Beyond the Surface: Enhancing LLM-as-a-Judge Alignment with Human via Internal Representations
Authors: Peng Lai
Jianjie Zheng
Sijie Cheng
Yun Chen
Peng Li
Yang Liu
Guanhua Chen
Venue: NeurIPS 2025 poster ()
Keywords: llm-as-a-judge
llm evaluator
Primary area: evaluation

Abstract: The growing scale of evaluation tasks has led to the widespread adoption of automated evaluation using LLMs, a paradigm known as “LLM-as-a-judge”. However, improving its alignment with human preferences without complex prompts or fine-tuning remains challenging. Previous studies mainly optimize based on shallow outputs, overlooking rich cross-layer representations. In this work, motivated by preliminary findings that middle-to-upper layers encode semantically and task-relevant representations that are often more aligned with human judgments than the final layer, we propose LAGER, a post-hoc, plug-and-play framework for improving the alignment of LLM-as-a-Judge point-wise evaluations with human scores by leveraging internal representations. LAGER produces fine-grained judgment scores by aggregating cross-layer score-token logits and computing the expected score from a softmax-based distribution, while keeping the LLM backbone frozen and ensuring no impact on the inference process.
LAGER fully leverages the complementary information across different layers, overcoming the limitations of relying solely on the final layer.
We evaluate our method on the standard alignment benchmarks Flask, HelpSteer, and BIGGen using Spearman correlation, and find that LAGER achieves improvements of up to 7.5% over the best baseline across these benchmarks. Without reasoning steps, LAGER matches or outperforms reasoning-based methods. Experiments on downstream applications, such as data selection and emotional understanding, further show the generalization of LAGER.

Beyond the Surface: Enhancing LLM-as-a-Judgg Alignment with Human via Internal Representations
Peng Lai', Jianjie Zheng', Sijie Cheng', Yun Chen', Peng Li?, Yang Liu?, Guanhua Chen
Southern University of Science and Technology. TTinngu University 3 Shanghaii University of Finance and Economics
Abstract
The growing scale of evaluation tasks has led to the widespread adoption of auto- mated evaluation using LLMs, paradigm known "LL--as-a-juugee" However, improving its alignment with human preferences without complex prompts or fine- tuning remains challenging. Previous studies mainly optimize based on shallow outputs, overlooking rich cross-layer representations In this work, motivated by preliminary findings that middle-to-upper layers encode semantically and task- relevant representations that are often more aligned with human judgments than the final layer, we propose LAGER, a post-hoc, plug-and-ple framework for improv- ing the alignment of LLM-as-a-Jude point-wise evaluations with human scores, by leveraging internal representations. LAGER produces fine- mne-grained judgment scores by aggregating cross-layer score-token logits and computing the expected score from a softmax- -ased distribution, while keeping the LLM backbone frozen and ensuring no impact the inference process. LAGER fully leverages the comple- mentary information across different layers, overcoming the limitations of relying solely on the final layer. We evaluate marks Flask, HelpSteer, and BIGGen using Spearman correlation, and find that LAGER achieves improvements of up 7.5% over the best baseline across these benchmarks. Without reasoning steps, LAGER matches or outperforms reasoning- based methods. Experiments on downstream applications, such as data selection and emotional understanding, further show the generalization of LAGER.
method the standard alignment bench-
Introduction
Large language models (LLMs) have witnessed significant progress in various tasks like math reasoning Ying al. 2024 Duan Wang 2024) and open-domain question answering (Allemang
Sequeda 2024) exhibit great generalization and reasoning abilities on unseen tasks and domains
(Li al.
2024c Ye 2024 Ni al. 2024), which makes possible evaluate model generations
with an LLM (Bavaresco et al. Zheng et al., 2023). LLM-as-a-judde (Lin & Chen 2023 Li
[ct al. 2024a| Wu al. [024] Shiwen et al. 2024), an emerging approach to text evaluation, uses large language models to perform automated and scalable assessment of textual responses, reducing the reliance on human annotation. This paradigm has found widespread applications
various scenarios
such as model evaluation (Lin & Chen 2023), data synthesis (Kim et al. 20224a] Cui et al. 2023b
Wang et al. 2024b), and model enhancement via verification and critic agents (Pace et al. 2024
Badshah & Sajjad 2024).
Researchers have explored various approaches improve the consistency of judgment with human
experts. Prompt- based methods (Lin & Chen 2023: Liu et al. 2023) improve the judge performance
with guidelines encouraging step-by-step reasoning (Chen et al. 2024 Lin Chen 2023 Zhuo 2024)
Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Figure 1: (a): Vanilla scores may overlook meaningful distinctions by relying solely on the most probable score token. Better evaluation requires leveraging deeper signals beyond surface-level outputs. (b): The framework of LAGER. LAGER fully considers candidate score probabilities and aggregates cross-layer logits, enabling LLMs to act as robust evaluators with probabilistic scoring for reliable assessment.
carefully curated examples (Song et al.) 2025). However, these methods rely chain-of-thought reasoning, which introduces additional computational cost (Gu et al. 2024). Other researchers propose to finetune LLM with specialized dataset (Ye et al.) 2024a Cui al. 2023a adapt
the LLM to the judgment task. Although effective, these methods face the generalization problem
(Doostmohammadi et al. 2024) they have been adapted to the domain of the training data.
In this paper. we propose an effective LLM-as-a-judge framework called LAGER, to enhance LLM- as-a-Judge alignment with human via internal representations. Inspired by prior studies (Wang et al.) 2020 Yang et al. 2022 Roh et al. 2024) showing that middle-to-uppe layers encode richer semantic and task-specific information, By applying a weighted combination followed by softmax, we obtain probability distribution over candidate scores, from which the final score is computed the expected value. LAGER leverages the semantic diversity across different layers, allowing the final score to integrate both low-level lexical cues and high-level reasoning signals, thereby providing a more comprehensive reflection of the model's understanding of the scoring task. LAGER is plug-and-play, leaving model parameters and next-token predictions unchanged. LAGER outperforms baselines alignment benchmarks such as Flask, HelpSteer, and BIGGen, with improvements of to 7.5% in Spearman correlation. Although reasoning- based evaluation methods provide more transparency by exposing intermediate reasoning steps, their reasoning is often shallow and fails to improve reliability, leading to inferior performance. contrast, without explicit reasoning, LAGER achieves comparable or superior results to these reasoning- based baselines. We further select instruction data with LAGER method and achieve better performance on the AlpacaEval-2.0 benchmark than various baselines. Experiments on more downstream applications show the effectiveness of the LAGER method.
propose to aggregate the logits of score tokens from different layers.
2 Preliminary
decoder-only LLM f consists of embedding layer femba, I decoder layers f and an output projection layer funcmbd- Given an input instruction x, the model generates response y through the
Our code is publicly available at huthtts:: http://wwww..eeeuuuuteeeee//////

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following computation:
y= = f(x) = funembu fasodder
f(1) f (2);
(I)
all decnder layers
where o denotes function composition, i.e., (f (x) f(((x)). To predict the next token 2;, the model typically relies on the hidden state produced by the final decoder layer, denoted
h (L) d
(
where Tec = (#1,..... 1i-1) represents the sequence of previous tokens. The output logits for token Iy are then computed as:
2, = fueembd h (2)
When incorporating general LLM as the judge for a model response, the prompt template includes the evaluation task description Tds user instruction z;, the response to evaluated Ty. and the scoring criteria and output format requirement Te (Liu et al. [223 2024 Hu et al.) 2024a). We denote the full input as X {ard, Ti, Fr, Je). and the set candidate scores as $ C where the model's vocabulary. Let hn (4) denote the final-layer hidden state at the position where the score token is to be generated (e.g., after "Score:"). The model produces output logits:
nn = funemba (h.")).
which are then passed through a softmax over the model's vocabulary V:
exp(2n (!]
Pt(t|X, Σrev (xp(2.(("))
(4)
The score token with the highest probability is the final score. referred to as the vanilla score:
arg max (s(ssX,Ven)) SEB
(5)
Figure 1 a) shows that vanilla overlooks informative score distributions by relying solely the top-probability score token, limiting its ability to distinguish response quality. More reliable and fine-grained evaluation requires the use of deeper internal representations beyond surface output.
Methods
3.1 Motivation
Hidden representations across different layers have been widely observed to exhibit distinct characteristics: the bottom layers focus more on local lexical information, while the middle and
LLaMA-3-8B-hstruuc
0.6
Spoaman Correlation
(Spsumert
0.4
top layers focus more on semantic and global in-
0.2
formation Wang et al. 2020 Yang al. 2022
Roh et al. 2024: Sun et al. 2025). ). Previous works (Sun al. 2025 Alabi et al. (2024) using techniques such as PCA and shared-space anal- ysis have shown that middle-layer hidden states are highly consistent and interchangeable across language adaptations, suggesting shared rep- resentation space. Thus, they can be directly transformed to logits with the shared LLM output unembedding layer f funembd-
0.0
10
20
30
0
10
20
30
Layer Index
Layer Index
Figure 2: Agreement Between Human Ratings and Internal Layer Scores of Different Models.
Previous works on LLM-as-a-Juder predominantly rely on the final-layer hidden state, while ignoring the intermediate representations across layers. Hence, investigate the judge scores derived from hidden representations at different layers to better understand the layer-wise evaluation behavior. Specifically, the logits at the let ( L.) layer be computed follows:
2 funcmba decoder
(fll))
(1) deccdeer femba (w)))) funembal (h("),,
(6)

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Following Equation 4 we can obtain the probability distribution P( X,, Ven)over the vocabulary for each token, which allows us to compute the final judge score at the 4eh layer:
87 = arg max V(())
Following the above setup, we conduct evaluations of different models' layer-wise scoring per- formance across multiple benchmarks and analyzed their alignment with human judgments. The results in Figure 2 show consistent pattern across various benchmarks and models: one or more intermediate layers yield better agreement with human evaluations than the final layer.
In this paper, we focus point-wise LLM evaluators without reference responsc. Inspired by preliminary observations, we explore incorporating the hidden representations from intermediate layers improve the judge score estimation. We propose the LAGER framework to enhance the consistency with judgment from human experts while maintaining the generalization ability of the LLM evaluator, and achieve better alignment with human score distributions.
3.2 Score Estimation Based on LLM Hidden Representations
For improved formality and clarity, we rewrite the LLM output unembedding layer funemba as W unembdd so & can rewrite as:
2 = (1)
decoder o Feemtaa (n W unembd = h W unembd-
((1)
(8)
Based on the results in Figure 2 identifying consistently well-performing layers is challenging, as the layers exhibit varying levels of alignment with human judgments across different datasets. To address this, we first aggregate the logits corresponding the set of candidate scores S from different layers using a set of weights = embedding layer. The above procedure can be represented as:
(Wo, w wr where wo corresponds to the output of the
Wi
we W unemhdd
caleulate integer judge score. However, illustrated in Figure [bb, instead of relying on single token, the full probability distribution over score candidates can be leveraged to capture richer evaluative information. This yields probability distribution the discrete score set, from which we compute a continuous, fine-grained score by taking the expected value. Therefore, we first extract the logits corresponding all candidate score tokens from the full vocabulary logits and then aggregate them:
following Equations 4 and
L.
1
1Mlg
Σ 2=0
w
Σ ==0
wi [h W unnembalM:
(10)
where M = ("ookenizes)]ls E 8) denotes the set of tokenized sequences from S. The final probability distribution of S is then obtained by applying a softmax over the aggregated logits:
exp (xp(2[s)) [s)
P(s)
E
(11)
Σ. es (x1))
by taking the expectation over the score distribution, we can obtain the final fine-grained judge score:
E P(s)
Σ x P(s).
(12)
SEB
Normalizing before aggregation removes the relative scale information of logits and overemphasizes less important layers. We compare both settings in the ablation study (Section 4.3)
For certain layers, if the calculated scores are identical across all samples, the Spearman correlation cannot be computed; such cases shown missing points in the figure.

