Language Model Uncertainty Quantification with Attention Chain
Authors: Yinghao Li
Rushi Qiang
Lama Moukheiber
Chao Zhang
Venue: COLM 2025 (2025)
Keywords: Uncertainty Estimation
Large Language Model
Attention
TL;DR: Investigates large language model uncertainty estimation with critical reasoning token backtracking using attention chain.

Abstract: Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers.
While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g., multiple-choice), involving intermediate reasoning steps in LLM responses is increasingly important.
This added complexity complicates uncertainty quantification (UQ) because the probabilities assigned to answer tokens are conditioned on a vast space of preceding reasoning tokens.
Direct marginalization is infeasible, and the dependency inflates probability estimates, causing overconfidence in UQ.
To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization.
UQAC iteratively constructs an "attention chain" of tokens deemed "semantically crucial to the final answer via a backtracking procedure.
Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens.
The resulting chain is further refined with similarity filtering and probability thresholding, which reduce the reasoning space, facilitating the approximation of the marginal answer token probabilities.
We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.

Published as a conference paper at COLM 2025
Language Model Uncertainty Quantification with Attention Chain
Yinghao Li, Rushi Qiang, Lama Moukheiber, Chao Zhang Georgia Institute of Technology, Atlanta, USA (yinghaoli, rqiang6, Imoukheiber3, (at.aaeeeeeerrcccchaaagagggg// chaozhang edu
Abstract
Accurately quantifying a large language model's (LLM's) predictive uncer- tainty is crucial for judging the reliability of its answers. Although current uncertainty quantification (UQ) research still concentrates on short, direct answers, typically in closed-form formats (e.g., multiple choice), interme- diate reasoning steps are becoming increasingly critical to LLM responses. It complicates UQ because the probabilities assigned to answer tokens are conditioned on vast space of preceding reasoning tokens. Direct marginal- ization is infeasible, and this dependency inflates probability estimates, causing overconfidence in UQ. To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization. UQAC iteratively constructs an "attention chain" of to- kens deemed "semantically crucial" to the final answer via a back back-tracking procedure. Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens. The resulting chain is further refined with sim- ilarity filtering and probability thresholding, which together reduce the reasoning space, facilitating the approximation of marginal answer-token probabilities. We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.
1 Introduction
As large language models (LLMs) become integral across domains, ensuring their reliability is increasingly important. This issue is especially pressing in high-stakes scenarios such as medical diagnosis (Fox, 1980; Simpkin & Schwartzstein, 2016; Shen et al., 2023), where incor- rect predictions can have severe consequences. such domains, uncertainty quantification (UQ) is crucial for estimating model's confidence in its answer, detecting when it operates beyond its knowledge scope, and mitigating phenomena like hallucinations (Li et al., 2023; 2024b; Xu et al., 2024). However, efficient methods for UQ in natural language generation remain scarce (Gawlikowski et al., 2023; Kuhn et al., 2023), underscoring the need for robust techniques to assess LLM reliability.
Unlike auto-encoding models (Peters et al., 2018; Devlin et al., 2019) that produce outputs within constrained spaces, autoregressive LLMs (Radford et al., 2018), particularly those prompted or fine-tuned to generate detailed reasoning steps (Wei et al., 2022; OpenAl, 2024; DeepSeek-AI, 2025), yield arbitrarily long reasoning sequences. These sequences can be seen as samples from an intractably large and high-dimensional language space, making direct marginalization of intermediate steps impractical. Existing approaches often rely on approximating this space with tractable semantic representation (Kuhn et al., 2023; Hou et al., 2024; Jiang et al., 2023; Ling et al., 2024; Lin et al., 2024b; Chen & Mueller, 2024) But they frequently employ Self-Consistency sampling (Lakshminarayanan et al., 2017;
Wang et al., 2023) to repeatedly generate answers using the same or paraphrased prompts, which can be computationally expensive. In another line, some methods focus isolating semantically critical tokens (Duan et al., 2024; Lin et al., 2024a), yet they are typically tailored to short outputs and struggle with extended reasoning sequences. Furthermore, approaches

