Sample Smart, Not Hard: Correctness-First Decoding for Better Reasoning in LLMs
Authors: Xueyan Li
Guinan Su
Mrinmaya Sachan
Jonas Geiping
Venue: ICLR 2026 Poster (2026)
Keywords: Sampler
model uncertainty
LLM reasoning
min-p
calibration
chain-of-thought
self-consistency
Primary area: foundation or frontier models, including LLMs
TL;DR: LLM sampling should be reduced at high uncertainty tokens

Abstract: Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two competing objectives: to inject enough stochasticity to explore multiple reasoning chains, and to ensure sufficient accuracy and quality in each path. Existing works pursue the first objective by increasing exploration at highly uncertain steps with higher temperature or larger candidate token sets, while others improve reliability by rejecting samples with low confidence post generation, implying that low confidence correlates with low answer quality. These two lines of thought are in conflict, as they conflate different sources of uncertainty. To resolve this, we argue that the decoding rule should be calibrated by *correctness*, not confidence alone. We should sample from tokens with higher estimated correctness, and reduce sampling where expected correctness is low. We propose simple strategies that achieve this goal: **Greedy-Threshold** makes sampling greedy at very low confidence steps. **Calibrated-TopK** and **Calibrated-ε** set truncation threshold based on estimated rank-wise correctness. Together, our findings challenge prevailing heuristics about decoding under uncertainty, showing consistent gains across math and general reasoning benchmarks.

SAMPLE SMART, NOT HARD: CORRECTNESS-FIRST DECODING FOR BETTER REASONING IN LLMs
Xueyan Li
Guinan Su²
Mrinmaya Sachan' Jonas Geiping
'ETH Zurich
Max Planck Institute for Intelligent Systems
3ELLIS Institute Tübingen
*Tübingen Al Center
ABSTRACT
Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two competing objectives: inject enough stochasticity explore multiple reasoning chains, and to ensure sufficient accuracy and quality in each path. Existing works pursue the first objective by increasing exploration highly uncertain steps with higher temperature or larger candidate token sets, while others improve reliabil- ity by rejecting samples with low confidence post-generation, implying that low confidence correlates with low answer quality. These two lines of thought are in conflict, as they conflate different sources of uncertainty. To resolve this, we ar- gue that the decoding rule should be calibrated by correctness, not confidence alone. We should sample from tokens with higher estimated correctness, and reduce sampling where expected correctness is low. We propose simple strate- gies that achieve this goal: Greedy-Threshold makes sampling greedy at very low confidence steps. Calibrated-Te old based on estimated rank-wise correctness. Together. our findings challenge prevailing heuristics about decoding under uncertainty, showing consistent gains across reasoning benchmarks, with up to 6% improvement in AIME.
and Calibrated-e set truncation thresh-
INTRODUCTION
Large Language Models (LLMs) are used for wide range of generation tasks, ranging from open-ended text to structured problem-solving. In many cases, producing more than one candidate output improves not only fluency, but also reliability, since different samples may capture alternative valid continuations (Wang et al., 2023; Lin et al., 2024). This practice highlights fundamental trade-off: introducing enough randomness to explore multiple options while still ensuring the accuracy and quality of each individual output (Tan al., 2024; Meister et al., 2024; Shi et al., 2024). Existing works optimize exploration by raising temperatures or enlarging candidate token sets step-by-step (Nguyen et al., 2025; Zhang al., 2024; Hewitt al., 2022). These methods assume that higher entropy is a signal of uncertainty between multiple valid next steps, warranting broader exploration. parallel, other works filter after generation, relying on the finding that low confidence correlates with low answer quality. Fu et al. (2025) accepts only samples with high token confidence and stops generation when uncertainty spikes. Hallucination detection also makes use of low- confidence segments (Chang et al., 2024).
These two perspectives are in conflict, because they conflate different sources of uncertainty. From a classical perspective, if probabilistic language model closely approximates the true distribution over next tokens, then high predictive uncertainty indicates that multiple continuations may be valid. In this case, uncertainty reflects aleatoric variability, and broader sampling is appropriate. However, low-confidence positions are instead those where the model most often wrong, then additional randomness amplifies epistemic uncertainty, which is systematic errors arising from the model's lack of knowledge (Yadkori et al., 2024). In such cases, drawing more samples from an unreliable distribution might compound the model's errors.
In this work, we start by analyzing the role of low pwwbbabbyyyy tokens in reasoning tasks. We observe that increasing exploration at low-confidence steps is indeed sub-optimal strategy, single

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Top-k
Top-p
Min-p
s-sampling
Top-k + Top-p
Confidence
Largest taken
Smallest
taken
Greedy-Threshold
Calibrated-Topt Calibrated-e
Truncation threshold source
Ours
token probabilities taken correctness
Figure Comparison common and our proposed truncation strategies. Each panel shows which tokens remain available for sampling, with tokens ordered from highest to lowest model-assigned probability (left to right). The y-axis represents the max token probability ("confidence"). Our methods explicitly suppress low- confidence tail tokens.
misstep can derail subsequent tokens (Arora et al., 2023). This is especially true for smaller models. Therefore, we propose using the counterintuitive, but simple, common sampling heuristics in the literature: when step's maximum probability falls below threshold, decoding becomes greedy. Greesy-Threshold can be used in addition to existing samplers and shows consistent gains in reasoning benchmarks, especially for smaller models.
rule that inverts
With this we build upon prior work on e-sampling (Hewitt et al., 2022) that drops every token below Previous work chose very small for machine translation MBR decoding (== 3 x 10-4 9 x 10 in the original paper) (Jinnai et al., 2024; Finkelstein & Freitag, 2024). We show that for reasoning tasks, larger safe. This based on the same conservative principle where less randomness is beneficial where the model is epistemically uncertain. An overview of our methods versus those in literature is shown in Figure
Finally, we unify these perspectives by showing that the rank-wise correctness of tokens provides better truncation signals than probabilities alone, and propose a learning-free way to approximate rank-wise calibration. Calibrated- Topk sets truncation threshold at each generation step based on estimated correctness for each confidence bin. Calibrated-E extends upon this by replacing discrete confidence bins with smooth mapping from probability to correctness. It improves from e-sampling by making the truncation threshold data-calibrated. Our paper makes the following main contributions:
We find that sampling low-confidence steps contributes little additional diversity, while increasing the risk of selecting low-correctness tokens that can harm overall performance, We verify this empirically by showing that Greedy-Threstee that eliminates unreliable tail tokens alleviates this trend and improves reasoning benchmarks when used in addition to existing samplers such as top-p, top-k and min-p.
We introduce rank-conditional calibration grid and derive Calibrated-Toptt and Calibrated-s, learning-fres correctness- aware truncation rules that align exploration with expected correctness and incur negligible inference cost.
We open-source unified, composable implementation of common samplers and our meth- ods one framework."
WHY WE NEED STRICTER SAMPLING FOR REASONING
Before introducing our samplers, we first examine how confidence relates to accuracy across models and how errors emerge at low-confidence steps. We show that token probabilities provide strong signals correctness: when the model is uncertain (low maximum probability), expected accuracy decreases regardless of model size, and correctness beyond the top-ranked token drops sharply.
hhtpp:://gii
http://ggttttttt.e thub. /ttp///eeeanaaeeeee 111 //1///mpleeee Seateee--mttttttttteeee
2

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These observations motivate clear definition of confidence, rank, and calibration, which to formalize stricter sampling rules that suppress error-prone low-probability tokens.
2.1 DEFINING RANK-WISE ACCURACY
For prompt- pair, define the gold answer token sequence as 21:L and the sequence generated at inference as y1:M. Let V denote the vocabulary. V = V. At any position t, the model outputs logit vector 2, IR' conditioned
context h, which is either the gold prefix Tet during calibration, or the generated prefix уę* during decoding. With temperature T > 0, the lemperature-scaled categorical distribution over the next token is
exp (zx
Pe(i TT; Eveyexp exp (z(v)/T)
for jorjeM V.
When we omit T and write Pc(i). Further, let pi 2 Pi (2) ... P denote the probabilities sorted in descending order, and let (j) {1,.... V) be the rank of token j
step i, then top-k sampling draws from tokens with rank{()) Σ k. We define confidence as the maximum token probability each step. Pt,max - maxjev Pt(f) p!
Confidence bins, We partition model confidence (0, 1] into n contiguous confidence bins, 10 in this work:
m
m n2
Bi
1, n.
n2
Each step is assigned to exactly one bin via the index (t) such that Pt.max Bm(t)-
Rank-wise probability and correctness. For each step the rank-wise probability at rank r is p!") Let 2; E V be the ground truth next token under teacher forcing. Let R < V be the maximum rank considered. We define the rank-wise correctness as
1, if the gold token appears at rank
Ifrank, = r]
0, otherwise.
We can estimate a calibration grid over confidence bins and rank just based on given text sequences which we score by teacher forcing. For each bin-rank pair (m, r), we compute the average probability Pon,ro and correctness êm,r within confidence bin Bm:
Calibration Grid.
B[r5" pt Pt,max E Bmm]
Pmr
E
Ōm.r Prrank (x;) Pt.max E Bm
(4)
In practice, with Nm steps whose Pt,max Bm
Pmr
N
Σ
Pi
(r)
Cm.r
Nm.
Σ
1ranke =r}.
E:pr, maae B.n.
te EB..
An example calibration grid with bins is shown in Figure for visualization. Full calibration grids can be found in Sec- tion A.10. These definitions apply to any next-token distribution Pt of a language model. If temperature scaling, or any other logit processing applied, then the cali- bration would be calculated based on the final probabilities, as in Equation (I).
0.8-10 43.41%
6-0.956
t=0.907
6=0.071
C=0.039
C=0.013
6=0.023
6-0.012
0=0.006
6=0.008
C-0.004
Confidence bin
0.6-0.8 16.86%
p-0 704
t=0.616
d=0.100
C=0.173
p=0.063
c=0.064
6-0.081
0.0.036
6-0.021
t=0.117
0.4-0.6 19.21%
t=0.439
d-0.505
(=0.286
2=0.233
600.104
t=0,106
p-0.054
t=0.0
(-0.035
2=0.029
0.20
0.2-0.4 15.92%
(=0.280
(=003316 316
6=0.223
č=0.188
(<0.140
2=0,117
5-0.084
E=0.073
(-0.056
E=0.052
Bin-wise expected accuracy. The ex- pected accuracy for each confidence bin. ie., the probability of selecting the correct next token, is given by the average rank- wise probability and correctness:
0.0-0.2 4.61%
6-0.1158
6w0.124
(-0.0097 097
6-0.077
0-0.069
(-0.060
C=0.057
0.01
Rank
Figure 2: Calibration grid of Qwen2.5-1.5h Insttrucct with bims shows the average probability á and correctness for each confidence-bin and rank. Correctness is notably low in (6) the lower-confidence bins, and decreases rank increases. Percentages indicate frequency of occurrence of this bin.
Cm Σ Pm. En,..
3