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3.3 Lightweight Training of Layer Weights
We propose two types of layer weights w. One is to apply average aggregation wy = 1/(L (denoted LAGER (w.o. tuning) in Table the other is to tune the lightweight L + 1 parameters (L is the number of transformer layers) with a small-scale validation set (denoted as LAGER (w. tuning)). With frozen backbone and minimal learnable parameters, to distinguish from finetning-basee based LLM evaluators. To enhance the model's s performance while closely with the distribution of human scores, adopt combination of
refer the dataset as validation set
aligning its predictions cross-entropy(CE)) loss and mean absolute error (MAE) loss, balanced by a weighting hyperparameter a.
F = o. -CE + (1 -x) LAAA
18
8
[8|
=
[(s = smuth log Ps(s) + (1--a
(s]
S rruth)
B
2|
(13)
where B is the batch of samples in a training step, and Strath is the numan-annotarn score for each sample. Please refer to Appendix E. for specific training settings and details. It is important to note that the weights are tuned only once for each backbone and subsequently applied across all benchmarks and downstream tasks. As the L.M remains frozen, no additional judge model is needed for scenarios like sef--improeement. Our method is implemented without altering the model's next-token prediction process or logits, thereby offering plug-and-pla, capability, In contrast, finetuning-baas based methods require domain-specific judge models and suffer from limited generalization due to scarce labeled data.
3.4 Discussion: Applicability under Restricted Access Settings
While LAGER relies on accessing the intermediate layers of the LLM, it can naturally adapt to more restricted scenarios. For instance, when only final-layer logits are available (e.g.. API-based models), we can extract the logits corresponding to score tokens, apply softmax, and compute the expected score (this method proposed in G-Eval (Liu al.) 2023)). ). We refer this setup as expectation score (E-Score). The evaluation uses the vanilla score, based on the most likely token, when only the final token prediction is observable. Both settings can be viewed as simplified special cases within our framework. We treat both scores comparable baselines in our experiments. Nonetheless, powerful open-source models still remain the mainstream for large-scale evaluation due to their lower cost and performance comparable to closed-source models (Lambert al. [024]] Gu et al.) Malik et al. 2025), making LAGER broadly applicable and easily extensible to future models.
2024
4 Experiments
4.1
Experiments Setup
Benchmarks. Due to potential preference leakage (Li et al.) 2025) between models, we evaluate our method on human-annotated datasets for reliable results. We chose three diverse point wise Flask (Ye et al. 2024a), HelpSteer (Wang et al.) 2023), and BiGGen Bench") (Kim et al. 2024b). In these benchmarks, human-annotated scores range from 1 to 5. Please refer to Appendix E.2 for the details.
benchmarks to ensure a comprehensive evaluation:
Models. We experiment with multiple backbone models of varying sizes and from different families, including Mistral-7B Mistral-7B-Innttuut--ddl (Jiang et al., 2023a). InternLM3-88 MM-M----BInsttue (Cai et al. 2024).
LLaMA3.1 B.aMMA..--BBIIsttre -nB-Innttruct (Grattationi et (0024). Qwwn-2.5-144-Innstee (Qwen et al.) 2025
Mistral-
Small-24B-Innstree and LLAMA-3.3-70B 3-0.---------.
Baselines. We compare LAGER with three baselines: GPTScore, vanilla score (VScore) and expectation score (E-Score). At the same time, we compare the commonly used API-based model GPT-40-mini. We also experiment with methods that explicitly train the LLM backbones, namely TIGERScore-7B and Prometheus2-7B. While LAGER does not modify the backbone models, these
hutss//iieeiiiiiccooeeeeeessoses Bench- Results Resut-
5

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Table 1: Spearman Correlation Results: LAGER vs. Baselines on Flask, HelpSteer, and BiGGen Bench. These results are statistically significant, with p-values less than le-5, See Table for the full Pearson correlation results.
Flask
HelpSteer
BIGGen Bench
Model
Average
Direct
Reasoning
Direct Reasoning
Direct
Reasoning
Fine-tuned Models
TIGERscore-7B
0.175
0.118
0.171 0.367
0.155
Prometheus2-7B
0.413
0.514
0.431
Close-source Model via API
GPI-4o-mini
Vscore
0.526
0.535
0,482 0,500
0.535 0.541
0.534
0.509
0.520
R-Score
0.579
0.561
0.573
0.530
0.547
Open-source Models
GPTScore
0.258
0.183
0.217
Vscore
0.266
0.269
0.364
0.138
0.280
0.264
E-Score
0.239
0.279
0,296
0.380
0.185
0.277
LAGER (w.o tuning)
0.338
0..995
0.401
0.377
0.353
0,329
0.349
LAGER (w. tuning)
0.347
0.298
0.403
0.376
0.357
0,333
0.352
LLaMA3.1-80-Imss
GPTScore
0.061
-0,022
-0.162
-0.041
Vscore
0.334
0.429
0.374
0.518
0.273
0.390
0.386
B-Score
0.386
0.446
0.464
0.525
0.352
0.403
0.429
LAGER (w.o tuning)
0,472
0.456
0.520
0.524
0.475
0.443
0.482
LAGER (w. tuning)
0.477
0.460
0,515
0.524
0.482
0.444
0.484
Intern IM3-8--nsttruct
GPTScore
-0.087
-0,022
-0.257
-0.135
Vscore
0.423
0.449
0.388
0.425
0.374
0.441
0.417
E-Score
0.515
0.472
0.453
0,430
0.470
0.470
0.468
LAGER (woo tuning)
0.449
0.468
0.426
0.429
0.374
0.469
0.436
LAGER (w. tuning)
0.545
0.489
0.515
0.474
0.507
0.490
0.501
Owen-2.5-14B-Instree
GPTScore
0.001
-0.014
-0,122
-0.052
Vscore
0.547
0.537
0.420
0.423
0.458
0.461
0.474
E-Score
0.579
0.555
0.447
0.452
0.502
0.457
0.499
LAGER (w.0 tuing))
0.572
0.567
0.433
0.473
0.503
0.507
0,509
LAGER (w. tuning)
0.612
0,572
0.443
0.472
0.567
0.524
0.531
Mistral-Small--2BB-nntttue
GPTScore
0.016
-0,008
-0,147
40.046
Vscore
0.528
0.505
0.420
0.459
0.542
0.533
0.498
B-Score
0.577
0.532
0.442
0.486
0.585
0.555
0,530
LAGER (w.o tuning)
0.591
0.542
0,452
0.485
0.589
0.562
0.537
LAGER (w. tuning)
0.596
0.542
0.449
0.487
0.598
0.566
0.540
LLAMAA-33-70B--mssrrru
GPTScore
0.042
0.014
-0.193
-0,066
Vscore
0,518
0.567
0.435
0.494
0.559
0.539
0.519
E-Score
0.464
0.540
0,444
0.488
0.530
0.495
LAGER (w.o tuning)
0.610
0.598
0.520
0.597
0.569
LAGER (w. tuning)
0.611
0.598
0.504
0.519
0.602
0.584
0.570
methods are included solely for reference and are not directly compared. Please refer to Appendix E.3 for specific details about the baselines.
Evaluation Metrics. Following previous works (Gu et al. 2024 Bai et al. 2023 Liu et al. 2025 ) we
use the commonly adopted Pearson and Spearman correlations to measure the consistency between LLM-predicted scores and human annotations. See Appendix E.4 for further details.
Evaluation Details. We adopt greedy decoding for its stability and consistency in evaluation (Lin Chen 2023). To comprehensively assess the effectiveness of our method, we conduct evaluations under two different conditions: Direct: Directly providing score during evaluation without reasoning. 2) Reasoning:
Previous work (Liu et al. [023 Wang et al.) 2024a] Hu et al. 2024a) shows that reasoning improves judgment quality, with reasoning- setups performing best
et al. 2024 Murugadoss et al. 2024 Gu et al. 2024). Thus, we adopt reasoning -irst approach in this study. The prompt template used in our work follows the standard configuration widely adopted
in prior studies (Kim al. 2024b Liu et al. 2023 Xu et al. 2023), please refer to Appendix G for

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the prompt templates. Unless otherwise specified, we highlight the best results in each table using bold, and denote the second-best with underlining.
4.2 Main Results
Tables I report Spearman results of LAGER compared baselines across three benchmarks. Sec- tion further analyzes the performance variation of LAGER and baseline methods across different model scales, under the setting where models from the Qwen2.5 family are used as frozen backbones, and compares their results on the same set of benchmarks. Specifically, LAGER (w. tuning) achieves near-best performance on these benchmarks and demonstrates strong stability, so it serves the main approach in our work.
The Effectiveness and Scalability of LAGER. LAGER with tuning consistently outperforms all non-training baselines across diverse LLM backbones on all three benchmarks. This highlights the importance of leveraging internal logits and output distributions for accurate scoring. Although Sastral-Saall-24-IInnttt and Qwen2.5-14Bh 10wen2.5-14B-Instruce underperform GPT-4o-mini on Vscore, they achieve comparable results when using LAGER GPTScore performs poorly due its reliance on generation probabilities, which overlook the semantic and logical quality. Due to its focus on егтоr detection, the fine-tuned TIGERscore-71 shows relatively limited performance. Compared the fine-tuned Prometheus2-7B, LAGER also enables BarrmLMM--BB-Inttrue and LLaMA3. I -8--Instruct, two models of comparable size, surpass it even though they initially have weaker performance on Vscore. Even without tuning. LAGER outperforms E-Score in 5 out of 6 backbone models, with an average improvement of 4.5%. the few cases where underperforms, the performance gap is within 3% Moreover, it consistently outperforms V-Score.
The Robustness of LAGER. The average E-Score performance of models like Qwen-2.5- 2.5--1B- Instruct, -LAMA-3.3-708% Iostttuuttt,tttt and Mistral Besstra--BBIIssiiie In--nntuuct--.... is sometimes lower than VScore. Specifically, the average E-score performance of LLAMA-3.. 3.3--33---ii-- 3-Btt-insttuct across all benchmarks is 2.4 points lower than Vscore. In contrast, LAGER with tuning achieves almost the best performance across all settings and benchmarks, consistently outperforms Vscore. LAGER can closely match human score distribution and incorporate more fine-grained information. More details are discussed in Section 5 Therefore, we primarily recommend the LAGER with tuning approach and conduct subsequent analyses based on it. The performance gains of LAGER stem not from large-scale fine- tuning, but from a more efficient and structured utilization the model's s internal representations.
Reasoning Is Not Always Better. The richness of information aggregation increases gradually from Vscore, E-Score to LAGER (with uning). Figure 6 shows that reasoning leads to an improvement in Vscore performance, divergence in E-Score performance (with half of the models improving and the other half declining), and consistently weaker results for LAGER (with tuning) under the reasoning setting compared to direct. We speculate that this phenomenon may be due to reasoning potentially causing the model become overconfident (Yang et al.) 2024; Wagner et al.) 2024), which in turn leads to inaccurate evaluation scores. This is also consistent with the findings of previous work (Gie et al. 2025 Guo et al. 2024) Li et al. (002d)): As the reasoning steps progress, the model's focus the original imput and the text be evaluated gradually diminishes, shifting more toward its self-generated reasoning trajectory.
Table 2: Ablation Study Results on FLASK and HelpSteer Datasets Evaluated by Spearman Corr.
Strategies For LAGER
InternalLM Flask
Mistral
ID
Exp.
Max.
Logits agg.
Proh. agg.
Tuning
HelpSteer
Flask
HelpSteer
0.545
0,515
0.347
0.403
2
0.452
0.448
0.299
0.344
3
x
/
0.373
0.374
0.268
0.264
4
x
X
/
0.367
0.379
0.268
0.267
5
V
0.449
0.426
0.338
0.401
6
V
X
0.442
0.445
0.306
0.358
X
X 0.379
0.367
0.265
0.264
x
X
0.363
0.268
0.267
9
V
0.515
0.453
0.239
0.296
0
x
X
0.423 X
0.388
0.266
0.267
7