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for explicit verbalization of confidence (Lin et al., 2022; Tian et al., 2023; Xiong et al., 2024) demand additional model training, creating extra barriers for end users.
To overcome these challenges, we introduce model-agnostic UQ method, Uncertainty Quan- tification with Attention Chain (UQAC), designed to accommodate intermediate reasoning sequences without extra fine-tuning. UQAC builds on the observation that not all tokens in reasoning sequence equally contribute to the final answer a concept aligned with "attention" mechanisms (Bahdanau et al., 2015; Luong et al., 2015; Vaswani al., 2017) and prior find- ings (Duan et al., 2024; Lin et al., 2024a). Specifically, UQAC traces "semantically crucial" tokens by iteratively backtracking through the reasoning sequence: starting from the final answer tokens and using attention weights to identify their most influential predecessors (Figure 1). This process continues until reaching the input tokens, forming an atfention chain that captures the reasoning steps most critical to the final outcome (S 4.1). To further refine the atfention chain, UQAC prunes peripheral tokens by assessing their similarity to the answer tokens ($ 4.2), thus filtering out syntactic auxiliary elements. We then apply probability thresholding to remove token combinations with minimal influence on the final answer's 's probability distribution, producing tractably small set of key reasoning paths (5 4.3). This pared-down set is used to compute marginal probabilities of the final answer, effectively measuring the model's confidence. Compared with existing methods, UQAC provides confidence scores bounded between 0 and in single pass, yielding more interpretable results and improved calibration. Overall, UQAC offers:
Applicability: Works with any white-box autoregressive language models without the need for model or hyper-parameter tuning.
Scalability: Handles responses of arbitrary length by isolating the most influential tokens.
Efficiency: Runs in parallel with autoregressive generation and requires no additional sampling or external model inference.
Calibration: Provides bounded scores that directly reflect the model's confidence.
Our experiments across diverse LLMs and datasets (S 5) demonstrate that UQAC delivers superior calibration performance among UQ methods with comparable overhead ($ 6). Code and data are available at https: thub. com/Yinghaao-LL/UQA.
2 Related Works
Early approaches to UQ in autoregressive models compute cumulative token-wise probabil- ities or entropies (Kadavath et al., 2022; Kuhn al., 2023), as well as their length-normalize variants (Malinin & Gales, 2021). However, these methods struggle with long reasoning se- quences, where semantic and auxiliary tokens are conflated in joint probability estimations. To address the intractable reasoning space, several works approximate it through semantic space composed of model outputs sampled from multiple runs (Kuhn et al., 2023; Hou et al., 2024; Jiang et al., 2023; Ling et al., 2024; Lin et al., 2024b; Chen & Mueller, 2024). For instance, Kuhn et al. (2023) propose semantic entropy, which clusters similar responses and measures uncertainty via normalized cumulative log probabilities, later extended by Lin et al. (2024b) to black-box models using a co-occurrence entailment matrix. Chen & Mueller (2024) combine semantic entropy with selffreffective evaluation for enhanced robustness. Similarly, Jiang et al. (2023) employ paraphrased prompts to gather multiple outputs, while Hou et al. (2024) differentiate aleatoric and epistemic uncertainty by appending various clarification sequences to the original query. All these methods require multiple model runs, mirroring Self-Consistency (Wang et al., 2023), which is expensive due to the autoregressive structure of decoder-based LLMSs. In addition, approaches like semantic entropy rely on external encoder models for clustering, further increasing computational overhead.
A second line of research, akin to UQAC, aims to isolate auxiliary tokens and evaluate token-level contributions to the final answer semantics (Duan et al., 2024; Lin et al., 2024a). Duan et al. (2024) propose SAR, which quantifies token importance as the negative similarity between the complete sequence and a version with the token removed, weighting token- level entropies accordingly. Although effective, SAR necessitates multiple forward passes for thorough sequence-level aggregation. Lin et al. (2024a) introduce CSL, which modifies sequence probabilities by weighting tokens based on attention scores captured during the
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Instruction Tokens
Ressoning Tokens
Answer Tokens
0.2
0.4
wise nan once said
Therefore
The answer \boxed 2
033
044
066
022
Step
Step 2
Step
Step
Sourue Tokens (2)
(2, answer)
(2, 1)
Taget Tokers
(2, answer)
(2, 1, (outuct bdow (rrshtdd)
(A (accuatt stop (intrudion), (istructizz, 1 (isstrution))
Figure 1: Construction of the attention chain Xattn with 3-step attention backtracking procedure. Arrows point from source tokens to target tokens with the top-2 attention weights (displayed on the arrows), Le., Lagt 2. Solid lines indicate valid target tokens, while dashed lines indicate invalid ones for various reasons explained below. For simplicity, we do not shift the source set Xare as described in appendix B.2.
model's prediction of selffveeriication tokens (eg.,, "Y" or "N"). While CSL requires only a single pass, it depends on a large in-domain validation set (egg, 1,000 samples) to select attention heads, which is impractical in most real-world contexts. Moreover, both SAR and CSL are limited to short responses, as SAR's complexity grows factorially and CSL's localized attention scores fail to capture long-range dependencies.
A third line of work explores prompting LLMs to express uncertainty in natural language (Lin et al., 2022; Tian et al., 2023; Xiong al., 2024; Amayuelas et al., 2024). Lin et al. (2022) demonstrate that GPT-3 can be fine-tuned to output well-calibrated Verbalized Uncertainty without relying on logits. Tian al. (2023) show that confidence statements produced by ELHF-trained models can outperform traditional probabilitt-basee approaches, even under distribution shifts. Meanwhile, Xiong et (2024) propose a black-box framework featuring tailored prompts, sampling, and aggregation to reduce overconfidence, and Amayuelas et al. (2024) improve calibration through targeted fine-tuning on on specialized datasets. Nonetheless, they typically require additional training domaif-specific adaptations, limiting their applicability to broader range of models and tasks.
3 Problem Definition
Consider an instruction sequence Xinstr E Vinnstr A [x1, X2, of length Linstry where V is a vocabulary set. A language model M generates response sequence Xresp E VLee of length Leep, which can be split into Chain-of-Thought (CoT; Wei al., 2022) reasoning
sequence Xcot E VLeat and the final answer Nans E VLare, We write Xresp Ncot ① Xans (Figure 1), where represents "concatenation" disregarding any tokens after Xans-
Our objective in UQ is to determine the model's confidence in its final answer, denoted by Winstr). Directly using the joint probability PM (Xresp Xinstr) PM (Nans, Xcot (instr) is not suitable, as the reasoning sequence Xoot typically includes both semantically crucial tokens needed for deriving the answer and auxiliary tokens that primarily serve syntactic or coherence purposes. These auxiliary tokens often make up the bulk of Xcot yet have minimal impact on the actual answer semantics. Consequently, using PM (Xrespl Xinstr) as confidence measure can be both biased and unintuitive: the probability tends to decrease monotonically with the length of the response, leading to small joint probabilities that are difficult to interpret. Moreover, conditioning the final answer's confidence on Xcot is unnecessary when the primary concern is the correctness and trustworthiness the final answer itself. Therefore, this confidence formally is expressed
(Xans Xinstr) (inst))
Σ Xxol
(Xans Xcotr Xinstr) PM (Xcot) Xinstr).
(1)
where X ranges over all possible reasoning sequences in Vlo However, the sunmation is compulationally intractable: even when the vocabulary dimension is on the order of
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10,000, the space grows exponentially with the sequence length Leot, which can reach into the hundreds. Accordingly, the main challenge in LLM UQ is to construct an accurate approximation PM = PM (Nansl Xinstr) that faithfully reflects the model's confidence, without explicitly summing over all possible reasoning sequences.
In the following, we focus on a single instance of a single model and thus omit the model indicator M and the instance index. Table 4 summarizes the notations used throughout.
Uncertainty Quantification with Attention Chain
4.1 Attention Chain
We first apply attention backtracking to identify semantically crucial tokens Xatin E Xcol where t is defined as a "proper (not necessarily consecutive) subsequence", i.e., x1 E
VN C x2 E VM <> 31 < i < .... < iN < M s.f. *L,K = x2,/%/)' vk E NI.N Attention backtracking itself is an iterative procedure governed by function f: Xsre + Xigi, which selects target subsequence Xigı E Xcot deemed most influential for predicting the source tokens Xsre [ Tresp, based on the model's attention weights. We impose buffer size
Ligt A max jigtt that bounds the number of tokens selected at each step. The process starts
with Xare = Xans and (0) = Ø. At each iteration 2, we compute
(2) fx (x()-1)) and update
igi
(z) [z)
Asrc igt This continues until no new tokens are extracted from Ncot- The final sequence
Xattn is then the concatenation of all target sequences Xatin igt @ xig assuming f is (2)
applied Z times. Xattn serves compact semantic approximation of the original reasoning
chain Xcot- Figure 1 provides an illustration of attention backtracking. Each step of f consists of three stages: 1) attention weight processing; 2) attention head selection and aggregation; and 3) target token identification, detailed in the following paragraphs.
Attention Weight Processing For sequence of length T, LLMs employ self-attention (Vaswani et al., 2017) to compute weight for each token in the prefix xşT (which includes the instruction, i.e,, Xinstr C xgg) to gauge its contribution to predicting the next token XT-1- In an L-layer, H-head Transformer model M, the attention weight vector for token x7 in the 1-th layer and h-th head is defined as
(1)) a
E [0,1)]= softmax
(K(M) (10) 47 1v5))
(2)
(1)) where 9T E Rd is the query vector for xy, K( E Tx4 the key matrix for the prefix NgT, and de is the dimensionality of the key vectors. This attention vector determines how much semantic information from X&T is transferred to Xy-1, thereby serving as an indicator of the relative importance of each token in the prefix.
However, LLMs often overemphasize tokens that are close to position T, irrespective of their semantic relevance. To mitigate this bias, reweight the most recent C attention weights by multiplying them with a sequence of decreasing factors y E [0,1]C. Moreover, since some LLMs tend to assign disproportionately high attention to the instruction's BOS token, we reset that particular attention weight to zero. After these modifications, the attention vector is renormalized as follows (with layer and head indices omitted for brevity):
[T(TTCCTT] & @ &TT[T-CTTJ *T,[1] + 0; a' = "/In,
(3)
where "o" denotes element-wise multiplication and the square brackets indicate a slice. Please refer to appendix B.1 for further discussion on the reweighting factors 7.
Attention Head Selection and Aggregation Different attention heads typically capture distinct aspects of the input sequence. Not all attention heads contribute equally when predicting XT+1, making it crucial to identify the most informative ones for discerning semantically significant tokens (Lin et al., 2024a). To enable a lightweight, training-free selection process, we leverage attention entropy, defined H(a) = Ea laloge a, which
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quantifies the uncertainty of the attention distribution. A higher entropy value indicates more uniform distribution, suggesting a less informative attention head. Consequently, we select the top-K heads with the lowest entropy:
(L, arg ming H(aT ((A))); k [N (13)
(4)
where the operator arg min; returns the index corresponding to the k-th smallest entropy value, and the subscript I' emphasizes that the computation is performed independently for each token Xy. Subsequently, we aggregate the selected attention weights into a single vector a E [0,1]T via element-wise maximization:
T = max 11
EE N
(5)
k
Due to the maximization, Eaj E (1, ie,, a no longer resides on probability simplex.
Target Token Identification Le E [1.]]] for NN denote the positions of source
tokens within the source token set Xsre & {xi,}s (with step index (z) omitted). Here we treat Vare and Figt as sets for convenience. Given the set of attention weights {a 1s corresponding to Xsrc, our goal is to construct Xigt by selecting the top-Ltgt tokens based on their cumulative attention weights. For each token position & E NLTT, we compute cumulative attention
weight and gather the target set
Lare
411
L A
Xigl
{x1
4H
0; [[x; É Wstop); t {arg max; Φi )=1))
Lig
(6)
where 0 is threshold to filter out weakly attended tokens, and the operator arg max; returns the indices corresponding the k-th largest cumulative weight.
Finally, we define the step-wise backtracking function f as the sequential composition of (2)- The attention chain Xattn is generated by iteratively applying f; at each step z, a new target set is produced, and the final attention chain is the concatenation of all these target sets, as discussed above. For further details, please refer appendix B.2.
4.2 Similarity-Basse -aasd Filtering
Since the backtracking function f does not explicitly regulate the attention chain length Lattn, the chain may be long, complicating the formation of a tractable reasoning space. Therefore, we employ a similarity-based filtering strategy for finer control. Given the answer tokens Xans and the attention chain Nattn, we compute the similarity between each token pair (Xm, Xn), where Xm C Xans and X2 C Xaun, by applying cosine similarity their last-layer output logits hn and hg- We calculate the similarity vector w E [-1,1] Lattt as:
sim, Xn) = l |T/ Illlll
[[]] Σ sim Xm Xn),
m E IN [1,7an))) n E N N(I.aam
We retain the tokens with the top-L/ttm weights to form the filtered sequence x xattm
Xatin'
Yuun [xaun, aatm, s.f. Wpx) 0; n; E {arg max; w
1/am w
(8)
where the threshold of 0 excludes tokens with negative similarity scores. Please refer to appendix B.3 for further discussion.
4.3 Model Confidence
Using the attention chain Xatin and its filtered version X we first define two confidence
approximations in (1) based on the joint probabilities the attention chain and answer
tokens: 1) attention approximation PM - P(Xans, Xattn Xinstr;; 2) similarity approxi-
mation PM A PXXans, X Xinstr). Since X Xattn, we have PMssim 2 P Both
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(DeepSeek-A1, Published as a conference paper at COLM 2025
approximations can be viewed as indicators of the model's confidence in the critical seman- tics captured by the final answer Tans- By marginalizing out the filtered attention chain xat in P.M.sim, we obtain 3) answer approximation PM - P(xans Xinstr), which more directly captures the model's confidence in Xans alone. The challenge to reduce the approximated reasoning space Vlannn to a manageable subset S so that the summarization in
PM =
Σ
P(Xans, Xattn Xinstr)
(9)
Xattn S
remains computationally feasible. Approximating Xcot by aattn significantly reduces the token count, and we constrain 1 S 10. Furthermore, language models typically assign very high probabilities (e.g,, > 0.99) to the selected tokens; hence, substituting chosen token x aattn]ji] with any other candidate X Xattn/il * x attn.]]i] often results in a negligible joint
Xiinsrr O. Consequently, we only consider probability, ie.,, P P(xans, X attn X attn. # |
alternative tokens that exceed 0.01 probability threshold, and we alter just one token at time while keeping the others unchanged. In our experiments, this yields on average only six such candidates per position (excluding aamm), so E||s|] 7. Although multiple forward passes are still required, all elements in S are independent and can be evaluated without any recurrent or sequential dependencies, in contrast to Self-Consistency approaches.
Experiment Setup
Datasets and Models We use three standard reasoning datasets: 1) GSMSk (Cobbe et al., 2021) for basic math; 2) MATH (Hendrycks et al., 2021) for advanced math; and 3) BBH (bench authors, 2023; Suzgun et al., 2023) for logical, mathematical, and commonsense reasoning. See appendix C.1 for details. We evaluate nine instruction-tuned white-box SOTA LLMs spanning 1B-9B parameters: Llama-3.2-11B,3B) Llama-3.1-8B (Llama Team, 2024), 2ermma-2-12b/// (Gemma Team, 2024), and SeepSeek-RI-Disttil-LLmmmm
(Qwen Team, 2024),
Baselines We compare three variants of UQAC, PM P and PM,, against the following baselines. 1) P |Ncot, Xinstr), ), the joint conditional probability of the answer; 2) PM (Xresp) X the joint conditional probability of the entire response; 3) P.M (Xans), the mean probability of answer tokens; 4) P.M(Xresp) (Xresp), the mean probability of response tokens;
5) Predictive Entropy H. = // -lmmerr Lresp
LiiLinet
Linetr 1 Ex, PM x=:)) log (x /xxx) (Kuhn et al., 2023);
6) LengaheNormalized Predictive Entropy H. = H Lresp (Malinin & Gales, 2021); 7) Self- Consistency (Wang et al., 2023), the probability averaged over 5 independently sampled answers; and 8) Verbalized Uncertainty (Xiong et al., 2024), model-generated confidence score via additional prompts. See appendix C.2 for further discussion.
Evaluation Metrics Prior works produce unbounded confidence scores (Kuhn et al., 2023; Duan et al., 2024) and thus rely on AUROC for its scale-invariance. However, while AUROC effectively captures the model's s ability to distinguish correct from incorrect predictions, it provides no indication of how well the predicted confidence scores align with actual accuracy, that is, it does not reflect calibration. Consequently, when queries originate from distributions different from those seen during training or from previously tested scenarios, relying solely on AUROC yields limited insight into the true reliability of the model's answers. Therefore, we emphasize Expected Calibration Error (ECE; Naeini et al., 2015) and calibration plots, while reporting AUROC for completeness. See appendix C.3 for details.
Implementation We set C = 10 in (3), K = 16 in (4), Ligt 3 and 0 = 0.5 in (6), and delay applying@ 0 until Lattn > 5 to avoid premature backtracking. We use L 10 in (8). For token prediction, The inference temperature is set as 0 and top-p as 1. We balance the numbers of correct and incorrect predictions through subsampling. All experiments run on an NVIDIA A100-SXM4-80GG GPU with bf16 precision. Results, reported as mean + standard deviation over five runs (seeds 0 0-4), are from our own implementations.