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1.0
Model
accuracy
50
Frequency
Frequency occurrencer (1%)
0.8
1.58
Expected accuracy
3B
-40
78
0.6
14B
30
20
10
0.0
0.
0.1
0.2
0.5
0.6
0.7
0.8
0.9
1.0
Confidence bin
Figure 3: Expected accuracy increases with confidence across all model sizes. In the lowest confidence bin, expected accuracy drops regardless model size. Frequency refers proportion of decoding steps whose maximum probability
Larger models assign more predictions to the 0.9-1.0 confidence range, where both accuracy and frequency are highest, reflecting stronger benchmark performance. In contrast, smaller models place more probability mass in low-confidence hins, where accuracy poor.
into each confidence
2.2 Low PROBABILITY SIGNALS Low CORRECTNESS IN REASONING TASKS
While calibration grids highlight how confidence and correctness align on average, it is less clear how these signals affect full generations. particular, one might expect that sampling from un- certain positions could encourage exploration which is beneficial over many samples. We test this assumption by analyzing the role of low-probability tokens self-consistency.
Figure 3 shows that high-confidence predictions occur most frequently, which amplifies diversity simply by providing more opportunities for stochastic sampling. However, this diversity does not necessarily translate into better performance, since rank-wise accuracy drops sharply beyond the top token (Figure 2). In the highest-confidenee bin (0.8, 1.0). correctness falls from 0.907 from rank to only 0.039 at rank 2. Figure 4 further demonstrates that restricting sampling the lowest-confidence bin does not yield measurable gains in majority-voted accuracy, while also contributing little to output diversity despite sampling from the full token distribution. This stands in contrast to the assumption that exploration at cww-coniieecc steps is beneficial. Instead, the largest improvements accuracy arise from sampling in cid-cconideece bins 0.3 0.6.
Figure presents two views of why low-confidence positions are dangerous. Figure 5a distinguishes between when low-probability token is actually chosen (blue) versus when the model is in a low- confidence state regardless of what is sampled (orange). Both conditions harm accuracy as they
0.74
Avg number unique answers
Confidence
Majority Voted Accuracy
[0.9.1.]
[0.8,0.9]
0.72
[0.7,0.8]
[0.6.0.7]
0.70
[0.5,0.6]
4
[0.4.0.5]
[0.3,0.4]
0.68
[0.2,0.3)
[0.1,0.2]
0.68
[0,0.1]
32
128
32
64
128
Number of Samples
Number of Samples
Figure 4: Plot of the majority voted accuracy and the number of unique answers as the number of samples increase. Sampling is greedy unless the maximum probability falls into certain confidence bin, in which case sample from the full token distribution. Sampling at the lowest confidence bin results in no gain in accuracy while contributing little diversity terms number unique answers.
4

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Low probabiiity token sampled p 0.1
Low-probability token sampled 0.1
0.5
0.5
Low confidence state 0.3
Low-confidence State Pmox 0.3
0.4
Accuracy
0.4
Accuracy
0.3
0.3
0.2
0.1
0.1
0.0
Number of low-confidence events
Mean sampled rank
(a) Accuracy vs the number of low probability tokens or states sampled each sequence
(b) Accuracy mean sampled rank
Figure 5: Effect of low-confidence events on sequence-level accuracy. (a) Accuracy decreases both when the model directly samples low-prohability tokens (p < 0.1, blue) and when it is in low-confidence state regardless of the sampled token (Pmax (l3,, orange). (b) Accuracy also drops as the rank of sampled tokens increases, showing drifting into lower-ranked tokens degrades sequence quality.
accumulate within a sequence. Figure 5b presents a rank perspective: once decoding drifts into higher-ranked tokens, accuracy drops. These findings motivate conservative truncation rules. By enforcing greedy decoding at low-confidence steps, Greedy-Threshold prevents the model from sampling higher-ranked, error-prone tokens and keeps the mean sampled rank low, Similarly, s- sampling blocks low- ow-probabilltty tokens entirely, which naturally caps the rank distribution. In both cases, the methods limit the propagation of errors and preserves sequence-level accuracy.
HOW TO CALIBRATE TRUNCATION SAMPLERS
The central idea is adapt the sampling process in autoregressive language models by filtering out tokens that are likely to be inaccurate, thereby refining the candidate set. Although this might initially seem infeasible, we will show that excluding tokens likely be incorrect is possible and effective. We call the restricted pool of permissible next tokens the active set at each step As reference, the active for the simplest truncated sampler, standard top-k sampling, always the set of the & most likely tokens, i.e. top-k
E V rank, (v) < k).
We this sampler exemplify claim that sampling less when confi- dence is low is beneficial. When using Greedy-Threshof we sample greedily when confidence is below a threshold PGT E (0, 1). and only the argmax token of & arg max Pc(v) is accepted. The active of tokens to sample from is
Freedy-Thresholde
f (ot V
if Pt,max < PGT,
AGT
if Pt,max PGT-
e-sampling. To draw connection with existing e-sampling (Hewitt al., 2022), we recap its definition. This rule only samples from tokens above a threshold s 2 0. The active set is
A ( : }...
(8)
Note that when the Greedy-Threshee parameter equals the e-cutoff, i.e. PGT and the maximum token probability at step 1. is below this level (pr,max < PGT)) both methods fall back to greedy. Motivated by the mismatch between raw probability and correctness, we adopt the same truncation principle but calibrate the cutoff to estimated correctness rather than probability alone.
-alibrated-TopK. Recall from the calibration grid (Figure 2) that we can estimate, for each con- fidence bin and token rank, the expected correctness of a token. This provides direct way to infer how far down the ranked list of candidates one can safely explore. The idea of Calibrated- Topk therefore simple. Instead of fixing & in advance, adaptively set it so that only ranks whose
5

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average correctness is above threshold are included. In this way, the method truncates exploration to the range of token ranks that are empirically likely to be correct. Given the maximum rank whose correctness is above the threshold CCT E (0, 1) in calibration grid C,,ri
Km (CCT) = max{ E {l,.... RJ õm,r 2 CCT
At step with bin m(t), the active set defined by the maximum rank
[ f EV: rank{(u) I Km(ecr) Km (CCT)) 2 1
(
(10)
Km (CCT)) =
Calibrated-e Since Calibrated-TopK sets thresholds based discrete confidence bins, we are motivated to find a solution that maps probability to correctness in a continuous way. A plot of all á and è shows near-linear relationship in log-log coordinates as shown in Figure 6:
109
logč - Blogå
Average correctness è
A D.506, 8 0.795
10-1
logıgë= A + B 10
10-2
We estimate the coefficients by least squares on the cal- ibration grid, fitting line in log-log space the pairs (p, é) aggregated over bins and ranks:
10-3
LinearRegression (logio P. logio é). Given these coefficients, we instantiate per-token cor- rectness predictor decoding step i, mapping each can- didate token j E V with probability Pc(j) to esti- mated correctness score (z) & 1)) Computa- tionally this is just a single sealar transform, adding negli- gible overhead decoding. We then define a correctness threshold ce E (0, 1), the active set at step becomes
A,
10-4
10
10-3
10
10-1
10
Average probability 6
Figure 6: A scatter plot of calibration grid averages (p,C) across confidence bins and ranks. Points concentrate along an approx- imately linear trend. We fit least-squares line and use this mapping to predict correct- ness at inference time for Calibrated-s.
(ce) = { {VEV= (v) 2 )=
i.e., we keep exactly those tokens whose predicted correctness exceeds the threshold. For all sam- plers, if no tokens satisfy this condition A, Ø, sample greedily A, {(r}} In general, we note that all truncated samplers can be used together by taking the intersection of their active sets. Lastly, given any active set A,, sample Ia ~ p-(()) from the renormalized distribution
Pc(u)
p((v) EWEA, (((w) for v E Ay.
(11)
CORRECTNESS-FIe SAMPLERS IMPROVE REASONING ABILITIES
We now study whether truncating low-confidence regions during decoding translates into better end- task reasoning. Our focus is on frontier LLMs evaluated on math and general reasoning benchmarks, where sequence-level correctness is the primary objective. We compare the proposed correctness- first samplers against standard temperature and probability- baselines.
4.1 EXPERIMENTAL SETTINGS
We evaluate models in the Qwen2.5 (Qwen al., 2025) and the Llama (Grattafiori al., 2024) family on short reasoning tasks (GSM8K (Cobbe et al., 2021), MMLU (Wang et al., 2024) and Big-Bench-HHee Hard (Suzgun et al., 2022)), and GPT-OSS (OpenAl et al., 2025) on long reasoning tasks (AIME*). We use Greedy-Threshold with par = 0.3, Calibrated-Topk with GeT = 0.05 (over n 10 bins), and Calibrated-E with c 0.05. We adopt higher threshold æ 0.05 than typically reported to emphasize the impact of truncating low cow-probayility tokens. We provide ab- lation on threshold value selection in Section A.4. Calibration performed on the training split of each benchmark. We additionally perform cross-domain calibration using ulpaca-gpt4-cr (Peng et al., 2023) For comparability with temperature-basee samplers, we use T = 1 unless otherwise noted. Further implementation details, ablations with threshold values, temperatures and calibration datasets are provided Section A.
htt.:/f......ctttttt///ttttattaa /

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Table 1: Majority voted (maj@k, results GSM8K, MMLU-PM and Big- Be--BBnch--aeee Hard for Qwen2.5-0.5B.
Instruct. Calibrated samplers achieve the largest performance gain from no restrictions baseline.
GSMSK
MMLU-Pro
Big- Tig-Bench-Haan
Method
maje @8
maj @ 16
maj @ @32
maj@@ @8
maj @ 16
maj @ 32
maj @8
maj @ 16
maj @ 32
No restrictions
30.2
35.2
38.6
16.4
17.0
17.3
17.9
17.0
16.2
top-k
32.6
38.7
41.9
16.8
17.5
18.0
22.0
21.7
21.5
top-p
35.5
40.8
43.6
16.8
17.5
18.1
25.5
25.9
25.9
min-p
38.7
43.1
46.6
17.7
18.2
18.6
30.6
31.5
31.7
EDT
40.2
44.1
46.7
17.7
18.1
18.4
30.5
31.1
31.7
7-sampling
31.6
37.2
41.0
16.5
17.3
17.9
20.6
20.3
19.6
s-sampling
39.2
44.3
46.7
17.5
18.1
30.4
31.6
Greedy-Threholld
31.2
37.0
40.6
16.9
17.8
18.2
20.8
20.3
19.4
Calibrated-Topp
39.3
44.5
47.1
17.9
18.3
18.7
30.4
31.1
31.6
Calibrated-E 40.8
44.3
47.1
18.9
18.4
18.6
30.6
31.5
32.0
Baselines We compare our methods against several widely used sampling strategies. Top-k 10) (Fan et al., 2018). Min-p (p 0.1) (Nguyen et al., 2025). Top-p (p 0.95) (Holtzman et al., 2020), EDT (Zhang et al., 2024) with
0.8, = 1, To 0.7. These parameters are selected from the original paper after small parameter search experiments to determine reasonable values. s- sampling (Hewitt et al., 2022) with higher = 0.05 than recommended. 17-sampling (Hewitt al., 2022) with the original recommended value 0.0009.
4.2 CALIBRATED TRUNCATION INCREASES MODEL PERFORMANCE.
We evaluate the effectiveness of our proposed samplers across benchmarks. Table shows that Calibrated-E and Calibrated-Toph achieve the largest improvement overall, showing rank-wise correctness is effective truncation signal. Greedy-Threshold activates only when the max- probability token falls below 0.3, an infrequent but high-risk regime (see Figure 2). Despite its low activation rate, this condition occurs often enough for Greedy-Threshen benefits. E-sampling (fixed threshold) performs on par with min-p and EDT, supporting the idea that simply removing tail tokens helps by shaping the cutoff where correctness actually drops. All cal- ibrated samplers add negligible runtime overhead at decoding, since they only require 2-parameter table lookup single vector operation over the vocabulary.
to yield measurable
4.3 EXISTING SAMPLERS BENEFIT FROM TREEDY--TURESIOLD
To test whether halting sampling at low-confidence steps is beneficial, we apply Greedy-Threshold on top of existing samplers that otherwise increase exploration at such positions. This preserves their original behavior when confidence is above 0.3, but forces greedy decoding when confidence falls below this threshold. Table 2 shows that Preedy-Threeshe improves performance in this set- ting, especially for smaller models. When no gains are observed, results remain comparable to the baseline, indicating that it does not degrade performance.
4.4 SCALING ADVANCED REASONING MODELS
We evaluate our proposed methods on reasoning orientte "thinking" model GPT-OSS- 20B (OpenAI al., 2025) and a challenging mathematics benchmark AIME that demands multi-step derivations. Thinking models differ from standard LMs in that they generate long sequences of intermediate tokens, making calibration on short, instruction-style datasets less representative of their actual be- havior. To capture
central idea of filtering out low-correctness tokens in this setting, apply e-sampling with a relatively high cutoff (s = 0.05). Our results show substantial gains. GPT-OSS- 20B benefits from both Greedy-Threshole Threshold and e-sampling. Output diversity is reduced, but the effect minimal. Over 32 samples, the number of unique answers decreases from 14.1 to 13.3 (roughly 1-2 fewer unique answers out of 14). This small drop coincides with higher maj @ k and pass @k @k,