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4.3 Ablation Study
To better understand each design choice of LAGER, we conduct a comprehensive ablation study on the direct setup using Baatrral----Isstuttt--oo and InternLMM-88B --Istrutt Table shows the results of the Spearman correlation. The expectation (Exp.) score and the maximum (Max.) score are alternative designs. Given the score distribution of certain layer, we use Eqn 12 to calculate the expected score or use the score with the highest probability. Logits agg. and prob. agg. are two alternative designs, aggregating information from all hidden layers at the logits level or output distribution level. Removing logits agg. and prob. agg. indicates that we do not use internal states. It is observed that the full configuration (Exp. score Logits agg. Tuning) achieves the best performance across all settings, with a maximum Spearman correlation of 0.545; Fine-tuning brings up to +0.10 improvement; expectation scoring outperforms maximum scoring (up to +0.17); and logits aggregation surpasses probability aggregation (up to +0.07). Multi-layer integration is generally effective, especially for Mistral; however, in untuned settings, InternalLM occasionally performs better without aggregation, indicating model-spe model-specific differences.
5 Analyses
5.1
Understanding Internal States
Mistrall7B-instructtoo
1.0
LLaMA.3-8B-Innae
1.0
Cosine Similarity Heatmap
Spearman Correlation
0.5
0.4
-X
Helpdroer [Speamman
Fask Spcoman)
3.8
Sprarmnn Correaatio
0.5
0.4
5.8
1900
0.3
0.3
0.2
0.2
2.4
-.4
0.1
0.0
0.2
0.0
0.2
500
20
30
10
20
30
Layer Index
Layer Index
(a)
10
Instruct- V0.3 using HelpSteer and Flask. (a) and (b) illustrate the performance of E-scores computed from different layers. (c) depicts the average cosine similarity heatmap of hidden states across layers.
Figure 3: Analysis of Llama3. 1-8B-Inntruce and -i-stret---Instruut--
Having observed that internal states contribute significantly to the success of LAGER, we now aim to understand how internal states in each layer contribute to the judgment score. Specifically, we apply LAGER to each layer of the backbone LLM, namely using the expected score from the output distribution of each layer, and report the consistency with human scores. Figure Jiluustttlsstrttt the results of the -B-itt--t---sst
and L.L.MA-3.1 ---8B-IInstree backbones. We observe the following: (1)The bottom layers exhibit low even negative correlation with human scores, indicating their limited utility in evaluation tasks. (h) middle-upper layers (approximately layers 20 to 30) show the highest correlation with human scores, suggesting they carry the most informative representations for judgment. However, there is a drop in correlation at the topmost layer, implying that certain judgment-relevant signals may be diluted lost in the final transformation stages. Thus, relying solely on the top layer is insufficient for precise evaluation.
To better understand the differences between internal and top layers, we visualize the cosine similarity between hidden states across layers at the position of the score token using the Flask and HelpSteer datasets. Based on Figure c), the similarity between layers generally decreases as the distance between layers increases. For the bottom layers, the representation changes rapidly with increasing layer number. In contrast, the representation changes relatively slowly for the middle-upper layers, and the representations across these layers remain similar over a broader range. The topmost layer exhibits low similarity to its neighboring layers, displaying distinct pattern.
Based on the above observations, we believe that: The middle-upper layers exhibit relatively consistent representations and stronger alignment with human scores, indicating that these layers may deserve more attention. Meanwhile, the topmost layer shows comparatively weaker judgment ability, likely because its focus on next-token prediction leads to the loss of fine-grinned evaluative information. Instead of searching for optimal layers, which vary across LLM backbones and are hard to identify, LAGER directly learns a weighted combination of all layers. This approach
8

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Spearman Correlation Qwen2.5 Models (direct condition)
flask
happSaer
BiG Bench
2.7
Venill
3.-
LAGENIA
65-
3.5
544
0.3
23
50-
01
Figure 5: Comparison of Spearman Results for Qwen2.5 Models Across FLASK, HelpSteer and BIGGen Bench Using Vanilla Score, E-Score, and LAGER (w. tuning) (Direct Condition).
both lightweight and effective, requiring only small validation and transferring well across benchmarks (Section 4.2 Appendix D.I Appendix D.2) and tasks (Section 6.1 Appendix D).
5.2 LAGER Yields More Human- Aligned and Fine-Grained Score Distributions
To better understand how LAGER improves over both the VScore and the E-Score, we evaluate LLaMA-3.1-8 Instruct on the Flask dataset to obtain the Vanilla Score, E-Score, and LAGER, and visualize the min-max normal- ized scores and human annotations using Gaussian kernel density estimation (KDE). Details of the KDE visualiza- tion procedure can be found in Appendix E. Figure 4 visualizes the score distributions. Compared to E-Score and VScore, LAGER yields distribution that more closely matches human judgments, with noticeably higher over- lap. LAGER mitigates the high-score bias of VScore and E-Score by shifting the score distribution to the left and producing more evenly distributed scores.
KDE Plot Different Score Distributions
Vanills Score
E-Score
Human
LAGER(W. tuningl
Densiy
Normalized Score
Figure 4: The KDE Plot of Different Score Distributions, evaluated on Flask with
backbone.
We also quantitatively compare LAGER, E-Score, and VS- core by evaluating the Kullback-Leibler (KL) divergence and the mean squared error (MSE). The KI. divergence of a candidate score 5 is computed as DKL (Pu.lll) where Ph. and P. represent the human score distribution and the candidate score distribution, respectively. The results in 3 demonstrate that LAGER more accurately approx- scores.
Table 3: Distribution distance of VScore and LAGER to human score, evaluated on Flask with LLaMA-3.1 1.---- 1-B---8B--mm -nn-trruuttttt backbone.
LLaMA-3.1 --18--IIIsttue
Dkr.(L)
MSE(L)
VScore
0.312
0.112
E-Score
0.102
0.092
imates the distribution of
LAGER (w. tuning)
0.087
0.060
5.3 From Tiny Huge: LAGER Brings Improvements Across Model Scales
To further investigate whether LAGER can enhance human alignment across broader range of model scales, we conducted experiments using three benchmarks on instruct models varying sizes from the Qwen2.5 family, including 0.5B, 1 1.5B, 3B, 7B, 14B, 32B and 72B.
The Figure 5 and Figure show the alignment effectiveness of Vanilla Score, E-Score, and LAGER (w. tuning) across Qwen2.5 models from 0.5B to 72B. Both direct and reasoning conditions show mostly upward trend in Spearman correlation coefficients as model size increases across Flask, Helpsteer, and BIGGen datasets, with LAGER leading (e.g., 0.658 in Flask for direct, 0.598 for reasoning). When the model size exceeds 14B, LAGER achieves greater performance gains over the backbone model than the VScore computed using GPT-4o-mnni Notably, on the BIGGen dataset, LAGER shows significant improvement on the 0.5B model scale, elevating the Spearman correlation from negative value (-0.4 for the Vanilla Score) to a positive 0.1, marking substantial gain compared to the baseline. These results demonstrate its effectiveness across different model scales and datasets, and the benefits brought by LAGER are scale-tramm traesfrranfe and synergistically amplified as model capacity grows.

---

Table 4: The Performance of LLaMA3-80 LaaMA338B-BBss Fine-tuning with Instruction Data Subsets on AlpacaEval 2.0: Sength-Controoi (LC) win rate against evaluated with GPT-4o-mini.
(805 Test Examples),
AlpacaEval-2.0
Filtering criteria
Ratio
LC win rate average length
No filtering
100%
7.73
1070
Longest instructions
10%
6.92
946
Highest VScore
10%
9.42
1206
Highest E-Score
10%
11.50
1282
SuperFitering
10%
10.69
1367
Longest responses
10%
11.82
1506
Highest LAGER (w.o. tuning)
10%
11.77
1325
Highest LAGER (w. tuning)
10%
12.65
1248
Applications of LAGER
6.1 Instruction Data Selection
Instruction data selection (Cao et al. data from given instruction dataset to enhance both the efficiency and performance of the tuning process. In this experiment, we use LAGER as scoring metric to select a 10% subset from the alpaca-cleaned-522 datase (Taori et al. 2023). We compare our subset, Highest LAGER, with four baselines on finetuning the LLaMA3-8B-ball model: Longest instructions, Longest responses (Shen) 2024). Highest VScore, and Superfiltering (Li al. (2024)). SuperFiltering is an explicitly designed instruction data filtering method. For methods that require a backbone LLM, we utilize LLaMA3.1- 8B-Instruct for fair comparison. More details are in Appendix
2024 Shen 2024) involves choosing subset high-quality
As shown in Table our method with tuning achieves the best performance, outperforming the second-best method, the Longest responses, and the explicitly designed method, SuperFiltering, by 0.83 and 1.96 LCC win rate, respectively. Even without tuning, our method outperforms most baselines, improving the VScore by 2.35 LC win rate. And the highest LAGER (w tuning) has relatively shorter average lengths than most baselines. This indicates that our tuning model does not achieve better scores by generating longer responses, but by learning to follow instructions more effectively.
In addition the application mentioned above, LAGER be applied other scoring-basse tasks, such as LLM emotional understanding and LLM Recognizing its Knowledge Boundaries. LAGER shows strong transferability, even when there is mismatch between the task's 's scoring range and that of the data used for training. Please refer to Appendix D.I and Appendix D.2 for detailed discussions.
7 Conclusion
In this work, propose LAGER, effective LLM-as-a-judge framework to estimate the judge score from the logits information from different LLMM layers. LAGER offers training-free and tunable options, allowing flexible integration with various LLMs to deliver fine-graine judgment services. Unlike previous methods that explicitly update LLM backbones, LAGER provides a lightweight tuning solution that only trains weights on a small validation dataset, and the learned weights can be transferred across tasks. Experiments on three comprehensive alignment benchmarks demonstrate the effectiveness of LAGER. Specifically, LAGER outperforms all baselines that do not explicitly train LLM backbones. Additionally, LAGER demonstrates strong performance in improving alignment with human annotations across models of varying scales and families. Even without explicit reasoning. LAGER outperforms various reasoning-buse -baed baselines. including those specifically trained for reasoning tasks, while requiring fewer generation tokens and offering higher efficiency. LAGER is quite general and can be applied to various use cases, including but not limited to instruction data selection, recognizing its knowledge boundaries and emotional understanding.
10