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GSM8k
MATH
BBH
AUROCT
ECE|
AUROCT
ECEL
AUROCT
ECE]
Pxa(s)n))
60.9+0.66
49.4+0.0
74.2+11.
48.1+0.2
65.0+0.9
44.6=+0.3
P. PM (xeepp))))
61.1+0.8
41.9+0..0
69.0+1155
41.5+0.11
59.3+11.
42.6+002
PM (Kans) Xoote Xinstr)
60.71:0.6
48.410.1
73.9=12
43.710..
66.110.8
38.1
PM (Xresp Kinstr)
66.7100.
50.010.0
79.0=1.1
50.0110.0
63.611.55
45.310.4
P7(a)
618810.8
33.210.11
6..3=1.5
35.31:02
59411.
33.510.4
H(la)
67.14-0.8
78.6-+1.1
63.6+:1.2
Self-Consistency Verbalized
66.41199
28,910.88
79.5=1.0
15.8:0.88
79.5+1.0
31.610.7
54.911.5
42,910.2
57.4=0.7
45.1+0.2
58,21122
39.7
UQAC-P PACC-PPMAN
M,attnn
58.4:0.8
37.400.6
68.6=122
42.8+00.5
64.6113
23
UQAC-P M,ssimm
60.7#1.0
28.0+
68.0=1.3
21.6#110
65.1
22.1=100
UQAC-PA PM
61.3++0.9
33.6+004
69.5=112
25.8++09
66.7+1.2
24.2=
()) We use 1 - and 1 - as higher entropy indicates higher uncertainty, different from proba- bilities. ECE is not applicable to predictive entropy 'H as its value is unbounded.
Table 1: Performance of different UQ methods. The scores (in %) are reported as μ d over 5 runs, averaged across all LLMs. Higher AUROC is better; ECE the opposite.
Results
Main Results Table summarizes the average performance across all LLMs, with ad- ditional details in appendix E, showing superior calibration from UQAC. Notably, the unnormalized baselines, ie., PMM(Xresp Xinstr) and H. achieve higher AUROC on GSM8k and MATH by leveraging pronounced differences in response lengths between correct and incor- rect answers (shown in Figure 4a and discussed in appendix D.2). Since longer sequences yield lower joint probabilities and higher cumulative entropy, this effect benefits the AUROC calculation. However, when response lengths are more balanced, as with DeepSeek-R on GSM8k (Figure 4c and Table 18) or across most models on the BBH dataset due in- context regularization, the advantage diminishes. Furthermore, H. cannot be calibrated, and (Xreppp Kinstr) suffers from 50.0% ECE, indicating that predicted probabilities are pushed toward extremes (1 as in Figure 3a or as in Figure 3b). This concentration harms the ability to distinguish correct from incorrect predictions based solely on confidence, yielding poor calibration. While the congth-normaiized predictive entropy performs comparably to UQAC on GSM8k, falters with longer inputs and extended reasoning chains, as evidenced by its inferior performance on the MATH and BBH datasets and a more centralized entropy distribution (Figure 3c). In general, UQAC provides descent AUROC scores well as delivers significantly lower ECE across datasets, aligning more closely with true predictive performance and offering more reliable uncertainty estimates (Figure 3).
External Baselines Without additional fine-tuning, Verbalized Un- certainty exhibits significantly inferior performance, consistently underperforming even the H. baseline. This suggests that it is not ef- fectively integrated into prevalent LLMs and requires extensive train- ing careful prompt engineering for practical utility. In contrast, Self-Consistency, a variant of Deep Ensembles (lakshminarayanan et 2017), generally achieves superior performance, albeit with sig- nificant computational overhead (shown in Figure 2 and discussed in appendix D.3), aligning with theoretical insights and prior empiri- cal evidence (Fort et al., 2019; Wang et al., 2023; Li et al., 2024a). When efficiency is not primary concern, it is possible combine Self-Consistency with UQAC to further enhances calibration performance.
MM. sim
PM
vu
sc
Figure 2: Run time.
UQAC Variants
Among the variants UQAC, PM yields lower AUROC and higher ECE. As reasoning becomes complex and the attention chain Latt lengthens, the
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Calimmtio Plot
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(c) (1 HA-MATH
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Estimated Answer Probability
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(d) MATH
(e) -BH
(f) P. -SM-G
Figure 3: Calibration plots and probability histogram for Llamm-3.1-81) 3.1-8B. The x-axis shows the centers of 20 probability bins. The calibration curve (blue line with μ = o*) displays actual accuracy per bin, while the gray shadow represents the probability proportion.
150
Count Samples
Count of Samples
Lazan Correct
Counnt of Samples
100
20
Corratt
Leepp
10
01
500
1000
0
250
500
750
500
1000
Number Tokens
Number of Tokens
Number of Tokens
(a)
(b)
(c) DeepSeck-RR
Figure 4: Histograms of response and attention chain lengths for correct & incorrect answers.
predicted probabilities concentrate around zero, leading to increased ECE. This highlights the need to control token count via similarity filtering to preserve a balanced confidence distribution. Conversely, PM, developed from PM,sim, consistently outperforms P PMM,im in terms of AUROC, albeit at the expense of higher ECE. Thus, the optimal variant depends on the specific application requirements.
Since similarity filtering (8) effectively controls the size of the estimated attention space S, and given that Laun inherently has higher similarity to Xans compared to Xresp (Figure 7, appendix D.2), we investigate whether using only similarity scores without the attention backtracking described in 4.1 is sufficient. Specifically, we set Xattn Xresp in S 4.2, ignoring $ 4.1. Table 2 compares the generalizable results of this similarity-only variant against UQAC on smaller-scale models. The similarity-only variant performs notably worse than UQAC, exhibiting higher ECF and lower AUROC scores. This indicates that attention backtracking crucial for effectively identifying semantically important tokens and enhancing calibration performance.
Ablation Study
Correlation Analysis Previous studies such as Li al. (2024a) report a negative correlation between model's prediction accuracy and its UQ performance, suggesting that higher
8

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Published as a conference paper at COLM 2025
Llama-3.2-1B
gemma-2-2b
Qwen2.5-1.5B
Average
AUC
ECE 4
AUC t
BCE
AUC
ECE +
AUC1 t
ECE
UQAC
64.75
19.54
68.10
35.45
57.97
34.76
63.61
29.92
GSM8k
w/o attns
61.56
22.06
66.17
32.22
60.09
35.22
62.61
29.83
UQAC 67.92
20.65
74.09
15.23
71.71
31.45
71.24
22.45
MATH
w/o attn
65.25
24.55
70.30
18.94
72.65
31.57
69.40
25.02
UQAC 61.91
21.05
60.78
26.01
65.90
21.35
62.86 61.49
22.80
BBH
w/o attm
62.17
22.52
60.06
25.60
62.25
22.82
23.65
Table 2: Performance differences when applying similarity-based filtering (8) to response tokens Xresp instead of only the attention chain Lattn, i.e., Xattn Xresp*
0.65
Accuraey
0.6
AUROC
AUROC
0.60
GSMSk MATII
0.55
0.4
0.50
0.4
0.4
0.3
ECE
ECE
ECE
(a) ECE-Accuracy model
(b) ECE-AUC model
(c) ECE-AUC hyper-parameter
Figure 5: Correlation analysis of ECE with accuracy and AUROC for UQAC-PM- In (a) and (b), different point types differentiate dataset; in (c) they distinguish models.
accuracy often coincides with poorer calibration. To verify whether this holds for autore- gressive LLMs, Figure 5a plots each model's ECE against its accuracy across all datasets. The strong correlation shown in the figure, evidenced by an average Pearson's coefficient of 0.760, confirms that the conclusion still holds for LLMs. This is further discussed in appendix D.1 from the dataset perspective.
We further analyze the relationship between ECE and AUROC under two conditions. Across different models (presented by the same type of points), Figure 5b reveals a negligible correlation (average coefficient of 00.147, indicating that calibration and AUROC capture distinct performance aspects and should be evaluated jointly, echoing $ 5. However, when examining РM with hyper-parameters, specifically, varying LAttn from 8 to 12 and the similarity threshold in (8) between 0 and 0.2, a more pronounced positive correlation (coefficient of 0.489) emerges. These findings suggest trade-off between calibration and AUROC, warranting further exploration in future work.
Hyper-Parameters As introduced in $ 5, we adopt a single, universal set of hyper-parameters for every model.
attn
AUROC (1)
ECE ())
0.5
10
58.11 =: 0.61
25.50 0.52
This configuration yields stable, com- petitive results in most situations, yet task-specific tuning can sometimes im- prove calibration further.
0.7
10
59.32 = 0.79
25.25
0.38
16
0.5
10
56.59 = 0.77
26.39 = 0.96
16
0.5
16
59.25 = 0.97
24.16 = 0.79
16
0.7
10
58.10 1.19
25.61 + 0.82
32
0.5
10
57.18 0.69
26.01 0.65
Table 3 on the right presents a small hyper-parameter sweep for gemma- 2-2b on BBH. Cells shaded in light blue correspond to our universal set- ting, while boldface highlights the best value achieved in each metric. Al- though our default choice falls slightly
32
10
58.83
1.04
25.45 0.68
Table 3: Hyper-parameter study with gemma-2-2b on BBH. K is the number of attention heads (4), 0 the attention weight threshold (6), and L the number of tokens in the similarity- filtereed token sequence X (8).