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Table Majority voted results GSM8K. In addition existing sampling conditions. Greedy-Threshold Threshold PGT 0.3 is applied. Greedy-Threshol improves majority voting performance, especially in models with lower starting accuracy. Statistically significant differences (p < 0.05) marked in bold.
1.55--trueett Qwen2.5-0.55 1-en2.5-005B-Instrrutt Owwn2.5-11.5B Instructtt
Qwen2.5-3B-Insteee
Method
maj maj@8 maj@ 16 maj@32 maj@y mij@8 maj @ 16 maj @32 maj @8 maj @ 16 maj@ 32
Baseline T=1
30.2
35.2
38.6
68.4
71.5
73.1
79.3
80.6
81.1
+ Greedy-Threshold
+1.0
+1.8
+2.0
+1.7
+2.1
+2.4
+0.1
+0.2
-0.1
top-k
32.6
38.7
41.9
68.5
72.6
73,9
79.0
80.3
81.0
+ Greedy-TThrshhne
+1.1
+0.5
+1.1
+2.6
+2.4
+2.8
+1.0
+0.5
-0.2
top-p
35,5
40.8
43.6
71.1
74.1
75.9
79.5
80.5
80.8
Greedy-Threshold
+0.4
+1.3
+1.5
+1.8
0.0
min-p
38.7
43.1
46.6
73.3
75.6
76.6
80.0
80.4
81.2
Greedy-Threshod
+1.4
+0.8
+0.6
+1.3
+1.2
+1.5
-0.2
+0.2
EDT 40.2
44.7
46.8
74.9
76.6
78.9
79.5
80.5
80.9
Greedy-Threshold
+0.2
-0.3
+0.1
-0.2
0.0
-0.1
+0.1
+0.1
+0.1
--sampling
31.6
37.2
41.0
69.0
72.4
74.2
78.8
80.1
81.0
Threshy-
+2.4
+1.8
+1.7
+1.7
+2.7
+2.7
+0.5
+0.3
+0.1
consistent with our goal: do not value diverse wrong answers. For reasoning tasks with single correct solutions, correctness is more important than diversity. Expanding exploration does not help when early steps emor-anmplifyngg. By steering decoding away from low-correctness regions, methods increase the fraction of valid solutions by up to 6.5% and improve overall answer quality,
DISCUSSION
Why does Greedy-Threed Threshold work? Our results suggest that in reasoning tasks, in spite of popular intuitions, the positions with low confidence not branch points among many valid continuations, but error-amplifying states. Two pieces evidence support this claim: rank-wise correctness de- creases beyond the top token (Figure 2), and performance degrades once low-probability tokens are sampled (Figure 5). Greedy-Threshon chooses a safe token where both risks are highest, and potentially prevent subsequent error. is targeted suppression of low-correctness steps.
Reordering uncertainties as epistemic first, aleatoric second. Common existing decoding strate- gies assume high entropy means alcatoric variability (many valid tokens) and sample more. Our results imply the opposite might be true in reasoning tasks with closed-form answers. High entropy
The result of AIME24 and AIME25 on GPT-OSS 20B with thinking mode enabled. "Unique An- swers" is the number of unique answers over all 32 samples. "Overall Correct" is the overall proportion of answers. Best result is in bold. Statistically significant difference (p < 0.05) is in italics.
Table 3:
Maj @k
Pass @k
Unique
Overall Correct
Model Method
Answers
8
16
8
32
AIME25
Baseline
75.4
84.4
87.8
90.0
85.6
90.0
91.1
92.2
13.6
56.1
Greedy-Threshold
71.1
87.8
88.9
91.1
85.6
91.1
93.3
94.4
12.0
59.9
e-sampling
68.9
85.4
91.1
86.7
90.0
93.3
95.6
13.6
56.1
AIME24
Baseline
71.4
83.3
88.7
92.6
83.4
90.7
92.0
93.3
15.1
48.7
Thresh-T
77.3
88.0
91.3
92.6
86.7
92.6
93.3
94.0
13.3
55.2
e-sampling
77.3
87.3
90.0
91.3
89.3
90.0
91.3
92.6
54.9
8

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often reflects epistemic uncertainty which is systematic lack of knowledge, especially in smaller models. When the distribution is wrong, sampling more from does not benefit correctness. In calibration-bast based methods, correctness is the focus. We increase sampling where expected cor- rectness is high and shrink it where the model lacks fundamental understanding. This perspective explains why stricter truncation (higher e, lower rank caps in top-k) consistently helps in reasoning. Randomness is less valuable in low-confidence regions where epistemic error dominates.
Robustness to cross-domain calibration data and fit quality. In-domain calibration dataset is not always available, we want to ensure our calibrated samplers are robust to domain shifts. We test cal- ibration using a general purpose instruction tuning dataset al alpaca-gpt 4-en and observe similar performance as in-domain calibration on GSM8K- trainning (Section A.5). This suggests that the confidence to correctness map transfers generally when the format matches (instruction to answer) and that out-of-domain calibration datasets can be used when in-domain dataset is not available.
6 RELATED WORK
Literature on decoding for LLMs largely follows two directions: (i sampling more to increase diversity of generations, and (ii) sampling less to increase accuracy and stability. Our work focuses on reconciling these perspectives for reasoning tasks.
Removing tail-end tokens. Classical truncation methods such top-k (Fan et al., 2018) and top-p (nucleus) sampling (Holtzman et al., 2020) reduce tail risk by discarding low- -wwobabbbility tokens. Temperature scaling (Guo et al., 2017), often with lower temperatures for math and reasoning tasks, has a similar intuition: sharpening the distribution so that low-probability tokens are rarely sampled. These classic methods are often used in combination (Yang et al., 2025). More recently, locally typical sampling (Meister et al., 2025) restricts to tokens whose information content is close to the local entropy. REAL sampling (Chang al., 2024) adaptively reduces top-p when hallucination risk is high. Our results on reasoning tasks support this risk-aware trend: sampling in high- uncerttncttantty steps introduces catastrophic errors, while removing tail end low probability tokens safer.
Selection after sampling, Another line of work improves reliability after generation. Self-certainty (Kang et al., 2025) and DeepConf (Fu et al., 2025) re-weigh or filter generations using confi- dence signals. The open-source effort Entropix (XJDR, 2024) pauses or resamples at high-entropy steps. These methods implicitly acknowledge that low-confidence steps are strongly correlated with low correctness. Our contribution is orthogonal. We intervene during decoding to prevent low- confidence tokens from being sampled the first place, so that downstream majority voting operates on stronger candidates.
Adaptive, aacer decoding. A complementary set of methods dynamically adjust sampling based on estimated uncertainty. Entropy-dependee 2024) increases temperature as entropy grows. "Hot or Cold" decoding (Zhu et al., 2023) applies higher temperature only the first token in code generation. Adaptive Decoding (Zhu et al., 2024) and Adaptive Contrastive Search (Garces Arias et al., 2024) adjust candidate sets or penalties step- by-step. Min-p (Nguyen al., 2025) scales truncation by the maximum token probability, enlarging candidate sets when uncertainty is high, which is shown to benefit creative text generation, although a subsequent study criticized its effectiveness (Schaeffer et al., 2025). Our study provides an explanation why high uncertainty correlates with lower accuracy while providing limited diversity.
temperature (EDT) (Zhang et al.,
Assessing model calibration. Calibration for L.MS is typically assessed with reliability diagrams and scalar errors such as ECE error on top-1 labels (Guo et al., 201 or on a sequence level (Huang al., 2024; Stengel-Eskin & Durme, 2023). Full-ECE (Liu et al., 2024) extends beyond top-1 by evaluating calibration over the entire token distribution, but it does not condition on token rank. We introduce a confidence and rank calibrated method that informs correctness-awan truncation.
7 CONCLUSION
Future work. This work can be extended tasks beyond math and reasoning, such open-ended and creative tasks, to characterize when diversity is the priority while ensuring correctness. There is also the potential to conduct online calibration with on-the-fly recalibration depending on the exact

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question task. Lastly, study how calibration evolve with model size, post- wost-training method and data regime.
Conclusion. In this work, re-examined decoding under uncertainty for reasoning tasks and gue for a correctness-firg perspective. By visualizing a novel rank-wise calibration grid, we present evidence token level that in low-confidence bins, all tokens have low expected correctness. On a sequence level, accuracy declines with more low-probability tokens and with higher ranks sam- pled. On dataset level, Threeyy-hreshold, Calibrated-TopK, and Calibrated-a raise performance in reasoning benchmarks by allocating randomness only where expected error is low. These meth- making them practical for inference use. We encourage
ods are consistent and compute-effice future work to consider uncertainty as a risk signal to truncate, rather than a signal to explore.
REPRODUCIBILITY STATEMENT
Implementation of our proposed sampling strategies, model behavior analysis and calibration mea- surements are released with our paper and hosted in our public repository. Details of evaluation and calibration, including model settings, hyperparameters, and prompting formats are documented in Section A.1. All benchmarks openly available, and provide complete code for running the benchmarks.
LLM USE
We used large language models (LLMs) only for light editorial assistance (e.g., grammar, spelling, phrasing), simple LaTeeX formatting, and typo checks. LLMs were also used to draft boilerplate code (e.g., code scaffolding, argument parsers) and to plot high-level diagrams. All such outputs were reviewed, and validated by the authors before inclusion. LLMs were not used to write substantive sections of the paper, design experiments or analyze results. All technical content, experiments, analyses, and conclusions were created and verified by the authors.
REFERENCES
Kushal Arora, Layla El Asri, Hareesh Bahuleyan, and Jackie Chi Kit Cheung. Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation, January 2023. URL httt: org/ abs 2204 01171. arXiv:2204.01 [cs].
Jacob Austin, Augustus Odena, Maxwell Nye, Maarten Bosma, Henryk Michalewski, David Do- han, Ellen Jiang, Carrie Cai, Michael Terry, Quoe Le, and Charles Sutton. Program Synthesis with Large Language Models, August 2021. /tthttp://ae htattt:://axxv..../// www.vv...rrgbbb//1..e. 1xXi::2108.07722 [es].
abs/
Haw-Shiuan Chang, Nanyun Peng, Mohit Bansal, Anil Ramakrishna, and Tagyoung Chung. REAL Sampling: Boosting Factuality and Diversity of Open Ended Generation via Asymptotic Entropy, June 2024. URL /tattt:///rxiie httpp:/ org/ abs 2406. 07735. arXiv:2406.07735 [es] version:
1.
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichir Nakano, Christopher Hesse, and John Schulman. Training Verifiers to Solve Math Word Problems, November 2021. URL http: / //arxiv.org/aaet www.org//bbs/11111 14168. 100 [cs].
Angela Fan, Mike Lewis, and Yann Dauphin. Hierarchical Neural Story Generation. In Iryna Gurevych and Yusuke Miyao (eds.), Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 889-898, Melbourne, Australia, July 2018. Association for Computational Linguistics. doi: 10. 11..1865//11/11-110000 URL https: / laallanhhology........ or82218-108//
Daniel Fein, Sebastian Russo, Violet Xiang, Kabir Jolly, Rafael Rafailov, and Nick Haber. LitBench: A Benchmark and Dataset for Reliable Evaluation of Creative Writing, July 2025. URL http: / waw.ivvorrggooooo..o..oooo.o...r 225p://///////......// 69. arXiv:2507.000 .07669 [cs].
10