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Acknowledgements
This project was supported by National Natural Science Foundation of China (No. 62306132). Guangdong Basic and Applied Basic Research Foundation (No. 2025A151501 1564), Natural Science Foundation of Shanghai (No. 452R140 We thank the anonymous reviewers for their insightful feedback this work.
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A Impact Statement
Limitation Our method relies on obtaining the hidden states from all model layers during the training and evaluation phases. This requirement means full internal access to the model's architecture and intermediate representations essential for optimization. Consequently, the method is applicable and can be optimized only for open-source models, where such internal states are accessible. In contrast, for closed-source or proprietary models, where access to internal hidden states is typically restricted, our method cannot be deployed to improve performance, limiting its applicability in those scenarios.
Wc affirm that this research adheres to the ethical standards in Al and machine learning. No personal, sensitive, proprictary data was used in the experiments. All datasets employed are publicly available and widely used in the research community. Our code is publicly available, and all experiments reproducible. We have carefully considered the potential societal impacts and are committed to applying the method responsibly, ensuring it has a positive and controllable impact on society.
Ethics Statement
Future Societal Consequences Our approach relies on comprehensive access to the internal states of models, which has profound implications for the future ecological landscape of Al development. As open- source models continue to evolve, this method helps drive the democratization of performance optimization, enabling researchers to improve models transparently and collaboratively, fostering innovation, and enhancing the accountability Al systems. However, it cannot be applied to dlosed-souree or proprietary models, highlighting the growing gap between open and closed Al ecosystems and potentially increasing dependence on few dominant providers. Furthermore, since this approach is primarily used for improving judgment models, there is a potential risk of misuse, such interfering with or manipulating evaluation results, reminding us to be mindful of possible negative impacts when promoting its application, ensuring responsible and controlled use.
B Related Work
B.1 Evaluation of Text Generation Tasks
Over the past decades, automatic evaluation metrics, including statistical methods and embedding-based approaches, have played a crucial role in assessing the quality of generated text. The metrics BL.EU (Papineni
ct al.
20X02) and ROUGE (Lin) (004) have long been standard for evaluating generated text. BERTScore (Zhang
2020) evaluates the similarity between two sentenees by using pre-trained BERT model to generate
contextual embeddings for each token and calculating the sum of their cosine similarities. BART (Yuan)
el al.
202T) evaluates the quality of generated text by calculating the weighted logarithmic probability of
one text given another text. Chung et al. (2023) found that these metrics cannot be accurately evaluated for semantically cquivalent expressions but syntactically different. Therefore, trying to evaluate harder- generrttd text requires more efficient methods. GPTScore (Fu et al. (023) evaluates text quality through conditional generation probabilities, enabling customizable assessments using natural language instructions. However, these methods all require reference answers for a stable evaluation.
B.2 LLM-as-a-Judge
The advancement of LLMs has made LLM-as-a-judee possible, where LLM-based evaluator judges the model responses based on user instructions and the criteria from different aspects the prompt. The evaluation is flexible as the evaluation criteria can be adjusted dynamically in the prompt instead of retraining the evaluator from scratch. The judgment can be interpretable and detailed criticism as well as feedback are generated before the judge score. The M.-.-based evaluator is more efficient and scalable than human experts much less expense. It is more effective and applicable than statistical evaluation metries like BLFU and embedding metrics like BERTScore.
Now there are three different categories of LLM judges: The Point wise judge model (Kim et al. 2024a
Lin & Chen 2023] Dong et al. 2024) evaluates individual responses independently. scoring them based on predefined criteria: The pair-wise judge model et al. 2024b Kim et al. 2024b Jung et al. 2024) compares two responses directly, determining which one is superior based on sct of evaluation dimensions; The List-wisc judge modelςLiu et al. (2025) ranks multiple responses in terms of quality, assigning rank to each based on the overall evaluation. Researchers explore effective approaches to apply LLMs as judges by prompt-based or finetuning-base -baeed methods in various scenarios. The prompt-based approaches aim to enhance judgment via step-by-step instructions as well as multi-turn optimizations. G-Eval (Liu el al., (023) evaluates NLG output quality using Chain-of-Thoon Thoughtt (CoT) and Form-Filling paradigms. Portia (Li et al. [0024] proposes evaluate
the responses with step-by- bt- reasoning guidelines. Active-critte critic (Xu al. (2024) first generates evaluation
criteria from data and iteratively refines them. However, the performance of prompt based LLM evaluators is
unsatisfactory (Gu et al. 2024). The finetuning based approaches further optimize the LLMs with the specialized dataset to adapt the LLMs judgment tasks either with instruction tuning (Ye & Ng
2024
Li et al. 2024b)
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18henetet
ILAM) 11704 sutrat
Vacore Tefformence
Eocam Petformance
luting Neformare
122
15
1.5
14
14.
Tedh Tyze
Task Tyze
Task Typa
Figure 6: Average performance comparison of different scoring methods across models on direct and reasoning tasks over three benchmarks.
Spearman Correlation Owen2.5 (reasoning condition)
Mirila LAGZEle
65
5p0
0.1
Model Stoe
Figure 7: Comparison of Spearman Correlation Coefficients for Qwen2.5 Models Across FLASK. HelpSteer and BIGGen Bench Using Vanilla Score, E-Score, and LAGER (w. tuning) (Reasoning Condition)
preference tuning et ct al. 2024b Hu et al. 2024b). InstructScore Xuu ct al. 2023 combines human guidance with implicit knowledge from models like GPT-4, finetuned on the LLaMA model, to provide both scores and human-readable diagnostic reports. TIGERScore (Jiang et al. 2023b) is finetuned on the LLaMA-2 model analysis, helping
understand each identified error and its associated penalty score. Prometheus (Kim et al. 2024a) Prometheus (Kim et al.) 2024b) are finetuned
generate detailed
fine-grained evaluation, achieving new state-ol-thc-art performance on judgment benchmarks. In this work, we focus on the LingleLLMM point-wise evaluator without reference response. Our proposed LAGER method improves judgment performance by estimation with aggregated layer-wise logits, which is different from the idea of prompt-based and finetuning-base based methods.
C Addition Experimental Results
In this section, Figure shows the comparison of the performance of different scoring methods models on direct and reasoning conditions. Figure shows the comparison of spearman correlation coefficients for Qwen2.5 models across FLASK. HelpSteer and BIGGen Bench Using Vanilla Score, E- E-Score, and LAGER (w. tuning) under the reasoning condition. In Table we present the Pearson correlation coefficients for all models, including LAGER and other haselines, on the Flask, HelpSteer, and BiGGen Bench.
D Addition Applications of LAGER
D.1 Emotional Understanding
LLMs have demonstrated strong capabilities to comprehend and interpret complex emotions and their meanings social contexts. Therefore, beyond merely assessing the quality responses, emotion judge. In the widely used emotion understanding benchmark EQ-Bench (Paech) 2024). EQ- BeBch a benchmark for language models designed assess emotional intelligence. It uses specific question format in which participants required read conversation and then rate the intensity of one character's emotional
can be used an
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Table 5: Pearson correlation coefficients of LAGER and other baselines Flask, HelpSteer, and BiGGen Benchmarks. These results are statistically significant, with p-values less than le-5. These results statistically significant, with p-values less than le-5.
Flask
Flask
HelpSteer direct
HelpSteer Reasoning
BIGGen Bench
BIGGen Bench
Model
Direct
Reasoning
Direct
Reasoning
Average
Fine-tuned Models
0.227
0.173
0.116
0.172
Prometheus2-78
0.453
0.502
Close-source Model via API
GPI-44-mini
Vscore
0.566
0.581
0.484
0,529 0.532
0.576
0.538
0.545
E-Score
0.588
0.587
0.503
0.543
Open-ource Models
LLaMA3J1-8I-Instme
GPTSeore
0.109
0.028
-0.109
0.009
Vscote
0.393
0.486
0.376
0.517
0.329
0.441
0.424
E-Score
0.386
0.494
0.427
0.525
0.380
0.452
0.444
LAGER muning)
0.481
(w, tuning)
0.493
0.512
0.486
0.524
0.485
0.482
0.497
Mistral-7B-Innttruuttt....
GPTScore
0.336
0.166
0.154
0.219
Vscore
0.292
0.305
0.302
0.355
0.194
0.321
0.295
E-Seore
0.307
0.313
0.333
0.363
0.221
0.329
0.311
tuning)
0,380
0,343
0.412
0,380
0.357
0.376
0.375
LAGER (w. tuning)
0.378
0.337
0.413
0.377
0.361
0.375
0.374
GPTSeore
0.104
-0.047
-0.128
+0,093
Vscore
0.468
0.516
0.374
0.429
0.399
0.475
0.444
E-Soore
0.544
0.532
0.441
0.489
LAGER (WLO tuning)
0.475
0,517
0.417
0.441
0.371
0.471
0.449
LAGER (w. tuning)
0,568
0.551
0.494
0.474
0.497
0.501
0.512
Qwen-2.5-14hh
GPTScore
-0.026
-0,065
-0,108
-0,066
Vscore
0.585
0.581
0.428
0.420
0.494
0.507
0.503
E-Score
0.612
0.594
0.448
0.436
0.517
0.515
0.520
LAGER (wLO tuning)
0.612
0.600
0.430
0.436
0.496
0.503
0.513
(w. tuning)
Mistraa-SSalll244---nee
GPTSoore
-0.020
-0.044
-0.088
-0.051
Vscore
0.440
0.575
E-Score
0.608
0.561
0.442
0.463
0.624
0.589
0.548
LAGER (w. tuning)
0.603
0.577
0.448
0.477
0.628
0.603
0.556
tuning)
0.608
0.569
0.448
0,477
0.634
0.604
0.557
GPTSe
0.022
-0.121
-0.044
Vscore
0.544
0.607
0.435
0.482
0.590
0.587
0.541
E-Score
0.554
0.610
0.444
0.485
0.597
0.588
0.546
LAGER (w.o tuning)
0.627
0.634
0,515
0.624
LAGER (w. tuning)
0.626
0.630
0.503
0.512
0.645
0.620
0.589
response. Each question is explanatory and aims assess the ability predict the intensity of four different emotions. The dataset originally contained questions, after processing, we obtain 430 instances, each corresponding to one emotion per conversation. The emotional intensity annotated by humans ranges from to 9, with higher scores indicating stronger emotions. The I.I.M asked to predict the intensity of the emotional states of characters in dialogue with score ranging from to 9. In this part, evaluate LAGER on FQ-Bench and report the consistency with human evaluations.
As shown Table LAGER significantly outperforms the widely used vanilla score across all LLM backbones consistency metries, with an average improvement 8.42 points without tuning and points tuning. This demonstrates that LAGER is effective not only for evaluating the quality of responses but also in other LLM-as-a-Judge scenarios, such emotional understanding. LAGER is tuned on the HelpSteer validation set, which has different scoring domain and range compared to EQ-Bench (ranging from 1-5 versus 1-9). This further highlights the robustness of LAGER with tuning, successfully transfers from one domain and score range other domains with different judging prompts and score ranges.
D.2 Enhancing LLM in Knowing When They Don't Know
Knowing when they don't know, also known self-knowledge (Yin et al. 2023). is erucial enhancing the reliability and trustworthiness
LLMs. In this section, we explore whether LAGER can improve an LLM's knowlegeee We evaluate the SelfAware dataset (Yin et al. 2023 using LLaMA3.1-4 I-8B-Instruct and Mistral-7B 7eeentBB-Innntttnneeeeeee Instruct-vO33 v0.3, which consists of 2337 answerable and 1032 unanswerable questions from five diverse

---

Table 6: The Spearman and Pearson correlation coefficient measures the consistency between reference sentiment intensity and the scores from LLaMA3.1-800 1--ttunsttttttt, Mistral- 77--Insrucct-0.33 Qwen-2.5-14BBIInsrruee on the processed EQ-Bench.
Processed-EC Baarssed-E--BBraee EQ-Bench
Model
Scoring Type
Pearson
Spearman
VScore
0.56
0.596
E-Score
0.574
0.618
Mistral-7B Binial-7B-Instuet--ie
LAGER (w.o. tuning)
0.593
0.632
LAGER (w. tuning)
0.598
0.635
VScore
0.456
0.478
E-Score
0.608
0.652
aLaMA-3.1 In-trrtr
LAGER tuning)
0.627
0.653
LAGER tuning)
0.634
0.657
VScore
0.706
0.707
E.Soore
0.739
0.759
Qwen-2.5 2.5-14B 1.5--14B-Instruct Instruct
LAGER (w.o. tuning)
0.745
0.758
tuning)
calegories. Specifically, given subjective question in SelfAware, ask LLM evaluate the answerability this question scale to score of indicates that question completely unanswerable based on the available knowledge, while a score of indicates a highly accurate answer is possible. Following the original paper, we normalize the certainty score to range of 0-1 and use threshold of 0.75 as the boundary to classify LLM as either "Know" (2 0.75) "don't It know" (< 0.75).
Then, can quantitatively calculate the Fl score to measure the model's level of self-knowledge. Table 7 compares LAGER with baseline methods, includ- ing the SimCSE baseline used in the original paper. The results show that LAGER (w. tuning) signifi- cantly enhances the LLM's 's's self- knowledge, achieving a +19.77% + +1.9% increase in score compared to SimCSE, and VScore on LLLMA-3311-88 respectively, and +11 111.1% 1%, and +4.8% increases in Fl score compared to SimCSE and VScore Mistral- 7B-Instrrct--0.33 respectively. By providing reliable measure LLM's self-knowledge, LAGER enhances the LLM's ability to understand their limitations, shows performance comparable to the E-score.
Table 7: Self-knowledge Comparison of LAGER and baselines. The evaluation metric is the F1- Score.
Chesifiration Metheds
SinCSE
VScore
E. Score
(sco tunings
[w. tuning)
Mistral Intract-vts LLMAN- L-B--uatrut
0,005
0.62
E
Experiment Details
E.1
Details About KDE for Score Distribution Visualization
We adopt kernel density estimation (KDE) to visualize the distribution of model-generated scores across evaluation samples. KDB provides smooth, non- parametric estimate of the underlying score distribution and is preferable to histograms for highlighting fine ane-grained density differences.
Given set of samples {01, .2,..., ). the estimated density point is computed
fa(x)
Σ
24
(14)
rufi
where (-)) is the kernel function and h is the bandwidth. We the Gaussian kernel:
K(u)
22
(15)
22T
All KDE plots are normalized to unit area for comparability. We employ kernel density estimation for visualiza- tion, with the handwidth parameter selected using Silverman's 's rule or cross-validation when appropriate. KDE is used in Figure compare the output distributions of LAGER and haseline models.
E.2 Details About the Benchmarks
FLASK We utilize the complete test prompt set from FLASK. Ye et al. 2024a). a fine- grained evaluation dataset that includes various conventional NLP datasets and instruction datasets. This dataset contains data
25

