Efficient semantic uncertainty quantification in language models via diversity-steered sampling
Authors: Ji Won Park
Kyunghyun Cho
Venue: NeurIPS 2025 poster ()
Keywords: uncertainty quantification
large language models
natural language generation
semantic diversity
importance sampling
Primary area: deep_learning
TL;DR: We inject a semantic-similarity penalty term into decoding for autoregressive and masked-diffusion LMs, generating semantically diverse answers and, with importance reweighting, enabling consistent estimation of downstream uncertainty metrics.

Abstract: Accurately estimating *semantic* aleatoric and epistemic uncertainties in large language models (LLMs) is particularly challenging in free-form question answering (QA), where obtaining stable estimates often requires many expensive generations. We introduce a **diversity-steered sampler** that discourages semantically redundant outputs during decoding, covers both autoregressive and masked diffusion paradigms, and yields substantial sample-efficiency gains. The key idea is to inject a continuous semantic-similarity penalty into the model’s proposal distribution using a natural language inference (NLI) model lightly finetuned on partial prefixes or intermediate diffusion states. We debias downstream uncertainty estimates with importance reweighting and shrink their variance with control variates. Across four QA benchmarks, our method matches or surpasses baselines while covering more semantic clusters with the same number of samples. Being modular and requiring no gradient access to the base LLM, the framework promises to serve as a drop-in enhancement for uncertainty estimation in risk-sensitive model deployments.

Efficient semantic uncertainty quantification in language models via diversity-steered sampling
Ji Won Park Prescient Design, Genentech park. ji_ won@gene. com
Kyunghyun Cho
Prescient Design, Genentech
Center for Data Science, New York University cho. www.kknnyuunggnne.com
Abstract
Accurately estimating semantic aleatoric and epistemic uncertainties in large language models (LLMs) is particularly challenging in free-form ques- tion answering (QA), where obtaining stable estimates often requires many expensive generations. We introduce diversity-steered sampler that discourages semantically redundant outputs during decoding, covers both au- toregressive and masked diffusion paradigms, and yields substantial sample- efficiency gains. The key idea is to inject a continuous semantic-similarity penalty into the model's proposal distribution using a natural language inference (NLI) model lightly fine-tuned on partial prefixes or intermediate diffusion states. We debias downstream uncertainty estimates with impor- tance reweighting and shrink their variance with control variates. Across four QA benchmarks, our method matches or surpasses basclines while covering more semantic clusters with the same number of samples. Being modular and requiring no gradient access to the base LLM, the framework promises to serve as drop-in enhancement for uncertainty estimation in risk-sensitive model deployments.
1 Introduction
Large language models (LLMs) excel generating fluent text yet remain prone to both intrinsic aleatoric ambiguity and epistemic gaps in their learned knowledge. The latter can lead to hallucinations confident outputs that factually incorrect. Quantifying these uncertainties is critical for building safe AI systems deployable in high-stakes applications. In free-form natural language generation (NLG) tasks like question answering, this is especially challenging, as lexically distinct responses can still be semantically equivalent.
Estimating uncertainty in language generation often relies on drawing large TID sample sets, which often contain semantically redundant outputs and waste compute. For example, semantic entropy has been proposed to quantify aleatoric uncertainty by clustering generated outputs into semantic equivalence classes [. while mutual information computed via iterative prompting has been used to lower-bound certain forms of epistemic uncertainty 2 Despite their conceptual appeal, both approaches require extensive sampling to produce stable estimates, limiting their use in low-resource settings. Diversity-oriented heuristics such as temperature scaling or nucleus sampling 3. on the other hand, do not account for semantics. More recently, Aichberger et al. 4 proposed method that steers generation toward semantic diversity, though it relies on token substitutions and remains restricted to autoregressive models (ARMs). We aim at extending this line of work.
While uncertainty estimation methods have focused on ARMs, masked diffusion models (MDMs) have recently emerged as strong alternatives. These models extend masked language
39th Conference on Neural Information Processing Systems (NeurIPS 2025).

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Previous generations:
Prompt:
The stance ladder methos
Namre ore say to measure the lubble constant.
Gsavilalions sigraals
Btrong gravitacional lenaing time delays Fine delays Zzom. lecsed quasars
Next generation (autoregresaive):
Next generation (masked diffusion):
Coanic [2RUNC)
Impose semantic similarity penalty
[MASK] microvave (ASK
[MASK]
Cosnic nacrowavs [ЛRENC]
Coeniic e microwave (MASKK [NASK]
Cosnic croooos backgreund (TRUNC)
Coanic nicrowave (MASK) and
Compute uncertainty estimate
semantic clusters
Figure 1: Our sampling workflow illustrated with prompt that induces high aleatoric uncertainty, Given previous generations, guide the LLM's next token away from semantically redundaut outputs. The semantic clusters of resulting generations are used estimate downstream uncertainly.
modeling by learning iterative denoising schedules to progressivcly resolve masked spans 5-10 Despite achicving text quality on par with statc-of- ARMs, MDMs remain largely overlooked in the context of uncertainly quantification.
We propose a unified, model-agnostic framework that (1) actively steers decoding away from semantically redundant hypotheses, (2) corrects the induced sampling bias via importance weighting, and (3) reduces estimation variance with control variates. Crucially, our sampler operates in both ARM and MDM settings using entailment-base penalties computed on truncated or masked spans. single natural language inference (NLI) model, fine- tuned minimally with new [TRUNC] token for prefixes masks, enables live semantic scoring without altoring the base LLM. Our experiments evaluate the method's ability to quantify established proxies for alcatoric and epistemic uncertainties, demonstrating improved uncertainty estimation across diverse NLP tasks. Practical enhancements, including adaptive luning of the diversity hyperparameter and online stopping based on estimator stability, further improve sample efficiency.
[MASK] token for diffusion
Estimating the predictive uncertainty of free-form responses
Let be an input (e.g., a question) and 0 the weights of pretrained language model. We wish to measure the total predictive uncertainty of the model's output under semantic clustering. Following Aichberger et al. 4 we define the predictive distribution semantic clusters e E C by marginalizing over all output sequences
p(c x 0) - / ly E I x, ply x 0) dy.
which can be approximated with the MC estimator
N
p(c x, 0) =
N Σ (
e cl. y()).... (2)) ~ p(y xx,0 x)
(1)
If is sequence of tokens (Vi,.... Jr), then p(y|:, 0) can be computed as the product of individual conditional token probabilities, or, in terms of log probability:
T
logp(y xx 0) logp(nn x, 0) log logr(y (,,,,, 0).
The total predictive uncertainty of a model parameterized by 0 can then be written as the expected cross entropy between the predictive cluster distribution associated with its own
The original presentation [ used the biased estimator, p(c x. 0) Eysc p(y 2, 0).

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SE (aleatoric weights and that associated with an independent draw from the weight posterior 11
!
Bgg [CF(p(c a. p)c a ar,
H (p(cl x. 0)) + Bg [T.( x.
|I p(c x. 0))
total
alcatoric
epistemic
where CE(:-) is the cross entropy, (+)- is the Shannon entropy, and BEg == E Bapp(-1D) denotes expectation over the weight posterior. As noted by Aichberger et al. [ the term,
(pllc 2,))) = - Epee| z, 2,0) log x, 0),
aEC
is the alcatoric semantic uncertainty, also called semantic entropy (SE) capturing the irreducible ambiguity in the meaning of valid outputs under a single model. The term,
Eg KL(p(c 0, |l p(c 22,0)].
(4)
is the epistemic semantic uncertainty, mcasuring our ignorance about which cluster is correct due to lack model knowledge or data coverage.
Let us consider possible answers to the question, "Name a way to measure the Hubble constant." Aleatoric uncertainty arises when multiple answers valid. Even reliable model may output multiple correct variations that reflect different measurement methods:
" "The distance ladder method, which uses Cepheid variable stars and Type supernovae as standard candles to determine distances and redshifts of galaxies."
"Gravitational lensing time delays, where the time differences in light arrival from multiple images of lensod quasar are used infer cosmic distances and expansion rate."
These two answers belong to distinct semantic clusters only to the extent that they report different measurement. methods; under single model they contribute uncertainty) but do not indicate that the model lacks knowledge of the phenomenon. To reduce aleatoric uncertainty, the user may rephrase the question to remove ambiguity (e.g., " "Name a way to measure the Hubble constant using quasars.)). On the other hand, if the model truly lacks knowledge or out-of-distribution, it may produce answers that conflict with scientific facts or admit ignorance:
" "Trccking the color shift of moonlight reflected off distant asteroids." (hallucination)
"Im sorry, you might need consult a scientific source or expert in cosmology for that.
These responses fall into semantically distinct clusters that reflect gaps in the model's knowledge (high epistemic uncertainty), signaling that the model is not locally trustworthy.
Methods
3.1 Diversity-steered sampling
Our proposed sampling scheme modifies token-level conditional distributions to explicitly discourage semantically similar samples. Let us omit. the conditioning 0 for notational clarity and let p(y. V<r) represent the original language model distribution for the gth token given previously generated tokens yeu. Our (unnormalized) sampling distribution is:
log 7(y I vcc))= p(u yer) Amma E(yc1, SES
(5)
where S is the set of previously sampled sequences and E(.,.) is a score quantifying the degree of semantic similarity between the inputs. We refer to the normalized version as = // q. In words, the tilting term repels the current sample away from the most similar existing generation. Aggregation schemes other than max, such as mean or median, may allernatively be used for softer guidance. Note also that we do not require gradients from the scoring function, and any scoring function that can handle partial sequences either input argument would work. For full consistency with the NLI model used to semantically cluster
3