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Published as a conference paper at COLM 2025
short of the sweep's optimum, it remains convenient, ready-to-use option that as demon- strated appendix delvvesierss solid performance across a wide range of tasks.
Conclusion
This work addresses UQ for LLMs, particularly in tasks where final answers are derived from the intermediate reasoning steps. We propose UQAC, a method that leverages at- tention chains constructed according to the autoregressive attention weights to efficiently identify and track semantically critical tokens within the reasoning sequence, significantly re- ducing the space for uncertainty estimation. UQAC provides reliable uncertainty estimates with minimal computational overhead, requiring only a few parallel forward inferences without additional fine-tuning, multiple recurrent response sampling, depending external models. Empirical evaluations across diverse benchmarks and model architectures confirm that UQAC achieves superior calibration, especially when intermediate reasoning steps substantially influence final outcomes. Moreover, UQAC is applicable to any white- box autoregressive LLMs, preserves reasoning interpretability, and scales efficiently with increasing model size and complexity. Limitations are discussed in $ 7.
Limitations
Although UQAC is, in principle, compatible with any Transformer-basse model that generates textual outputs, we do not explore tasks in the vision-only or multimodal domains. Due to resource constraints, our empirical analyses primarily focus smaller LLMs. Theoretically, the conclusions in this paper should generalize to larger models, we have not empirically verified this assumption. UQAC may also underperform in certain cases, e.g,, gemma-2-99 on GSM8K, when run with its default hyper-parameters. Performance can be improved by tweaking the hyper-parameters, as shown in 6, but such tuning deviates from our aim of providing plug-and-play UQ method. Finally, although UQAC consistently achieves better calibration than baseline methods, its performance is still imperfect, leaving room for further improvement.
Acknowledgments
This work was supported in part by NSF IIS-2008334, ITS-2106961, IIS-2403240, CAREER TIS- 2144338, and ONR MURI N00014-17-1-2656. This research has benefitted from the Microsoft Accelerate Foundation Models Research (AFMR) grant program.
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A
Notations
Table summarizes the notations and definitions included in this paper.
Category
Notation
Definition
V
Vocabulary
V Stop
Set of stop words.
Sets & Spaces
ILM
Set natural numbers from N.
Reduced reasoning space.
Empty set.
A sampled token.
X
A random token variable.
A sampled token sequence/vectun
x
A random sequence variable. Instruction sequentce.
Misstr
Tokens Sequences
Nyes
Response sequence.
Xoot
Reasoning (CoT) sequence.
Answer token sequence.
Nac
Source sequence/ set backtracking step
Target sequence /set backtracking step Attention chain token sequence.
Xattn
Similarity-filee filtered attention chain sequence.
Attention weights at step in layer head ht
Re-weighted attention weights.
Aggregated attention weights at step T.
Attention Bachtracking
Re-weighting factors.
Cumulative attention weights from all source tokens.
T
Similarity vector.
P
Exact probability:
Probabilistic Metrics
P
Approximated probability.
Length-nornulized approximated probability. Entropy
H
Linerr
Length the instruction sequence.
Lesp
Length of the response sequence.
Leo
Length reasoning sequence.
Lura
Length of the answer sequence. Length the attention chain.
Latn
Latn
Length the similarity- filtered attention chain.
Leg
Length of the target sequence/ses
Token index sequence. Index of the latest predicted token during inference. Generic indices (comlet--dpennden)) Layer and head indices model M.
Numbers & Indices
T
1
L H
Total number of layers and heads in model M.. Attention backtracking step index.
s,e
Position indices in source/ target sequences or sets.
f,
Specific token positions in source and target soquences.
C
Number of tokens selected for re-weighting. Attention weight threshold. Similarity threshold.
Step-wise atlention backtracking function. Indicator function.
Functions
Cardinality of a htt///eueeeeeeeeeeeeeeeeeee
2-norm of vector.
sim
Cosine similarity.
Concatenation of sequences.
Pruper subsequence relation (non--onsecctivve allowed).
C
Subsequence relation. Transpose of vector or matrix.
T
Exponentiation by T.
Operators
.(T)
Superscript T.
arg min, arg max,
Index of the k-th smallest element in vector largest element vector A vector from (du (2....... indexed by subscript j-th element the vector d. Subvector/sie ssurecttr/subett Subvector of a; from the j-th to k-th elements (inclusive).
Index
Auj
Agvl
excluding the j-th element.
A.
Table 4: Summary of Notations and Definitions
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B UQAC Details
B.1
Attention Re-Weighting
As discussed in $ 4.1, to mitigate the inherent bias of LLMs toward emphasizing more recent context, we apply sequence of decreasing re- weighting fac- tors E [o, 1j to adjust the attention weights cor- responding to the most recent C. tokens. To obtain these re-weighting factors, we first compute an av- erage attention vector a. Specifically, we randomly select 1,000 samples from the GSM8K training par- tition and use Llama-3.2-1B generate answers for each sample. We then average the attention weights from all heads and layers for the last 50 tokens in each generated response:
0.20
Average Attention Weight
0.15
0.05
0.00
11
21
Token Distance
Mnnstrtaon (h,)
Figure 6: Averaged attention weights.
E [0,1]50
ΣΣ E
HLLresp 1t-1==1 Linstr
1[1-50:]
(10)
To simplify subsequent analysis, reverse the
order of the computed average attention weights, placing the most recent token at the first position, i.e., "[j < A|50-1]- Next, project into two-dimensional space, with
the y-axis representing attention weights and the x-axis representing token indices. We then fit a linear regression line that passes through the points (C + 1, (,d(c11)) and (L(50- - C)
This regression line is defined as:
α 30 C
ā [C11]
8(i) = [[++]]
+
- (C+1) (i (i-(1)))
(11)
50
C
Subsequently, each re-weighting factor 7 is calculated as:
g(i) i
CC-i+1
Vi Np.c..
(12)
We emphasize that the resulting y values are approximations, as high precision is not critical for this adjustment. Consequently, we adopt these GSM8k and Llama-3. 2.2-IB-deri factors
universally across all models and datasets. In our experiments, we consistently set C 10, yielding the following re-weighting factors:
0.93925344
0.87378443
0.81274293
0.73914525
0.67549127
(13)
0.59304059
0.46061748
0.32959151
0.20938152
0.116444488
which is hard-coded our implementation. The averaged attention weights and the fitted
line are visualized in Figure 6.
B.2 Attention Chain Construction
When transferring the target set Xigt to serve the new source Xsrc for the next iteration
(z) (x)
(i.e,, updating x x for iteration + 1), it is important to differentiate between token
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generation and token attention. During token generation, based on the input token x7, with the attention computation operating between xy and the preceding context ggT. In contrast, during token attention, the projected key and value vectors are computed directly from the token x; as it is fed into the model.
token X7+1 is produced
Suppose that XT is identified tokens that contributed to its prediction via attention backtracking. In this case, we focus on the attention vectors generated during the token's generation. These vectors, computed with respect to the input token XT, are defined by (2) (reproduced here for clarity):
semantically crucial token and wish to trace back the
KTqr
at (0, 1] softmax
(14)
Vdg
Assume further that a token X, E Xigt is the most attended token in the target set, i.e.
T = max T.jf max ,
(15)
where ky, - Kr.j]] denotes the i-th key vector in the key matrix Ky corresponding to token Xz. In this scenario, x, serves as model input (generated from x;-1) rather than an output. Consequently, when propagating the target set to the next iteration, the indices are shifted
back by one position [i = (xi 1 X; ()) The same index-shifting principle applies to the initial source set X {x-1 Xi Xans).
(0)
B.3 Similarity- Filtering
Our similarity calculation (7) is practical and efficient it leverages model M's hidden states I rather than external Sentence-BEKT embeddings (Reimers & Gurevych, 2019; Kuhn et al., 2023; Lin et al., 2024b). Because these hidden states are produced "for free" during autoregressive decoding, no additional computational overhead is incurred. In contrast, extracting Sentence-BERT embeddings would require multiple extra forward passes through separate model that employs different vocabulary and tokenization scheme. Moreover, due to the autoregressive nature of M, the hidden states corresponding to the same token at different positions are not necessarily identical:
Im # hn and 0 < h < 1, Vm, 11 S.f. Xm = Xn, 111 # 11,
(16)
This property helps reduce the risk of inadvertently filtering out short indicator tokens, such as "yes", "no", or multiple-choice options, when relying on external embeddings. Although several studies indicate that last-layer hidden states may be suboptimal for capturing semantics (Li & Li, 2024; Liu al., 2024), our current configuration performs adequately in practice. We therefore leave systematic search for improved semantic representations to future work.
C Experiment Setup Details
C.1 Datasets and Processing
We evaluate our approach using three widely recognized reasoning datasets that span vari- ous domains, including mathematical problem solving, logical reasoning, and commonsense reasoning. Only fest partitions of the datasets are used for evaluation.
GSMSK (Cobbe et al., 2021): A dataset comprising 8,792 (7,473 for training and 1,319 for test) high-quality grade school math word problems that require multi-step reasoning. Each problem includes a question and a detailed, step-by-step solution.
MATH (Hendrycks et al., 2021): A collection of 12,500 (7,500 for training and 5,000 for test) challenging competition-level math problems covering subjects such as algebra, geometry, calculus, and more. Each problem is paired with a detailed solution.
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BIG-Bench Hard (BBH) (bench authors, 2023; Suzgun et al., 2023): A subset of BIG- Bench consisting of 23 tasks identified as particularly challenging for LLMs, summariz- ing to 6,511 test instances in total. These tasks span domains such as logical reasoning, mathematics, and commonsense reasoning. In addition to providing the correct an- swers, BBH includes detailed CoT reasoning annolations for each question, thereby enabling the evaluation of both final answers and intermediate reasoning processes.
For the mathematical reasoning tasks on GSM8K and MATH, we employ zero-shot prompt- ing strategy without additional formatting instructions, ensuring that models generate responses directly from the input questions. In most cases, the answers from all models are straightforwardly extractable. However, gemma-2 models require additional guidance; they are explicitly instructed to enclose their final answers within |boxed wrapper to facili- tate easier extraction. For BBH, we utilize 3 provided in-context examples, supplemented with explicit instructions and modified prompts. These modifications direct the models to encapsulate their final answers within the (boxed{) wrapper, ensuring consistent and reliable answer extraction across the dataset.
During our experiments, we set the maximum sequence length to 1,024 tokens for GSM8K and MATH, and to 1,536 tokens for BBH to accommodate the in-context examples the latter dataset. For DeepSeek-R1, we further extend this limit by an additional 512 tokens to incorporate the "deep thinking" tokens.
Our implementation separates answer generation from the uncertainty quantification step. Once an answer is generated, we first extract and evaluate it to verify its correctness. If no answer is extracted, the instance is excluded from the UQ evaluation. Next, we subsample the instances to balance the number of correct and incorrect predictions, ensuring reliable estimation of the calibration metrics. Specifically, if the number of correct predictions is lower than that of incorrect ones, we randomly sample a matching number of incorrect predictions. If both groups exceed 500 instances, we randomly select 500 instances from each group. Although this step does not affect the UQ scores, it does influence both the AUROC and ECE metrics. Therefore, we repeat the subsampling process five times and report the mean and standard deviation of the results.
C.2 Baselines
In $ 5, we compare the three variants of our proposed method, UQAC, namely PM, P.M.smm/ and PMM, against diverse set of baselines. These baselines are selected to cover broad spectrum of uncertainty quantification techniques, incorporating both token-level and response-level approaches. In particular, we consider the following methods:
1. PM (Xans Xcot, Xinstrr: The joint conditional probability of the answer, conditioned on both the CoT reasoning and sequence and the instruction sequence.
2. PMM (Xresp ):nstr): The joint conditional probability of the entire response given the instruc- tion.
3. P PM (Xans:: The mean conditional probability computed over the answer tokens.
4. P M (Xres)): The mean conditional probability computed over all tokens in the response.
Predictive Entropy H (Kuhn et al., 2023): A token-level uncertainty measure that aggre- gates entropy over the response, where the value do not have fixed range:
Linstr Laesp
H. E 10, Leepp]
Σ
Σ (o PM X
(17)
L= +1
Length-Normalized Predictive Entropy (Malinin & Gales, 2021): It normalizes the predictive entropy by the response length to account for variations in output size:
H
H E 0,
(18)
Lresp
7. Self-Consistency (Wang et al., 2023): The probability averaged over 5 independently sampled answers, thereby reflecting the consistency of the model's outputs. We use temperature of 0.5 to balance the samples' accuracy and diversity.
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8. Verbalized Uncertainty (Xiong et al,, 2024): A modee--generaeed confidence score obtained via additional prompting.
The first six baselines derive their uncertainty estimates directly from token probabilities, while the latter two rely on aggregating information from multiple or additional model outputs to capture uncertainty at higher level. It is important to note that earlier ap- proaches, such as the semantic entropy methods proposed in (Kuhn et al., 2023; Lin et al., 2024b), provide only a weaker approximation of Self-Consistency. These methods focus capturing lexical diversity but do so at the expense of substantially higher computational overhead, In addition, the semantic ambiguity are minimal in our reasoning tasks, making these methods less relevant. Consequently, we neglect such methods.
In appendix E, we report additional experimental results for several UQAC variants and baselines that were not included in the main discussion. These additional methods, although derived from our primary baselines, possess less rigorous theoretical foundations and exhibit inferior performance in our experiments. They are detailed below:
9. Averaged Attention Approximation UQAC-P Mattnn This variant approximates the predictive distribution using attention scores, which are averaged over all tokens in the attention chain Xattm (see $ 4.3).
10. Averaged Similarity Approximation UQAC-P Similar to the previous variant, this method employs similarity-based approximations of the predictive distribution, averaging over tokens in the similarity-filteree attention chain xaunn (refer to 4.3).
11. Predictive Answer Entropy H. (Nans): This metric is analogous to the predictive entropy but is calculated exclusively over answer tokens. It is defined as
Linstr Leesp
H. (Xans) =
E (x)lxe))) log PM (x(xxx)))) Linstr 1
Σ
(19)
12. Predictive Answer Length-Normalized Entropy (Xans): This is the length-normalized version of the predictive answer entropy, computed as
H (Xaas)
H. (Xans) =
(20)
Lans
where Laans denotes the length of the answer.
In our results tables (e.g,, Table 1), we present the full mathematical expressions for baselines that have a robust theoretical basis and are computed exactly as defined. For methods lacking such foundations, we adopt a shorthand notation (e.g., (Xans) or P MM, for clarity. All reported entropy metrics are computed using - H. as shown in Table 1.
C.3 Evaluation Metrics
The receiver operating characteristic area under the curve (AUROC) is a widely used metric in binary classification tasks. The ROC curve is constructed by plotting the true positive rate (TPR, also known recall) against the false positive rate (FPR) for varying decision thresholds E (0, Given the counts of true positives (TP), true negatives (IN), false positives (FP), and false negatives (FN), the TPR and FPR are computed as
AUROC
TP
FP
TPR
FPR
(21)
TP
FP + TN
The AUROC represents the probability that randomly selected positive instance is ranked higher than randomly selected negative instance. Formally, it is defined as
d ROC-AUC = TPR((), FFR(()) dt, dt
(22)
and in practice, it is often approximated using numerical integration methods.
We scikit-learn's auc score function in our implementation.
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While AUROC is effective in evaluating the discriminative ability of a classifier, i.e. its capacity to separate correct from incorrect predictions, it does not assess the calibration of the predicted confidence scores. Calibration refers to the degree of agreement between the predicted probabilities and the actual likelihoods of the outcomes. For instance, consider scenario with three instances having predicted confidence scores of 0.9, 0.5, and 0.1, where the first two predictions are correct and the third is incorrect. In this case, AUROC would yield score of 1, indicating perfect separation. However, the same AUROC score of 1 would result even if the predictions were assigned extremely low and uninformative confidence values (e.g,, 9 10 3, 8 x 10 10 and 7.99 x 10 10), despite the fact that such scores lack meaningful interpretation. Consequently, high AUROC does not guarantee that the confidence estimates reflect the true probability of correctness. If model outputs maximum estimated confidence of only 1 10- across 10,000 instances, users might be misled about the model's overall certainty despite an ostensibly perfect AUROC.
To address this limitation, also incorporate calibration metrics into our evaluation, with a particular focus on the Expected Calibration Error (ECE; Naeini et al., 2015). ECE quantifies the average discrepancy between predicted probabilities and the corresponding empirical frequencies. In the binary classification setting, the set of predicted probabilities
ECE
{Pn J is partitioned into S equal-width bins (with S = 20 in our experiments). Formally, for each bin s E {1,..., S}, we define
B: = {n E (I,...,N) Pn E (Ps.Pstal)
(23)
The ECE is then calculated
Bg (B.) conf(B.)),
ECE
(24)
1
acc(B,)
Vn,
co,)(B,)
Σ B
Pm.
Bg
B&g
REB,
In this formulation, (B,) represents the empirical accuracy within bin and conf(B.) de- notes the average predicted confidence. Here, [B, is the number of instances in bin s (while the notation |- denotes the absolute value when applied real numbers). By quantifying the calibration error, ECE provides critical insights into how well the predicted confidence scores align with actual prediction accuracy, thereby complementing the discriminative evaluation offered by AUROC.
D Result Discussion
D.1 Potential Overfitting
On GSM8k, nearly all uncertainty quantification methods show a significant performance gap compared to those on more challenging datasets. As illustrated in Figure 3f versus Figures 3d and 3e, GSM8k exhibits a marked overconfidence: the probability distribution is highly centralized around 1 and the calibration curve deviates substantially from the ideal diagonal. This behavior suggests that state-of-the-art LLMs may be overfitting on GSM8k, thereby questioning its reliability benchmark for evaluating LLM capabilities.
D.2 Response Lengths
Figure 4 illustrates the lengths of the entire response sequences Leesp and the attention chain Laun, categorized by answer correctness. The lengths of the similarity-filereed chain (In)))) are omitted as they are controlled. Across all models, Laun is less than 10% of Lresp, demonstrating that the attention backtracking function f effectively reduces computational overhead. Additionally, while Leesp is noticeably longer for incorrect predictions, this difference is less pronounced for Lattn- Given that tokens in the attention chain have a higher average similarity to the answer tokens (shown in Figure/ 7 with sim (ans, Nattm) 0.257 versus sim Nans, Xresp) = 0.206), these results confirm that f successfully captures the reasoning process and identifies critical tokens.
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1.2-1=33.-11B
Llamu-3.2-11
Llamo-3.2-1B
Llama-3.2-3B
Llame-3.2-3B
Llama-1.2 1.2-3B
Llama-3.1-88
Llama-3.
Lluma 3.1-a-311-81
gemma2-2h
gemmal-2b-
gemmaa-22
gemma2-9h
gemmas-9bb
gemmal-99b
Qwen2.5- 5-1.5.511.58
Qwea2.5-1
Qwen2.5 5-55B
Qwen2.5-38
QwenZ: 5-3B
Qwen2.5-38
Qwen2.5-78
Qwen2. 5.B
Qwen2.5.77
DeepSeek RI
DeepSeek R1-8B
DeepSeek RI R1-SB-
Similarity
Similarity
Similarity
(a) GSM8k
(b) MATH
(c) BBH
Figure 7: Average token similarity between the answer tokens Xans and 1) the attention chain tokens Xattn (blue bars) and 2) the response tokens Xresp (gray bars). The similarity scores are computed by averaging the cosine similarities of token embeddings over all examples. It shows that Xattn tokens are inherently more similar to Xans tokens than average Xresp tokens, indicating that the attention chain is more likely to capture the answer-relevant context.
D.3 Computational Overhead
Figure 2 illustrates the average computational overhead (excluding T/O) measured on the Llama-3.1-8B model when generating outputs of approximately 500 tokens. Here, "Infer" refers to the baseline inference time needed to generate responses; "VU" denotes the Verbal- ized Uncertainty approach; and "SC" indicates Self-Consistency with sampled responses. Compared to standard inference, UQAC introduces only slight computational overhead, demonstrating higher efficiency compared to the Verbalized Uncertainty method. con- trast, although Self-Consistency achieves superior calibration performance, it substantially increases computational requirements. This overhead makes Cols-Connsttncyy less feasible for real-time applications, particularly in scenarios demanding extensive output generation or strict latency constraints.
D.4 Syyee-PPraamelee
Tables 5-9 present additional experiments that analyze how various hyper-parameters affect UQAC's performance. Specifically, K denotes the number of attention heads in (4); is the attention-weight threshold in (6); L/ttn is the length of the similarity-filee -ilttered token sequence x defined in (8); and represents the similarity threshold. The configuration highlighted in light blue corresponds to the setup reported in the main paper.
K
0
AUROC
ECE
attn
0.3
10
0.0
65.38 + 1.05
18.08 0.75
0.5
10
0.0
65.09 + 1.12
18.62 0.98
0.7
10
0.0
65.61 + 1.08
17.64 + 0.82
16
0.3
10
0.0
64.42 1.21
18.71 1.07
0.5
10
0.0
64.15 115:110
18.88 1.02
16
0.7
10
0.0
64.62 1 1.38
19.10 1 1.11
32
0.3
10
0.0
63.88 1 1.45
19.52 1 1.37
32
0.5
10
0.0
63.76 1.33
19.24 = 1.24
32
0.7
10
0.0
63.30 + 1.45
19.32 1.38
16
0.5
0.0
65.14 1.04
23.85 0.97
16
0.5
8
0.2
64.81 + 1.00
24.10 1.00-00 0.96
16
0.5
8
0.5
61.90 + 1.01
31.33 + 0.91
16
0.5
10
0.2
64.21 1.22
20.02 1.30
0.5
10
0.5
6
29.47 1.16
16 0.5
12
0.0
63.60
19.67 0.95
16 0.5
12
0.2
63.01 - 1.14
20.12 +
16
0.5
12
0.5
61.55
+ 1.08
29.32 + 1.01
Table 5: Hyper-parameter study of -lama-3.2-11 on GSM8K.
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0
L
attn
AUROC
ECE
0.3
10
0.0
58.30 + 0.70
34.90 = 0.34
0.5
10
0.0
58.68 - 0.87
34.85
0.7
10
0.0
59.28 1: 0.51
34,62 4.23
16
0.3
10
0.0
57.73 +: 0.55
34.98 + 0.30
16
0.5
10
0.0
57.53 +: 0.60
35.11 0.28
0.7
10
0.0
58.27 0.41
34,94 0.20
32
0.3
10
0.0
58.16 + 1.01
35.38 0.05
32
0.5
10
0.0
58.62 = 0.98
35.69 = 0.25
32
0.7
10
0.0
58.57 + 0.82
34.99 0.43
16
0.5
0.0
60.30 + 0.40
38.86 0.37
16
0.5
0.2
60.66 + 0.49
38.93 0.34
16
0.5
0.5
48.07 + 0.64
49.87 0.85
16
0.5
10
0.2
58.17 + 0.73
35.20 + 0.32
16
0.5
10
0.5
47.75 0.55
47.87 0.66
16
0.5
12
0.0
58.13
31.74 0.56
16
0.5
12
0.2
58.64 - 0.79
32.05 0.64
16
0.5
12
0.5
47.65 + 0.57
46.08 0.64
Table 6: Hyper-parameter study for Qwen2.5-1.5B on GSM8K.
attn
T
AUROC
ECE
0.3
10
0.0
68.36
35.77 0.43
0.5
10
0.0
68.43 = 0.61
35.72 0.40
0.7
10
0.0
68.80 + 0.52
35.94 0.33
16
0.3
10
0.0
68.30 + 1.06
35.28 0.39
16
0.5
10
0.0
68.10 1: 0.99
35.45 0.47
0.7
10
0.0
67.99 0.93
35.68 0.34
32
0.3
10
0.0
69.24 + 0.99
34.70 0.26
32
0.5
10
0.0
68.99 + 0.93
34,92 = 0.21
32
0.7
10
0.0
69.19 0.75
35.05 0.11
0.5
0.0
69.14 0.77
38.97 0.35
16
0.5
0.2
69.18 + 0.76
38.99 0.36
16
0.5
8
0.5
67.92 + 0.68
40.32 + 0.36
16
0.5
10
0.2
68.14
35.47 0.49
16
0.5
10
0.5
66.7010.7
37.78 0.32
0.5
12
0.0
67.89
30.59 0.44
16
0.5
12
0.2
67.94
0.91
30.60 0.47
16
0.5
12
0.5
66.43 0.63
33.98 0.26
Table 7: Hyper-parameter study for gemma-2-2b on GSMSK.
K
0
L'
AUROC
ECE
attn
0.3
10
0.0
73.31 0.64
15.77
0.71
0.5
10
0.0
73.56 1 0.67
15.01
1.83
0.7
10
0.0
73,87
1 0.73
1..2
16
0.3
10
0.0
73.92
1.07
15.68 0.56
16
0.5
10
0.0
74.08
1.19
0.73
16
0.7
10
0.0
+ 73.97#111
1..96
32
0.3
10
0.0
74.22
0.90
14.62 + 0.64
32
0.5
10
0.0
74.41
+ 0.84
14.59 4 0.45
32
0.7
10
0.0
74.02
+ 0.85
13.86 0.44
0.5
0.0
74.86
0.96
17.25 0.41
16
0.5
12
0.0
74.18 + 1.16
14.11 0.93
Table 8: Hyper-parameter study for gemma-2-2b MATH.
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K
0
attn
L
T
AUROC
ECE
0.3
10
0.0
57.60 + 1.01
25.76 1
0.5
10
0.0
58.11 0.61
25.50
0.7
10
0.0
59.32 1 0.79
25.25 1.38
16
0.3
10
0.0
56.43 1: 0.81
26.76
16
0.5
10
0.0
56.59 0.77
26.39 06.99:0066
0.7
10
0.0
58.10
32
0.3
10
0.0
56.73 - 0.65
0.65
32
0.5
10
0.0
57.18 + 0.69
26.01 0.65
32
0.7
10
0.0
58.83 + 1.04
25.45 + 0.68
16
0.5
12
0.0
56.63
+ 1.05
25.87 0.97
0.5
16
0.0
59.25 - 0.97
24.16 0.79
Table 9: Hyper-parameter study for Gemma-2-2b on BBH.
E
Complete Results
Tables 10-36 present the complete results for all experiments in the main paper.
AUROC
ECE
P. Pa (Xans)
62.85 + 0.31
48.93 0.14
M (Xresp)
65.47 + 0.80
36.81 0.05
Token Probability
PM (Nans Acot, Xinstr)
63.62 + 0.32
48.47 + 0.15
PM (Krespl Kinstr)
68.71 0.41
50.00 0.00
H
65.27 + 0.95
20.22 + 0.13
H (Xans)
62.65 + 0.27
47.56 + 0.28
Token Entropy
H
67.54 1 0.74
H (Xans)
63.46 0.29
Verbalized Uncertainty
53.75 0.57
30.85 0.43
Multi-Round Prompting
Self-Consistency
72.77 + 0.95
14.21 + 0.77
M,attn
62.40 1.23
38.49 0.11
P M,siim
63.04 1.20
42.35 0.14
UQAC
M,,
61.39 0.88
44.01 0.21
M
63.33 1.17
20.95 0.62
PM
64.75 1.19
19.54 1.27
Table 10: Llama-3.2 3.1--1----------------- results on the GSM8k dataset.
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AUROC
ECE
M (Nans)
59.19 0.74
49.23 0.05
M (Xresp)
64.03 0.62
38.79 0.03
Token Probability
PM (Kans) &eot, Xinstr)
59.76 + 0.74
49.06
0.05
PM (Fresp Xinstr)
68.75 0.51
50.00 0.00
H
64.72 0.54
24.18
0.07
H Xans)
60.00 0.78
48.25 0.05
Token Entropy
H
68.22 + 0.67
H (Xans)
60.55 0.77
Verbalized Uncertainty
63.31 + 0.40
38.60 + 0.22
Multi-Round Prompting
Self-Consistency
70.35 + 0.76
28.80 0.35
M,attn
61.99 + 0.62
41.08 + 0.04
M,sim
59.06 0.52
44.50 0.05
UQAC
Mattn
60.94 + 0.74
38.55 + 0.58
M,sim
58.85 + 0.50
22.80 + 0.47
PM
59.08 + 0.55
27.51 + 0.20
Table 11: Llama-3.2 3.2-3B-Insttunet results on the GSM8K dataset.
AUROC
ECE
P. PM (Xans)
68.71 1.12
49.64 0.02
M (Xresp)
61.14 1.10
41.65 0.05
Token Probability
PM (Xans Kcol Xinstr)
68.90 + 1.11
49.47 0.03
PM (Kresp Kinstr)
68.17 1 0.98
49.99 1 0.00
H
61.07 1.09
30.12 0.11
H Xans)
72.10 1.24
49.32 0.08
Token Entropy
H
67.59 + 1.05
H (Xans)
72.30 1.23
Verbalized Uncertainty Self-Consistency
62.27 1 0.48
45.24 1 0.10
Multi-Round Prompting
67.53 1 1.04
37.01 1 0.44
M,attn
53.35 + 1.11
42.08 + 0.09
M,sim
57.72 + 1.54
47.45 + 0.06
UQAC
P a,a
52.41 + 1.42
41.25 + 1.19
P MMa
57.64 + 1.58
31.16 + 0.56
PM
58.66 + 1.03
36.39 + 0.22
Table 12: Meta-Llama-3. 3.1---.-1-11-tttt results on the GSM8k dataset.
24