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on 2,001 entries, each consisting of human feedback score and evaluation score from GPT-4, We utilize 12 scoring rubrics: Conciseness, Metacognition, Insightfulness, Readability, Commonsense Understanding. Logical Robustness, Factuality, Comprehension, Completeness, Logical Efficiency, Logical Correctness, and Harmlessness.
HelpSteer HelpSteer [Wang al. 2023) is an open-source Helpfulness Dataset. For each response in the dataset, it is evaluated based on live criteria: helpfulness, correctness, coherence, complexity, and verbosity. These evaluation scores are annotated by humans, ensuring that each instruction in the dataset is paired with responses of varying quality. We process these data, combining the prompt, response, and corresponding criteria into individual data samples. A total of 8.95k data points are generated, with the first 2k used for our evaluation.
BiGGen Bench BiGGen Bench (im al. 2024b) is comprehensive evaluation benchmark designed assess the capabilities large language models (LLMS) across a wide range of tasks. This benchmark focuses on free-form text generation and employs fine-gres greeggrined instance-speciff evaluation criteria. BiGGen Bench evaluates nine distinct generation capabilities (e.g., instruction following, reasoning. tool usage, etc.) across 77 tasks, providing model outputs and scores for 103 different language models. We utilize the human evaluation set.
E.3 Details About the Baselines
Due to the limitations of the GPTScore method, we do not report its results under the reasoning condition. Since TIGERScore-75 and Prometheus2-7B cannot directly output single score, do report their results under the direct condition.
TIGERScore TIGERScore(iang al. 2023b) trained metric designed for explainable, reference-
free evaluation of text generation tasks. Unlike other automatic evaluation methods that only provide scores, TIGERScore uses natural language instructions to guide error analysis, identifying specific mistakes in the generated text. It is based on the LLaMA-2 model and trained on carefully curated dataset, Metriclnstruct, which includes 42K quadruples covering text generation tasks and 23 datasets. TIGERScore is capable of generating detailed error analysis, including the error location, error type, error explanation, and revision suggestions, along with a penalty score for cach error.
(/1, le.. Am The core GPTscore method lies in leveraging LLM to evaluate the quality of text by computing the average log probability 1 >> logp(h, [d, a, S); () under specific context S and task instruction T(d, a, S). The prompt m2
GPTScore Assuming the text to evaluated
template T(-) is composed of a task description and aspect definition.
The process of constructing the Prometheus-2 model (Kim et al., 2024b involves the following steps: First, fine-grained pairwise ranking dataset, PreferenceCollection,, containing 1000 custom evaluation critcria, created to support evaluation based on user-defined standards. Next, Mistral- selected as the base model, and it trained separately on the direct evaluation dataset FEEDBACK COLLECTION and the pairwise ranking dataset PreferenceCollection Finally, by merging the weights of the models trained on these two formats, the final Prometheus-2 model is obtained.
Prometheus-2-7B
E.4 Details of Evaluation Metrics
PEARSON Pearson correlation cocfficient indicates the strength and direction of the relationship between two variables, ranging from -1 to 1. For the two sets of data x.y. we can calculate their Pearson correlation coefficients pxy as follows:
Coo(X, YX
PXY
(16)
aXOY
SPEARMAN Spearman rank correlation coefficient a non-paramett paramereetrric measure that evaluates the statistical dependence between the ranks of two variables. It determines how well the relationship between these variables can be described using monotonic function. We can calculate Spearman r. according to the following formula:
6 6.. de nn 1)
(17)
where d represents the rank difference hetween the two variables for each observation (pairwise difference). and n denotes the number of fraction pairs.
Since the Spearman correlation coefficient effectively measures nonlinear monotonic relationships, is robust to outliers, and does not require data to follow a normal distribution, it is particularly suitable for handling ordinal data. Therefore, this work primarily presents results based on the Spearman correlation coefficient.
26

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Table 8: Parameters and settings used for instruction fine-tuning of the Llama-3-8B model.
Training Parameters
Setting
stage
sft
finetuning type
full
template
alpaca
flash atin
fa2
cutoff
2048
learning_ret _aae
2
num num_train_ee
sum_train_epochs
3
size
4
gradient_accumulle
4
ir_scheduler_tyie
cosine
warmup_ratio
0.03
packing
FALSE
bf16
TRUE
tf32
TRUE
optim
adamw_torch
include_nume num pwt__nnmt_______eeeeeeeee wtwptnnttotss__sttt_ttt toweestkeeeeseeeee seen
TRUE
seed
42
E.5 Details of layer-wise weight training settings
We randomly select 1,000 samples from the HelpSteer dataset as held-out validation set, ensuring that does not overlap with the test to tunc the layer-wise weights of LAGER. The training is performed using the Adam optimizer with an initial learning rate of 0.01, and batch size of 4. A random seed of 42 set ensure the reproducibility
also apply ReduceLROnPlatee learning rate scheduler factor of 0.S, patience value of I, and a minimum learning rate specified by min_lr. Since some models in the Qwen2.5 family may not converge with just epoch, we set the number of training epochs to 2 for all models in the Qwen2.5 series. For other backbone models, we set the number of training epochs to 1. All experiments are implemented using Py Torch.
experiment.
decay
F Details of SFT
For LAGER, E-Score and VScore, establish dimensions (including answer accuracy, logical sistency, relevance, fluency and clarity, length appropriateness, diversity, instruction difficulty) and utilize the average score of each dimension, evaluated using the LLaMA3.1-880 1-8--333--BBInttttue model, for data selection. The specific definitions and scoring standards for these seven dimensions can be found in Table SuperFiltering is explicitly designed instruction data filtering method. We strictly follow the original paper's methodology, except for using LLaMA3.1 1-8B-Instruct the backbone model for fair comparison. During the SFT training of the Llama-3-8B model, we use L40 GPUs, and total batch size during the training phase 64. The specific training parameters and settings are detailed in Table
G Prompt Template
this section, we present all the prompt templates used in this paper, with the blue text indicating the parts where corresponding content should be inserted. For the direct evaluation scenario, Figure 9 is the prompt template for direct evaluation in point-wise scenario that outputs only single score. Figure T0 the prompt template for reasoning evaluation in point-wise scenario, including (reabac)(reasoning))
27

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Prompt Template for Emotional Understanding
Your prodict the emotional response
dinlogue:
[dinlogne]
[Fad dialogue]]
At the end of this dialogue, rate how strongly [human]] likely feeling [emotionn_type on scale
You only to oulput rating, with additional commentary:
Figure 8: The prompt template for Emotional Understanding experiment.
Prompt Template for Point wise Direct Evaluation
#o0 Task Description:
(might include Input it), responee
score mibric representing evaluation are given.
a detailed feedback that assess the quality the response strictly besed on the given score rubric, evaluating general. After writing feedback, witte score that is an integer between and You should refer the score rubne.
#ee The instruction to evaluate: (instruction)
wee R Response to evaluate: [output]
Score Rubrics:
(Definition)
Snore (criteria for 1}
Score (criteria for
Score 3: (ctiteria, for 3)
(criteria for
Score 5:
(criteria for: 5)
##B O Output format:
The output formet should look follows: "Seere: -give your score heres" Remember that you only need to provide the scone. There need generate explaination forit.
Figure 9: The prompt template for direct evaluation in a point-wise scenario that outputs only single score.
Prompt Template for Point-wol wise Reasoning Evaluation
#90 Task Description:
An instraction (might include an Ingut inside it), a response to evaluate and score nibric representing evaluation criteria are given.
Write a detailed feedback that assess the quality of the response strictly based on the given score rubric, not evaluating in general. that integer between. and should refer cubric.
ffter writing feedback,,
instruction (instruction)
#ee Response evaluate: [output)
#88 Score Rubrics:
(Definition)
Score 1: (criteraa for 1}
Score
(criteria for 2]
Score 3:
(ontertaa, for 3)
Score (criteria for 4}
Scone (criteria for:
Output format:
The output formet should look as follows: ('Feedback: owrite your feedback here> Score: <give your score herest" Remember you should with the Pleese generate any opening, closing, explainations
Figure 10: The prompt template for reasoning evaluation in point-wise scenario, including (eedback(reasonnng)
28

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Prompt Template for ata Filterng
oraliator
trm based otterta the of
488 Evaluation Task:
Assess grren tata entry lesed the tollaningg aspert.
ve (eeclattion sxpectynn for task, your grel evalante bess well the (ecalesbor, tepad) demondtmeed the prestded "instrctor"" and "Heggrree" Be ram consider the fellowag::
(eratuatoo aspectien niters to speciti qualrt oc charutetiss the entyy.
dearmddieut directow sani shouldl lssed dlecily accunially mileaaaly mny
feeporaath corgast provided arower to insrostion)
nutiilled accening
grven "Istruction" "Rsposser"
660 Defiaiiion Eovalattion
(evalaation
(Detrittin)
448 Soaeing Criteri:
SSooo 1
(cmeeta toz 1)
.rccom 2*
(crteta, tor 2)
145co00 3+
[cdaataa for 3]
1*5coo f+*
[cdiatia tor 4)
(crsene
comegende spettic lenel quaiity from (loweet) (igheet) Lee grondde enterts select
#00 Data Entry Evaluate:
""isstudiioo" (Isttactoo):
eet Himponse Fermab
Prreiie chrgge score" from formot of aoom soom you groso beed or your eraluation **Istratton** *"oegoraa""
Figure 11: The prompt template used for data filtering in SFT task.
Prompt Template for SelfAware
Your task evaluate whether question can be answered and provide an answerable level, represented by number between Here the question and evaluation criteria:
<question>
(question)
</question>
<evaluation criterla>
1: No relovant knowledge available; question cannot answered
either general sperulative, lacking precision. Level 3: Moderate knowledge available; the be constructed but lacks depth clarity.
Level22 2:
Limited outdated knowledge;
evel 4: The answer is mostly accurate and comprehensive, but may have small details missing require minor clarification.
Fully answerable with certainty; cloar, procise, and complete response based on solid knowledge. <levaluation criteria>
Level 5:
Provide answerable lovel based on the ev avaluation critria. Your response should be in the format of nsswraable Level: <An integer from to showing answerable the question not generate content.
Figure 12: The prompt template used in the SelfAware dataset in section 7.2.
29

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Table Definitions of different dimensions and their specific scoring standards, with each dimension scored on a scale ranging from to 9, each score corresponds to a specific standard.
Dimension-1 & Definition
Answer Accuracy: Evaluate whether the response accurately addresses the instruction and completely fulfills the task.
I: Completely incorrect, irrelevant to instruction.
2: Partially correct, major omissions emors in fulfilling the instruction.
3: Contains significant errors, unable to fully address the core task.
4: Partially correct, missing key details or addressing wrong aspect of the instruction.
Scoring Standards
5: Mostly accurate, but contains
emrrr omissions.
6: Mostly correct, though missing small details or has minor inaccuracies.
Largely accurate and complete, but may lack small details have minimal errors.
8: Fully accurate, completely addresses the instruction, minimal flaws.
9: Perfectly accurate, fully aligns with the instruction, no omissions.
Dimension-2 & Definition
Logical Consistency: Assess whether the response maintains logical consistency, fol- lowing the reasoning the instruction without contradictions.
1: Completely incoherent, self-contradictory. does not follow the instruction.
2: Major logical errors or contradictions, docs not follow the instruction.
Logic unclear, unable to fully support the instruction's 's requirements.
4: Contains some logical inconsistencies, but overall understandable, with minor devia-
tion from the instruction.
Scoring Standards
5: Mostly consistent, but has slight logical flaws or areas that could be clearer.
6: Largely logical and clear, but small inconsistencies or areas for improvement exist.
7: Logical and coherent, only minimal inconsistencies remain.
8: Completely logical, reasoning is sound and aligns perfectly with the instruction.
Perfectly logical, tightly reasoned, flawless adherence to instruction's 's requirements.
Dimension-3 & Definition
Relevance: Evaluate whether the response is relevant to the instruction, directly address- ing the key aspects of the task.
1: Completely irrelevant, deviates from the instruction' 's theme.
Minimal relevance, strays from the core task.
3: Poor relevance, does not adequately address the main parts of the instruction.
4: Somewhat relevant, but deviates from key details or task elements of the instruction.
Scoring Standards
Mostly relevant, but lacking some precision or key aspects of the instruction.
6: Mostly relevant, covers the main aspects of the instruction, but can be improved for accuracy detail.
7: Directly relevant, clearly and adequately responds to the instruction.
8: Highly relevant, fully addresses the core aspects of the instruction with precision.
9: Perfectly relevant, fully and comprehensively addresses all aspects of the instruction.
Dimension-4 & Definition
Fluency Clarity: Evaluate the fluency and clarity of the response, ensuring it follows the expression requirements of the instruction and easy understand.
I: Completely unclear, frequent grammar errors, hard to understand.
2: Very unclear, poor structure, difficult to follow.
3: Unclear, sentence structure issues, parts are hard to understand.
4: Somewhat unclear, lacks fluency, but overall understandable.
Scoring Standards
5: Clear, but could he improved in flow conciseness.
6: Clear and fluent, but slight improvements in clarity conciseness could be made.
7: Fluent, easy to understand, clear expression.
Continued on next page
30