---

Mara Finkelstein and Markus Freitag. MBR and QE Finetuning: Training- time Distillation of the Best and Most Expensive Decoding Methods. In The Twelfth International Conference on Learning Representations, October 2024. URL https:/ bkNx300sND.
Yichao Fu, Xuewei Wang, Yuandong Tian, and Jiawei Zhao. Deep Think with Confidence, August 2025. URL http:://azee
15260. arXiv:2508. 15260 [es].
Esteban Garces Arias, Julian Rodemann, Meimingwei Li, Christian Heumann, and Matthias Aßen- macher. Adaptive Contrastive Search: Uncertainty-Guided Decoding for Open-Ended Text Generation. In Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen (eds.), Findings of the Association for Computational Linguistics: EMNLP 2024, pp. 15060-15080, Miami, Florida, USA, November 2024. Association for Computational Linguisties. doi: 10. 10.18653/v1/2024 finding--emnl.8855 URL pettss:/accantthol/e wwtp:/loooo.og////////// wttpr//224....nn...... sanndinngsemm/// 885/.
Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, and 548 other authors. The Llama 3 Herd of Models, November 2024. URL 21783. arXiv:2407.21785 [cs].
org. wtgp/r/////bb//go/
Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q. Weinberger. On Calibration of Modern Neural Networks, August 2017. URL http:://tt///t/ wwg. awaaabass///// 04599. [cs].
John Hewitt, Christopher D. Manning, and Percy Liang. Truncation Sampling as Language Model Desmoothing, October 2022. URL
arXiv:2210.15191 [cs].
Ari Holtzman, Jan Buys, Du, Maxwell Forbes, and Yejin Choi. The Curious Case Neu- ral Text Degeneration, February 2020. URL http:://tt/t wwwaaiivvvoooooooooooooo htrg/abs/1900 09751.
arXiv:1904.09751 [cs].
Yukun Huang, Yixin Liu, Raghuveer Thirukovalluru, Arman Cohan, and Bhuwan Dhingra. Cal- ibrating Long-form Generations from Large Language Models, October 2024. URL http: // //aaxiiv.oo wwtpxiiwrg//ab////// 2402 06544. arXiv:2402.06544 [cs].
Yuu Jinnai, Tetsuro Morimura, Ukyo Honda, Kaito Ariu, and Kenshi Abe. Model-Based Mini- mum Bayes Risk Decoding for Text Generation, June 2024. URL
org/abs/
2311.08 05263. 1xXiv:231..0526 [es].
Zhewei Kang, Xuandong Zhao, and Dawn Song. Scalable Best-of-N Selection for Large Language Models via Self- self-Certainty, February 2025. URL http: /tap:::///axvvv..///a wwtp://wwwooog///////bobee/ 18581.
arXiv:2502.1 18581 [es].
Lei Lin, Jiayi Fu, Pengli Liu, Qingyang Li. Yan Gong, Junchen Wan, Fuzheng Zhang, Zhongyuan Wang, Di Zhang, and Kun Gai. Just Ask One More Time! Self-Agreement Improves Reasoning of Language Models in (Almost) All Scenarios, May 2024. URL httttt////aaiii www.aiiwi.....oaeeoooooooooooooe /
2311.00 08150015000 54. arXiv:231 1. 1.08 154 [cs] version: 3.
Han Liu, Yupeng Zhang, Bingning Wang, Weipeng Chen, and Xiaolin Hu. Full-ECE: A Metric For Token-level Calibration on Large Language Models, June 2024. URL http::t/axii...oo abs/2405 11345. arXiv:2406. 1345 [cs] version: 1.
Clara Meister, Tiago Pimentel, Luca Malagutti, Ethan G. Wilcox, and Ryan Cotterell, On the Effi- cacy of Sampling Adapters, January 2024. URL http:://azdd..org//baa arXiv:2307.03749 [cs].
03749.
Clara Meister, Tiago Pimentel, Gian Wiher, and Ryan Cotterell. Locally Typical Sampling, June 2025. URL http: tatttp:/arxiin //tra//aavvv///////////eee/aaavv org/obrg// //bp/////22....///////////////// 2202. 60666. arXiv:2202.00666 [cs].
Minh Nhat Nguyen. Andrew Baker, Clement Neo, Allen Roush, Andreas Kirsch, and Ravid Shwartz-Ziv Ziv. Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs, June 2025. URL httpt httttt:://wxwi..orgg//o/oo
01082. arXiv:2407.0100 [cs].

---

OpenAI, Sandhini Agarwal, Lama Ahmad, Jason Ai, Sam Altman, Andy Applebaum, Edwin Arbus, Rahul K. Arora, Yu Bai, Bowen Baker, and 113 other authors. gst 120b & gpt-oss-20b Model Card, August 2025. htthttp/// waw.ii.iiii.////ii//.aaaaaiaaiia org/
10925. 1XXi:2508.10025 [es].
Baolin Peng. Chunyuan Li, Pengcheng He, Michel Galley, and Jianfeng Gao. Instruction Tuning with GPT-4, April 2023. URL htlthttpp//axiii [es].
abs 2304. 03277. arXiv:2304.03277
Qwen, An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang. Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin. Tianhao Li, Tianyi Tang, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu. Qwen2.5 Technical Report, January 2025. URL http: /ttp//axxvvvv//////////e///a.avl org/ abs/ 2412 15115. 11Xiv:2412.55115 [cs].
Rylan Schaeffer, Joshua Kazdan, and Yegor Denisov-Blande Blanch. Min-p, Max Exaggeration: A Critical Analysis of Min-p Sampling in Language Models, June 2025. URL abs/2506... 13681. arXiv:2506.1368 [cs].
Chufan Shi, Haoran Yang. Deng Cai, Zhisong Zhang, Yifan Wang. Yujiu Yang. and Wai Lam. A Thorough Examination of Decoding Methods in the Era of LLMs, October 2024. URL http:
/
..e.2.69922 06955. arXiv:2402.06925 [cs].
Elias Stengel-Fskin and Benjamin Van Durme. Calibrated Interpretation: Confidence Esti- mation in Semantic Parsing, July 2023. URL http:://axxxi/ wwwperiwwi.o.ooooeeeeeeeeeeeeeee htrrgg/ab///211..
MtXiv:2211.07445 [es].
Mirac Suzgun, Nathan Scales, Nathanael Schärli, Sebastian Gehrmann, Yi Tay, Hyung Won Chung, Aakanksha Chowdhery, Quoe V. Le, Ed H. Chi, Denny Zhou, and Jason Wei. Challenging BIG- Bench Tasks and Whether Chain-of-Thoughh Can Solve Them, October 2022. URL http:
//arxiv. owr.iiorrrraooooo abs////////// 22122221...22 09261. arXiv:2210.0922 [cs].
Naaman Tan, Josef Valvoda, Tianyu Liu, Anej Svete, Yanxia Qin, Min Kan, and Ryan Cot- terell. A Probability-Qual Quality Trade-off in Aligned Language Models and its Relation to Sampling Adaptors. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pp. 14805-14829, Miami, Florida, USA, 2024. Association for Computational Lin- guistics. doi: 10.118633/1/2024..oo 2024. ewnee-maimmim...e. 822.
main.82) URL https: httpss//acaaaathhoocooo . org/
Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoe Le, Ed Chi, Sharan Narang, Aakanksha Chowd- hery, and Denny Zhou. Self-Consistency Improves Chain of Thought Reasoning in Language Models, March 2023. URL [es].
httpr//www..rrg/b/////eee 11171. arXiv:2203.1117.
Yubo Wang, Xueguang Ma, Ge Zhang, Yuansheng Ni, Abhranil Chandra, Shiguang Guo, Weiming Ren, Aaran Arulraj, Xuan He, Ziyan Jiang, Tianle Li, Max Ku, Kai Wang, Alex Zhuang, Rongqi Fan, Xiang Yue, and Wenhu Chen. MMLU-Pro: A More Robust and Challenging Multi- Task Lan- guage Understanding Benchmark, November 2024. URL http:// httttp://axxv..oo org. org/ abs 2406. 01574. arXiv:2406.01574 [cs].
XJDR, Entropix - Entropy Based Sampling and Parallel CoT Decoding, 2024. URL https:
Yasin Abbasi Yadkori, Ilja Kuzborskij. András György, and Csaba Szepesvári. To Believe or Not to Believe Your LLM, July 2024. URL http:///aaa http://arxiv..oo http:///w...oggg///////000// 02543. arXiv:2406.02544 [cs].
An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, Chujie Zheng, Dayiheng Liu, Fan Zhou, Fei Huang, Feng Hu, Hao Ge. Haoran Wei, Huan Lin, Jialong Tang, Jian Yang. Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jing Zhou, Jingren Zhou, Junyang Lin, Kai Dang, Keqin Bao, Kexin Yang.
12

---

Le Yu, Lianghao Deng, Mei Li, Mingfeng Xue, Mingze Li, Pei Zhang, Peng Wang. Qin Zhu, Rui Men, Ruize Gao, Shixuan Liu, Shuang Luo, Tianhao Li, Tianyi Tang, Wenbiao Yin, Xingzhang Ren, Xinyu Wang, Xinyu Zhang, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yinger Zhang, Yu Wan, Yuqiong Liu, Zekun Wang. Zeyu Cui, Zhenru Zhang, Zhipeng Zhou, and Zihan Qiu. Qwen3 Technical Report, May 2025. URL http::/ttaaaee arXiv:2505.099 0,9388 [cs].
org/ httggabbs/500000995 09388.
Shimao Zhang, Yu Bao, and Shujian Huang, EDT: Improving Large Language Models' Generation by Entropy-based Dynamic Temperature Sampling, April 2024. URL htt.:httt//xii.ooortt abs /2032240... 14541. arXiv:2403. 14541 [cs].
Wenhong Zhu, Hongkum Hao, Zhiwei He, Yiming Ai, and Rui Wang. Improving Open-Ended Text Generation via Adaptive Decoding. In Proceedings of the 41st International Conference Machine Learning, pp.
PMLR, July 2024. URL http::://procceediggss mlr.press. / v23.222552//2 2hd html. ISSN: 2640-3498.
Yugi Zhu, Jia Li, Ge Li, YunFei Zhao, Jia Li, Zhi Jin, and Hong Mei. Hot Cold? Adaptive Temperature Sampling for Code Generation with Large Language Models, December 2023, URL http:// aawxiv v.v.v. org/ abgg/////// /209, 02772. arXiv:2309.02772 [cs] version: 3.
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A APPENDIX
A.I
DATASETS AND PARAMETERS
We provide detailed experiment setups and parameters for reproducibility. We evaluate on reasoning and math-focused benchmarks commonly used to assess Mhain-of-thouge robustness. We follow the community-standard evaluation scripts to ensure comparability across papers and release the detailed configuration files in our public GitHub repository.
Datasets
GSM8K (Cobbe al., 2021): with 5-shot chain-of -ttii- prompting. The train split is used to construct in-distribution (ID) calibration grid.
MBPP (Austin et al., 2021): ID calibration grids are built using the training split, with evaluation the test set. Results are reported in Section A.6
Big- Big-Bench-HHard (Suzgun al., 2022): we report unweighted average accuracy across all categories. Since this benchmark does not have train split, we use alpaca-gpt4-en for calibration.
MMLU-Pro (Wang al., 2024): we report unweighted average accuracy across all cate- gories, using the validation split for ID calibration.
Alpaca-gpt4-en (Peng et al., 2023) 7: used as an out-of-distribution (OOD) dataset for calibration. This OOD calibration is applied once derive a general Calibrated- setting, which can then be used across tasks. In contrast, ID) calibration offers more precise task-specific signals, but may always be feasible for new domains. Effect of ID OOD) calibration dataset is compared in Section A.5
AIME25 and AIME24": used to evaluate "thinking" models with extended reasoning
traces.
For all benchmarks, performance is measured the average maj @k or pass@k across three runs. Popular Python package 1m_eval generation for benchmarking. Calibration is done using code bootstrapped to torchtune".
6 is used to evaluate all tasks. vLLM' is used to run large scale
For all calibration procedures, the input question is masked, and only cor- rectness with respect ground-truth answers is considered. Unless otherwise specified, we set Steedy-Threshold pGr = 0.3, cCT = 0.05 for Siubratte-Tookk and = 0.05 for Calibrated-s. The maximum number of ranks considered is R
Calibration Setup
Baselines
We compare methods against several widely used sampling strategies:
Top-k (A = 10) (Fan et al., 2018)
Min-p (p = 0.1) (Nguyen et al., 2025)
Top-p (p 0.95) (Holtzman et al., 2020)
EDT (Zhang al., 2024) with N 0.8, 1, To 0.7. These parameters are selected
from the original paper after small parameter search experiments to determine reasonable
values.
sampling (Hewitt et al., 2022) with higher 0.05 than recommended.
. sampllin (Hewitt et al., 2022) with the original recommended value ' 0.0009.
Long-Form Reasoning To assess robustness on extended reasoning chains, we test on AIME25 and AIME24 using GPT-OSS's recommended setting (T' = 1.0), averaged across three runs. Ad- ditionally, we restrict baseline comparisons to Sreedy-Threshon with Pcr 0.3 and e-sampling with e 0.05. As thinking models exhibit substantially different behaviors from standard models,
*https: httpaaa.///atttoo.oo/////////o/r
14