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the generations downstream, we fine-tune the same NLI model to accept partial sequences, as detailed in Section 3.2 Concretely, we opt for the bidirectional entailment score:
E s) = 1/2 (entailment(gg.. entailment(s, Vgi)),
(6)
where entailment is the entailment probability reported by an NLI model fine-tuned to handle partial sequences. The pseudocode for our sampling strategy is given in Algorithm
Algorithm 1 Diversity-stoored autoregressive sampling
Require: Prompt z; base model p(- x); bidirectional NLI scorer E(:-)) from Equation 6 trained with a special marker [TRUNC] for incomplete text; diversity penalty X; number of samples N;
candidate tokens V
Ensure: Set of semantically diverse generations
-
2: for i= to do
3: prefix + tokenize(2)
4: token <BOS>
while token # <EDS> do
for next in V do
Can alternatively consider the top-k tokens only
7:
{(next) + log p(next prefix) 8 - decode(prefix |nex) [TRUNC]] Similarity with the most similar existing generation Repel toward semantic novelty
b Base-model logits Mark that is unfinished
8:
9:
max (5,
10:
e' (next) f(next) A= end for token (stegorical(sottmxx())
11:
12:
13:
prefix + prefix[|token
14:
end while
15:
(0) decode(prefixx
16:
S Su (8)
17:
end for
return S
Extension to masked diffusion models. In MDMs, decoding proceeds by iteratively refining a partially masked sequence y( through denoising steps. At each step t, subset of masked positions is selected for infilling. Our diversity-steered strategy applies by modifying the denoising distribution ((y(() | ((+1) to discourage infillings that are semantically similar to those from previous trajectories. To compute similarity, we construct an intermediate input (1) by substituting the current proposal (tth) into the masked positions of (t++)) and evaluate the unnormalized distribution:
log ((y (t) (t+!)) = (ogr(y ((++)) Amxx E(z(9,
(7)
ses
The NLI model here is fine-tuned to handle masked partially masked spans. This allows our method to promote semantic diversity across the entire denoising trajectory. Algorithm provides the analogous pscudocode for MDMs.
Adaptivoly tuning the diversity parameter. The divorsity strength parameter significantl influences the semantic novelty of generated samples: too small value yields redundancy as in vanilla IID sampling, while loo large risks incoherent outputs. To navigate this trade-off, adaptively lune À during both token-level sampling within sequences and across multiple sampled sequences. See [eccion B.3 for details on adaptive tuning.
3.2 Pine-tuning NLI for partial sequences
Standard NLI models expeet full gremisc-hypothess pairs, but our sampler requires entail- ment scores for partially generated or masked text. To adapt an off-tho-sholf NLI model with minimal overhead, we begin by loading a model fine-tuned on a natural language under- standing datasel such as the MNLI benchmark dataset 12] (e.g., DeBEITTalarge-MMNN
[3] and freezing all of its existing paramelers. We then consider special token: [TRUNC] in the case of ARMs and [MASK] in the case of MDMss The token embedding and the model's final classification layer the only components allowed to update during fine-tuning.

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Premise:
Premise:
don't know do you do of camping
You and your friends welcome here, said Severn.
p p(entailment)
True label: contradiction
True label: entailment
know
exccyy
vaza
said
the
people
Were
not
welcome
there
Hypothesis
Hypothesis
Figure 2: Predictions of the line-tuned NLI each truncated point of the hypothesis, on two examples from the GLUE MNLI ieriidationmaattiee split [4]
Next, we construct an augmented dataset by corrupting one side of each NLI training example. The corruption mechanism is truncation for ARMs and masking for MDMs. For each promiss-sypothesis pair, we randomly determine whether to сorrupt the premise or the hypothesis. For ARMs, we truncate the selected sequence of length at point drawn uniformly at random from & (I...., T} and append the token [TRUNC] if < T. This procedure exposes the model to cases where either the premise or the hypothesis ends abruptly, teaching it to interpret [TRUNC] as signal of incompleteness. For MDMs, we randomly select the masking probability uniformly in [0, 1] and independently replace tokens with [MASK] with that probability.
We then fine-tune using the standard cross entropy loss, updating only the [TRUNC] or [MASK] embedding, [CLS]] embedding, and the classification head, which corresponds to only 0.3% of the model parameters (around 3M parameters) in the case of DeBERTa-large-MNLI [3] This adaptation is thus lightweight and preserves the model's original NLI performance. At inference time, for ARMs, whenever we need to score partial prefix against full previous sample (or vice versa), append [TRUNC] to the truncated side and query the fine-tuned NLJ model for the probability of entailment. For MDMs, no preprocessing needed to query the fine-tuned NLI model, as its vocabulary already contains the [MASK] token.
Figure traces the probability that the fine-tuned NLI model assigns the "entailment" class as progressively longer prefixes of each hypothesis are revealed. In both panels, the trajectory converges the ground-truth label long before the final token appears, suggesting that even partially generated hypotheses already contains enough signal for identifying entailment. See Figure 3 for similar demonstration for the MDM case. In another view, Figure 6 plots the classification accuracy of the fine-tuned NLI model at varying corruption levels. For both ARMs and MDMs, the accuracy matches that of the NLI model prior to fine-tuning and slowly falls to the "random guess" accuracy at complete corruption.
3.3 Importance-reweiihted estimators of uncertainty
As we sample from the biased proposal q(.) in Equations 5 and 7 instead of the true model dist.riuutio p()), we apply importance reweighting correct for the introduedd bias. For set of N generated sequences {s(0) L.V where each s(0) was drawn from ((s(1), compute the unnormalized and self-normalized importance weights:
w/ = p(s(1) (((())
W
Σ
Wj
with the densities computed from the conditionals as in Equation 2. In this section, illustrate how importance reweighting and semantic clustering interact for the purpose of estimating SE [ and MI [] proxies of alcatoric and epistemic uncertainty, respectively. Note that these are meant to serve as illustrating examples and we do not advocate for these particular uncertainty metrics
alternatives.
Keeping the [CLS] frozen had little effect performance.

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Premise:
yeah think my favorite restaurant always been the oue closest you know the closest as long as it's it the minimum criteria you good food
Premise:
I'm what the overnight low was
1.0
0.8
True label: contradiction
True label: entailment,
p(entailment)
0.6
Hypothosis:
My favorite restaurants always at least a hundred miles away from my house.
Hypothesis:
0.4
I don't know how cold it last night.
0.2
0.0
90
100
90
100
% tokens masked
% tokens masked
Figure 3: Predictions the fine-tuned NLI at each masking percentage of the hypothesis, on two examples from the GLUE MNLI validation_mat oaatichedddeeee split [4].
Semantic (aleatoric) uncertainty. Let C be the set of semantic clusters. The probability of each cluster e can be estimated using the importance-weighee
version of Equation
p(c) ~0 En [s(() E c] wi- This yields the eepportacc- version Eqqation 4
---E j(c) log log((c). GEC
Epistemic uncertainty. We use the MI proxy introduced in Algorithm 2 of 22, restricted here to the pairwise case n=2, as worked example of how one quantify epistemic uncertainty with our semantically diverse sample set. Rather than a faithful reproduction of the original MT implementation, aim at demonstrating our diversity sampling within importance sampling framework. The MI proxy operates on the assumption that successive answers are conditionally independent under the ground-truth distríbution p" that ís, p" (111 x) = p" (y1 x))p (y/ -) so that any observed dependence between them can be ascribed epistemic uncertainty.
We draw N pairs 200 = (s (()) from the tilted distribution d" by iterative prompting.
(6) Each response token sequence is mapped to semantic cluster Cj EC using the NLI-reported bidirectional entailment score, rather than using the Fl score as originally done in Yadkori et al. 2. We find cluster centers S defined by all tuples j. k such that E(2(), 2(k) < and each cluster center = ES is associated with a cluster e(z*) = (x' E(z",'' 2 T).
While sample from the proposal qf the target distribution for MI is the model distribution pº, so each pair receives a self-normalized weight
of (x( ())
182))))
Wi.joint
joijt
ge( (s (
Σ
Wyjoint
After clustering the response pairs, we evaluate the joint and marginal cluster probabilities:
N Σ
((c(21,2))
1 1(
(0)) E ((211222) Wijoint
1=1
839 (c(2),
Σ
p(c(21, 2))) Σ
p(o(=")
22)=
22))]
E'S
E"ES
Finally, the importance-rewwighted MI estimator becomes:
Σ p(c) log p(c)
i
(c(c)

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A large signals strong dependence between successive clusters (hence high epistemic uncertainty) whereas I x 0 is consistent with the conditional independence assumption and suggests that the model's parameters are locally trustworthy for the given query.
3.4 Variance reduction via adaptive control variates
The importance-weigghan weighted estimators for SE and MI can exhibit high variance, particularly when the proposal 9(-) differs substantially from the model distribution p(-). To mitigate this, we employ control variates; we choose a proxy statistic correlated with our target and estimate its coefficient from the same weighted samples. They may optionally be applied adaptively on the running samples. Appendix E. provides additional background and derivations.
Semantic entropy. We define a control variate based on the log probabilities from the basc model. Denote Y, = log (())s where c(s()) is the cluster containing s The estimator
in Equation 8 is then Σi=1 Wi Y,. Now define X; = - log logp(s()), and let X = X; - μx and
y Y, jy represent the centered versions, with empirical means μxx Li=1 X and
.
My = E W;Y, Our adjusted entropy estimator then:
Hev
W.YY
x
(10)
A in Eq. (10)
control variate
Σ E x
where the optimal cocfficient a that minimizes variance is computed ase
Em ú,
This scheme uses the correlation between the log model probabilities and the cluster entropy to reduce variance without extra inference cost, as X; already required to compute w;.
Mutual information. Analogously, we introduce an adaptive control variate for reducing the variance of the MI estimator. Letting Y, log(p(c(21, (2(c(((()))))///// 22)p//)()((((/ 22))) represent the log ratio appearing in Equation 9 we similarly define the control variate using the joint log probability under the base model, X; = logp(s)") 882 ,s(),, with means and centered variables defined analogously to the SE case. Our control variale-corrected estimator is thus:
NV fov == Σ Wi.ooine Y₁ - aMI Σ
N
wú joint X₁,
(11)
i=1
ΣN Wagoins X/ Din
with the adaptively computed coefficient given by axM
X!
Related Work
Uncertainty estimation. Common approaches for uncertainty quantification for machine learning include Monte Carlo dropout 15. deep ensembles 16 and evidential methods including prior networks [7 18 and deep evidential regression 19. While these methods
have also been adapted for text classification and regression NLP 20, semantic invariances inherent in generated texl. present challenge in mulliple-choice QA 25 26 and the challenge is even more pronounced free-form QA [I- Several studies have proposed prompt.ing or fine-tuning language models to explicitly articulate their confidence levels [7 34, though this typically requires additional supervision. Attention values may contain information about relevance confidence 35 86
Alternatively, exssmiaamint leverages a secondary language model to evaluate uncertainty in another model's outputs 37 Predictive entropy quantifies the token-level entropy of the predictive distribution 28 20
Semantic entropy [ offers an unsupervised mothod that clustors multiple outputs into semantic equivalence classes based on bidircctional entailment and then computes entropy on these clusters. Complementary strategics using the conformal framework can provide bounds on errors under stronger theoretical assumptions 38 39
When a question has multiple valid answers, it can be useful to differentiate epistemic uncertainty from aleatoric uncertainty, expected to be high. Classically, the former is defined