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Published as a conference paper at COLM 2025
AUROC
ECE
P. M (Xans)
61.54 0.44
49.60 0.03
P. M (Xresp)
70.09 0.29
42.23
0.04
Token Probability
PM (Xans) Keoot Xinstr)
60.20 + 0.43
49.14 + 0.04
PM (Xresp Kinstr)
73.24 0.78
49.99 + 0.00
H
71.47 0.42
33.54 1 0.11
H (Xans)
61.54 0.44
48.84
0.07
Token Entropy
H
73.22 + 0.77
H (Xans)
60.05 0.42
Verbalized Uncertainty
58.14 + 0.69
41.91 + 0.09
Multi-Round Prompting
Self-Consistency
38.75 10.00
34.13 = 3.36
M,attn
65.71 + 1.10
44.52 + 0.04
M,sim
66.31 1.02
46.94 + 0.04
UQAC
M,attn
65.76 + 0.79
32.48 + 0.26
P. M,Msim
65.83 + 1.02
27.70 + 0.84
PM
68.10 + 0.99
35.45 + 0.47
Table 13: gemma-2-2b-tt results on the GSM8K dataset.
AUROC
ECE
P. P.M (Xans)
50.35 0.61
49.90 0.01
M (Xresp)
55.62 1.55
45.51 0.05
Token Probability
PM (Xans Kcol Xinstr)
49.45 + 0.71
49.92 0.03
PM (Kresp Kinstr)
60.31 1 0.59
50.00 1 0.00
H
59.60 1.43
41.62 0.08
H (ans)
43.75 0.52
49.85 0.02
Token Entropy
H
64.90 + 1.25
H (Xans)
43.01 0.43
Verbalized Uncertainty Self-Consistency
51.38 1 0.08
49.75 1 0.01
Multi-Round Prompting
53.45 1 1.82
31.82 1.35
M,attn
57.16 + 0.94
46.81 + 0.02
M,sim
66.76 + 1.12
48.59 + 0.02
UQAC
P PMM
58.64 + 0.77
26.15 + 0.56
MMa
66.47 + 1.11
36.54 + 0.24
PM
65.39 1 1.05
44.48 + 0.10
Table 14: gemma-2-9b-it results on the GSM8k dataset.
25