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using question-ansenn answer pairs with short ground tround-truth -tuth answers would produce misleading calibration values.
Temperature Sensitivity To ensure fairness against lemperature-baser samplers, all main results are reported with 7 = 1.0. Since math and coding tasks often benefit from lower sampling tempera- tures, we additionally evaluate with 7 0.6. In this setting, calibration grids are recomputed using scaled logits (Equation (I), and thresholds (PCT, 7) and CCT) are adjusted accordingly. Detailed hyperparameter values and results are provided in Section A.8.
A.2 PARAMETERS FOR FIGURES
Figure 2 uses 5 confidence bins with 0.2 increments on Qwenn..5-0.5-IImsrruc using GSM8K train dataset.
Figure 3 Models are in the Qwen2.5 instruct family. Expected accuracy is calculated from the top R 20 ranks at each step. Dataset used is alpaca-gpte with questions masked, so correctness is only calculated from answers.
on GSM8K set with T' 1 and no other sampling con- ditions. Each final numerical answer is extracted, excluding the reasoning chains. Only different final numerical answers are counted. Different reasoning chains that arrive the same final answer will count as the same answer. The number of unique answers is averaged over all questions at each number of samples. If no valid final answer can be extracted, the final answer becomes null This means all reasoning chains without valid final answer will count one unique answer.
Figure Uses Owen2.5-1.5B-Innstte
Figure uses Qwen2.5-0.55 3-0.5B-Insstrue on GSM8K test set. All reasoning chains up to and including the final numerical answers are considered. Sometimes the model continues generate the next in-context question after answering the current question. All subsequent generations are excluded.
Figure uses Qwwe2.5500.BB-Instree on GSM8K train set.
A.3
EXAMPLE OF LOW-CONHDENCE CASES
has
them for 6. She 8 She sells them for 4 = You Solve this invested
eggs to sell.
She eats
6
answer expertise in financial matters. Your task is to solve these financial problems. with the reasoning scheme. After years, he gat Rs. To determine the rate
=$
with
financial problem, and then provide Rs.
What the
rate interest Options text
C) 7 D)
interest, we can use formula
simple interest text Simple Interest text Time Given
text
Principal
times
Rate
times
Principal
Simple
0.3
p 0.6
0.6 <.88
0.8
Figure 7: Example of an answer for GSM8K by Qwen2.5-0.5B Instruct under greedy generation. The lowest confidence typically do not occur the start of sentence.
We illustrate a simple case of where low-confidence tokens arise. As shown in Figure 7, the be- ginning a sentence where aleatoric variability is expected, typically exhibits moderate confidence (p 0.3). In contrast, very low-confidence tokens (p < 0.3) are rarely observed while the model still producing coherent initial sentence. Over-sampling at this stage risks introducing irrelevant tokens that derail the generation. Once the model finishes answering the question and shifts to pro- ducing the next in-tontext example, however, both aleatoric variability and epistemic uncertainty increase, and the model's confidence drops substantially.
15

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A.4 HYPERPARAMETER SEARCH ON PROPOSED METHODS
0.44
0.48
0.42
0.46
0.40
Accuracy
Accuracy
0.44
Gready Threshold TreesyTTheeshlld
sampling
0.1
0.36
0.40
0.03
0.34
0.3
0.38
0.32
0.09
0.6
0.36
0.30
64
128
64
maj@k
maj@k
(a) s-sampling
(b) Giresdy-Treehood
0.50
Calbrated
0.500
0.48
0.475
0.05
0.46
Accuracy
0.450
Accuracy
0.09
0.44
0.1
0.425
Talp
0.42
0.400
0.03
0.05
0.375
0.09
0.38
0.350
16
32 maj@k
128
maj@k
(c) Calibrated-Tope
(d) Calibrated-e
Figure 8: Values of each threshold E, par, cer and varied study their effect self-consistency performance. Higher number samples generally benefit from smaller truncation thresholds.
We conduct parameter search for each our main methods to find the optimal E, PCT, CCT and Ce values. Figure 8a confirms our hypothesis that much larger value than suggested in the original c-sampling paper is beneficial. is 0.0009 in the original paper (Hewitt et al., 2022). We find that performs best around threshold benefit more at higher number of samples. The optimal par is 0.3 at 128 samples and 0.6 32 samples. Calibrated- Toop yields the best performance cCT 0.05 0.09 range. Calibrated-e shows the strongest gains at = 0.03.
regardless of the number of samples. For Srredd-Threshhe
lower
In general, larger sample sizes benefit from smaller truncation thresholds. This is intuitive: looser thresholds retain more candidate tokens, promoting diversity that enables the model to explore mul- tiple reasoning paths and recover the correct answer often enough dominate in majority voting. Figure 8 illustrates that optimal threshold selection is inherently sample-size dependent, reflecting the complex trade-off between accuracy and diversity.
In addition, we test various binning methods, including different number of bins and bin widths. Even bins (default) use fixed, uniform bin widths over confidence. Quantile bins adapt their widths so that each bin contains approximately the same number of tokens. This tests whether calibration quality depends on uniform spacing or sample-balanced partitioning. Since high confidence steps a lot more common, quantile bins would fit high confidence steps more. This results in different linear value compared to even bins and worse performance as shown in Table 4. Thus, it is not adviced to quantile bins. Using different number of evenly spaced bins results in similar performance, We do not overtune the number of bins to avoid overfitting on certain dataset and model combinations.
16

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Tabbe Effect of bin size and binning strategy Qwen2.5-0.5B - performance GSM8K. Even bins (default) use fixed, uniform widths over confidence. Quantile bins adapt their widths so each contains approximately the same number of confidence samples. n indicates the number of bins. A and B are the bias and gradient for log-log linear fit.
Bins
B
maj @8
maj @ 16
maj @ 32
71 5 even
-0.574
0.791
41.2
45,4
47.6
71 5 quantile
-2.290
0.435
33.9
34.1
34.0
10 even -0.506
0.795
40.8
44.3
47.1
10 quantile
-2.232
0.442
33.5
33.9
33.7
10 5 even -0.537
0.795
40,4
44.4
47.6
20 quantile
-2.214
0.444
33.5
33.6
33.6
30 even
-0.500
0.802
40.6
44.5
47.1
A.5 EFFECT OF CALIBRATION DATASET
In many cases, in-domain datasets are not available for calibration. To test robustness under this setting, we also perform calibration on a general instruction dataset, a alpaca- e-en. As shown in Table 5, performance with alpaca calibration is close to that obtained with in-domain data. While one might expect in-domain calibration to provide stronger correctness signals, alpaca still offers sufficiently reliable guidance.
A plausible reason out-of-domain calibration works that the mapping from model confidence expected correctness appears relatively stable across settings. In Figure 3, models of differ- ent sizes exhibit similar curves of expected accuracy as function confidence. Larger models place more mass in higher-confidence bins, which aligns with better benchmark scores. If this confi- dence-correctness relationship is driven by general properties of autoregressive modeling (rank-wise correctness decaying with rank) rather than dataset specifics, then calibration that matches the format of the target task ieatruction-aanswenrn this is hypothesis rather than causal claim. We lack direct evidence that models possess an "in- trinsic sense" of token-level correctness. Still, the observation that confidence-correttees correctness curves are similar across model sizes suggests that correctness- calibration can transfer because leverages structural, model-internal uncertainty signals rather than domain-specific features.
may suffice even when its domain differs. We stress
Table S: Calibrated-Topi with cer 0.1 using alpaca or GSM8K-train for calibration. Similar performances are observed. The test dataset GSMs.-test.
alpaca-gpt4-en gpt4-en
GSMSK -aMik-train Set
Model
maj @
maj @ 16
maj @10 32
maj @8
maj @ 16
maj @ 32
Qwen2.5-0.58
40.1
44.3
46.5
41.0
45.7
47.4
1ren2.5-1.5B-Instruee
72.4
74.8
76.1
72.9
74.8
76.5
Qwen2.5-3B-Instmee
79.9
80.8
81.0
79.1
80.7
80.7
Owen2.5-14BBIInttre
92.9
93.4
93.3
93.0
93.4
93.8
Qwven2.5-3BB-Instruuc
92.6
93.3
93.6
92.9
93.3
93.3
Llama-3.2-1B
4.4
4.4
5.1
4.8
5.3
6.0
Llama-3.22 2-1B-Instruct
40.5
42.7
44.6
39.4
43.0
43.9
17

---

Tabbe MBPP performance by Qwen2.5-0.5B-Inst Innstructt and 1.en2.55-..B-Instruuee Using out-of-domaal
calibration dataset -apaca-gpt--en results better pass@k @k performance than using in-domain data.
Qwen2.5-0.5B-Insteee
Qwen2.5-1.5B
Method
pass @8 pass 16
pass @ 32
pass@8 pass@ 16
pass @ 32
No restrictions
41.6
50.1
57.6
55.6
65.2
72.5
Top-k
45.3
53.5
59.8
59.0
68.0
74.3
Top-p
47.0
55.3
63.0
60.2
68.6
74.9
Min-p
51.1
58.9
65.0
62.2
69.7
76.0
EDT
50.5
58.1
65.0
50.4
57.9
64.3
1--ampling
44.3
53.4
61.2
57.9
63.2
74.0
Greedy-Threshold
44.0
52.8
60.6
56.8
65.9
72.7
e-sampling
49.2
56.1
61.8
62.0
69.6
75.4
Calibrated-Topk (ID)
50.3
57.9
64.2
62.6
69.3
74.6
Calibrated-s (ID)
48.6
53.8
57.8
62.1
68.2
72.8
Salibrated-Tople (OOD)
49.7
61.2
65.2
62.4
70.1
76.1
Calibrated-e (OOD)
51.0
64.2
62.3
76.3
10a
109
log ė = + Blog
log = A Blog
-0.506 0.795
A 00733,
0.697
Average correctness
10-1
Average correctness
10
10
10-2
10-3
10-3
10-4
10
10-3
10-7
10-1
10"
10
10-3
10-2
10-1
10
Average probability 6
Average probability P
(a) GSMSK-train set calibration MSE loss= 0.134.
(b) MBPP-validation set calibration MSE loss 0.237
Figure Twen2.5-00B-Il. calibrated MBPP-validation set poorer linear than GSM8K, which might lead to worse performance.
A.6 FAILURE CASE STUDY- POOR CALIBRATION SIGNALS
We provide case study on MBPP (Austin al., 2021), code generation benchmark where our truncation strategies underperform compared to min-p that prioritize diversity. Unlike reasoning tasks, MBPP requires directly producing executable code without intermediate steps, so every token is critical. A single incorrect token causes the program to fail its tests. Moreover, the pass@k @ metric rewards diversity, since success only requires one valid solution among the k samples. this setting, broader exploration increases the chance of producing at least one correct variant. Nevertheless, Greedy-Threshold still improves over unrestricted sampling, reinforcing our argument that sampling from low-confidence bins is harmful.
Calibration on MBPP also presents challenges. The validation set produces noisier signals, with larger linear fit loss (Figure 9), which likely reduces the reliability of predicted rank-wise cor- rectness and helps explain the weaker performance of Calibrated-E on Qwen2.5B-0.5B -.nn..55-o.SBInsttrrct. Despite this, Calibrated TopK performs comparably to existing methods in the literature, suggesting that correctness- aware truncation remains useful even in diversity-dee driven domains. Additionally, the less-noisy alpaca calibration variant, performance becomes better than using in-domain
18