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by an expectation over possible weight realizations (Equation 4), which vanishes when weights agree. Recent work, however, suggests that one can probe it with a single fixed network by measuring the consistency of multiple answers it produces to the same query 2 40 42
Diversity-promoting sampling. Sampling heuristics aimed enhancing output diversity, such as temperature scaling, top-k, and nucleus sampling ] do not account for semantics. Diverse beam search (DBS) introduces diversity heuristics within beam search optimization 43. Contrastive decoding enlists a secondary, weaker language model whose output tokens are penalized encourage diverse token selection by the primary model 1 Cluster- based beam search methods apply semantic clustering [5 to prune beam candidates and diversify subsequent selections 40, but this heavily depends on initial candidate diversity. Semantically Diverse Language Generation (SDL.G) substitutes the most informative token in a fully generated sample and allows standard sampling to proceed from that token onward [.. It does not, however, explicitly account for diversity within rumning sample set and, because the token scoring involves a gradient of the NLI loss with respect to the NLI token space, requires additional implementation (e.g., [7)) if the base LLM does not share the tokenization scheme or vocabulary with the NLL. Our approach differs by integrating a contimuous semantic penalty directly into the logits during generation in gradient-free manner. For a comparison of diverse decoding strategies, see Ippolito et al. 48
Semantic clustering and paraphrase detection. Grouping model outputs based on semantic equivalence often reduces to paraphrase detection. Casting semantic equivalence as bidirectional entailment dates back to early linguistics work [9] and was later adopted in NLP 50
Early methods relied on lexical overlap 53 or vector embedding similarities 54 55
56 explored the use of bilingual parallel corpora for paraphrase extraction and ranking. BERT-style encoders can be used to build binary "paraphrases" vs. "not paraphrases"
classifiers
[3 57 60. The entailment probability from NLI models has been used to cluster
LLM generations into meaning- eeriiingg-uivllentt sets, enabling uncertainty estimation 1
5 Experiments
We evaluate diversity-pronee promoting sampling scheme for estimating SE [ and MI [2] The target estimators are the importance-reweighted versions with control variates: Hev in Equa Lion 10 and fov in Equation 11 respectively. Due space constraints, implementation details. additional results for H including ablations, and results for lov are deferred to Appendices B to D As observed by Aichberger et al. E it is common to employ diversity heuristics during sampling without correcting for the introduced bias with principled importance rewcighting (o.g., 2). Although one of our contributions is the application of importance correction with control variates, we apply the same estimation procedure to the final generations from all sampling schemes to enable a fair comparison. Estimation is performed on lop of the semantic clusters created using Algorithm 1 of [I. In brief, clustering works by querying the model [3], fine-tuned on the NLI dataset. MNLI [2], every pair of sampled responses. If the model returns "entailment" " for both directions, the answers belong in the same cluster, and otherwise, new cluster is created.
DeBERTa-large-NNN
Sampling basclines. As the main contribution of our mothod to promote semantic diversity in the samples, we compare against other sampling schemes. Our ARM baselines include (1) slandard IID sampling with lemperat ures T E [1,2), 2]. (2) diverse beam search (DBS) 43 with penalty hyperparameter of 0.5, and (3) our re-implementation of SDLG 4. where we handle the differing vocabularies of the base LLM and NIII by decoding each OPT/LLaMA token to its raw string and then re-tokenizing that string with the DeBERTa NLI tokenizer, so that substitution candidates and gradient attributions live in the same NLI embedding space. For the MDM, we compare with Gumbel temperatures of E 2).
We perform experiments on four question-answering (QA) benchmark datasets covering both closed- and open-book lasks: 907 validation matched instances with shorter stories from CoQA 62. a closed-book abstractive QA; 1,000 instances from the validation no-context reading comprehension split of TriviaQA
Datasets.
63 blosed-book. extractive QA;
8

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Table AUROC of SE I computed on generations from various sampling schemes. Each scheme uses N6 sequences. All numbers are meanistd over 5 jackknife samples of size 200. The symbol indicates that the sampling scheme does not apply to MDMs. "Vanilla" refers to standard sampling without any tempering (r 1). Best methods based mean are bolded. For AmbigQA, we omit results for OPT-6.7B, as generated a high fraction nonsensical responses.
Dataset
Model
Vanilla
==2
DBS 43
SDLG 4
Ours
OPT-6.7B
.591.06
.694.04
.684.04
.714.02
.751.02
OPT-13B
.70..04
.761.04
.73:.04
.72:.02
.754.03
CoQA
LLaMA 3
.681.03
.724.04
.715.05
.744.02
.77+.02
LLaDA 8B-Instruce
.78:.02
.814.05
.81:.04
OPT-6.7B
.66+:00
.67+.00
.71..04
.78+.03
.82+.03
OPT-13B
.72+-04
.70+.05
.734.04
.86+.03
.8++-03
TriviaQA
LLaMA 8B-Instruct
.791.04
.701.04
.702..03
.791.04
841.03
LLaDA 8B-Instruct
.11.111
.831.05
.861.04
OPT-13B
.65t.10
.684.11
.78+.08
.71
.8+..04
LLaMA 3 8B-Instruct
.70+.04
.55+.07
.71
.77+.05
76+.00
AmbigQA
LLaDA 8B-Instrucl
.701..99
.711.08
.761..33
OPT-6.7B
.0.1.04
.801.05
.771.02
.781.06
.811.06
OPT-13B
.73+.06
.74#.08
.79
.81.004
.85..04
TruthfulQA
LLaMA IB-Instruct
884.04
.88..05
.89:.04
.86..04
.89..02
LLaDA SB-Instruct
885.00
.81.00
.94
800 instances from the validation split of TruthfulQA 64
closed-book generalive QA;
and the light validation split AmbigQA 65 an open-book open-domain QA. Because AmbigQA contains multi-answer questions requiring question disambiguation, it serves test environment where He is expected to be large.
Models. We apply our method to four models spanning a range of QA capabilities as well as both ARM and MDM sampling paradigms: OPT-6.7B 7B, OPT-13B 66 for comparisons
with prior work [I 4 43]; LLaMA 3 8B-Instruct 67 6S as modern instruction-fine fineiin--ieetuueee backbone; and LLaDA 8B-Instruct
10, an instruction-fine-tueel MDM.
Metrics. Following the evaluation procedures in prior work, we report the Area Under the Receiver Operating Characteristic curve (AURÔC), where the correct answer is defined by ROUGE-L (F1 score) 0.3 against the reference answer. When there multiple reference answers, we take the maximum score across the answers. We also evaluate the average mumber of clusters and the effective sample size (ESS) 69 of the importance weights.
Discussion and limitations
By design, our sampling scheme covers more semantic clusters than the baselines while using the same number samples (see Figure 4). Meanwhile, applying importance correction with control variates preserves the rank agreement between estimated uncertainties and correctness, as reflected in competitive or superior AUROC across models and datasets (see [able 1). we find that aomanntic-agnostte heuristics such simple
Consistent with Aichberger et al. 4 temperature scaling or DBS 43 are insufficient to fully explore the semantic space. The advantage of our method is more evident in free-form and ambignous datasets like CoQA and AmbigQA than in TriviaQA, for which there is a single, usually short, unambiguous answer. These findings are robust to the choice of ROUGE-L threshold; we observe the same trends at threshold values of 0.1 and 0.5 (ppenndxx C As a complementary threshold-fres metric, the Spearman p between the negated ROUGE- scores and our estimated uncerlainties were 5% and 6% greater on average than those of DBS and SDLG, respectively. We suspect SDLG's weaker rank correlation may be due our simplified handling of differing tokenizations between
and the NLI model. Finally, the ratio ESS/N N stays above 0.4, which would suggest acceptable variance even without control variates.
We omit OPT-30B, the AUROC improvement from OPT-13B has been insignificant
36
9