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
58.28 0.74
49.77 0.01
M (Xresp)
65.32 0.70
43.32 0.03
Token Probability
PM (Kans) &cot, Xinstr)
58.06 + 0.70
49.69 0.05
PM (Tresp Xinstr)
71.01 0.55
50.00 0.00
H
65.58 0.70
33.02
0.06
H Xans)
58.32 0.73
49.30 0.02
Token Entropy
H
71.43 + 0.53
H (Xans)
58.06 0.70
Verbalized Uncertainty
52.08 + 0.44
42.96 + 0.09
Multi-Round Prompting
Self-Consistency
75.12 + 0.47
27.65
0.23
M,attn
59.48 + 0.71
43.32 + 0.03
M,sim
58.18 0.98
46.79 0.07
UQAC
Mattn
58.96 + 0.67
40.42 + 0.41
M,sim
57.82 + 0.97
28.13 + 0.63
PM
57.97 + 0.60
34.76 + 0.27
Table 15: S.wen2.5-1.5B-Insttuu results on the GSM8k dataset.
AUROC
ECE
P. PM (Xans)
57.17 0.18
49.82 0.03
M (Xresp)
57.29 0.89
42.45 + 0.04
Token Probability
PM (Xans Kcol Xinstr)
56.52 + 0.22
49.44 + 0.07
PM (Kresp Kinstr)
67.71 + 0.42
50.00 1 0.01
H
57.26 0.90
30.84 0.10
H Xans)
57.40 0.12
49.53 0.07
Token Entropy
H
68.44 + 0.34
H (Xans)
56.00 0.20
Verbalized Uncertainty Self-Consistency
51.68 1 0.10
49.77 1 0.01
Multi-Round Prompting
71.88 1: 0.31
33.92 1 0.14
M,attn
52.84 + 1.20
42.74 + 0.08
M,sim
57.13 + 1.42
46.42 1 0.10
UQAC
P MMatttn
56.48 + 0.58
43.01 + 0.68
MMa
56.96 + 1.41
31.85 + 0.46
PM
56.78 1 1.10
36.90 + 0.46
Table 16: Doven255-3B-Instee results on the GSM8k dataset.
26

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
53.54 0.95
49.82 0.01
M (Xresp)
54.21 1.24
44.53
Token Probability
PM (Kans) &eot, Xinstr)
52.92 + 0.99
49.58
0.03
PM (Kresp Xinstr)
61.27 1.26
49.98 0.02
H
54.70 1.07
36.19 0.07
H Xans))
49.25 1.01
49.65 0.04
Token Entropy
H
61.88 + 1.11
H (Xans)
46.73 1.11
Verbalized Uncertainty Self-Consistency
53.77 + 0.37
49.04 + 0.05
Multi-Round Prompting
64.74 + 1.06
41.17 0.35
M,attn
50.55 + 1.21
46.80 + 0.07
M,sim
53.08 0.95
47.61 0.05
UQAC
Mattn
53.18 + 1.18
27.35 + 0.89
M,siim
52.91 + 0.93
33.34 + 0.23
PM
49.98 + 0.83
42.39 + 0.26
Table 17: Dwven..5-7B-nnsfie results on the GSMSk dataset.
AUROC
ECE
P. P. (Xans)
76.36 0.46
47.62 0.03
M (Xresp)
56.52 0.22
41.55 0.02
Token Probability
PM (Xans Kcol Xinstr)
77.25 + 0.40
41.03 + 0.07
PM (Kresp Kinstr)
61.04 1 0.74
50.00 1 0.00
H
56.49 0.27
31.02 0.10
H Xans)
76.10 0.49
44.46 0.08
Token Entropy
H
61.06 + 0.84
H (Xans)
77.39 0.39
Verbalized Uncertainty
48.06 1 1.25
37.65 1 0.98
Multi-Round Prompting
Self-Consistency
82.62 1 0.59
11.41 1 0.40
M,attn
55.93 + 0.45
41.38 + 0.02
P M,sim
63.58 1 0.71
46.10 + 0.05
UQAC
P a,a
57.92 + 0.54
43.37 + 0.31
MMa
66.38 + 0.70
19.82 + 0.61
PM
70.96 1 0.85
25.06 + 0.24
Table 18: DeepSeek-Rl-Distiie -itamall--Lam--BB results on the GSM8K dataset.
27

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
69.59 0.85
48.91 0.17
M (Xresp)
66.19 1.58
40.13 0.06
Token Probability
PM (Kans) &cot, Xinstr)
68.90 + 0.86
46.71 + 0.26
PM (Fresp Xinstr)
79.93 0.90
50.00 0.00
H
65.87 1.59
27.73 0.09
H Xans)
69.52 0.81
48.02 0.30
Token Entropy
H
78.93 + 0.73
H (Xans)
68.79 0.81
Verbalized Uncertainty
55.25 + 0.74
44.05 + 0.51
Multi-Round Prompting
Self-Consistency
82.03 + 0.80
9.77 + 1.04
M,attn
66.92 + 0.95
39.64 + 0.10
M,sim
65.90 1.33
44.94 0.10
UQAC
Mattn
69.48 + 1.41
47.48 + 0.49
M,sim
67.22 + 1.19
17.48 + 0.96
PM
67.92 + 1.07
20.65 + 0.51
Table 19: Llama-3.2 results on the MATH dataset.
AUROC
ECE
P. PM (Xans)
70.93 1.37
47.15 0.17
M (Xresp)
64.72 1.00
40.57 0.12
Token Probability
PM (Xans Kcol Xinstr)
70.82 + 1.46
42.62 + 0.25
PM (Kresp Kinstr)
75.37 1 1.50
50.00 1 0.00
H
64.56 0.99
28.73 0.28
H Xans)
70.87 1.35
45.18 0.37
Token Entropy
H
74.59 + 1.59
H (Xans)
70.79 1.45
Verbalized Uncertainty Self-Consistency
60.98 1 0.90
41.51 1 0.21
Multi-Round Prompting
74.04 1 0.55
12.66 0.88
M,attn
63.62 + 1.13
40.69 + 0.12
M,sim
65.04 + 0.76
44.75 1 0.06
UQAC
P a,a
63.95 + 1.61
46.88 + 0.68
MMa
66.58 + 0.83
20.92 + 0.84
PM
68.40 1 0.89
21.14 1 0.81
Table 20: Saama-3.2-3B-Insttt results on the MATH dataset.
28

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
77.71 1.72
48.10 0.25
M (Xresp)
68.62 1.80
40.41 0.13
Token Probability
PM (Kans) &eot, Xinstr)
76.59 + 1.69
44.93 0.48
PM (Tresp Xinstr)
81.03 1.16
50.00 0.00
H
68.19 1.73
27.52
0.26
H Xans)
77.72 1.69
46.83 0.48
Token Entropy
H
80.38 + 1.20
H (Xans)
76.45 1.68
Verbalized Uncertainty
60.17 + 0.75
46.44 + 0.33
Multi-Round Prompting
Self-Consistency
82.01 + 1.53
14.99 0.54
M,attn
65.01 + 1.63
39.46 + 0.17
M,sim
66.53 1.24
44.92 0.18
UQAC
Mattn
64.70 + 0.68
45.17 + 0.45
M,sim
67.86 + 1.02
18.57 + 1.02
PM
70.00 + 1.14
21.97 + 1.62
Table 21:
results on the MATH dataset.
AUROC
ECE
P. PM (Xans)
73.22 0.73
45.91 0.18
M (Xresp)
71.01 + 1.38
37.54 0.09
Token Probability
PM (Xans Kcol Xinstr)
72.82 + 0.82
34.13 - 0.25
PM (Kresp Kinstr)
78.88 1 0.62
50.00 1 0.00
H
71.46 1.31
21.70 0.22
H Xans)
73.33 0.75
40.67 0.23
Token Entropy
H
77.26 + 0.76
H (Xans)
72.76 0.85
Verbalized Uncertainty Self-Consistency
60.26 1 0.65
40.80 1 0.26
Multi-Round Prompting
77.26 1 0.80
18.44 1.93
M,attn
72.97 + 1.27
39.76 + 0.05
M,sim
70.97 + 1.06
43.38 1 0.10
UQAC
P aMM
74.57 + 1.32
43.64 + 0.21
MMa
72.91 + 1.29
15.74 + 1.48
PM
74.09 1 1.18
15.23 + 0.73
Table 22: gemma-2-2b-it results on the MATH dataset.
29