---

calibration dataset and methods in literature too. This could be explained by in-domain dataset being 'vverfit' that impose too strict sampling conditions as seen by higher gradient (B value). This results in more greedy-like behavior and better performance at pass@8 but worse behavior at pass@32 where diversity is more valuable.
To examine how the quality of the linear fit in calibration grids (log-log space) impacts perfor- mance, we plot the regression Mean Squared Error (MSE) alongside model accuracy in Figure 10. To isolate the effect of calibration quality from majority voting, use maj @ I (single-sample curacy). If the linear interpolation provides reliable correctness estimates, models should generate more accurate single completions. If the fit is poor, the predicted correctness signals may be uninfor- mative or even harmful. To quantify this effect, we measure the improvement of Calibrated-s over the unrestricted baseline in maj Figure 10 shows that as model size increases, regression MSE rises and the performance gain diminishes. While part of this effect reflects the general difficulty of improving already-strong large models, the trend also suggests that noisier calibration weakens the benefit of Calibrated-s. This pattern is consistent with previous observation, where MBPP's noisy validation signals lead Calibrated-E to underperform Calibrated-Topt Importantly, however, maj @1 I accuracy never drops below the no-sampling baseline, indicating that even poor calibration not harmful.
0.18
Ulama3-80
0.16
0.14
at maj@@1
0.12
Owen2.5-0.58-lnse
Qwen2.5-1.5 1.5.5---1BBB/sttrrcc
0.10
Lama-3.2-BBlInstrud
0.08
Qwen2.5 B-3.l.-unc
0.06
0.04
Qwen2.5-2 5-32-------l
0.02
Qwen2.5 Ins-ruutt
0.1
0.2
0.3 MSE Loss
0.4
0.5
Figure 10: Effect of calibration fit quality. Larger models yield noisier linear fits (higher MSE), which corre- lates with smaller gains of Calibrated-s the unrestricted baseline.
19

---

'Tbble 7: Majority voting performance for Qwen2.5-1.5B-Instiee performance.
Calibrated- TopK has the strongest overall
GSMSK
MMLU-Pro
Big-Bench-IHe
Method
maje @+
maj @ 16
maj @ 32
maj@8
maj @ 16
maj @ 32
maj @8
maj @ 16
maj @2j@32 32
No restrictions
68.4
71.5
73.1
32.9
34.4
35.4
38.9
41.8
43,0
Top-k
68.5
72.6
73.9
33.7
35.0
35.9
41.7
44.2
45.6
Top-p
71.1
74.1
75.9
34.1
35.4
36.4
44.0
46.2
47.1
Min-p
73.3
75.6
76.6
35.3
36.2
36.9
45.5
47.2
47.6
EDT
74.9
75.6
77.0
34.7
36.2
36.8
45,5
47.8
48.2
7-sampling
69.0
72.4
74.2
33.6
34.8
35.7
41.1
43.6
45.3
s-sampling
73.4
76.4
78.2
35.0
36.2
36.9
46.9
47.7
Greedy-Threholld
70.1
73.6
75.5
33.6
34.9
36.1
40.3
42.9
44.4
Calibrated-Toph
72.3
75.2
76.3
35.6
36.4
37.0
45.8
47.7
48.5
Calibrated-s 74.3
77.2
78.4
34.8
35.9
36.9
46.2
47.2
48.2
Table 8: Majority voted results on GSM8K and Big-Bench-Hiie Hard using O0wen..5-1.5B-Instt In addition to existing sampling conditions, Thredy-Thresholdd pGr 0.3 is applied and shows strong consistent gains in addition to base samplers. Statistically significant differences 0.05) marked in bold.
GSM8K
Big B--e--Bnnhadd Hard
Method
maj
maj @8 maj @ 16 maj @ 32 maj@
maj@@ maj@ 16 maj @
Baseline T=1
17.3
30.2
35.2
38.6
17.4
17.9
20.0
16.2
-Treeyy-Treehold
+0.3
+1.0
+1.8
+2.0
+1.9
+2,9
+0.3
+3.2
top-k
18.8
32.6
38.7
41.9
20.5
22.0
21.7
21.5
Greedy--hreshold
+0.2
+1.1
+0.5
+1.1
+1.1
+1.6
+1.5
+1.5
top-p
22.4
35.5
40.8
22.3
25.8
25.9
Thresh-T
+0.6
+0.9
+0.4
+1.3
+1.6
+1.5
+1.5
+1.9
min-p
25.3
38.7
43.1
46.6
27.5
30.6
31.5
31.7
Greedy- Thress--h
+1.9
+1.4
+0.8
+0.6
+0.3
+0.2
+0.1
+0.1
EDT
28.0
40.2
44.7
46.8
27.0
30.4
31.1
31.7
Greedy-Threshold Threshold
0.0
+0,2
-0.3
+0.1
+0.5
+0.3
+0.5
+0.3
1) sampling
19.0
31.6
37.2
41.0
19.7
20.6
20.3
19.6
Threshlld
+4.3
+2.4
+1.8
+1.7
+0,9
+1,9
+2.2
+2.7
A.7 FURTHER CALIBRATED TRUNCATION AND GREEDY-TUREESIOLD RESULTS
We further compare our proposed methods against other existing methods across different bench- marks. Calibrated-Topp has the strongest overall performance for 1..5B55-1.-BIIttte as shown in Table 8.
We extend our analysis of Greedy-Threshie for up to 32B parameters models in Table 9, con- sidering both instruct and non-instruct models. As expected, larger models with stronger baseline performance are more challenging to improve. Existing samplers provides little improvement on the baseline. Nevertheless, Greedy-Threshold does not degrade performance. It either provides modest gains or remains comparable to existing samplers. One explanation for this diminishing effect is that larger models produce high-confidence predictions more frequently (Figure 3), leading to fewer low-confidence steps. Since Greedy-Three Threshold only intervenes under low-confidence conditions, its impact naturally diminishes as model size increases. Similarly, the effect of majority voting in larger models (Table 11) also diminishes in larger models due to reduced stochasticity.
20

---

Table 9; Majority voted results on GSM8K. Creedy-Threehole improves performance more smaller models.
Statistically significant difference (p 0.05) marked in bold.
Llama-3.2-1B
Qwen2..5 Qwen2.5511B-IIstrruc
Qwenn..5-32B-Instruuc
Method
maj@8 maj@ maj@32
maj@8 @8 maj @ 16 maj @:22 maj @
maj @ 16 maj@
Baseline T=1 + Greedy-Threshold
0.7
0.6
0.2
92.8
93.4
93.5
92.8
93.4
94.0
+0.7
+0.5
+0.5
+0.2
+0.2
+0.3
+0.1
+0.3
Top-k
2.6
1.7
1.4
93.3
93.5
93.7
92.9
93.7
93.9
Greedy-Threshool
-0.3
+0.6
+0.1
0.0
-0.1
0.0
+0.1
-0.1
0.0
Top-p
1.7
1.4
93.3
93.5
93.5
93.1
93.5
Greedy-Threshold
+0.3
+0.5
+0.4
+0.1
-0.1
0.0
-0.2
-0.1
-0.2
Min-p
3.9
3.6
93.2
93.1
93.3
92.8
Greedy-Threshold
+0.9
+0.5
+0.9
-0.3
+0.2
+0.1
+0.3
0.0
-0.2
EDT
4.2
3.8
3.9
92.9
93.3
93.4
92.7
93.3
93.5
TrrehhyTrreshold
+0.9
+0.3
+0.1
+0.1
-0.1
0.0
-0.1
-0.1
+0.1
s-sampling
1.1
0.8
0.5
93.5
93.6
93.7
93.2
93.6
93.9
Greedy-Threshold
+0.7
+0.5
+0.7
-0.4
-0.3
+0.1
-0.1
0.0
-0.1
Table 10: GSM8K performance by Qwen2.5-7B and Wwven255-BBIInsrruee
Qwen2.5-7B
Bwwe2.5-7B-Inssten
Method
pass@8
pass 16
pass 32
pass@8 pass 16
pass 32
No restrictions
82.8
86.8
88.4
86.7
88.4
89.4
Top-k
83.3
87.6
88.9
87.2
89.3
89.3
Top-p
84.9
88.2
89.6
87.2
88.3
89.3
Min-p
86.2
88.7
89.9
87.2
88.3
88.8
EDT
83.4
87.3
88.7
87.0
89.1
y-sampling
83.8
87.2
89,5
87.8
89.3
89.7
Greedy-Threshold
83.8
86.6
88.9
86.8
88.8
89.6
e-sampling
86.6
88.5
89.9
87.4
88.7
88.8
Calibrated-TopK
86.5
88.7
87.4
89.6
Calibrated-e
86.5
87.6
89.3
88.0
88.7
89.4
Table 11: MMLU-Pro performance by Qwen2.5-14B. Inntstruu and Qwwnn2.533B-Innstt Instruct.
Qwen2.5-14BBInsse
Qwen2.5-32BB --eenl.--32B-nsttuuu
Method
pass @8
pass @ 16
@2
pass@8
pass @ 16
pass @ 32
No restrictions
63.4
63.7
64.1
68.1
68.5
68.7
Greedy-Threshol
63.4
64.1
68.1
68.5
e-sampling
63.6
64.2
64.2
68.6
68.9
68.9
Tolpbrated-TopK
63.7
64.2
64.6
68.3
68.7
69.0
Calibrated-e
63.8
63.7
64.1
68.3
68.6
68.9
21

---

A.8 EFFECTIVENESS AT Low TEMPERATURES
Since lower temperatures are used for math and coding tasks, we test our proposed methods using T 0.6. The reason for temperature scaling is make probability distribution more peaked so that top-1 probability increases while the tail probabilities shrink. Consequently, probability-ban pruning becomes implicitly more aggressive. Many low-rank tokens become unlikely to be sampled even without changing any thresholds. This aligns with our thesis that low ranked tokens should be broadly sampled due their correlation with low correctness. Given the same non top-1 ranked token, after temperature scaling, its probability will decrease. Thus, to remove the same token as without temperature scaling, the probability cutoff needs to be lower. choose s = 0.01, PGT 0.1 and cCT 0.01.
Given the same Pmaz: its scaled probability would be bigger. Thus, we should set higher Greedy- Threshold than before. However, in practice found that this limits diversity significantly that the benefit from self-consistency diminishes. The maj @ accuracy increases but performance gain from maj @k reduces. We hypothesize that this is because more lower temperature already results diminished diversity. Further restrictions results diversity collapse. From Table 12, we can see that further gains from baseline is much smaller than with T 1. Nevertheless, by setting lower truncation thresholds, we still see performance gains from using our proposed truncation methods.
Relation between temperature and E-sampling. We derive how temperature scaling interacts with probability thresholding in e-sampling. At a fixed decoding step let 25( denote the logit of token j and (j) the corresponding next-token probability under temperature 0.
exp( (z((T)
pT(i) = Σ, exp 24 (v)/TT
(12)
Let j be the top-1 token this step and define centered logits Azj = 20) 2(i²) s 0. Subtracting 21 (j** from all logits leaves the softmax invariant, so
exp(Az,/T)
exp( exp(Az;/T)
pr(j)
(13)
I+ EKEE exp(A2x/T)
Dr
where we introduced the normalizer
D= : 1+ Σ exp(A2x/T).
(14)
Azjj"
In particular, for we have
exp(Aej) D1
pı(s)
D1 1+ Σ exp(Azk).
(15)
We can now eliminate the logits A2, and obtain a direct relation between Pr(j) and (i()) at the same decoding step. From the T expression get
exp(Azz)= = Pi() DI,
exp(Az,/T) = (exp(Az,)) = (i) Di)
(16)
Table 12: Majority voted results on GSMSK with scaled temperature 7 0.6, E = 0.01, PGr = 0.1 and
cor 0.01
Qwen2.5-0.5B- Instrucct
Owee2..511.5B-1 Instrucct
Method
maj@ @8 maj @1 16 maj@ 32
maj@ @8 maj 16 maj@
No conditions
40.7
44,9
46.9
73.7
76.3
76.9
e-sampling
41.4
45.2
46.8
74.4
75.8
77.0
Greedy-Threshodl
41.2
45.2
47.2
74.3
76.9
77.1
Calibrated-Topt
40.9
44.5
46.7
74.1
76.0
77.3
Calibrated-e
41.4
45.2
48.4
74.2
75.6
77.0
22