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If the fine-tuned NLI models systematically overestimate entailment on the partial generations, is possible for the steering to be biased. We empirically observe, however, that the predicted entailment probability sharply peaks at the "random guess" value of 1 1/3 when the input generation has one token revealed Figure 5p. That is, the fine-tuned NLI models are not biased toward high entailment when there is minimal semantic signal. The value of 1/3 motivates our default schedule for À (Section B.3), where we increase À when the score of the current generation with respect to the most similar existing generation is higher than 1/3,
In general, sampling algorithms face a trade-off between encouraging exploration by introducing a joint steering (repulsion) term on the walkers and facilitating parallel sampling by preserving walker independence. Our method can be viewed as prioritizing the former; we enforce di- versity sequentially in the rumning sample set [70], at the expense of computation time that grows linearly with N. By contrast, SDLG can parallelize the generation of sub- sequent tokens once an initial sample is produced and ions are identified, although its diversity gains de- pend on the quality of the initial sample. Our experiments suggest that the extra cost of sequential diversity steering may be justified by the improved accuracy of downstream semantic uncertainty estimates. As future work, could investigate hybrid approaches, such as batch sampling, to balance exploration with parallel throughput. Note also that, although fixed N for all sampling schemes here, the online stopping mechanism based estimator stability, described in Appendix B can help with sample efficiency.
10a
ITD r-?
DBS
Frequency
SDLG
10
5
Number of semantic clusters
Figure 4: Number of semantic clus- ters captured by various sampling schemes on the CoQA dataset.
Conclusion
We presented diversity-steered sampling, simple plug-in that adds repulsion term to both ARM and MDM decoding, and then corrects the resulting bias with importance weights to recover consistent estimates of SE (alcatoric uncertainty) and MI lower bound on epistemic uncertainty. Because these uncertainty estimators group outputs into semantic clusters defined by the very same entailment metric, enforcing that metric during sampling is coherent; generation and estimation are aligned by design, so each draw already respects the sample space of the rewmstream estimator. To our knowledge, this is the first framework that (1) applies to both ARM and MDM decoding paradigms (including recent models such as LLaMA-v3 68 and LLaDA IQ]. ) (2) has been demonstrated on both aleatoric and epistemic proxies, and (3) requires no gradient access to the NLI or the base LLM.
Several opportunities for improving robustness remain. While we inherit the NLI-based clustoring schome from prior work, real text often straddles several plausible semantic clusters and NLI scores noisy; treating the cluster assignments as random and marginalizing over them could make downstream estimates more robust. The cluster inference may be performed on the token level, the embedding level, or jointly on both. Moreover, our current pipeline conditions on a single prompt realization. We can instead sample multiple paraphrased prompt templates and marginalize over them, yielding uncertainty estimates that are robust to prompt wording. Specifically in the QA setting, we may even generate paraphrases of the question itself using the base model.
Looking ahead, the same can, in principle, be embedded inside on-policy RL fine-tuning methods such as Proximal Policy Optimization (PPO) 71 and its grouped-reward variant GRPO 77.. During roll- outs, the repulsion term would drive the policy toward novel semantic clusters, while the accompanying importance weights would keep relurn estimates unbiased.
plus self-normalized importance-weighting scheme
Acknowledgmentss
We thank Aya Ismail for helpful discussions MDM decoding.
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Technical Appendices and Supplementary Material
A Extension to masked diffusion models
Algorithm 2 provides simplified pseudocode of our diversity steering scheme for MDMs. assuming a denoising schedule where one masked token is predicted at a time. Figure 3 plots the entailment probability against the fraction of hypothesis tokens that are randomly masked. In the contradiction example (left) the score remains near zero throughout, while in the entailment example (right) it stays high until roughly two-thirds of the words are hidden. The model thus settles on the correct label long before the sentence is fully revealed, showing that even heavily masked hypotheses still carry signal for guiding MDM generation.
A Algorithm 2 Diversity-steereed masked-diffusion sampling
Require: Prompt z; base masked-diffusion model p(: :); bidirectional NLI scorer E(;,) from Equation 6 trained with a special marker [MASK] for masked text; diversity penalty A; number of samples N; total denoising steps T
Ensure: Set of semantically diverse generations
S
2: for i= to do
3: T²² 4- MASKTOKENS(C
Initialize with masked sequence
4: for t== 7-11 downto do
.M + SELECTMASK(Y
Choose subset of masked positions to fill step
6:
for each position m E Me do
7:
for each candidate token next E V do b Alternatively consider the top-k tokens only ((next) + logp(y nnxt y(++))
8:
b Base model logits for current mask P. Temporarily fill mask with candidate token Form partially denoised sequence & Similarity score with the most similar existing generation
9:
g( ((++1); Um + next
10:
+ decode()
11:
क - max F3 (8)
EES
12:
(next) + {(ext)) - Av
Repel toward semantic novelty
13:
end for y Categorical(sottnx((())
14:
Sample token for the current masked position
15:
end for
16:
y (4) + FILMMAKS( ((+)) ..))))
Update denoised sequence
17:
end for
18: ((
"ecode(y""))
19: S-Su (s(0))
20:
end for
21: return S
3.0
lengtis 1 hypothesis
lengthe1 hypothesis
6
rondomi guess
2.5
random
2.0
Deusity
4
Density
1.5
3
1.0
2
0.5
0.0
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1.0
0.0
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1.0
P(entailment)
P(entailment)
(a) Prefix truncation
(b) Masked tokens
Figure 5: Distributions of entailment probability predicted by the fine-tuned NLT on the hattttiiiommmtceeeeeeee
GLUE MNLI validation matched dataset when (a) truncating or (b) masking all but one token of the hypothesis. Both distributions are peaked at the "random guess" probability of 1 1/3.
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0.9
random gues (1/3)
0.9
random guess (1/3)
0.8
0.8
0.7
Aceracy
0.7
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0.0 0.1
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0.6 0.9 1.0
Masking fraction
Truncation fraction
(b) Masked tokens (averaged over 20 realiza- tions)
(a) Prefix truncation
Figure 6: Classification accuracy of fine-tuned NLI models at varying corruption levels for (a) prefix truncation and (b) masked tokens. At zero corruption, the accuracy matches that of the pretrained model and slowly falls until it reaches the "random guess" accuracy of 1/3 at complete corruption.
B Additional implementation details
Our sampling pipeline is implemented at httper//gthu.cco//vvvoaaa///airr steered sampling C
B.1 NLI fine-tuning
Prefix truncation. We start from the micrrssfff//eeeett--aarggemlll checkpoint cor- responding to the DeBERTa model [3] fine-tuned on the GLUF Multi-NLI matched dataset 14. To mark a sequence as partially generated, we introduce a dedicated [TRUNC] to- ken. The MNLI dataset is augmented as follows. Every MNLI pair is deterministically unrolled into (i) the original sentence pair, (ii) all proper prefixes of the hypothesis (lengths 1... Ln 1) each followed by [TRUNC], and (iii) all proper prefixes of the premise (lengths Lp - similarly tagged. A single example with tokenized lengths (Lp, LA) thus con- tributes 1 + (Ln - + (Lp 1) training instances, covering every possible truncation. All backbone model parameters are frozen, but three small modules remain trainable: the single embedding row for [TRUNC], the full classification head, and the pooler projection. We fine-tune on the angmented version of the GLUE MNLI matched training split and evaluate on the correspondingly augmented validation split, while also monitoring the classification accuracy on the original (unaugmented) validation split to ensure that the performance on the original sentence pairs does not degrade. Optimization uses ADAMW 73 (initial learning rate 5x 5x10-5, weight decay 0.01) with batch size of 8 for two epochs. The final validation accuracy on the augmented set was 73.3% and that on the original was 91.0%. which was similar to the accuracy prior to fine-tuning (90.8%).
Masked tokens. Starting from the we first ensure that the tokenizer exposes a [MASK] token. During training, each MNLI example expanded on-the-fly into one intact pair plus 20 stochastic variants in which either the premise or the hypothesis has a uniformly random fraction of tokens (f- 1)) replaced by [MASK]. The training mirrored that of the truncation case, but progressed for just one epoch. The final validation accuracy on the augmented set was 73.9% and that on the original set was 91.1%. which was similar the accuracy prior fine-tuning (91.2%).
mi microsoft/
checkpoint,
B.2 Prompts
We use the following prompt for the SE experiments on CoQA 62
<context> Answer in sentence. Q: <question> A:
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0.15
0.10
0.05
0.00
20
30
Token position
Figure 7: Trajectory of the diversity parameter X over token positions for different autore- gressive samples shown in different colors. The parameter usually increases monotonically with as the partially generated sample becomes more semantically similar to the running sample set.
For the MI experiments on CoQA, we modify the prompt in Yadkori et al. 2 We sample the first answer with the above prompt and the second answer using the following.
<context> Consider the following question. Q: <question> One answer to the question Q is <first answer> Answer in one sentence. Q: <question> A:
B.3 Adaptively tuning the diversity parameter À
Within sequence, we dynamically adjust by monitoring token-level entailment scores and increasing when semantic similarity with existing samples exceeds a target threshold. Formally, at token position update:
Ae+1 d + Thok
max Elyse, 8) Esarget)
eES
with small learning rate Took Empirically, Erarget 0.3 and Ao = 0 work well. We observe that X, tends to increase monotonically over autoregressive sampling time, as shown in similarly tune À by tracking the variance and stability of SE estimates computed so far. Specifically, entropy variance across samples is excessively high, we slightly increase to encourage greater diversity; if too low, decrease it accordingly:
Figure Across sequences,
Anext seq Acurrent seq + 1/aeq (Var( Viarget)
with sequence-level learning rate Tseq These adaptive schemes, though simple, substantially reduce the need for manual hyperparameter tuning, ensuring stable, efficient, and semantically diverse generations in practice. While À can similarly be calibrated using Eiarget or Viarget as target values [e.g.. (2, we do not opt for a separate calibration step, as this expends additional compute and it is difficult to curate an IID calibration dataset in practice.
held-out dataset
B.4 Semantic clustering
As observed by Kuhn et al. [1, semantic equivalence depends on the context. Two answers may be scmantically distinct the absence of any context (c.g., "I'm not an astronomer." and "You should consult cosmology textbook.") while being semantically equivalent conditioned on the context. If the question were to be "Name one way lo measure the Hubble constant," the responses would be semantically equivalent in the sense of acknowledging ignorance. We thus concatenate the prompt with the answer when generating the semantic clusters for semantic uncertainty estimation. For the SE experiments, the clusters generated greedily
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following their Algorithm 1 using the binary bidirectional entailment criterion (1 if predicted "entailment" both ways and otherwise). For the MI experiments, they are also generated greedily but by clustering the bidirectional entailment distances defined by 1 E(s,, 83) for every pair 8j of iteratively prompted responses (see Equation for the definition of the bidirectional entailment score E(::))) Each 8, is a concatenation of the prompt and the iteratively prompted responses separated by a special delimiter ||.
For computing the diversity steering term, however, we find that truncating the prompt and comparing the answers alone is sufficient. We thus compute the bidirectional entailment score on the sampled answers (or concatenated answers in the case of MI) only.
B.5 Computational complexity
When using no diversity penalty, standard autoregressive sampling involves forward pass through the language model and softmax/sampling over the vocabulary. This incurs per-token cost of ( + V), where Mgen is the cost of one forward pass through the language model and V the vocabulary size. Over T tokens per sequence and N sequences, the total cost is (NT(MMge + V)).
