information, and alignment methods. Relying solely on token probabilities as a measure of uncertainty may affect the reliability and generalizability of the conclusions drawn. A model with a higher output probability is likely just over-confidence.\n  - In my opinion, rather than an evaluator that consistently outputs results with high probability, what we require is a well-calibrated evaluator, one whose output probabilities accurately reflect the precision of its assessments.\n- The authors claim that this is the first study to investigate uncertainty for LLM-as-judge paradigm. However, many prior studies have also addressed the analysis of evaluation uncertainty, albeit employing different methods for estimating uncertainty. For example, position bias refers to the evaluator providing inconsistent evaluation results when the positions of candidate responses are swapped. This, too, is a method for estimating the uncertainty of an evaluator.", "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": "fCvLtIaRgc", "reviewer": "Reviewer_2uFv", "summary": "The paper mainly discusses uncertainties in evaluations/generations of LLM-based-evaluators. The major contributions of this paper are: \n- First, an in-depth evaluation uncertainty of various models across 2 types of tasks (direct-assessment, pairwise-evaluation), 3 prompting strategies (Default, CoT, Self-generated-Reference), 6 LLMs and 2 Benchmarks\n- Finetune a new uncertainty aware LLM-evaluator (ConfiLM), that shows lesser uncertainty while evaluating responses.\n- The authors also augment the model with a new OOD test set curated from the Olympics website to assess the models for this task.", "questions": "- When training the second model, `Llama-3-8B-Instruct-Finetune`, why was the learning rate lowered to 3e-5? If anything, for consistency and comparison, the exact same setup as `ConfiLM` should be used, by just removing $u_1$ and $u_2$. \n- What happens when $u_1$ and $u_2$ are not verbalized? That would really be an interesting find. Will the model gain more insights from the exact numbers or falter as per previous works? The confidences are converted to discrete classes (Table-8) is slightly dubious as close values on the boundaries of these classes (ex. 0.59, 0.61) see an abrupt jump, which I understand is unavoidable. That's why, a simple experiment without this verbalization should also be studied. \n- What is the distribution of $u_1$ and $u_2$ in the finetuning set?\n- I feel a very significant portion of the paper is dumped in the appendix. Without referring to the examples in the appendix Table 7-12) the write up about the Olympics Testset and `ConfiLM` evaluation is quite unclear and incomplete. I really urge that content be added to the main paper itself. \n- The speculation on line 393 is unclear and needs further support. \n- Also, why is the confidence modelled as an arithmetic mean, and not a geometric mean? Geometric mean provides a tighter estimate of the probability, and also goes along with the language-modelling objective.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Firstly, I appreciate the dataset and model created in this paper. These can surely benefit the community in future research in this domain. \n- The paper is well-written and provides cogent and coherent arguments till the end. \n- The problem discussed in the paper is also quite interesting and important as there is a significant shift towards LLMs as evaluators, however, there are several uncertainties and interpretability issues associated with those judgments, that need to be acknowledged and studied in depth. \n- The paper aggregates several tiny established yet undocumented/poorly documented ideas into one place as a formal work.", "weaknesses": "- The paper claims to the first to study uncertainties in LLMs as evaluators, which might be incorrect given a previous work already delves in to the same topic of inaccuracies: [Finding Blind Spots in Evaluator LLMs with Interpretable Checklists](https://arxiv.org/abs/2406.13439). I really urge the authors to acknowledge this work in the Related Works section and show the difference with the current work. \n- Somehow, I fail to see the use of `Self-Generated Reference`. What is the rationale behind it as compared to `Default` and `CoT`? Also, if the LLM-evaluator has to generate a \"good\" reference answer, it should first be well-versed with the domain and possess enough knowledge, and this might be difficult of smaller models. For example, the Olympics test set might be OOD for the evaluator as well, and the generated reference answer also might not be optimal, and this might lead to an inaccurate evaluation. \n- The paper lacks novelty in some places and feels like a reiteration of existing facts, i.e., most of the findings in section 4.2 are well-known and documented. For example, the second point on self-bias is a long-standing idea and has been proven across multiple tasks and models. Also, there have been several discussions across LLMs excelling at `LMSys ChatBotArena`, however they fail on general tasks. and the last line in the third point of Section 4.2 is also obvious as evaluation is a hard task, and unless models are explicitly trained for it, they will not be suitable for it. Similarly, evaluation is a thorough reasoning task, as the evaluator has to take a proper decision based on the criterion, and input content, so `CoT` performing well in such a case is not a surprise. But, going by my last point in the Strengths, I do not wish to penalize the paper much for this, as these findings are known, but poorly documented, and this paper does a good job of collating them in one single research with appropriate justifications and experiments. \n- While building `ConfiLM`, I see that the training instances are < 700 for an 8B model, and FFT was used to train the model. This is slightly concerning as the generalization of the model might be quite less, and there is a good chance of overfitting, especially with 6 epochs. Were any regularizations put into place during this finetuning?", "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)