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Table 9: Definitions of different dimensions and their specific scoring standards, with each dimension scored on scale ranging from to 9, each score corresponds specific standard. (Continued)
8: Very clear and fluent, perfect adherence to the instruction's 's expression requirements.
9: Perfectly fluent, natural, and clear, fully aligned with the instruction's 's expectations.
Dimension-5 & Definition
Length Appropriatenes:: Evaluate whether the response length appropriate, providing sufficient information without being too brief or too long according to the instruction.
1: Extremely short overly long, irrelevant to the instruction' expected length.
2: Too short or too long, fails to meet the instruction's 's requirements.
brief, lacks key details, or too lengthy with unnecessary information.
4: Slightly short or slightly long, lacks important details or includes redundancy.
5: Reasonable length, but could be more concise or include more details as per the instruction.
Scoring Standards
6: LLngth is appropriate, but could refined by removing unnecessary parts or adding small details.
7: Length is well-suited, adequately covers instruction's main points without redun- dancy.
8: Perfect length, concise yet comprehensive, fully meets the instruction's requirements.
9: Optimal length. precisely conveys all required details, no redundancy, aligns perfectly with the instruction.
Dimension-6 & Definition
Diversity: Evaluate whether the response shows diversity in language, structure, and viewpoints, and avoids repetition or overly uniform expressions required by the instruction.
1: Extremely repetitive, no variation, fails to meet the instruction's 's diversity requirements.
2: Lacks diversity, repetitive or formulaic expression, no innovation.
3: Some diversity, but much of the content is repetitive uniform.
4: Some variation, but significant repetition or lack of diverse viewpoints.
Some diversity, but certain sections are somewhat repetitive or conventional.
Scoring Standards
6: Largely diverse, offers different perspectives or expressions, but with minor repetition.
7: Strong diversity, rich in varied language and structure, aligns with the instruction's expectations.
8: Very diverse, with significant creativity and variety in language and perspective.
9: Extremely creative, highly diverse, fully meets the instruction's innovation and diversity requirements.
Dimension-7 & Definition
Instruction Difficulty: Assess the complexity of the instruction, considering whether it requires deep reasoning. multiple steps, specialized knowledge, and how well the response reflects the difficulty of the task.
I: Very simple instruction, requires only basic information with no reasoning.
2: Simple task, requires basic common knowledge or simple answers.
3: Slightly complex, requiring some background knowledge understanding of specific content.
4: Moderately complex. involving reasoning moderately difficult tasks.
Scoring Standards
5: Instruction requires multiple steps or specialized knowledge across domains.
6: Complex instruction requiring advanced reasoning or wide range knowledge.
7: Highly complex, requires deep reasoning or tasks that span multiple domains.
8: Very complex, involves multi-layeree reasoning or highly specialized knowledge.
9: Extremely complex, requiring professional-level knowledge or intricate reasoning fulfill.
31