---

Plugging this into the definition of pr (j) gives
(p1(j) D1)
1/r
D
pr(j)
Pi(i)
(17)
Dr
Dr
Kr
Thus, for any fixed decoding step l and any temperature T > 0,
pr(j) Kr KrPi
(18)
where the factor
DV/ Kr = DT
(19)
depends the full logit configuration that step and T, but does not depend the particular token j. In other words, temperature rescales per-token probabilities via power law in their 7 = probabilities, up step-wise constant multiplier Kr shared by all tokens. This leads to natural scaling rule for s-sampling. Suppose that at T 1 we apply e sa-samlling and discard all tokens with
(i()) - E1
(20)
The same tokens have probability, at temperature T.
pr()) Kr pi(j) S KrTYT. 1/T
(21)
If we want temperature-7 cutoff to remove least all the tokens that would have been removed
by E1 es-mamlling at = 1, a natural choice is
1/T
ET E
(22)
with the proportionality constant absorbing average the step-wise factors Kr. In practice we use the simple global scaling rule
(23)
For T < 1 (sharper distributions), 1/T > 1 and hence εT < Temperature already suppresses www-prbbbbilty tokens, the probability threshold must be lowered in order to prune a comparable part of the tail of the logit distribution.
Intuition for the E = 0.01 choice. In our main experiments we use E = 0.05 at 1. Applying Equation (23) to T = 0.6 yields the theoretical value
E.6
theory
1/0.6 = 1/05 ~ 6.8 x 10
(24)
For our low-temperature runs at 0.6 we instead adopt e = 0.01, which is slightly more conser- vative (it removes a bit more of the tail) but remains close to the theoretical prediction.
23

---

TTbble 13: GPT-4-mini judges performance of various samplers LitBench prompts generated Qwen2.5- 7B Instructtc.. Human written baseline is the etosen_story column from the original benchmark. Each category is scored from 1-5, Higher is better.
Method Greedy
Relevance
Coherence
Emotional impact
Originality
Total
4.50
3.27
2.70
2.68
13.15
T-1
4.48
3.15
2.81
2.67
13.11
Min-p=0.1
4.48
3.38
2.80
2.69
13.35
Human written baseline
4.50
3.81
3.03
3,20
14.54
Calibrated-Topk
4.58
3.52
2.77
2.68
13.55
Calibrated-e
4.60
3.47
2.77
2.69
13.53
A.9 WHAT ABOUT CREATIVE WRITING?
Our main experiments target reasoning tasks with closed-form answers. A natural question is whether the same correctness-aware perspective applies open-ended generation. We provide an illustrative case study on creative writing using LitBench (Fein et al., 2025), treating the chosen story as proxy for ground truth. We construct calibration grids and probability robability-correetness correctness scatter plots and observe qualitatively similar patterns. As confidence decreases, expected correctness declines. rank increases, correctness drops sharply. Compared with GSM8K and Alpaca calibration, cre- ative prompts exhibit systematically lower confidence, with low-confidence bins occurring more often (e.g., lowest-bin frequency: 6.01 % for LitBench vs. 0.17 % for Alpaca and % for GSM8K). mapping in log-log space is also stronger in this setting, with slope closer to one. Full calibration diagrams and scatter plots are provided in Section A.10.
The
We conduct simple evaluation of our samplers compared to min-p (Schaeffer al., 2025), which advertised to excel at creative writing. We prompt Qwen2.5-7B 7-B-ntrruettt to generate short stories using the prompts given in LitBench with the following prompt: Given the following writing prompt, write a short story that is original, relevant, emotional and coherent correct in less than 500 words. [Prompt] Your story:
The stories generated are evaluated by GPT-5-mini uusin the following prompt: Evaluate a creative writing task and give scores. Each category is scored from 1 (lowest) to 5 (highest). Consider these categories: Originality: unique concepts, unexpected elements. Relevance: story follows the writing prompt. Emotional impact: how the writing affects the reader. Coherence: logical flow and narrative structure. Writing prompt: [prompt] Judge the writing in the following format: Reasoning: lyour evaluation with scores for each category]
The scores given by the judge model is parsed and averaged for each category averaged over three runs. As shown in Table 13, our calibrated samplers outperforms min-p and no-samplers baseline by improving coherence and relevance. While originality stays the same and emotional impact is slightly reduced. The improvement in coherence and relevance is essential for a small model like Swee2.55-B-IInstren which is prone drifting off-topic at a high temperature.
A.10 EXAMPLE CALIBRATION DIAGRAMS
"https::/ /openaii /gpt- m-mini
24

---

10a
lagê-A Blogé
10a
Jogé=A+ #log
lgg -A+ Riog/
10
-0.413, 0 0.791
Average correctnees
10-1
correctiness
10
10-2
10-2
10
10
10a3
10:3
10-4
10
10-2
10-2
10-1
10
10
10-1
Average probubility 6
Average probability 0
Average probability
(a) GSM8K
(b) alpaca-gpt4-en
(c) LitBench
Figure 11: Calibration scatter plots Qwen2.5-1.5B 10ven2.--15B-Inntruee
10a
I B
10a
logê= A Blog
-0.506, 8 0.795
-0.217,
correctness
Average correctness
10-1
10-1
10
10
10
10
-4
10-1
10-2
10-1
10-4
10-1
10-2
10-1
Average probability 6
Average probability p
(a) GSM8K
(b) alpaca-gpt4-cn
Figure 12: Calibration scatter plots S.ve22.--0.5B-Instmre
25

---

[0.9,1.0] 70.80%
(-0.000
2-0.010
j-0.001
(-0.000
2-0.002
2-0.00
0000000
2-0.001
Aina aco
(-0,000
E-0.001
[0.8,0.9] 7.31%
2-0.023
3-0.010
[-0.021
2-0.005
015
2-0,009
6-0
A-0 DC1
2-0.004
(m0,001
2-0.002
(0.7.0.8] 5.43%
fm0.752
1500.157
2-0.171
2-0.037
3-0.015
2-0.000
fm0.000 000000
2-0,012
1+0.005
902
2-0.002
2=0.003
0.6
(0.6.0.7] 4.64%
(-0.651
2-0.053
f-0.007
C=0.010
2w0.007
2-0.005
003
2-0.002
2-0.004
0..4
Confidence bin
(0.5.0.6 4.58%
6-0.009
2-0.017
2-0.010
6=0.005
2-0.005
2-0.003
2-0.005
Correctness
(0.4.0.5) 3.59%
A-6.015
6-0.010
4-0.007
6-0.006 006
2-0.008
2-0.004
0,2
(0.3,0.4) 2.31%
$-0.249
2-0.041
6-6.026
6-0.018
A-0.013
5-0.017
6-0.010
2-0.008
[0.2,0.3] 1.12%
A-6.043
6-0
6-0.023
6-0.00
[0.1,0.2 0.22%
A-6.058
6-0.037
829
[0.0,0.1] 0.00%
6.0.035
830
2w0.000
7
10
Rank
Owen2.5-0.5B --.......0.BB-sstrucc on GSM8K
(0.9,1.0] 33.21%
$-0.978
E-0.337
6-0.012 012
Eu0.022
200.007
6-0.003
6-0.002
6s0.003 003
Á- 001
2u0.000 6002
A.0.001 0.0.001
Es00001
6 000
200.003
6-o 000
$s00001
dun 000
$s0.001
6-0.000
2=0.00
0.8
[0.8,0.9] 9.11%
Bu0.522
2e0.786
6u0.079 079
2e0.105
6.0.023
2m0.035
6u0.011
Em0.010
Au0.007 000.007
2mb 611
6s0.004
2m0.007
6w0.003
8e0.005
$s0.002
Ew 000
Aua 002
000.003
6.0.001
2m0.007
[0.7.088] 8.31%
A-0.700
F-0.867
Amo
2-0.152
2-0.058
Gm0.019
6m0.019
6-0.031
Am0.011
2m0 015
6m0.007
2-0.010
6m0.005
2-0.007
Am0.004
t-0.006
And 061
0.0
6m0.002
7-0.0
(0.6,0.7] 8.67%
2-0.566
$-0.669
A-0.188
2-0.191
2-0.054
2-0.077
4-0.026
2-0.041
6m0.016
2-0.020
6m0.010
2-0.014
6m0.007
2-0.009
fr0.006
2-0.007
A-2 064
2-0.006
6-0.004
2-0.005
donfidence bin
[0.5,0.6] 9.61%
$-0.549
2-0.477
ji-.235
2-0.230
2-0.098
(-0.070
$-0.034
2-0.046
2-0.000
2-0.025
de0.015
2-0.017
6-0.010
2-0.012
f-0.007
2-0.009
4-2 006
t-0.007
(-0.005
2-0.006
Correctness
[0.4.0.5] 9.91%
S=0.451
E.0.357
ji-0.243
2u0.233
2=0.114
2=0.005
$=0.047
E.0.056
2.0.033
2-0.028
fmc.019
E=0.023
6-0.014
E.0.017
5-0.010
5w0.013
p=0.008 008
E.0.010
2-0.007
2.0.008
[0.3,0.4] 9.11%
$=0.351
E=0.317
$50.2115
2m0.205
2m0.122
2-0.119
$=0.066
Es0.070
2m0.041
Em0.040 06.
2m..003
fw0.028
6=0.021
Em0.024
S=0.016
Ew00.000
p-0.00
2w0.015
2mb.012
0=0.010
[0.2,0.3] 7.38%
Aeo.251
F-0.233
Am0.177
E-0.166
2-0.115
6m0.116
$m0.078
F.0.079
Em0.054
2mb 658
2m0.041
$mc.039
6m0.000
F=0.033
$s0.023
Em0.00%
Am0. 519
2=0.021
6e0.01
2+0.017
[0.1,0.2 4.12%
Ae0.158
E-0.149
A14..119
2-0.115
2-0.091
(-0.001
$=0.071
[-0.072
Em0.056
2=0.557
2-0.045
fmc.045
6-0.206
2-0.057
$m0.000
2-0.033
Ai2 206
2-0.026
6-0,00
2+0.225
(0.0.011] 0.59%
j=0.078
E=0.075
Ai3 063
2-0.061
2-0.051
6-0.05 35.
f-0.045
(-0.044
2m0.030 0-0.038
2-c C37
fmc.033
2-0.032
2-0.030
0.0.029
f=0.026
2-0.021
Ai2 224
2-0.024
(-0.001
2+0.025
Rank
(b) Qwen2.5-0.3. 5..en2.5-0.5B-- --5--turtttttt on aapaca-gpt4-en
Figure 13: Calibration grids on various Qwen models and GSM8K or alpaca-gpt4-en
26