With full-vocabulary diversity steering, each token step additionally computes the entailment probability for all V candidates against prior samples at cost. MNLI per entailment. The per-token cost becomes O(Mgen + VPMNLI +
By restricting the penalty computation to the top-k tokens (k < V), where the top-k ranking is done using the base language model only, the entailment work per token drops to only k candidates, yielding OM + &PM + V) per token. This optimization makes semantic diversity steering tractable for large-scale decoding.
B.6 Computing resources
All experiments were conducted on an NVIDIA A100 GPU, with each sampling scheme requiring under 32 GB of VRAM.
C Qualitative case studies
We explore the LM's responses to the following prompt: Answer in one sentence. Q: Name one way to measure the Hubble constant. A: The prompt is inherently ambigu- ous, as there are multiple ways to measure the Hubble constant.
C.1 Sample answers: ARM
Here are some sample answers (N=8) by LLaMA 3 8B-Instruct 68 without any diversity stcering. The answer set covers two distance-ladder measurement methods: one using Cepheid variable stars and another using Type la supernovae standard candles.
Use Cepheid variable stars. Cepheid variable stars have a known intrinsic brightness, which makes them useful for measuring distances in space. (cluster 1)
By analyzing the distances to Cepheid variable stars in the Milky Way and other galaxies. (cluster 1)
One way to measure the Hubble constant is by comparing the brightness and redshift of Type la supernovae, which are used standard candles. (cluster 2)
By measuring the distances to Type la supernovae in different galaxies and then using these distances to calculate the Hubble constant. (cluster 2)
The Hubble constant can be measured using the light curves Type Ia supernovae, which have consistent maximum brightness allowing for distance estimation. (cluster 2)
One way to measure the Hubble constant by observing the distance to Type Ta supernovae and using the recession velocity of the expanding universe. (cluster 2)
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The method of standard candles involves using supernovae "candles" to measure distances and then infer the Hubble constant from redshift data. (cluster 2)
One way to measure the Hubble constant is by using the distance-luminosity rela- tionship for Type la supernovae. (cluster 2)
With diversity steering, the answer set becomes more diverse. In addition to the Cepheid variable stars (cluster 1) and supernovae (cluster 2) measurement methods covered above, it now includes low-likelihood nonserssical ones but also covers an answer addressing the cosmic microwave background method (cluster 5).
Name one way to measure the Hubble constant. The Hubble Space Telescope Key Project found a good estimate by analyzing Cepheid variable star distances (cluster 1)
The expansion (cluster 3): nonsensical
Parallax distance method is one way to measure the value of the Hubble constant from Type supernovae. (cluster 2)
Find the word answer (WA). think. Haha (cluster 4): nonsensical
1) By observing how light coming from the cosmic microwave background (cluster 5)
way measure the Hubble constant... (cluster 6): nonsensical
Measuring cosmic distances of supernovae at fixed redshift, comparing observed luminostities (cluster 2)
A value of the Hubble constant (H subscript 0 equal to 67 kilometers per second...
(cluster 7): nonsensical
C.2 Sample answers: MDM
Similarly, here are some sample answers by LLaDA 8B-Instruct 10 to the same prompt as the above. The answers all refer to single measurement method, of mapping the redshifts (rates of recession) and distances of distant galaxies hosting supernovae.
One way to measure the Hubble constant is by observing the distance and apparent work of celestial objects/ standard candles such as Type la supernovae.
One way measure the Hubble constant is by observing the redshift of supernovae, which provides direct evidence of the expansion the universe.
One way to measure the Hubble constant by observing the expansion of the universe through the measurement of the redshift of the light from distant supernovae.
One way measure the Hubble constant is by obscrving the redshift of distant supernovac, as their distance changes relates to the expansion of the universe.
One way to measure the Hubble constant is by observing the rate of recession of distant galaxies, which allows astronomers to determine the expansion rate of the universe.
One way to measure the Hubble constant is by observing the redshift of distant supernovae, which allows astronomers to determine the expansion rate of the universe.
One way measure the Hubble constant is by observing the redshift of distant supernovae, which allows astronomers to determine the expansion rate of the universe.
One way to measure the Hubble constant is by observing the redshifts of distant galaxies, which indicate stretched light due to the expansion of the universe.
Diversity steering makes the answer set more diverse for MDMs well. It consists mostly of answers addressing the same supernovae-based measurement method covered above (cluster 2) and also includes low-likelihood vague nonsensical ones, but also covers answer addressing the cosmic microwave background method (cluster 6).
One of the better methods is to measure the Hubble constant (known as Ho) using modern techniques, resulting in better accuracy than listance-ladder observations. (cluster 1): vague
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One method around the red complex within the past few years of water resources is estimate it using radiation and other methods. (cluster 5): nonsensical
The Hubble constant can be measured using standard galaxy-distance measurements by comparing the brightness of distant supernovae to their redshift. (cluster 2)
One way to measure the Hubble constant is by observing Type la supernovae and creating the standard distance ladder (LZ ladder diagram). (cluster 2)
One way to measure the Hubble constant is through observations remote galaxies, such with the Hubble Telescope or Lemlint. (cluster 3); vague
One way to measure the Hubble constant involves measuring the distance between seemingly related astronomical objects. (cluster 4): vague
One method to mcasure the Hubble constant is by observing the cosmic microwave background using microwave receivers and other sophisticated tochniques. (cluster 6)
To measure the Hubble constant, one can use observations and discoveries of Type la supernovae, also known supernovae HO. (cluster 2)
D Mutual information results
AUROC gains over baselines for MI are modest, and the results exhibit high variance. One possible explanation is that the clustering based on NLI (which applies to all methods in the comparison) introduces noise.
As shown in Table
Table 2: AUROC of MI 2 computed on generations from various sampling schemnes. Each scheme uses N-8 pairs of iteratively generated answers. The correct metric Rouge-L. (F1 score) was thresholded at 0.2. All numbers are meantsst over 5 jackknife samples of size 200. "Vanilla" refers standard sampling without any tempering (r =). Best methods based on mean are bolded.
Dataset
Model
Vanilla
DBS
SDLG
Ours
LLaMA 8B-Instruce
.61=.07
.66:.09
.584. 12
.64+.08
.68=.07
CoQA
LLaDA 8B-Instruct
.51+.03
.54+-066
.56-.06
LLaMA 8B-Instruct
.492.07
.51:.04
.541.08
.57..11
.54 07
TriviaQA
LLaDA SB-Instruct
.52:.08
.5311.06
.551.06
LLaMA 8B-Instruct.
.56+.04
.55+-.07
.51+.08
.564.08
.56=1.66
AmbigQA
LLaDA 8B-Instruct
.53+.09
.514.12
.53+.05
LLaMA 8B-Instruct
.581.06
.5711.07
.5911.0
.631.08
.63...0
TruthfulQA
LLaDA 8B-Instruct
.60.1.06
.67.1.10
.691.08
E Variance reduction with control variates
In this section, we provide additional justification for using control variates to reduce the variance of importance-weigheer estimators SScciin 3.3, For self-contained treatment, begin with brief introduction to control variates.
Let ~ p be a random variable and assume we wish to estimate its moment
/ = E<(
using iid samples ZNN. The classical estimator takes the form
N
h(Z)).
N
which has variance Var[ā] Var(b(Z))
N
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The idea of control variates is to pick any auxiliary function g whose mean Me = Ep]o(Z)) is known in closed form. For any coefficient R,
1 Σ (ev(a)= = N
- -(z.)-a(((2)) [pl
unbiased, because Ep(g(Z) - Mgl =0
It then remains to choose the optimal coefficient. o* that minimizes the variance. Define
of Var[h(Z]], of Varlg(Z)), and Thg = ())()(Z)) Writing H h(Z) - 1 and
G = =Z)
Mg: we have
1 Var -aG]- N
1 (o 2000g + a)og).
[ar[Mev(a)]
N
Differentiating with respect to and setting the result to zero,
Var -20 + 2a0 =0 a' hg
Cov(h (or(h(Z),co g()
da
oy [arlg(Z)]
Substituting a* back yields
1 [ p²), N
Var Per
where p The the correlation between h and 9, so variance is reduced by the factor is to 1, the greater the reduction in variance.
on
1 - p² such that the closer
Semantic entropy The estimator proposed in Equation 10 uses
x
X, as the control variate. The centered negative log probabilities = px with X,
(()))(s()) are strongly correlated with the negative cluster probabilities Y; = = log logg(c(s(()) being based on the same sample g(0), In natural language generation, likely samples with low X, lend to be mapped to dominant clusters, so Y, becomes more negative when X is more negative.
The proposed control variate does not incur extra inference cost, as the log probabilities were already computed for evaluating the importance weights wy Particularly the context of norfalormd importance sampling, log probabilities behave nicer than, e.g,, a function of the ratio p/g. g. which can take higher moments.
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Reviews:
[{"review_id": "T3vWakjqcm", "reviewer": "Reviewer_Nwdr", "summary": "This paper proposes a novel and modular method for improving semantic uncertainty quantification in language models (LLMs), applicable to both autoregressive (AR) and masked diffusion models (MDM). It introduces diversity-steered sampling using a semantic repulsion term derived from a fine-tuned NLI model, and applies importance weighting to correct for bias and reduce variance in downstream uncertainty estimates. Across four QA benchmarks, the approach outperforms baselines like random sampling, diversity-based beam search.", "questions": "1. What is the reasoning behind specific weights in equation (8)? Is it possible to provide mathematical details to support these, and can we have weights such that there is equality in equation (9)?\n\n2. A suggestion: Sections 3.3 and 3.4 could be better with some interpretation, examples, or simulations to ground the intuition and understanding of these quantities in the context of language models.", "limitations": "yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n The proposed solution for semantic uncertainty quantification is interesting, novel, theoretically grounded, and clearly presented. Specifically, the formulation of diversity-steered sampling introduces a “repulsive” term that discourages sequences semantically similar to previously sampled sequences. Semantic similarity between two sequences is estimated using NLI models with bidirectional entailment scores. Further, the new distribution is corrected with importance weighting to debias the estimates of semantic entropy, mutual information, etc. \n\nThe same technique applies to the popular autoregressive language models and emerging masked diffusion models. \n\nEmpirical evaluation on several models and datasets is provided. The results demonstrate that the introduced diversity-based sampling strategy performs better than baselines, including random sampling and diversity-based beam search. \n\n\n\n**Weaknesses**\n\nThe use of entailment models for semantic similarity is not well justified. Moreover, the paper deals with measuring the semantic similarity of partial sequences, which can be significantly challenging, given that the presence of a single word (or token, e.g., not) can change the semantics significantly. Such mistakes in similarity measurements can eventually lead to erroneous samples coming out of the process.\n\nComputational efficiency is another major issue here. Given that semantic similarities need to be computed using an entailment model after generating each token. This can significantly slow down the inference procedure. \n\nThe experiments are focused on generating the correct sequence, i.e., the evaluation seems to be similar to any other inference technique and does not focus much on the uncertainty quantification aspects, which is a major focus of the paper.", "was_revised": true, "final_justification": "Rebuttal addressed my questions and I am happy to keep my current scores.", "rebuttal": "Thank you for your positive evaluation of our method's novelty, theoretical grounding, and clarity. We appreciate the constructive suggestions that have helped improve our paper. Please find below our point-by-point responses and new results motivated by your suggestions.