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
69.26 0.78
48.62 0.15
0.15
M (Xresp)
67.87 1.50
43.17
Token Probability
PM (Kans) &cot, Xinstr)
69.22 0.72
43.89 + 0.35
PM (Fresp Xinstr)
76.38 1.18
50.00 0.00
H
70.38 1.38
34.50 0.12
H Xans)
69.35 0.76
46.85 0.25
Token Entropy
H
77.39 + 1.10
H (Xans)
69.33 0.72
Verbalized Uncertainty Self-Consistency
57.55 + 0.51
49.01 + 0.05
Multi-Round Prompting
84.51 + 1.13
19.22 - 0.50
M,attn
67.12 + 1.43
44.10 + 0.10
M,sim
62.52 1.04
47.07 0.11
UQAC
Mattn
70.35 + 1.68
38.73 + 0.63
MMsii
63.72 + 1.07
24.12 + 1.09
PM
64.21 + 0.88
31.06 + 0.93
Table 23: gemma-2-9be results on the MATH dataset.
AUROC
ECE
P P. (Xans)
79.43 1.85
48.69 0.11
M (Xresp)
73.66 2.22
44.35 0.04
Token Probability
PM (Xans Kcol Xinstr)
79.72 + 1.66
46.07 = 0.32
PM (Kresp Kinstr)
82.17 1 1.66
50.00 1 0.00
H
73.73 2.22
35.76 0.09
H Xans)
79.44 + 1.85
46.53 0.37
Token Entropy
H
82.14 + 1.63
H (Xans)
79.75 1.64
Verbalized Uncertainty Self-Consistency
55.09 1 0.90
44.61 1 0.32
Multi-Round Prompting
78.30 1 0.53
14.58 0.34
M,attn
67.87 + 1.14
44.10 + 0.06
M,sim
69.33 + 2.06
47.25 + 0.10
UQAC
P a,a
68.17 + 0.84
39.55 + 0.46
MMa
70.17 + 2.09
22.90 + 0.90
PM
71.71 +: 2.01
31.45 + 0.72
Table 24: Swwe2.5-11.B.. Instrrutttt results on the MATH dataset.
30

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
79.03 0.83
49.34 0.08
M (Xresp)
71.05 1.11
44.50 0.10
Token Probability
PM (Kans) &eot, Xinstr)
78.94 + 0.89
47.61 0.10
PM (Tresp Xinstr)
79.30 0.72
50.00 0.00
H
70.92 1.14
36.13
0.24
H Xans)
79.21 0.77
48.08 0.19
Token Entropy
H
79.53 + 0.67
H (Xans)
79.14 0.87
Verbalized Uncertainty
52.46 + 0.34
49.56 + 0.04
Multi-Round Prompting
Self-Consistency
78.26 + 1.77
20.61 0.43
M,attn
67.15 + 0.95
45.03 + 0.10
M,sim
66.73 1.31
48.29 0.05
UQAC
Mattn
68.94 + 0.67
37.92 + 0.37
M,sim
67.37 + 1.45
31.73 + 0.44
PM
69.92 + 1.24
38.80 + 0.63
Table 25: 1eee2..53--Instruue results on the MATH dataset.
AUROC
ECE
P. PM (Xans)
77.65 1.05
49.26 0.10
M (Xresp)
68.63 1.31
45.43 0.05
Token Probability
PM (Xans Kcol Xinstr)
77.97 + 1.16
47.78 + 0.15
PM (Kresp Kinstr)
79,42 1 0.57
50.00 1 0.00
H
68.82 1.32
38.54
0.12
H Xans)
79.34 + 0.95
48.09 0.19
Token Entropy
H
79.53 + 0.54
H (Xans)
79.12 1.08
Verbalized Uncertainty Self-Consistency
61.96 1 0.46
47.34 1 0.12
Multi-Round Prompting
74.83 1 0.42
25.52
0.47
M,attn
57.85 + 0.59
47.46 + 0.13
M,sim
58.33 + 0.94
48.04 + 0.12
UQAC
P MMMtttn
59.28 + 0.66
25.96 + 0.94
MMa
59,42 + 0.91
34.36 + 0.64
PM
62.58 1 1.19
40.80 + 0.43
Table 26: S.wen2.5-B-Innstree results on the MATH dataset.
31

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
82.39 1.01
48.62 0.00
M (Xresp)
37.31 2.22
39.63
Token Probability
PM (Kans) &cot, Xinstr)
81.40 + 1.12
44.91 0.15
PM (Tresp Xinstr)
33.70 1.31
50.00 0.00
H
36.18 2.30
26.65 0.35
H Xans)
82.22 1.06
46.54 0.03
Token Entropy
H
30.75 + 1.81
H (Xans)
81.28 1.18
Verbalized Uncertainty
47.36 + 3.65
36.77 + 2.41
Multi-Round Prompting
Self-Consistency
65.51 + 1.39
22.00 1.70
M,attn
56.11 + 1.24
40.43 + 0.11
M,sim
67.82 1.06
46.39 0.07
UQAC
P Mattn
52.44 + 1.61
44.73 + 0.78
M
69.00 + 0.99
20.92 + 1.65
PM
69.94 + 1.08
27.94 + 0.59
Table 27: DeepSeek-R1- results on the MATH dataset.
AUROC
ECE
P. PM (Xans)
53.05 0.69
36.02 1.03
M (Xresp)
58.98 2.07
40.69 0.19
Token Probability
PM (Xans Kcol Xinstr)
58.57 + 0.41
25.95
PM (Kresp Kinstr)
56.71 1 1.36
33.73 1 0.99
H
62.18 1.79
31.12 0.46
H Xans)
52.12 0.96
29.82 1.10
Token Entropy
H
57.68 + 1.37
H (Xans)
61.60 0.75
Verbalized Uncertainty Self-Consistency
66.67 1 0.00
46.67 1 0.00
Multi-Round Prompting
71.37 1 1.44
22.10 1 0.52
M,attn
56.81 + 2.01
38.76 + 0.22
M,sim
54.66 1 2.13
36.56 + 0.57
UQAC
P a,a
60.97 + 1.40
24.97 + 1.09
MMa
59.65 + 1.63
24.11 + 0.94
PM
61.91 1 1.21
21.05 1 0.69
Table 28: Llama-3.2-1BB- 3.2--1B-Innstruct results on the BBH dataset.
32

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
64.01 1.24
40.60 0.32
M (Xresp)
63.39 0.47
44.14 1 0.14
Token Probability
PM (Kans) &eot, Xinstr)
64.22 1.08
27.21 + 0.82
PM (Fresp Xinstr)
66.29 2.03
45.21 0.49
H
61.60 0.49
36.92 0.26
H Xans)
64.23 1.16
31.08 0.39
Token Entropy
H
63.66 + 1.99
H (Xans)
64.48 0.66
Verbalized Uncertainty
59.56 + 2.39
29.45 + 0,49
Multi-Round Prompting
Self-Consistency
87.90 + 1.67
27.41 1.04
M,attn
66.16 + 1.15
42.98 + 0.17
M,sim
65.93 0.91
42.65 0.31
UQAC
Mattn
65.81 + 1.17
22.58 + 0.80
M,sim
66.17 + 0.54
18.94 + 0.66
PM
65.86 + 0.36
19.63 + 0.69
Table 29; Llama-3.2233 1amma-3.2--BInsstuuae results on the BBH dataset.
AUROC
ECE
P. PM (Xans)
61.51 1.04
46.34 0.27
M (Xresp)
66.05 1.04
43.92 0.05
Token Probability
PM (Xans Kcol Xinstr)
61.77 + 1.02
42.12 0.41
PM (Kresp Kinstr)
73.38 1 0.83
46.61 1 0.23
H
63.96 1.11
34.84 0.13
H (ans)
61.54 + 1.05
42.15 0.43
Token Entropy
H
71.76 + 0.98
H (Xans)
61.97 1.03
Verbalized Uncertainty Self-Consistency
58.82 1 1.27
30.91 1 0.53
Multi-Round Prompting
84.08 1: 0.97
35.61 1 0.56
M,attn
67.65 + 0.61
43.65 + 0.06
M,sim
67.79 + 0.37
44.15 + 0.07
UQAC
P a,a
68.79 + 1.14
21.15 + 1.17
MMa
68.58 + 0.33
19.79 + 0.44
PM
69.75 1 0.71
23.04 1 0.56
Table 30: Meta-Llama-3.11 1iaa-LLlaaa331---IInstttee results on the BBH dataset.
33

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
59.94 1.00
46.09 0.22
M (Xresp)
52.70 1.19
42.80 0.33
Token Probability
PM (Kans) &eot, Xinstr)
61.29 + 0.89
39.62 0.75
PM (Kresp Xinstr)
59.84 1.34
50.04 0.06
H
53.84 0.80
36.99
0.49
H Xans))
59.91 0.88
40.89 0.40
Token Entropy
H
59.85 + 1.49
H (Xans)
61.84 0.70
Verbalized Uncertainty
53.77 + 0.83
37.84 + 0.07
Multi-Round Prompting
Self-Consistency
82.82 + 0.89
29.16 1.05
M,attn
58.62 + 0.76
43,41 + 0.21
M,sim
58.05 0.93
44.05 0.15
UQAC
P Mattn
62.12 + 1.41
25.24 + 0.42
MMsim
59.94 + 1.20
27.45 + 1.20
PM
60.78 + 1.65
26.01 + 1.46
Table 31: gemma-2-2b-it results on the BBH dataset.
AUROC
ECE
P. PM (Xans)
72.17 1.37
46.10 0.32
M (Xresp)
59.17 + 1.49
43.57 0.05
Token Probability
PM (Xans Kcol Xinstr)
73.26 + 1.39
40.54 + 0.13
PM (Kresp Kinstr)
63.81 1 1.72
49.53 1 0.04
H
60.96 1.61
35.69 0.13
H Xans)
72.08 1.38
42.18 0.50
Token Entropy
H
66.54 + 1.61
H (Xans)
73.44 1.39
Verbalized Uncertainty
61.37 1 0.58
45.23 1 0.14
Multi-Round Prompting
Self-Consistency
77.89 1 0.98
34.13 0.20
M,attn
67.20 + 1.30
44.88 + 0.08
M,sim
71.03 + 1.28
45,43 1 0.09
UQAC
P aMM
68.17 + 1.33
22.51 + 1.26
MMa
72.46 + 1.25
19.99 + 0.82
PM
72.16 1 1.56
24.45 1 0.82
Table 32: gemma-2-9b-it results on the BBH dataset.
34

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
70.39 0.91
46.39 0.22
M (Xresp)
57.94 0.87
43.11 0.20
Token Probability
PM (Kans) &eot, Xinstr)
70.39 + 1.04
42.32 0.32
PM (Kresp Xinstr)
62.49 1.16
46.93 0.29
H
57.72 0.88
33.39
0.34
H Xans)
70.31 0.91
40.41 0.19
Token Entropy
H
62.74 + 1.22
H (Xans)
70.54 1.06
Verbalized Uncertainty
50.47 + 1.95
38.19 + 0.81
Multi-Round Prompting
Self-Consistency
74.05 + 0.65
32.22 - 0.51
M,attn
64.12 + 1.39
43,41 + 0.17
M,sim
62.08 1.40
44.14 0.17
UQAC
Mattn
64.53 + 1.20
21.12 + 0.94
M,sim
63.51 + 1.53
19.04 + 1.70
PM
65.90 + 1.38
21.35 + 1.37
Table 33: @0wen2.5-1.B-Instttue results on the BBH dataset.
AUROC
ECE
P. P. (Xans)
68.61 0.60
46.75 0.16
M (Xresp)
53.15 2.47
39.20 0.22
Token Probability
PM (Xans Kcol Xinstr)
69.10 + 0.57
42.10 0.18
PM (Kresp Kinstr)
58.17 1 2.18
49.10 1 0.05
H
52.67 2.47
25.96 0.87
H (ans)
68.67 0.66
42.47 0.28
Token Entropy
H
58.46 + 2.07
H (Xans)
69.37 0.60
Verbalized Uncertainty Self-Consistency
53.68 1 1.23
46.94 1 0.23
Multi-Round Prompting
81.87 1 1.20
33.08 1 0.89
M,attn
58.28 + 2.10
41.15 + 0.25
M,sim
61.23 + 1.84
43.21 1 0.20
UQAC
P a,a
59.01 + 1.78
28.70 + 1.57
MMa
62.06 + 1.94
23.29 + 1.74
PM
65.82 1 2.09
24.61 1 0.94
Table 34: Qwenn.5-3B-Inssfee Instruct results on the BBH dataset.
35