Reviews:
[{"review_id": "gQsGYdVUXN", "reviewer": "Reviewer_HC1G", "summary": "LAGER introduces a training-free (optionally tunable) way to boost LLM-as-a-judge quality by looking inside the model: it linearly combines the logits that every decoder layer assigns to each candidate score and outputs the expectation of that cross-layer distribution. Because middle-to-upper layers encode semantics that correlate more closely with human opinions, this fusion yields finer-grained, better-calibrated judgements than the usual “take the top token” heuristic. Tested on three alignment benchmarks, namely, Flask, HelpSteer and BIGGen, LAGER raises Spearman agreement with human scores by up to 7.5 % over the strongest existing baseline, while requiring no chain-of-thought prompting. It further enhances tasks such as instruction-data selection and emotional understanding, all while maintaining the backbone's frozen state for speed and portability.", "questions": "See my comments above.", "limitations": "See my comments above.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Pros:\n- LAGER (esp. the one with fine-tuning) significantly improves alignment with human preferences. Its innovative cross-layer scoring yields up to a 7.5 percentage-point Spearman correlation boost over GPTScore, VScore, and E-Score across three benchmarks.\n- The method keeps the backbone model frozen, training only a small set of fusion weights (or none in the zero-tuning variant). This means inference is as efficient as a single forward pass, and it avoids the expensive reasoning prompts used by many judges.\n\nCons:\n- The paper does not compare LAGER against several relevant evaluators that also target human alignment, such as G-Eval (reasoning-based) or HD-Eval (which also leverages multi-layer information). These comparisons are important to contextualise LAGER’s gains.\n- GPT-4o-mini achieved very strong results, raising questions about the impact of model scale. However, the current experiments focus only on cross-family comparisons. It would strengthen the work to test LAGER across different sizes within the same family (e.g., Qwen 2.5B, 7B, 14B).\n- While LAGER with tuning performs best overall, the tuning appears to succeed on some backbones (e.g., Qwen) but fails or regresses on others (e.g., Mistral, LLaMA). Yet the discussion (p. 6) focuses only on LAGER w/ tuning (without comparing to the ones w/ tuning), making the discussion a bit insufficient.\n- Compared to E-Score, LAGER without tuning performs worse (or on-par) on several backbones (e.g., InternLM, Qwen), suggesting that the observed gains largely stem from fine-tuning. This makes the comparisons not quite fair, comparing a tuned model to unturned baselines.\n\nReferences:\nYang Liu, Dan Iter, Yichong Xu, Shuohang Wang, Ruochen Xu, and Chenguang Zhu. 2023. G-Eval: NLG Evaluation using Gpt-4 with Better Human Alignment. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 2511–2522, Singapore. Association for Computational Linguistics.\nYuxuan Liu, Tianchi Yang, Shaohan Huang, Zihan Zhang, Haizhen Huang, Furu Wei, Weiwei Deng, Feng Sun, and Qi Zhang. 2024. HD-Eval: Aligning Large Language Model Evaluators Through Hierarchical Criteria Decomposition. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 7641–7660, Bangkok, Thailand. Association for Computational Linguistics.", "was_revised": true, "final_justification": "The response has addressed most of my concerns. Though I still think the discussion should be further improved, this is not a major reason for rejecting the paper.", "rebuttal": "Thank you for your thoughtful feedback and constructive suggestions. Our key responses are summarized below:\n\n> Q1: The paper does not compare LAGER against several relevant evaluators that also target human alignment, such as G-Eval (reasoning-based) or HD-Eval (which also leverages multi-layer information). These comparisons are important to contextualise LAGER’s gains.\n\n**A1**: \n\n  - **G-Eval and E-Score: Essentially the Same**. We would like to clarify that G-Eval is essentially the same as the E-score baseline included in our experiments. Moreover, the G-Eval(reasoning-based) evaluation results you mentioned are also incorporated within our experimental comparisons (see the performance of E-score under the reasoning setting on each dataset in Tables 1 and 6). \n  \n  - **LAGER outperforms HD-Eval.** Regarding the HD-Eval baseline, we would like to clarify: HD-Eval enhances the alignment between LLM evaluators and human judgments by **decomposing evaluation into fine-grained criteria (\"layers\" refer to fine-grained decomposition stages, not model layers)** and employing human-guided aggregation. This is fundamentally different from our approach, which utilizes **intermediate layer representations of the model**. We compared HD-Eval (chat task setting) with LAGER in evaluation performance. As shown in the table below, HD-Eval's performance is lower than our method, primarily because **it requires manually customizing fine-grained criteria for different tasks**, making it difficult to generalize effectively across the diverse evaluation datasets used in our paper.\n\n| Model                      | Method  | Flask  | Helpsteer | BigGen |\n|----------------------------|---------|--------|-----------|--------|\n| Llama-3.1-8B-Instruct | HD-Eval | 0.29   | 0.243     | 0.214  |\n|                            | LAGER (w. tuning)   | 0.46   | 0.524     | 0.444  |\n| Mistral-7B-Instruct-v0.3 | HD-Eval | 0.256  | 0.271     | 0.248  |\n|                            | LAGER(w. tuning)   | 0.298  | 0.376     | 0.333  |\n| InternLM3-8b-Instruct       | HD-Eval | 0.321  | 0.254     | 0.351  |\n|                            | LAGER(w. tuning)   | 0.489  | 0.474     | 0.49   |\n| Qwen2.5-14B-Instruct     | HD-Eval | 0.443  | 0.231     | 0.372  |\n|                            | LAGER(w. tuning)   | 0.572  | 0.472     | 0.524  |\n\n> Q2: GPT-4o-mini achieved very strong results, raising questions about the impact of model scale. However, the current experiments focus only on cross-family comparisons. It would strengthen the work to test LAGER across different sizes within the same family (e.g., Qwen 2.5B, 7B, 14B).\n\n**A2**: \n\n  - **LAGER brings improvements across model scales.** In fact, we have already conducted such an analysis in Section 5.3. This section includes extensive experiments across multiple sizes within the same Qwen2.5 family, ranging from 0.5B to 72B. These results demonstrate that LAGER consistently improves evaluation performance across a wide range of model scales. Moreover, larger models generally tend to achieve better performance.\n\n> Q3: While LAGER with tuning performs best overall, the tuning appears to succeed on some backbones (e.g., Qwen) but fails or regresses on others (e.g., Mistral, LLaMA). Yet the discussion (p. 6) focuses only on LAGER w/ tuning (without comparing to the ones w/ tuning), making the discussion a bit insufficient.\n\n**A3**：\n\n  - We would like to clarify that **across all evaluation datasets, LAGER(w. tuning) outperforms E-score by an average of over 6% on both backbones**. The number of instances in which LAGER with tuning underperforms E-Score is 3 out of 36. It is worth noting that in these cases, the performance of LAGER with tuning is comparable to that of E-Score, with differences of less than 0.5%.\n  \n  - We would like to emphasize that our tuning-based method demonstrates strong transferability, as validated by the multi-task experiments in Section 6. Even without tuning, our method outperforms E-Score in 5 out of 6 backbone models, with an average improvement of 4.5%. In the few cases where it underperforms, the performance gap is within 3%. Moreover, it consistently outperforms V-Score. Therefore, we primarily recommend the LAGER with tuning approach and conduct subsequent analyses based on it.\n\n> Q4: Compared to E-Score, LAGER without tuning performs worse (or on-par) on several backbones (e.g., InternLM, Qwen), suggesting that the observed gains largely stem from fine-tuning. This makes the comparisons not quite fair, comparing a tuned model to unturned baselines.\n\n**A4**: \n\n  - Our method does not involve fine-tuning the backbone language model. LAGER only **introduces L+1 lightweight parameters (where L is the number of transformer layers)** to aggregate multi-layer logits for more accurate scoring. This approach is fundamentally different from traditional fine-tuning: **we do not update any of the original backbone model's parameters**. \n  \n  - Except for InternLM, our method outperforms E-Score by an average of 4.5 points across all other model backbones, even without introducing any additional weight parameters. As a result, LAGER introduces minimal computational overhead and is highly scalable. The performance gains of LAGER stem not from large-scale fine-tuning, but from a more efficient and structured utilization of the model’s internal representations.\n\n---\n\nThank you again for your time and effort in the review process. We will carefully revise the manuscript based on your suggestions and hope that our responses adequately address your concerns. We remain open to any further suggestions or requests for clarification you may have."}, {"review_id": "HhXRWvqV3c", "reviewer": "Reviewer_Yh62", "summary": "The paper proposes LAGER (Layer Aggregation for Enhanced Representation), a lightweight framework to improve the alignment of LLM-based evaluators (\"LLM-as-a-judge\") with human judgments. Instead of relying solely on the final output layer (which may overlook nuanced signals), LAGER aggregates internal representations from multiple intermediate layers of frozen LLMs to generate finer-grained, probabilistic evaluation scores. On standard alignment benchmarks, this approach is reported to enhance judgment quality by up to 7.5% over the best baseline, and also lead strong downstream applications.", "questions": "Apart from the weaknesses, I want to see a bit more insights in why reasoning leads to weaker results for LAGER (with supports from concrete examples if possible).", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\n- The paper researches into LLM-as-a-judge, a popular topic within the NeurIPS community.\n\n- The presented approach has a high efficiency in that it works under frozen backbone LLMs and requires minimal computational cost during training.\n\n- 3 human-annotated datasets are chosen for evaluation to avoid preference leakage, making the results robust and reliable.\n\nWeaknesses:\n- In spite of the discussed in Section 3.4, the approach is mainly restricted to open-sourced models with accessible intermediate layers for idealistic performance, so its applicability is still limited.\n\n- The evaluation is limited to point-wise benchmarks, while the pairwise/listwise evaluation are not involved.", "was_revised": true, "final_justification": "The paper proposes LAGER (Layer Aggregation for Enhanced Representation), a lightweight framework to improve the alignment of LLM-based evaluators (\"LLM-as-a-judge\") with human judgments. It is technically solid and sufficiently validated in a comprehensive evaluation. My only concern is that it may not be applicable to proprietary LLMs. Overall, I recommending accepting this paper to the main research track.", "rebuttal": "We are truly grateful for your insightful feedback on our manuscript. Our key responses are summarized below:\n\n> Q1: In spite of the discussed in Section 3.4, the approach is mainly restricted to open-sourced models with accessible intermediate layers for idealistic performance, so its applicability is still limited.\n\n**A1**: \n\n  - We acknowledge that our method relies on access to intermediate layer logits. However, closed-source models could provide access to internal representations (e.g., via enterprise APIs or special access programs), our method could be readily applied without modification, and would perform similarly.\n\n> Q2: The evaluation is limited to point-wise benchmarks, while the pairwise/listwise evaluation are not involved.\n\n**A2**: \n\n  - In our study, we focus on point-wise evaluation, because **pairwise and listwise methods have high computational complexity and limited scalability**, which restricts their use in large-scale data synthesis and filtering. In contrast, point-wise evaluation is **computationally simpler, adaptable to various standards**, and thus better suited for practical applications.\n  \n  - Following your suggestion, we evaluated our method on the RewardBench dataset, which is designed for pairwise comparisons. The results in the table indicate that although our approach is primarily designed to enhance performance in point-wise evaluation, it also leads to certain improvements in pair-wise judgment. We will include these experiments and provide further analysis in the next version of the paper.\n  \n| Model                     | Method  | Score |\n|---------------------------|---------|-------|\n| Meta-LLaMA-3.1-8B-Instruct | Vscore  | 0.671 |\n|                           | E-score | 0.736 |\n|                           | LAGER   | 0.749 |\n| Mistral-7B-Instruct-v0.3  | Vscore  | 0.610 |\n|                           | E-score | 0.701 |\n|                           | LAGER   | 0.711 |\n| InternLM3-8B-Instruct     | Vscore  | 0.714 |\n|                           | E-score | 0.772 |\n|                           | LAGER   | 0.773 |\n| Qwen2.5-14B-Instruct    | Vscore  | 0.776 |\n|                           | E-score | 0.821 |\n|                           | LAGER   | 0.823 |\n\n> Q3: Apart from the weaknesses, I want to see a bit more insights in why reasoning leads to weaker results for LAGER (with supports from concrete examples if possible).\n\n**A3**: \n\n  - Through experimental analysis of the model’s internal attention scores, we found that the weaker performance of LAGER under the reasoning setting is closely related to the drift in attention distribution. This is consistent with the findings of previous work[1][2][3]: **As the reasoning steps progress, the model’s focus on the original input and the text to be evaluated gradually diminishes, shifting more toward its self-generated reasoning trajectory**. This attention shift weakens the model’s direct perception of the source text, causing it to rely on its own reasoning chain when information is insufficient, thereby exhibiting overconfidence. As a result, the model tends to exaggerate supporting evidence while overlooking potential errors or shortcomings, leading to inflated scores. Below, we present real evaluation examples (assessed by the llama3.1-8b-instruct model)：\n  \n---\n\n**A Real Evaluation Example(assessed by the LLaMA3.1-8B-Instruct model)：**\n\n- Instruction: Solve this equation. Input: x^3 - 4x^2 + 6x - 24 = 0\n\n- Response: Sure, I can help you with that. The equation x^3 - 4x^2 + 6x - 24 = 0 can be solved using the following steps: Factor the equation. Set each factor equal to 0 and solve for x. The factors of the equation are (x - 4)(x - 3)(x + 2) = 0. Setting each factor equal to 0 and solving for x, we get the following solutions: x = 4, x = 3, x = -2. Therefore, the solutions to the equation x^3 - 4x^2 + 6x - 24 = 0 are x = 4, x = 3, and x = -2.\n\n- Evaluation Feedback: The response provides a clear step-by-step approach and attempts to factor the cubic equation. However, the factorization presented, (x - 4)(x - 3)(x + 2), is incorrect as it does not satisfy the original equation upon substitution. This is a significant flaw since correct factorization is critical for solving the equation properly. **Despite this, the explanation is well-structured and easy to follow, which demonstrates solid reasoning skills. The response presents the solutions clearly and in an organized manner**. Based on the rubric, considering the clarity and structure of the explanation alongside the attempt at solving, I would rate this response as highly accurate and logical. Score: 5\n\n---\n\nThank you again for your time and effort in the review process. We will carefully revise the manuscript based on your suggestions and hope that our responses adequately address your concerns. We remain open to any further suggestions or requests for clarification you may have.\n\n---\n\n**Reference**：\n\n[1] [When Backdoors Speak: Understanding LLM Backdoor Attacks Through Model-Generated Explanations](https://aclanthology.org/2025.acl-long.114/) (ACL 2025)\n\n[2] [Mechanistically Demystifying Extreme-Token Phenomena in LLMs](https://neurips.cc/virtual/2024/107912) (NeurIPS 2024)\n\n[3] [Measuring and Controlling Instruction (In)Stability in Language Model Dialogs](https://openreview.net/forum?id=60a1SAtH4e) (COLM)"}, {"review_id": "mAuPvwhUDx", "reviewer": "Reviewer_DQpf", "summary": "This paper proposes LAGER, a framework for improving LLM-as-a-judge performance by aggregating score-token logits from all decoder layers of a LLM. Sepcifically, LAGER computes a weighted combination of layer-wise distributions and taking the expected score. Experiment results demonstrate the improvements over several LLM judge baseline methods.", "questions": "1. Will LAGER become better if scale more training data and params?\n2. Please also see the weaknesses.", "limitations": "NA", "rating": 2, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 1, "strengths_and_weaknesses": "**strengths**  \n1. The multi-layer aggregation approach is very simple and straightforward, using frozen backbones without modifying core LLM parameters.\n2. Empirical results demonstrate improvements across several selected benchmarks and model scales.\n\n**weaknesses**  \n1. The proposed method relies on accessing the internal representations of the LLM, thus this limits applicability to open-source models; closed-source or API-only LLMs cannot benefit.  \n2. The supervised weight-tuning step still requires human-annotated validation data. \n3. The experimental results are not thorough, missing important baselines, for example RewardBench and DPO rewarding. Also, LLM-as-a-Judge heavily rely on the prompt templates, so it would be better to test on different popular prompts which you can find in recent papers such as self-rewarding LLM.", "was_revised": true, "final_justification": "I appreciate the authors’ effort in addressing individual points, but the core issues remain unmitigated, and the manuscript requires major revision. I therefore stand by my original negative assessment.\n\n1. My major concern is about the contribution and realistic application of the proposed method.\n\nThe proposed aggregation mechanism fundamentally depends on accessing hidden states inside the base LLM. As the authors acknowledge, this effectively confines the method to open-source backbones. SOTA closed-source models (e.g., GPT Series, Claude, Gemini) do not expose these internals for even enterprise access, **yet they dominate the usage of LLM-as-a-Judge workflows**.\n\n2. The authors’ defense that “supervised weight tuning is common” sidesteps the critique: the paper claims to require no additional annotations, yet it does. Also, the authors overclaimed Non-Modification of Backbone, while they do require introducing additional params for fine-tuning.\n\n3. Despite the rebuttal, the evaluation still omits critical baselines which can further enhance the paper: RewardBench’s leaderboard models including DPO rewarding.", "rebuttal": "We appreciate the reviewers’ time and effort in evaluating our work. Below, we present our main responses to the key concerns raised:\n\n> Q1: The proposed method relies on accessing the internal representations of the LLM; thus, this limits applicability to open-source models. Closed-source or API-only LLMs cannot benefit.　