\n\n> ... use of entailment models for semantic similarity is not well justified\n\nThe use of entailment models is well established in the literature of analyzing natural language generation, particularly in hallucination detection (please see [1-5] for some well-cited examples). It has been shown to outperform embedding-based or lexical similarity methods for clustering semantically equivalent generations [1, 2]. More generally, the detection of entailment has been extensively studied in linguistics [6]. We will make this positioning clearer in the Introduction and Related Work sections.\n\n> measuring the semantic similarity of partial sequence ... can be significantly challenging, given that the presence of a single word (or token, e.g., not) can change the semantics significantly\n\nWe agree that predicting semantic entailment between a complete sequence and a partial sequence, rather than between two complete sequences, can be subtle. In fact, the right panel of Figure 2 illustrates exactly the flipping of the polarity upon revealing the token \"not.\" So far as we are using bidirectional entailment for *steering generation*, this behavior (sensitivity to a few important tokens) is desired. Taking the Figure 2 example, if the fully generated sample were \"You and your friends are not welcome here, said Severn,\" and the partial generation so far were \"Severn said the people were,\" then we would be discouraging the choice of \"not\" as the next token, as this would result in semantically redundant generations, and instead steer the sampling toward something like the token \"welcome,\" for which the model would predict a low entailment score.\n\nTo ensure that the model generalizes well to partial-sequence input, we finetune it to treat [TRUNC] or [MASK] as *unknown* context. While only 0.3% of the model parameters are updated, the model is capable of predicting the correct label long before the entire text is revealed. In Appendix A, we report a validation accuracy of 73-74% averaged over all levels of truncation/masking. To complement this, we will add plots of accuracy **at every level** of truncation/masking. Accuracy goes up steeply from 34% to 72% as corruption level decreases from 90% to 50%, and continues going up to 91% at no corruption. The intuition is exactly as the reviewer described: the meaning of the full text can be gathered as soon as few semantically important tokens are revealed. \n\nThe reviewer raises an important point that we do not want to be biased toward high or low entailment in the **absence** of information. This motivates our choice to use P(entailment) scores directly rather than the class predictions. Overall, we find that models tend to output P(entailment) of ~33% when provided input with almost no information, as supported by Figures 2 (leftmost) and 4 (rightmost). The specific value of 33% can be understood as the maximum-uncertainty prediction in the three-way (entail/contradict/neutral) NLI classification task. In Appendix A, we will add plots of the **distribution of predicted P(entailment)** sharply peaked at 33% for single-token inputs and 90% masking, to demonstrate that the model is correctly uncertain in settings with very little information about entailment. In this no-information regime, the desired behavior is to default to iid sampling, which is why we initialize the steering strength hyperparameter at $\\lambda_0 = 0$ and only dynamically adjust it upwards when sample redundancy is significantly above 0.3 in terms of bidirectional entailment. Empirically, we find that $\\lambda_t$ tends to monotonically increase over sampling time as we acquire more information about the text being generated (Figure 5).\n\nLastly, to further justify our use of predicted entailment probabilities, we'd like to present a perspective of our framework as model-guided online decision making, similar to delayed feedback scenarios in reinforcement learning or Bayesian optimization. The entailment model serves as a cheap \"surrogate\" that helps guide our \"decisions\" (which token to choose next) toward maximizing \"utility\" (full generation that is semantically different from existing samples). There is signal in partial sequences for us to construct our belief of whether the one-token-ahead partial sequence will be semantically equivalent to a running sample set.\n\n> Computational efficiency\n\nWe acknowledge that the semantic repulsion term adds computational overhead due to look-ahead NLI model scoring. However,\n- In practice, we restrict similarity computation to the top-$k$ tokens at each decoding step (Appendix B.5) with $k=32$, as most tokens are not relevant to the query at hand. The extra per-token cost relative to standard iid sampling is $O(k P M_{\\rm NLI})$, where $P$ is the size of the running sample set and $M_{\\rm NLI}$ is the cost of computing NLI entailment.\n- Our experiments run on a single A100 GPU with <32 GB of VRAM and remain tractable for typical N=16 samples (Appendix B.6).\n- Importantly, the user can optionally implement online stopping (Appendix B.3), which allows termination of sampling once uncertainty estimates stabilize, potentially reducing the required sample size below the >20 samples typically required by standard iid baselines.\n\nThat said, we agree that hybrid approaches using batch sampling are promising for further speed gains.\n\n> evaluation [focuses on correctness] ... does not focus on the uncertainty quantification aspects\n\nWe would like to clarify a possible misunderstanding. Our evaluation focuses on (frequentist) calibration quality of our uncertainties, as is standard in the uncertainty quantification literature [1-3, 5]. The AUROC metric evaluates rank calibration; it gives the probability that we assign lower uncertainty to a randomly selected correct answer than to a randomly selected incorrect answer; good calibration would yield AUROC scores ~1 while poor calibration would score ~0.5. That is, while we report AUROC against correctness, the SE and MI are the ranking variables. The ROC curve is obtained by sorting the uncertainties from highest confidence to lowest (call the negated uncertainties $z_i$), sweeping a threshold $t$ through them, and computing for each $t$,\n$${\\rm TPR}(t)=\\frac{\\text{num positives with }z_i \\ge t}{\\text{num positives}}$$\n$${\\rm FPR}(t)=\\frac{\\text{num negatives with }z_i \\ge t}{\\text{num negatives}}.$$ AUROC is then $\\int_0^1 {\\rm TPR}({\\rm FPR}) d({\\rm FPR})$. We will add more details about the evaluation metric in the appendix.\n\nThe AUROC metric requires us to threshold the ROUGE-L score to determine correctness, so we have also reported Spearman $\\rho$ between ROUGE-L scores and SE/MI as a complementary metric and find that ours outperform DBS and SDLG by 5% and 6%, respectively, as well.\n\n> reasoning behind specific weights in equation (8)\n\nEquation (8) defines the standard **importance ratio** $w_i = p(s_i) / q(s_i)$ used to correct for the fact that we sample from the biased (diversity-steered) proposal distribution $q$ when we seek to analyze $p$, and its self-normalized form $\\tilde w_i$ satisfying $\\sum_i \\tilde w_i = 1$.  \n\n> equality in (9)\n\nEquation (9) is a consistent estimator (equality holds in the limit $N \\to \\infty$) for the cluster probability under usual regularity assumptions for self-normalized importance sampling -- finite second moment of $w$ being sufficient. Rewriting as $\\frac{\\sum_{i=1}^N w_i 1[s^{(i)} \\in c]}{\\sum_{i=1}^N w_i}$, applying the strong law of large numbers to the numerator and denominator separately guarantees almost-sure convergence to $\\frac{\\mathbb{E}_{s \\sim q}[w(s) 1[s \\in c]]}{1} = p(c|x, \\theta)$. The estimator has bias $O(1/N)$ and the usual $1/\\sqrt{N}$ precision. We had omitted the proofs of consistency, finite-sample bias, and asymptotic variance, because they are standard results in self-normalized importance sampling (e.g., Theorem 9.2 of [7]), but they may be helpful to include given our particular definition of $q$ (which justifies the finite second moment assumption) and treatment of the indicator function $1[s \\in c]$. We will expand on the main text around Equation (9) and add the proofs to the appendix.\n\n> Sections 3.3 and 3.4 could be better with interpretation, examples, or simulations \n\nThank you for this suggestion. While our applications of importance sampling and control variates are standard, we agree that the definitions of SE and MI have quite a bit of detail that can benefit from explanations to guide the intuition. To supplement Section 3.3, we will include figures illustrating SE and MI for the running \"Hubble constant\" example in the appendix, with each generation $s^{(i)}$ illustrated as dots in the \"semantic\" space and the clusters shown as different colors. As Section 3.4 is more difficult to capture visually, we will include a step-by-step worked example of MI estimation for AR and MDM (Algorithms 2-3) for a simple QA pair. \n\n\n[1] Farquhar, S. et al. (2024). Detecting hallucinations in large language models using semantic entropy. Nature.\n\n[2] Kuhn, L. et al. (2023). Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation. ICLR.\n\n[3] Lin, Z. et al. (2023). Generating with confidence: Uncertainty quantification for black-box large language models. TMLR.\n\n[4] Manakul, P., et al. (2023). Selfcheckgpt: Zero-resource black-box hallucination detection for generative large language models. EMNLP.\n\n[5] Aichberger, L., et al. (2025). Semantically diverse language generation for uncertainty estimation in language models. ICLR.\n\n[6] MacCartney, B. Natural Language Inference (2009).\n\n[7] Owen, A. B. (2013). Monte Carlo theory, methods and examples."}, {"review_id": "0bP4Rr1TeH", "reviewer": "Reviewer_1ALS", "summary": "In this paper, authors propose to use \"diversity-steered sampling\" to generate diverse samples, which is then used for downstream uncertainty estimations. The key idea is to use Natural Language Inference model to score semantic similarity between generated outputs as a diversity signal to modify model's output. They show that their method  improves uncertainty estimation across QA tasks and outperforms strong baselines like temperature sampling, beam search etc. Importantly, their framework is unified: it works for AR as well as diffusion-based models.", "questions": "See weakness", "limitations": "No,  the authors adequately addressed the limitations and potential negative societal impact of their work", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n  1.  Principled and Efficient Sampling for Semantic Uncertainty\n\nThe paper introduces a well-motivated sampling strategy that leverages NLI entailment-based similarity to bias sampling. Unlike prior diversity-promoting methods (e.g., temperature scaling or diverse beam search), this approach operates at the level of meaning rather than surface form and is applicable to both autoregressive (AR) and masked diffusion models (MDMs).\n\n  2. Clear Presentation with Reasonable Baselines and Fair Assessments\n\nThe chosen baselines—temperature sampling, DBD, and SDLG—are appropriate and closely related to the proposed method. I appreciate that the authors acknowledge the effectiveness of simple baselines in certain settings while demonstrating that their proposed method excels in others. This balanced assessment enhances the credibility of their evaluations.\n\n  3.  Modular, Gradient-Free, and Practical for Deployment\n\nThe framework is entirely gradient-free and requires no modifications to the base language model, making it broadly compatible with pretrained models. The use of a lightweight, partially fine-tuned NLI model for scoring semantic similarity is computationally efficient and easy to integrate, highlighting its practicality for real-world applications.\n\n\n**Weaknesses**\n\n  1. Limited Evaluation of Epistemic Uncertainty\n\nWhile the paper claims to estimate both aleatoric (via semantic entropy) and epistemic (via mutual information) uncertainty, the empirical evaluation predominantly focuses on semantic entropy. Only a single result pertaining to mutual information is reported in Appendix D. Despite detailed discussions on epistemic uncertainty quantification in Section 3.4, the experimental validation appears minimal.\n\n  2.  Lack of In-Depth Analysis and Ablation Studies\n\nThe paper attempts to cover multiple aspects: diversity-steered sampling (the main contribution), uncertainty quantification, and applications to both AR and MDMs. While this breadth is good, it comes at the expense of depth. For instance, more comprehensive ablation studies on various components—such as the impact of variance reduction techniques, the performance of the NLI model on truncated sentences, and the influence of tuning the diversity parameter λ—would strengthen the paper. It might be beneficial to move detailed discussions on mutual information, aleatoric, or epistemic uncertainty to the appendix, allowing the main paper to focus more on elucidating the proposed method with clear ablations.\n\n  3.  Minor Clarity Issues in Section 3\n\nI found Section 2 to be more comprehensible because authors included examples and intuitive explanations. In contrast, Section 3 is somewhat dense, with mathematical formulations presented without sufficient accompanying intuition or explanatory text, making it harder to follow.", "was_revised": false, "final_justification": "", "rebuttal": "We are grateful for your positive evaluation of our work regarding the motivation, practicality, design of experiments, and clarity. Your constructive suggestions have helped improve our paper. Please find our point-by-point responses below and summaries of new results motivated by your comments.