---

[0.9,1.0] 75.80%
690.990
6-0.000
2-0.015
j-0.001
(-0.000
002
pim
2-0.003
2-0.000
1-0.000
2-0,003
Aina ac0
(-0.00
E-0.000
[0.8,0.9] 6.26%
t-0.667
10.13
2-0.021
$-0.009
t-0.023
2-0.000
2e0.014 014
2-0,008
0000
2-0.003
DC1
(m0,001
C-0.003
(0.7.0.8] 4.63%
jm0.752
2-0.1
2-0.035
059
2-0.007
2-0,012
0.005
002
(m0.001
0.6
(0.6.0.7] 3.95%
$-0.650
2-0.05
2-0.011
fm0.007
2w0.007
fm0
2-0.003
002
2-0.002
2-0.004
0..4
Confidence bin
(0.5.0.6] 3.86%
$-0.550
f-0.009
2-0.017
2-0.013
6=0.004
2-0.005
2-0
2-0.004
Correctness
(0.4.0.5) 2.85%
$000300
2-8.014
6-0.010
2-0.013
4-0.007
6-0.005
2-0.007
005
2-0.004
0,2
(0.3,0.4] 1.72%
$-0.253
6-6.026
6-0.817
A-0.012
2-0.010
6-0.009
2-0.007
[0.2,0.3] 0.77%
6-0.198
6-6.043
6-0.031
A-0.023
6-0.018 018
[0.1,0.] 0.16%
040
6-0.034
2.0.00
828
2.0.053
[0.0,0.1] 0.00%
822
2w0.000
7
10
Rank
O.en2.5-1.55-Innstee on GSM8K
[0.9,1.0] 41.00%
$-0.979
E=0,934
6-0.013 013
Eu0.024
2u0.010
$-0.003
6-0.001
6s0.005
2u0 602
8-0.001
A.0.000 0.0.000
Eu00001
6-0 000
2.0.001
6-o 000
$s00001
6un 000
$s0.001
6-0.000
2=0.00
0.8
[0.8,0.9] 9.79%
Au0.522
2e0.750
Aug 088
2e0.127
6.0.024
2m0.041
6u0.011
Em0.010
A.0.000
2mo 610
2m0.00
6s0.004
2m0.004
003
Em0.003
$s0.002
Aua 061
2e0.00
6.0.001
2m0.007
[0.7.088] 8.48%
A-0.700
F-0.864
Am0.147 147
2-0.171
2m0.040
2-0.055
6m0.018
0m0.025
6m0.010
2-0 61.
6m0.007
2-0.01.
6m0.004
2-0.007
Am0.001
5-0.005
And 062
0.0004
6m0.002
0.000
(0.6,0.7] 8.42%
2-0.566
$-0.850
A-0.204
2-0.222
2-0.070
2-0.057
6-0.026
2-0.037
2-0.020
6m0.015
6m0.009
2-0.012
6m0.008
2-0.008
fm0.005
2-0.008
A-2 004
2-0.006
6-0.003
2-0.004
Confidence bin
[0.5,0.6] 9.15%
$-0.549
2-0.482
2-0.256
2-0.257
2-0.087
2-0.074
4-0.034
E-0.040
2-0.022
2-0.018
fe0.012
2-0.018
6-0.009
2-0.013
f-0.006
2-0.010
4-0 0c5
t-0.007
2-0.004
2.0.005
Correctness
[0.4.0.5] 8.85%
S=0.451
Ew0.356
ji-0.26
2u0.251
2=0.110
2-0.104
$=0.050
Es0.081
2u0.033
2m0.020
fe0.019
E=0.024
6-0.013
E.0.017
5=0.010
5.0.010
p=0.007 007
E.0.011
/-0.006
2.0.008
[0.3,0.4] 7.14%
$=0.352
E=0.009
Em0.216
$50.229
2m0.124
2=0.132
G=0.072
Em0.070
2m0.044
Em0.050
fw0.020
2m00003
6=0.021
2m0.023
S=0.015
Ew00.008
p-0.00 002
Ew0.014
(-0.009
2=0.011
[0.2,0.3] 4.95%
Aeo.255
F-0.229
6m00.181 183
P-0.159
2-0.188
6m0.127
$m0.087
F.0.085
2mb 66.
5m00060
fsc.042
2m0.044
6m0.001
Fm0.033
$m0.024
Em0.004
Am0. 519
2-0.022
6e0.01
2-0.017
[0.1,0.] 2.04%
A=0.167
E-0.135
#27.1127
2-0.105
2-2.096
(-0.100
$=0.078
[-0.078
6m0.061
2-c .63
fmc.049
2-0.044
6-0.040
2-0.036
fe0.033
2-0.035
Am0 208
2-0.026
2-0.00
2+0.024
(0.0.011] 0.17%
j=0.081
t-0.050
Aim 069
2-0.050
(-0.058 85.8
2-0.079
4-0.050
2-0 050
2m0.043
2-o .48
fmc.030
2-0.029
d-0.033
2-0.017
$=0.090
Em0.042
C-0.029
(-0.004
2+0.006
Rank
(d) Qwen2.5- 1.55----t1.- Instructt on alpaca-gpt4-ent
Figure 13: Calibration grids on various Qwen models and GSM8K or alpaca-gpt4-en
27

---

[0.9.100] 9.38%
A-0.98
1-0.448
8-0.013 033
2-0.017
2-0.004
2=0.005
6-0.002
(-0.003
2-0.00 00.002
00.0002
2-0.002
2-0.001
6-0.001
2-0.001
A-0.001
5-0.001
6-0.00 001
2-0.001
2-0.000
2-0.001
[0.8,0.9] 4.64%
8-0850
t-0.797
8-0 960
2-0.068
2-0.021
2-0.025
6-0.012
tw0.014
2-0.0 000
2m0.000 009
A- 00.000
2-0.007
6-0.004
2=0.005
E-0.004
0.0.003
6-0 003
2-0,003
2-0.002
2-0.003
[0.7.088 5.08%
8.0.749
2w0.508
6u0 858
2-0.103
2.0.036
2-0.041
2-0.023
6.00020
2-0 033
2=0.015
2-0.011
6.0.007
2-0.008
A-c 000
2-0.007
pud 004
2-0.005
2-0.005
004
(0.6,0.7] 6.29%
Am0.668
2-0.604
2-0.135
114
6e0.051
2-0.056
6=00028
2-0.031
2-0.021
#ec.013
2-0.014
6m0.010
2-0.011
Ano 008
2-0.009
2-0.007
806
200.00
2-0.006
0..4
Confidence bin
[0.5.0.6 8.27%
$-0.547
E-0.508
6-0.170
2-0.170
2-0.065
2-0.069
6-0.036
2-0.029
2-0.024
2-0.026
2-0.019
2-0.017
6-0.013
2-0.015
$-0.010
5-0.011
6-0 008
2-0.009
2-0.007
2-0.007
(0.4.0.5) 11.22%
$-0.448
2-0.418
6-0.110
2-0.186
6-0.081
2-0.081
6-0.046
2-0.047
2-0.030
2-0.033 0.3
B-0.021
2-0.023
6-0.016
2-0.018
6-0.013
5-0.014
p-0 000
2-0.012
2-0.009
6-0.009
0,2
(0.3,0.4) 14.73%
5-0.348
Eu0.322
E-0.174
E-0.096
6-0.096
6-0.057
2:00 050
2-0.038 0.0.088
2-0.027
2-
6-0.021
2-0000
6-0
5-0.017
E=0.015
p-o 004.004
6-0.002
2-0.012
(0.2,0.3) 17.66%
$-0.249
p.a.1152 152
Eu0.166
2=0.093
6.0.096
6.0.064
6x00
2w0.034
6-0.027
2u0.028
6=0.022
pud 018
Ew0.018
6w0.005
Ew0.016
(0.1,0.2] 16.73%
#e0.152
piu0.105 105
6..00766
$..0.057 Ewc.
2mb
6m0.000
$e0.025
pid 822
6.0.009
2m0.019
[0.0,011] 6.01%
jm0.072
jimó
(m00.04
pmm
Amo 023
Aia 819
6m0.017
Rank
(e) Qwen2.5-1.5B 1.55e255- on LitBench
Figure 13: Calibration grids on various Qwen models and GSM8K, sipaca-gpt4-en or LitBench
28


Reviews:
[{"review_id": "DeAwGbtMb5", "reviewer": "Reviewer_2ZR5", "summary": "This paper re-examines predicting tree search in reasoning models by characterising the difference in uncertainty pertaining to randomness and that due to model uncertainty (aleatoric vs. epistemic uncertainty).  The authors then retrofit the sampling model to differentiate between these two potential sources of uncertainly through their proposed **Greedy-Threshold** sampling, where they calibrate the model's own certainty prediction (as modeled by final-layer logit) against that of the ground truth through Calibrated-$\\epsilon$ mapping.", "questions": "* Why choose 10 bins?  Could you better fit this as an optimisation parameter where the bin sizes also correlate with transitions in the calibration bin to improve performance?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "* I enjoyed reading this paper.  It is well-structured and presents well-founded arguments for the need for a calibration grid and its derivates that are then used to decide on rollouts.\n* Analysis that mid-confidence bins benefit from diverse sampling is intuitive and shown in S2.2.  This is intuitive but needed to be shown in contrast to the prevailing notion that low-confidence requires diverse sampling. \n* The paper uses open-weight models Qwen2.5 and Llama, and later the recent GPT-OSS 20B as an advanced LRM.  This aids reproducibility.  \n* The paper also experiments over various task datasets that are relevant to show cross-task applicability.", "weaknesses": "* I wished more information from the Appendix on failure cases (e.g., A.3 and A.6) could make it into the paper proper.  It helps to give a more concrete form with respect to sampling when grounded to an example.\n* Same with respect to A.8, the relation to temperature could be given stronger theoretic guidance and derivation.  This part should tie in elegantly, but in the current submission, does not give a sufficiently unified presentation.\n* The non-monotonicity of the calibration grids on page 23 deserve a bit of discussion.  The bottom of the grids somewhat reinforce your arguments, but here is is not clear whether sample sparsity also plays a role.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "aXtfaWneR7", "reviewer": "Reviewer_7oG6", "summary": "The paper argues that current decoding for reasoning mixes up two kinds of uncertainty:  good uncertainty (many valid continuations) and bad uncertainty (the model is just wrong). So instead of sampling more when the model is low-confidence, they propose “correctness-first” decoding: Greedy-Threshold (go fully greedy when max prob < τ), Calibrated-TopK (adapt k per step using a confidence×rank correctness grid), and Calibrated-ε (a continuous version that maps prob to expected correctness).On GSM8K, MMLU-Pro, BBH, and AIME (with GPT-OSS) these rules consistently give small-but-real maj@k / pass@k gains and can be layered on top of normal samplers which I found to be good.", "questions": "Please refer to weaknesses", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Very clear problem framing\n- Easy to implement and add to existing samplers and inference is cheap\n- The experiments were on broader side and showed consistency across range of models", "weaknesses": "- The paper seems to relies on task/data calibration; when calibration is noisy or OOD, gains shrink , so it’s not always free wins.\n- From the paper it seems like improvements are incremental, few points  maj@k, big models already strong.\n- The claim low confidence = epistemic, so always sample less is shown mainly on math/reasoning; creative/open-ended generation is only discussed, not tested", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZBh225Cr4d", "reviewer": "Reviewer_2drS", "summary": "paper presents an interesting and ambitious analysis of Correctness-First Decoding for Better Reasoning in LLMs. It’s well-structured and follows a logical argument, but several areas could be strengthened for clarity, rigor, and reader engagement.", "questions": "N/A", "limitations": "", "rating": 4, "confidence": 2, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The introduction effectively frames the research question and contextualizes the problem within existing literature.\n2. The Methods section provides an appropriate research design and statistical treatment. The inclusion of comparative baselines is a strong point.\n3. The experimental design and analytical approach are sound and appropriate for the research question.", "weaknesses": "1. The abstract summarizes methods more than findings; it doesn’t highlight the key quantitative results or main contributions.\n2. Some information about sample selection, data splits, or parameter settings is missing, which could affect reproducibility.\n3. The discussion section mostly restates results instead of analyzing their implications or addressing possible alternative explanations.\n4. The conclusion doesn’t emphasize broader implications or concrete future directions, making the ending feel abrupt.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "E0ZCZbwgcz", "reviewer": "Reviewer_cpeR", "summary": "The paper proposes a new method that samples based on correctness during the decoding process. The authors conduct comprehensive experiments to demonstrate the effectiveness of their approach.", "questions": "NA", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The idea is both novel and elegant. The authors approach the problem from a fresh perspective and achieve the goal of evaluating correctness without relying on complex architectures.\n\n2. The motivation behind the work is strong, and the authors provide a comprehensive and convincing analysis.\n\n3. The paper is well written and easy to follow.", "weaknesses": "1. The experimental results indicate only marginal improvements. In the main results table, the accuracy gain is approximately 1%, which appears to be relatively minor.\n\n2. It's valuable that the paper includes results on GPT-OSS; however, the evaluations on Qwen are limited to smaller model sizes. It would strengthen the paper to include results on larger models, such as the 7B or 8B variants, or even larger if available.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)