The proposed method relies on accessing the internal representations of the LLM; thus, this limits applicability to open-source models. Closed-source or API-only LLMs cannot benefit.\n\n**A1**: \n\n  - We acknowledge that our method relies on access to intermediate layer logits. However, closed-source models could provide access to internal representations (e.g., via enterprise APIs or special access programs), our method could be readily applied without modification, and perform similarly.\n\n> Q2: The supervised weight-tuning step still requires human-annotated validation data.\n\n**A2**: \n\n  - **This is a common requirement for most supervised training methods and should not be viewed as a weakness**, especially for approaches focused on human alignment, as evidenced by the paper [1] cited by Reviewer HC1G.\n\n  - **Minimal human-annotated data and lightweight training parameters.** Our method trains only dozens of lightweight parameters using a few hundred annotated data points (about 5% of the data required by traditional methods), avoiding the need to fine-tune billions of backbone parameters.\n  \n  - **Strong generalization ability.** Furthermore, as demonstrated in Section 6, our method demonstrates strong generalization ability, effectively transferring to other domains while requiring substantially fewer annotations and incurring no significant additional costs, thus offering clear advantages over traditional approaches.\n\n> Q3: The experimental results are not thorough, missing important baselines, for example RewardBench and DPO rewarding. Also, LLM-as-a-Judge heavily rely on the prompt templates, so it would be better to test on different popular prompts which you can find in recent papers such as self-rewarding LLM.\n\n**A3**: \n\n  - It is our view that RewardBench is fundamentally **an evaluation benchmark** intended to measure the performance of reward models, rather than a specific evaluation method. Moreover, we are unable to find a directly comparable baseline method reported in the RewardBench study.\n\n  - Similarly, DPO rewards are typically obtained by **fine-tuning the base language model itself**, which differs from our approach that only introduces lightweight aggregation parameters **without altering the backbone model**. So we believe that the DPO reward cannot be used as a directly comparable baseline in our setting. If our understanding is incorrect, we would appreciate clarification on the role of RewardBench and DPO rewarding in the comparisons.\n  \n  - Our primary prompt is adapted from templates widely adopted in prior evaluation studies[2][3][4], which have demonstrated strong and reliable baseline performance. While prompt design can influence performance, it is not the primary focus of our work. Nevertheless, we also tested two popular prompt variants (T1 refers to the template used in Self-Rewarding LLM, and T2 refers to the template used in G-Eval), and the conclusions were consistent with those obtained using our primary prompt, further confirming the robustness of our approach.\n  \n  | Model| Flask(T1) | Flask(T2) | Helpsteer(T1) | Helpsteer(T2) | BiGGen Bench(T1) | BiGGen Bench(T2) |\n|-----------------------------|-----------|-----------|---------------|---------------|------------------|------------------|\n| **LLaMA3.1-8B-Instruct**    |           |           |               |               |                  |                  |\n| Vscore                      | 0.339     | 0.325     | 0.380         | 0.346         | 0.264            | 0.245            |\n| E-Score                     | 0.389     | 0.370     | 0.454         | 0.445         | 0.361            | 0.354            |\n| LAGER (w. tuning)           | 0.470     | 0.466     | 0.521         | 0.502         | 0.472            | 0.477            |\n| **Mistral-7B-Instruct-v0.3**|           |           |               |               |                  |                  |\n| Vscore                      | 0.266     | 0.270     | 0.260         | 0.256         | 0.139            | 0.141            |\n| E-Score                     | 0.240     | 0.245     | 0.299         | 0.289         | 0.191            | 0.192            |\n| LAGER (w. tuning)           | 0.344     | 0.351     | 0.402         | 0.396         | 0.358            | 0.347            |\n| **InternLM3-8B-Instruct**   |           |           |               |               |                  |                  |\n| Vscore                      | 0.427     | 0.417     | 0.381         | 0.381         | 0.366            | 0.362            |\n| E-Score                     | 0.504     | 0.523     | 0.447         | 0.456         | 0.465            | 0.464            |\n| LAGER (w. tuning)           | 0.521     | 0.534     | 0.503         | 0.481         | 0.476            | 0.493            |\n\n> Q4: Will LAGER become better if scale more training data and params?\n\n**A4**: \n\n  - **Increasing the model parameters with an MLP and enlarging the dataset did not result in significantly better performance.** In preliminary experiments, replacing simple weighting with an MLP led to unstable training, likely due to increased complexity and limited data. Our current L+1 parameter approach is simpler and achieves great performance. We also observed performance saturates as data scales, with limited gains from additional data. In future work, we will explore larger datasets and more complex aggregations to evaluate scalability.\n\n---\n\nThank you again for your time and effort in the review process. We will carefully revise the manuscript based on your suggestions and hope that our responses adequately address your concerns. We remain open to any further suggestions or requests for clarification you may have.\n\n**Reference** \n\n[1] [HD-Eval: Aligning Large Language Model Evaluators Through Hierarchical Criteria Decomposition](https://aclanthology.org/2024.acl-long.413/) (ACL 2024)\n\n[2] [G-Eval: NLG Evaluation using Gpt-4 with Better Human Alignment](https://aclanthology.org/2023.emnlp-main.153/) (EMNLP 2023)\n\n[3] [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://openreview.net/forum?id=8euJaTveKw) (ICLR 2024)\n\n[4] [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://aclanthology.org/2024.emnlp-main.248/) (EMNLP 2024)"}, {"review_id": "fdww4A8VTm", "reviewer": "Reviewer_8jsL", "summary": "The paper introduces an approach that utilizes the internal hidden states, specifically, cross-layer logits, of a judge LLM to produce evaluation scores, moving beyond the conventional reliance on final-layer token probabilities. The method involves tuning L + 1 scalar weights on a held-out validation set, keeping the LLM backbone entirely frozen. The authors assert that these learned weights generalize across different benchmark datasets. The core experiments focus on comparing the model’s correlation with human judgments across three evaluation benchmarks.", "questions": "- As noted in the weaknesses, have you explored the method’s performance in more general or open-ended evaluation settings beyond predefined integer scores?\n- Do you have additional experimental results on recent benchmarks that are very different from the 1,000 samples of the HelpSteer dataset used for training?", "limitations": "Their limitations should also acknowledge the narrow scope of benchmarks used, as well as the restricted evaluation scenario that assumes predefined, discrete integer score ranges.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths\n- The writing of the paper is clear and easy to follow.\n- The main goal of the paper itself is interesting and potentially useful in building a more effective LLM-as-a-judge system.\n\n### Weaknesses\n- The method lacks novelty. As the authors themselves acknowledge, the idea of using internal hidden states has been explored extensively since the introduction of BERT.\n- My key concern is whether the lightweight training of layer weights can truly generalize across diverse evaluation benchmarks without additional fine-tuning. Fig. 2 illustrates that the correlation with human scores fluctuates significantly across layers, suggesting potential dataset dependency. This argument would be stronger if tested on a broader and more diverse set of benchmarks. The current evaluation, limited to three datasets, does not convincingly establish generalizability.\n- Increasingly, modern evaluation benchmarks are label-scarce, more complex, or dynamically generated without human-annotated scores. It is unclear whether the proposed method is applicable or effective in such settings where scalar labels are unavailable or ill-defined.\n- The work focuses exclusively on evaluations that assign discrete integer scores within a predefined range. It does not explore more general evaluation scenarios, such as those involving natural language feedback or descriptive labels. It remains uncertain whether the proposed method would be robust and adaptable in these more open-ended evaluation settings.", "was_revised": true, "final_justification": "The authors’ response has addressed some of my concerns regarding the diversity of benchmarks. I have adjusted my score accordingly.", "rebuttal": "We sincerely appreciate the time and effort you have devoted to offering insightful and constructive comments on the paper. Below, we present our main responses to the key concerns raised:\n\n> Q1: The method lacks novelty. As the authors themselves acknowledge, the idea of using internal hidden states has been explored extensively since the introduction of BERT.\n\n**A1**: \n\n  - We would like to clarify that there might be a misunderstanding, as we did not make such a claim in our paper. In lines 77–79, we specifically pointed out that “hidden representations across different layers have been widely observed to exhibit distinct characteristics”. We will revise and clarify this description in future work to prevent potential misunderstandings. \n  \n  - **This work introduces a new perspective to enhance point-wise evaluation by leveraging intermediate layer representations of the model**. Unlike traditional methods that rely solely on final layer outputs, we build a distinct evaluation framework based on an in-depth analysis of internal layers, laying the groundwork for further improving evaluation capabilities through deeper exploration of internal representations.\n\n> Q2: My key concern is whether the lightweight training of layer weights can truly generalize across diverse evaluation benchmarks without additional fine-tuning. Fig. 2 illustrates that the correlation with human scores fluctuates significantly across layers, suggesting potential dataset dependency. This argument would be stronger if tested on a broader and more diverse set of benchmarks. The current evaluation, limited to three datasets, does not convincingly establish generalizability.\n\n**A2**: \n\n  - In Section 6, we conduct experiments across diverse scenarios, including sentiment understanding, data selection, and large model knowledge boundary recognition (**without any additional training**), and found that LAGER effectively generalizes to these scenarios while outperforming the baselines.\n\n  - Regarding the fluctuations in layer-wise correlations shown in Figure 2, the datasets (FLASK, BiGGen Bench, HelpSteer) **indeed differ significantly in their design and objectives, yet we observe similar fluctuation trends across them**. This suggests that while dataset-specific characteristics may have some influence, the inherent properties and representational differences of the model's intermediate layers exert a more dominant effect on evaluation performance.\n  \n  - Our experiments cover **multiple widely used benchmark datasets spanning diverse domains and evaluation criteria** [1–6,10]. Broader validation could enhance generalizability, but our current results already demonstrate strong performance.\n\n> Q3: Increasingly, modern evaluation benchmarks are label-scarce, more complex, or dynamically generated without human-annotated scores. It is unclear whether the proposed method is applicable or effective in such settings where scalar labels are unavailable or ill-defined.\n\n**A3**：\n\n  - In this paper, we focus on the point-wise evaluation setting. Our method requires only a small amount of annotated data, demonstrates strong transferability, and incurs an acceptable cost for obtaining a limited set of high-quality annotations. While we appreciate your suggestion, it is beyond the scope of this paper, and we will address this issue in future work.\n  \n  - In fact, this relates closely to recent studies [7][8][9], which have leveraged LLMs to automatically generate scoring rubrics and annotations, effectively addressing challenges related to scarce, unavailable, or ill-defined scalar labels. Meanwhile, our method focuses on enhancing the generalization and efficiency of structured scalar scoring tasks, ensuring stability and reliability. **These directions are complementary: the former mitigates label scarcity, while the latter strengthens the robustness of evaluation methodology**.\n\n> Q4: The work focuses exclusively on evaluations that assign discrete integer scores within a predefined range. It does not explore more general evaluation scenarios, such as those involving natural language feedback or descriptive labels. It remains uncertain whether the proposed method would be robust and adaptable in these more open-ended evaluation settings.\n\n**A4**: \n\n  - **Unstructured scoring performs worse than structured scalar scoring**. In our early experiments, we also explored unstructured scoring methods (i.e., not confined to predefined discrete integer ranges), but found that the model's performance degraded significantly compared to structured scalar scoring.\n  \n  - **Point-wise evaluation suits open-ended tasks.** Previous studies [1][10][11] have shown that point-wise scoring is widely adopted in LLM-as-a-judge research, being well-suited for open-ended tasks without unified standards and demonstrating strong generality and scalability. Notably, **models can first perform explicit reasoning before providing a score**, thereby enhancing the transparency and rationality of the evaluation. \n\n  - This work leverages the core idea of **utilizing intermediate layer representations and lightweight weight training, aiming to capture a better mapping relationship between the model's internal states and the evaluation criteria**. While the current focus is on structured scalar scoring to establish a solid foundation, this core idea is **not** confined to integer scoring tasks. This lays the groundwork for future extensions to handle more complex and open-ended feedback forms (e.g., natural language descriptions). \n\n> Q5: As noted in the weaknesses, have you explored the method’s performance in more general or open-ended evaluation settings beyond predefined integer scores?\n\n**A5**: \n\n  - We have also explored more general evaluation settings, as presented in Section 6, including **sentiment understanding, data selection, and large model knowledge boundary recognition** (all without any additional training). These tasks typically involve greater task variability and weaker supervision signals, yet our method consistently demonstrates strong robustness in such scenarios. While we have not yet extended the method to fully open-ended evaluation formats, its strong generalization across diverse tasks suggests promising potential for application in more open-ended evaluation settings, which we plan to pursue in future work.\n\n> Q6: Do you have additional experimental results on recent benchmarks that are very different from the 1,000 samples of the HelpSteer dataset used for training?\n\n**A6**: \n\n  - We emphasize that our experimental benchmarks cover **diverse evaluation scenarios and exhibit significant heterogeneity in task design, evaluation dimensions, and target scenarios**, rather than being highly similar. Specifically, the FLASK dataset includes 12 fine-grained scoring dimensions, covering tasks from multiple different domains (e.g., Culture, Health, History); BiGGen Bench encompasses 77 tasks (e.g., Semantic Constraints and Code Revision) that evaluate various capabilities such as reasoning and instruction following; HelpSteer contains data annotated with multiple evaluation criteria, including helpfulness, correctness, coherence, complexity, and verbosity. And the results on downstream tasks (as presented in Section 6) are also sufficient to comprehensively evaluate the generalization ability of our method.\n\n---\n\nThank you again for your time and effort in the review process. We will carefully revise the manuscript based on your suggestions and hope that our responses adequately address your concerns. We remain open to any further suggestions or requests for clarification you may have.\n\n**Reference**\n\n[1] [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://openreview.net/forum?id=8euJaTveKw) (ICLR 2024)\n\n[2] [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://aclanthology.org/2024.emnlp-main.248/) (EMNLP 2024)\n\n[3] [Aligning to Thousands of Preferences via System Message Generalization](https://arxiv.org/abs/2405.17977) (NeurIPS 2024)\n\n[4] [Evaluating the Evaluator: Measuring LLMs' Adherence to Task Evaluation Instructions](https://arxiv.org/abs/2408.08781) (AAAI 2024)\n\n[5] [Evaluating Scoring Bias in LLM-as-a-Judge](https://arxiv.org/abs/2506.22316)\n\n[6] [RewardAnything: Generalizable Principle-Following Reward Models](https://arxiv.org/abs/2506.03637)\n\n[7] [G-EVAL: NLG Evaluation using GPT-4 with Better Human Alignment](https://arxiv.org/abs/2303.16634) (ACL 2023)\n\n[8] [MCRanker: Generating Diverse Criteria On-the-Fly to Improve Point-wise LLM Rankers](https://arxiv.org/abs/2404.11960) (WSDM 2025)\n\n[9] [Rationale Behind Essay Scores: Enhancing S-LLM’s Multi-Trait Essay Scoring with Rationale Generated by LLMs](https://aclanthology.org/2025.findings-naacl.322.pdf) (NAACL 2025)\n\n[10] [FLASK: Fine-grained Language Model Evaluation based on Alignment Skill Sets](https://arxiv.org/abs/2307.10928) (ICLR 2024 Spotlight)\n\n[11] [CODEJUDGE:Evaluating Code Generation with Large Language Models](https://aclanthology.org/2024.emnlp-main.1118.pdf) (EMNLP 2024)"}]

Author rebuttal:

Meta-review: This work proposed a fine-grained judgement framework to enhance the alignment between human and LLM-as-a-judge from the internal representations across different layers. They mainly use aggregated cross-layer logits with softmax distribution to provide a score-based judgement. This method is evaluated on different alignment benchmarks, and demonstrates that their method can improve performance across those benchmarks. They also evaluate their method on downstream emotional understanding and data selection tasks to show the effectiveness of their method.

The main strengths of this work include: (1) the proposed method is lightweight (only tuning small set of weights or none in the zero-tuning variant) to improve large performance across different benchmarks; (2) the evaluation is comprehensive plus the analysis about internal layers of different LLMs; (3) this work only requires few annotated data samples to finetune the model.

The main weakness of this work comes from: (1) it needs more discussion about different evaluators on this task; (2) the explanations about using L+1 lightweight parameters without updating original backbone models should be much clearer. Although the major concern from the reviewer DQpf is about the limitation of this work only for open-source LLMs, the performance of open-source LLMs-as-a-judge is not significantly behind of close-source ones. As this work focuses on the internal layers of LLMs, which make it impossible to access close-source LLMs.
Decision: Accept (poster)