\n\n> limited evaluation of epistemic uncertainty\n\nWe have added new evaluations for MI since the manuscript submission. We now report results for both LLaMA 3 8B-Instruct and LLaDA 8B-Instruct (to represent MDMs) on CoQA, TriviaQA, AmbigQA, and TruthfulQA. Previously in the literature, MI has only been evaluated on TriviaQA and AmbigQA for the Gemini 1.0 Pro and Nano-1 models [1], so we believe our experiments using new models and datasets will serve as useful benchmarking results for the community. To summarize briefly, our sampling method shows comparable or slightly better mean AUROC (0.57 ~ 0.64) across TriviaQA, AmbigQA, and TruthfulQA relative to vanilla iid sampling with $\\tau=1$ and $\\tau=2$, but performs similarly to DBS and SDLG on AmbigQA. DBS results carry high variance, about 30-40% higher than ours. LLaDA shows similar patterns but slightly lower AUROC by 1-2 overall. \n\nTo complement the quantitative results, we also added case studies demonstrating that diversity steering uncovers relevant semantic clusters, leading to meaningful SE/MI values. We consider three settings briefly summarized below.\n\n**(1) When the LM hallucinates.** If the prompt asks about a domain-specific, long-tail fact, models tend to hallucinate. We expect to see one cluster containing the correct answer and a few hallucination clusters. MI should be high, as the model easily \"changes its mind\" when conditioned on its own response. SE should depend on the hallucination pattern -- low if there are a few dominant modes of hallucination and high if hallucinations are varied and diffuse. We manually analyze responses to a well-defined biomedical question (with a single correct answer) for this setting.\n\n**(2) When the LM is legitimately uncertain due to ambiguity in the prompt.** If the prompt is vaguely worded or asks to name one item among many, models can output several valid semantic clusters. We expect SE to be high and MI to be moderate or low, as the model would not be internally conflicted about a given answer. We manually analyze responses to a precisely worded and easy question with multiple correct answers, taken from the AmbigQA dataset.\n\n**(3) A mix of both.** In Appendix C, we provided sample responses for the ambiguous, domain-specific question with multiple possible correct answers: \"Name one way to measure the Hubble constant.\" Given 8 sample generations, our method is able to surface more valid clusters corresponding to different methods of measuring the Hubble constant as well as hallucination clusters with made-up physics facts.\n\n> ablation studies on ... the impact of variance reduction\n\nWe have added an appendix section with the following items, briefly summarized:\n\n1. A brief primer on control variates (CVs). We present the concept in general terms and notation that apply clearly to the SE and MI cases.\n2. Justifications for why our proposed CVs are reasonable choices: We define our CVs as the mean-centered log probabilities of each generation. In natural language generation, high-likelihood samples tend to be mapped to dominant clusters, so our CVs correlate well with the cluster probabilities, as desired. Moreover, we can reduce variance \"for free,\" at no additional inference cost -- that is, they do not require extra forward passes through the base LM, as the log probability of each generation is already needed to evaluate the importance weights $w_i$. We will revise the text of Section 3.4 to make this benefit clearer as well.\n3. Average percent variance reduction achieved (ablation results): We can express the percent reduction in variance in terms of the correlation between the original semantic entropy functional $\\tilde w Y$ and our proposed CV $\\tilde w X'$, where $Y = -\\log {\\hat p}(c(s^{(i)}))$ and $X'$ is the mean-centered version of $X = -\\log p(s^{(i)})$. More precisely, if $\\sigma_X^2, \\sigma_Y^2$ are their respective variances and $\\sigma_{XY}$ is their covariance, then the percent reduction in variance is a direct function of the correlation $\\rho = \\sigma_{XY}/(\\sigma_X \\sigma_Y)$. We find that $\\rho \\approx 0.3 - 0.4$, translating to 10-15% variance reduction.\n\n> the performance of the NLI model on truncated sequences\n\nWe now provide additional results in Appendix A showing the performance of our finetuned NLI model at **every level** of corruption (trunc/mask) in addition to the average across all levels (73-74% accuracy) reported previously. Accuracy goes up steeply from 34% to 72% as corruption level decreases from 90% to 50%, and continues going up to 91% at no corruption. This is consistent with the intuition that the meaning of the full text can be gathered as soon as few semantically important tokens are revealed.\n\nWe also show that our model is not biased toward high or low entailment when the partial sequences do not carry sufficient information: \n- Models tend to output **entailment probabilities of ~33%** when provided input with almost no information (new histogram figures in the appendix). The existing examples in Figures 2 (for input 1-2 tokens long, leftmost) and 4 (for near 100% masking, rightmost) support this. The specific value of 33% can be understood as the maximum-uncertainty prediction in the three-way (entailment/contradiction/neutral) classification.\n- We will also provide **distributions of predicted P(entailment)** for single-token inputs and 90% masking. They are both sharply peaked at 33%, demonstrating that the model is correctly uncertain in settings with very little information about entailment.\n\n> influence of tuning the diversity parameter $\\lambda$\n\nTo avoid biasing the sampling unnecessarily, it is important for $\\lambda$ to default to iid sampling when the partial sequence carries no information about semantic redundancy with the sample set. This is why we initialize the steering strength hyperparameter at $\\lambda_0 = 0$ and only dynamically adjust it upwards when sample redundancy is significantly above 0.3 in terms of bidirectional entailment. Under our adaptive scheme for setting $\\lambda_t$, we find that $\\lambda_t$ tends to monotonically increase over sampling time as we acquire more information about the text being generated (Figure 5). We will justify our adjustment scheme more clearly in the text.\n\n> accompanying intuition or explanatory text [for Section 3]\n\nThank you for this suggestion. While our applications of importance sampling and control variates are standard, we agree that the definitions of SE and MI have quite a bit of detail that can benefit from explanations to guide the intuition. To supplement Section 3.3, we will include figures illustrating SE and MI for the running \"Hubble constant\" example in the appendix, with each generation $s^{(i)}$ illustrated as dots in the \"semantic\" space and the clusters shown as different colors. As Section 3.4 is more difficult to capture visually, we will include a step-by-step worked example of MI estimation for AR and MDM (Algorithms 2-3) for a simple QA pair. \n\n[1] Yadkori, Y. A., Kuzborskij, I., György, A., & Szepesvári, C. (2024). To believe or not to believe your llm. NeurIPS."}, {"review_id": "Uv2uSyfKWn", "reviewer": "Reviewer_mfGz", "summary": "In this work authors present a more efficient sampling method for estimating semantic uncertainty in LLMs. Authors sample from a modified LM proposal distribution that is steered by a fine tuned NLI entailment model to produce a set of semantically diverse responses. They then use importance sampling and control variate techniques to recover low variance estimates of uncertainty under the original model distribution (entropy and mutual information-type quantities). The resulting method on average outperforms vanilla SE for a fixed number of samples across a few different autoregressive and diffusion-based language models.", "questions": "* Do authors assume full entailment holds between premise and hypothesis examples at all levels of corruption when training the NLI model?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n* This method is well grounded in theory and flexible enough to work with most models and most UQ methods requiring MC sampling (I.e. consistency based methods)\n* The NLI fine tuning method for prefix entailment I think is interesting in its own right\n\nWeaknesses:\n\n* I am not sure whether this proposal distribution is compatible with more complex methods such as DRAGIN (Su et al. 2024), claim conditioned probability (Fadeeva et al. 2024), which select a subset of ‘important’ tokens to calculate uncertainty from. \n* Relying on an external entailment model introduces the hyperparemter lambda which needs recalibration for each new model. Although the authors propose an adaptive scheme there are no guarantees that this will be optimal for new queries", "was_revised": true, "final_justification": "In the rebuttal the authors provided additional discussion on how their diversity steered sampling method could be used in a variety of downstream UQ methods, and added further clarification about hyperparameter choice and finetuning data. While I am a bit skeptical about some of the implementation details (such as maintaining original labels for heavily corrupted entailment pairs), the overall method seems well grounded and fairly general.", "rebuttal": "We thank the reviewer for the positive feedback and are happy that you found the paper theoretically grounded, flexible, and clearly written. We appreciate the comment that our finetuned NLI is interesting in itself. Please find below our point-by-point responses.\n\n> compatibility with DRAGIN (Su et al. 2024)\n\nThank you for this interesting question that has helped us consider the implications of semantic diversity steering in the dynamic RAG context, beyond single-turn QA settings we focused on in our work. One possible entry point into DRAGIN is the RIND module that decides when to retrieve. RIND uses a product of attention weights, token entropy, and stopword indicators to detect the position when the model begins to hallucinate. This type of scoring can be prone to false positives, which would waste retrieval augmentation compute. In particular, token entropy is susceptible to over-estimating uncertainties if softmax weights are shared across multiple tokens with the same meaning. To improve on this, when RIND classifies a position as requiring retrieval, we can *verify* this prediction by generating a few partial phrases starting from that position with diversity steering and quantifying a measure of semantic uncertainty. The finetuned NLI model can be used for both steering and estimation to accommodate partial sequences. While using the finetuned NLI model would be new, this approach would naturally extend prior work using NLI for hallucination detection (e.g., [1]).\n\n> compatibility with claim-conditioned probability (Fadeeva et al. 2024)\n\nThank you for bringing the CCP metric to our attention. While we have used SE and MI as illustrative examples, our method is compatible with any downstream uncertainty metric defined on semantic clusters. CCP quantifies uncertainties only on the factual \"claim,\" after marginalizing over semantic clusters (thus removing uncertainties on \"surface form\", or style, as SE does) and conditioning on claim type/order. Instead of drawing multiple generations, however, it processes a single complete generation *post hoc* by substituting the token at each position with top-$k$ alternatives and computing the CCP of each alternative token based on NLI predictions: (1) if the text up to position $j$ with the $j$-th token swapped is predicted to \"entail\" the original text, then they are assumed to have the same meaning and claim type, (2) if \"contradict\", then they are assumed to have a different meaning but same claim type, and (3) if \"neutral,\" they belong to different claim types. The CCP of the entire claim is then 1 minus the simple product of the (non-stopword) words constituting the claim.\n\nWe can think of plugging into CCP in a couple of ways:\n- For a given generation $x$, the authors take a pretrained DeBERTa-large model *as is* to predict NLI relationships between prefixes $x_{1:j}$ and $[x_{<j}, \\textrm{substituted token}]$ for each position $j$. This can be risky, as DeBERTa-large is trained on *full* premise-hypothesis pairs and the CCP scoring relies heavily on its predictions to determine membership to meaning/claim types. We can use the finetuned NLI model instead to better deal with prefixes.\n- Instead of post-processing a single generation $x$ by swapping each token $x_j$, we can consider drawing multiple full generations with diversity steering (with the finetuned NLI model) and computing the claim-level CCP with the original NLI model, as done in our paper. Importance reweighting and optional variance reduction proceed as usual by reweighting the token probabilities. This sampling-based approach also eliminates the need to separately handle sub-word token substitutions.