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Published as a conference paper at COLM 2025
AUROC
ECE
M (Nans)
70.11 0.14
48.29 0.21
M (Xresp)
63.18 1.15
43.02 0.17
Token Probability
PM (Kans) &cot, Xinstr)
70.60 + 0.20
44.73 0.18
PM (Kresp Xinstr)
68.21 1.27
40.91 0.69
H
62.42 1.05
32.88
0.35
H Xans)
69.92 0.14
45.44 0.37
Token Entropy
H
67.78 + 1.25
H (Xans)
70.61 + 0.21
Verbalized Uncertainty
61.12 + 1.06
42.73 + 0.18
Multi-Round Prompting
Self-Consistency
75.88 + 0.60
39.17 0.53
M,attn
65.00 + 1.12
44.97 + 0.19
M,sim
66.28 1.04
45.51 0.20
UQAC
Mattn
67.59 + 0.93
20.65 + 0.72
M,sim
68.22 + 1.07
24.28 + 0.69
PM
71.39 + 0.93
33.48 + 0.50
Table 35: S.wen2.5-7B-Instren results on the BBH dataset.
AUROC
ECE
P. P.M (Xans)
64.72 0.88
48.12 0.11
M (Xresp)
46.56 0.33
35.82 0.13
Token Probability
PM (Xans Kcol Xinstr)
66.02 + 0.80
45.11 + 0.20
PM (Kresp Kinstr)
41.66 1 0.42
50.00 1 0.00
H
46.42 0.31
19.97 0.49
H Xans)
63.81 0.94
45.11 0.17
Token Entropy
H
41.62 + 0.50
H (Xans)
65.76 0.81
Verbalized Uncertainty
64.20 1 1.41
35.54 1 0.21
Multi-Round Prompting
Self-Consistency
74.27 1: 1.41
20.63 1 0.84
M,attn
49.70 + 1.35
39.82 + 0.10
P M,sim
45.75 1 0.87
42.87 + 0.13
UQAC
P a,a
53.17 + 1.30
42.15 + 0.98
MMM
48.97 + 0.62
34.50 + 0.28
PM
48.89 1 0.76
27.62 + 0.91
Table 36: DeepSeek-R1-Distie Dit-Disttil-Llam---1 results on the BBH dataset.
36


Reviews:
[{"review_id": "NIT33lytf2", "reviewer": "Reviewer_tYEK", "summary": "The paper tackles the problem of quantifying the uncertainty of LLM's responses. The paper uses the common general assumption that we can quantify the uncertainty of an LLM's response by using the LLM's probability of the output sequence it generates. The paper argues that this probability is intractible to compute since the search space would be too large (though the paper doesn't mention it explicitly, I assume the search space is the size of the vocabulary raised to a number of tokens in the output). The proposed method cuts down the search space of which vocab terms to consider when creating an uncertainty measure, using the uncertainty of the attention distribution to determine which attention heads should be considered and then the tokens at each attention heads by using cumulative attention weights.\n\nThe paper uses quantitative experiments to demonstrate that the propose methods outperforms baselines in terms of quantifying the uncertainty of LLM's responses.", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "Paper provides sufficeint motivation, is well written and clear to understand.\nThe paper makes a nice contribution to the important problem of quantifying uncertainty and calibrating probabilities of LLM's outputs.\nThe paper includes good thorough quantitative experiments and analysis", "reasons_to_reject": "None really from my perspective. The paper articulates the problem, a proposed method, and experiments to demonstrate how the approach can improve model calibration. There might be better techniques or baselines to compare against but I'd rely on those who are more familiar with state-of-the-art methods for model calibration for LLMs. \n\nThe method relies on generating a chain of thought response and an open-source LLMs, neither issues I see as strong reasons to reject the paper.", "questions_to_authors": "- I am about confused about the baselines 1 and 2. Based on the paper, I thought these methods would be intractable and to hard to compute directly? Can you provide more information on how these baselines were implemented. If they are intractible to fully compute, was the a simple approach used where at each answer token, we just keep the vocabulary words that have the highest probability and then just recompute a soft-max on just those tokens?\n\n\n- When I click through to the anonymous github, most of the “requested files are not found”. Only args.py in utils is available, There is no need to include the link in the submission if the code is not ready. its better not to include the link then\n\n- related work starts out strong with discussing the issues with using comulative token-wise probabilities or entropies\n- It would be nice for the transition from related work to section 3 (problem definition) to be a bit smoother, its a stark change with no smooth transition, though I understand this writing style\n\n\n- In figure 1, it would be nice to show the final quantify for uncertainty. Is it close to 0 in this example?\n\n\n- What if a Chain of thought sequence is not provided? It seem like this method won't work, am I correct or misunderstanding? its ok if this method requires a CoT sequence, just make that clearer in the intro and/or abstract\n\n- lines 121-124 are redundant since this was already made clear in the related work, on the other hand I guess its good to repeat it, but its unnecessary \n- the paper assumes that taking the probability of the response is a good way to quantify uncertainty, this is a common assumption so thats ok but more justification for this idea would be appreciated.\n\n- line 254, put a footnote here reminding reading what these specific hyper-parameters control so that the reader doesnt have to jump back to those equations and discussion about those equations\n\n- It would be nice if the paper included some qualitative examples & analysis\n\n(this is a mix of comments & questions, no need to respond to all of them)", "extra_scores": {}}, {"review_id": "kYOWvIzVnj", "reviewer": "Reviewer_5EYn", "summary": "The paper proposes UQAC, a new method for uncertainty quantification in LLMs, which uses attention chains to identify important tokens in the reasoning process, and calculates the marginalization of these selected tokens as uncertainty.", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "This paper uses attention chains to filter the crucial tokens in CoT, which is an innovative approach in UQ. This method doesn't need finetuning or multiple times inference, which is computationally efficient.\nThe entire paper framework is well-founded and logically coherent, especially for the extraction of the attention chain and the utilization of it (attention approximation, similarity approximation, answer approximation).\nThe experiments in the paper are comprehensive: the authors use multiple reasoning datasets and compare UQAC with numerous baselines using multiple evaluation metrics, such as AUROC and ECE.", "reasons_to_reject": "In the Similarity-Based Filtering, the cosine similarity metric relies solely on the model’s hidden states and suffers from saturation zones that lead to vanishing gradients, yet the paper does not compare it against other effective similarity measures, such as[1]. Also,\nrecent studies find that the last hidden layer may not the best choice for semantic information extraction, such as[2].\n\nIn line 254, the setting of several hyperparameters, value lacks detailed evidence or ablation studies.\n\nFrom the experimental results (Table 1), it can be seen that Self-Consistency remains the best-performing method overall, while some variants of the proposed UQAC method show better performance than Self- Consistency in very few cases.", "questions_to_authors": "EXTRA REFS:\n\n[1] AoE: Angle-Optimized Embeddings for Semantic Textual Similarity (ACL 2024)\n[2] Fantastic Semantics and Where to Find Them: Investigating Which Layers of Generative LLMs Reflect Lexical Semantics (ACL 2024）\n\nTYPOS:\n\n- Line 17: reduces --> reduce\n- Line 44: Further --> Furthermore\n\nSUGGESTIONS\n\n- Given reproducibility, the authors should include the prompt, and settings of parameters such as temperature and top_p in the experiments setting within the paper.\n\n-Figure 4 shows that there is a significant difference in the reasoning sequence lengths between correct and incorrect answers on the MATH dataset, which may have influenced the results. Authors can consider conducting a controlled\nvariable experiment to analyze the impact of sequence length on the UQ methods.\n\n- The experimental results (Table 1) show that UQAC exhibits significant performance differences across different datasets and models. Additionally, different variants of UQAC also show considerable variation in performance on the same dataset. Authors can try to include more analysis to explain the reasons behind these differences.", "extra_scores": {}}, {"review_id": "kKIfl3t9bD", "reviewer": "Reviewer_4Zzx", "summary": "This paper proposes UQAC (uncertainty quantification with attention chain) for estimating the predictive uncertainty of LLMs in tasks that involve multi-step reasoning. Traditional uncertainty quantification methods suffer from overconfidence or poor scalability when applied to long, complex outputs. UQA addresses by tracing an attention chain via attention-based backtracking from the final answer tokens. Authors also propose similarity-based filtering and probability thresholding to enable efficient approximation of the models' answer confidence without out retraining, sampling or external models. Experiments are conducted on GSM8L, MATH, and BBH using various versions of LLM (from 1B to 9B), and the results show that UQAC achieves state-of-the-art calibration with low computational cost, outperforming baselines such as self-consistency and predictive entropy.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. This paper is well-written and the motivation is easy to follow.\n2. The method is novel. The attention backtracking mechanism is both intuitive and well-justified. \n3. This method is efficient and applicable.\n4. The experimental results (especially the ECE) mostly prove the efficiency of this method.", "reasons_to_reject": "1. Lack of ablation study. Several core hyperparameters are manually chosen without any ablation study, including the number of attention heads (K) and the attention threshold ($\\theta$). It would be better to add more ablation studies to see how the experimental results change with the hyperparameters.\n2. The performance is not consistently higher than other baselines in Table 1. Although the authors give comprehensive explanations on this, the worse performance of this method compared to other baselines in some tasks will hinder the application of this method.", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EqhAa42GtV", "reviewer": "Reviewer_ZMZs", "summary": "This paper studies the uncertainty quantification (UQ) research problem in LLMs.  The authors propose UQAC, a confidence calibration method that iteratively constructs an attention chain of \"important tokens\" to the final answer via backtracking. The experimental results prove the effectiveness of UQAC.", "questions": "", "limitations": "", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. The research problem, LLMs' uncertainty quantification, is an interesting and important direction. This paper makes a concrete step to make some progress in this field. \n2. The paper is well-written and easy to follow. \n3. The proposed method UQAC, is well-formulated, and its effectiveness is proven on several benchmarks.", "reasons_to_reject": "1. The key foundation of the proposed method is based on the attention weights distribution. This is not a very reasonable intuition to me, since there is a long debate about the reliability of the attention weights. This paper also lacks corresponding proof or experimental results to prove this fundamental assumption. \n2. The authors argue the scalability of the UQAC by saying that it can handle responses of arbitrary length by isolating the most influential tokens. But I don't think the scalability should be measured in terms of handling responses of varying lengths. The method uses repetitive backtracking, similarity filtering, and probability thresholding to get the uncertainty quantification, which adds multiple layers of complexity. Compared to other methods that directly train LLMs to generate confidence scores, the proposed method is not that scalable. \n3. The experimental results are weak. Only some variants (ablations) and weak baselines are considered for comparison. Maybe the authors should include more advanced LLMs calibration methods for comparison [1,2]. In addition, the proposed UQAC lags behind the self-consistency uncertainty quantification method. \n\n[1] R-Tuning: Instructing Large Language Models to Say `I Don't Know'. Hanning Zhang et al\n\n[2] SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales. Tianyang Xu et al", "questions_to_authors": "N/A", "extra_scores": {}}]

Author rebuttal:

Meta-review: For many applications we wish to estimate the *marginal* probability that an LM produces an output $y$ for an input $x$ following any reasoning chain $z$. But computing $p(y | x) = \sum p(y|z, x) p(z|x)$ is intractable if $z$s are very long strings, and Monte Carlo estimates tend to be high-variance because there are many ways to realize $z$ that don't ultimately affect a model's final answer. This paper presents a method that speeds up this calculation by using attention to identify "critical tokens" in the reasoning chain and approximating the marginal probability of generating those critical tokens, reducing the variability in $p(z|x)$ across different $z$ and ultimately the quality of the approximate $p(y|x)$. A majority of reviewers found the method well-motivated, the presentation clear, and the experimental results convincing. Reviewer ZMZs recommended against acceptance, on the basis that the interpretation of attention scores is itself contentious (e.g. https://arxiv.org/abs/1902.10186). But I agree with the authors that these concerns aren't really relevant in the context of this paper, as the particular use being made of attention here clearly *does* lead to improved results.

[Automatically added comment] At least one review was discounted during the decision process due to quality]
Decision: Accept