\n\n> lambda ... needs recalibration for each new model and query\n\nWe acknowledge that $\\lambda$ is an important hyperparameter that must be tuned. In Section B.3, we describe an adaptive schedule for $\\lambda$ that empirically transferred across models and across queries, and yielded ${\\rm ESS}/N$ > 0.4 for all models and datasets in Table 1. The schedule goes as follows: $\\lambda$, initialized at zero (no steering), increases only when the maximum entailment exceeds $E_{\\rm target} = 0.3$ ($\\approx 1/3$), corresponding to the maximum-uncertainty prediction in three-way NLI classification. Empirically, we find that $\\lambda_t$ tends to monotonically increase over sampling time as we acquire more information about the text being generated (Figure 5). We will justify our adjustment scheme in more detail in the text.\n\n> Do authors assume full entailment holds between premise and hypothesis examples at all levels of corruption when training the NLI model?\n\nNo. During finetuning we retain the original MNLI gold label for each corrupted pair, so contradiction and neutral examples remain even when corrupted. Specifically, for every premise–hypothesis pair we (1) randomly choose one side, (2) truncate or mask it at a random position, without flipping the label, and (3) finetune only the new [TRUNC]/[MASK] embedding and the classifier head. This teaches the model that an incomplete sequence can entail, contradict, or be neutral wrt the other side, depending on the already-revealed content, as illustrated in Figures 2 and 4. Details of the NLI training can be found in Appendix B.1. \n\n\n[1] Manakul, P., et al. (2023). Selfcheckgpt: Zero-resource black-box hallucination detection for generative large language models."}, {"review_id": "Kvdl7zvlrB", "reviewer": "Reviewer_ozCj", "summary": "This paper introduces a novel framework to estimate both aleatoric and epistemic uncertainty in large language models (LLMs) for free-form question answering. The method centers on a diversity-steered sampling technique that penalizes semantically redundant generations during decoding using an NLI model (fine-tuned to work on partial or masked texts). The approach is model-agnostic, applicable to both autoregressive (AR) and masked diffusion models (MDM), and uses importance weighting and control variates to debias and reduce variance in the uncertainty estimation.", "questions": "NA", "limitations": "NA", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n* The paper proposes a principled, gradient-free method to enforce semantic diversity during decoding, using NLI-based similarity scoring, which is cleverly applied in both AR and MDM settings. This aligns the generation process with the uncertainty estimation objective.\n* The framework unifies semantic clustering, importance-weighted sampling, and variance-reduction via control variates, offering a comprehensive pipeline for both aleatoric and epistemic uncertainty quantification.\n* The method works with existing LLMs without requiring access to their gradients or architectures, and experimental validation spans multiple datasets, models (OPT, LLaMA, LLaDA), and decoding paradigms.\n\nWeaknesses:\n* The method introduces a sequential sampling cost due to diversity enforcement, which scales linearly with sample size. While effective, it may be less scalable in large-generation scenarios compared to parallelizable approaches like SDLG.\n* The accuracy of uncertainty estimation heavily depends on the quality of semantic clustering derived from the fine-tuned NLI model. Noisy or ambiguous entailment judgments may distort both SE and MI estimates.\n* The paper focuses on quantitative metrics but lacks qualitative examples or failure cases to illustrate how the method handles edge cases, hallucinations, or ambiguous prompts—key aspects for uncertainty estimation.", "was_revised": true, "final_justification": "Thank you for the rebuttal, I decide to remain the score", "rebuttal": "Thank you for your encouraging comments on our paper's novelty, applicability, and comprehensiveness. Please find below our point-by-point responses and new qualititative case studies motivated by your suggestions.\n\n> less scalable in large-generation scenarios compared to parallelizable approaches\n\nWe acknowledge that the sequential sampling cost prevents fully parallel generation. The scenario we consider is not all-purpose large generation but **targeted generation** with the specific goal of estimating a downstream uncertainty metric. As long as the target uncertainty metric is defined on top of semantic clusters, like SE or MI, steering sampling toward covering more clusters can help estimate it with fewer generations. Baseline iid sampling methods, in contrast, can \"waste\" sampling resources with semantically redundant generations. Figure 3 shows that our method helps cover more semantic clusters relative to baselines, and Appendix C presents case studies illustrating the improvement in semantic diversity. Moreover, Appendix B.3 presents an optional **online stopping** method that enables termination of sampling once uncertainty estimates stabilize, potentially reducing the required sample size below the >20 samples typically required by standard iid baselines. \n\nAs derived in Appendix B.5, the extra per-token cost relative to standard iid sampling is $O(V P M_{\\rm NLI})$, where $P$ is the size of the running sample set, $V$ is the vocabulary size, and $M_{\\rm NLI}$ is the cost of computing NLI entailment. In practice, we seek speed gains by restricting similarity computation to the top-$k$ tokens at each decoding step (Appendix B.5, L931–933) with $k=32$, as most tokens are not relevant to the query at hand. This reduces the extra cost to $O(k P M_{\\rm NLI})$ per token. Please note that diversity penalty can still be computed in parallel over $k$ tokens at each step.\n\nAn interesting avenue for future work would be to combine batch iid sampling with diversity steering in a hybrid approach. Our method is still parallelizable over beams or batches given a running sample set, so we could allow the model to sample $M$ generations in parallel before applying the diversity penalty for the next generation if the semantic redundancy is high. We could also consider alternating block tokens of iid sampling with diversity-steered sampling.\n\nWe will revise the text to clarify which aspects of our added computational cost are parallelizable and elaborate on hybrid extensions.\n\n> accuracy of uncertainty estimation heavily depends on the quality of semantic clustering derived from the fine-tuned NLI model\n\nWe would like to clarify that we use the finetuned NLI for sampling (our method contribution) but the original NLI without finetuning for final uncertainty estimation, as done in prior work [1-3, 5]. We will clarify this distinction in the Methods section. That said, our finetuned NLI model can be used in place of the original NLI model as well; both the TRUNC and MASK finetuned models scored similar validation accuracies as the original model (~91%), as reported in Appendix A.\n\nNo matter what sampling scheme is used, be it ours or any of the baselines, incorrectly clustering the final samples can distort the SE/MI estimates, as pointed out by the reviewer. Semantic clustering is an interesting and challenging problem in its own right, for which bidirectional entailment has been shown to outperform embedding-based similarity or lexical similarity methods [1, 2]. While we agree that improving semantic clustering can improve the accuracy of semantic uncertainty estimates, it lies beyond the scope of this work. We instead focus on how to generate semantically diverse samples **assuming** our goal was to estimate SE/MI defined on top of bidirection entailment clusters.\n\nIf the reviewer was referring instead to the accuracy of the *diversity-steering term* used in sampling, we now provide additional results showing that our finetuned NLI model is not biased toward high or low entailment when the partial sequences do not carry sufficient information. Overall, we find that models tend to output entailment probabilities of ~33% when provided input with almost no information -- the examples in Figures 2 (for input 1-2 tokens long) and 4 (for near 100% masking) support this. The specific value of 33% can be understood as the maximum-uncertainty prediction in the three-way (entailment/contradiction/neutral) NLI classification task. We will add to Appendix A the accuracy of the entailment model **at every level** of truncation/masking in addition to the average across all levels (73-74%) reported previously. Accuracy goes up steeply from 34% to 72% as corruption decreases from 90% to 50% and reaches 91% at no corruption. We will also provide a **distribution of predicted P(entailment)** for single-token inputs and 95% masking, to demonstrate that the model is correctly uncertain in settings with very little information about entailment. In this no-information regime, the desired behavior is to default to iid sampling, which is why we initialize the steering strength hyperparameter at $\\lambda_0 = 0$ and only dynamically adjust it upwards when sample redundancy is significantly above 0.3 in terms of bidirectional entailment. Under our adaptive scheme for setting $\\lambda_t$, we find that $\\lambda_t$ tends to monotonically increase over sampling time as we acquire more information about the text being generated (Figure 5).\n\n\n> qualitative examples or failure cases to illustrate how the method handles edge cases, hallucinations, or ambiguous prompts\n\nThank you for this suggestion. We have added case studies to the appendix demonstrating that our method can surface meaningful SE/MI values by uncovering relevant semantic clusters in three settings: (1) when the LM hallucinates, (2) when the LM is legitimately uncertain due to ambiguity in the prompt, and (3) a combination of the two. We summarize them briefly below.\n\n**(1) Hallucination.** If the prompt asks about a domain-specific, long-tail fact, models tend to hallucinate. We expect to see one cluster containing the correct answer and a few hallucination clusters. MI should be high, as the model easily \"changes its mind\" when conditioned on its own response. SE should depend on the hallucination pattern -- low if there are a few dominant modes of hallucination and high if hallucinations are varied and diffuse. We manually analyze responses to a well-defined biomedical question (with a single correct answer) for this setting.\n\n**(2) Ambiguous prompt.** If the prompt is vaguely worded or asks to name one item among many, models can output several valid semantic clusters. We expect SE to be high and MI to be moderate or low, as the model would not be internally conflicted about a given answer. We manually analyze responses to a precisely worded and easy question with multiple correct answers, taken from the AmbigQA dataset.\n\n**(3) A mix of both.** In Appendix C, we provided sample responses for the ambiguous, domain-specific question with multiple possible correct answers: \"Name one way to measure the Hubble constant.\" Given 8 sample generations, our method is able to surface more valid clusters corresponding to different methods of measuring the Hubble constant as well as hallucination clusters with made-up physics facts.\n\n\n[1] Farquhar, S. et al. (2024). Detecting hallucinations in large language models using semantic entropy. Nature, 630(8017), 625-630.\n\n[2] Kuhn, L. et al. (2023). Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation. ICLR.\n\n[3] Lin, Z. et al. (2023). Generating with confidence: Uncertainty quantification for black-box large language models. TMLR.\n\n[4] Manakul, P., et al. (2023). Selfcheckgpt: Zero-resource black-box hallucination detection for generative large language models.\n\n[5] Aichberger, L., et al. (2025). Semantically diverse language generation for uncertainty estimation in language models. ICLR."}]

Author rebuttal:

Meta-review: The paper proposes a modular method for semantic uncertainty quantification in language models using diversity-steered sampling with importance weighting and variance reduction. The approach is gradient-free, theoretically motivated, and broadly applicable to autoregressive and diffusion models. Reviewers highlighted the novelty of the method, the clarity of exposition, and empirical gains in estimating semantic entropy and mutual information, with additional ablations and case studies in the rebuttal further strengthening the work.

Main concerns were the computational overhead of semantic repulsion, reliance on entailment models for similarity (especially with partial sequences), and limited evaluation of epistemic uncertainty. The rebuttal addressed these by clarifying the role of entailment, showing robustness of fine-tuned natural language inference (NLI) models, and expanding evaluation and ablations. Reviewers agreed these additions improved the paper, though scalability and dependence on the NLI component remain open issues.

Overall, reviewers converged on a cautiously positive stance, with three leaning borderline accept and one more strongly supportive. Given the novelty, sound methodology, and empirical support despite some limitations, I recommend acceptance.
Decision: Accept (poster)