DiffSampling: Enhancing Diversity and Accuracy in Neural Text Generation
Authors: Giorgio Franceschelli
Mirco Musolesi
Venue: Accepted by TMLR ()

Abstract: Despite their growing capabilities, language models still frequently reproduce content from their training data, generate repetitive text, and favor common grammatical patterns and vocabulary. A possible cause is the decoding strategy: the most common strategies either consider only the most probable tokens, which reduces output diversity, or increase the likelihood of unlikely tokens, compromising output accuracy and correctness. In this paper, we propose DiffSampling, a new decoding method that leverages a mathematical analysis of the token probability distribution to ensure the generation of contextually appropriate text. In particular, the difference between consecutive, sorted probabilities can be used to truncate incorrect tokens. In addition, we also propose two variations of the proposed method that aim to correct the subtle inconsistencies of common sampling strategies.
Experiments involving four different text-generation tasks demonstrate that our approach consistently performs at least on par with the existing methods it builds upon in terms of quality, despite sampling from a larger set of tokens.

Published in Transactions on Machine Learning Research (12/2025)
DiffSampling: Enhancing Diversity and Accuracy in Neural Text Generation
Giorgio Franceschelli
sionio.fnamceschell@lnnio
Alma Mater Studiorum Università di Bologna, Bologna, Italy
Mirco Musolesi
wwmuuskeei@uull.cccoo
University College London, London, United Kingdom
Alma Mater Studiorum Università di Bologna, Bologna, Itly
Reviewed on OpenReview:
https: // openreveee....... net/ per/form?? id= HXy
Abstract
Despite their growing capabilities, language models still frequently reproduce content from their training data, generate repetitive text, and favor common grammatical patterns and vocabulary. A possible cause is the decoding strategy: the most common strategies either consider only the most probable tokens, which reduces output diversity, or increase the like- lihood of unlikely tokens, compromising output accuracy and correctness. In this paper, we propose DiffSampling, a new decoding method that leverages a mathematical analysis of the token probability distribution to ensure the generation of contextually appropriate lext. In particular, the difference between consecutive, sorted probabilities can be used to trun- cate incorrect tokens. In addition, we also propose two variations of the proposed method that aim to correct the subtle inconsistencies of common sampling strategies. Experiments involving four different, text-generation tasks demonstrate that our approach consistently performs at least on par with the existing methods it builds upon in terms of quality, de- spite sampling from a larger set tokens.
1 Introduction
In recent years, large language models (LLMs) have demonstrated remarkable performance (Bubock et al. 2023), driven by the availability large-scale datasets, advances in computational power (Bom- masani al.) 2021), and the development of in- novative learning strategics (c.g., Stiennon et al.) 2020 Rafailov et al. 2023) While training pro- vides LLMs with the information and skills required to process natural language, another aspect plays a key role at generation time: the decoding strategy, that is, the method used to extract text sequences from the model. The choice of decoding scheme sig- nificantly impacts the generated output, there is pronounced trade-off between quality and diver- sity (Ippolito et al. 2211).. The most straightfor- ward strategies, such as greedy decoding (selecting the highest- probabbiiy token) or sampling, tend to repeat the same tokens multiple times (Su et al.) 2022), reproduce training data (Carlini et al. (202)), flatten the lexicon in favor of the most common
PROBABLITY
200
DITSANPUNG-LO
DITTSAPPLIN--ANN
Figure 1:
In the top-left square, the original dis- tribution. In the top-right square, DeffSampling-cut truncates after the minimum discrete derivative. In the bottom-left square, DiffSampllig-lh also imposes a total probability lower bound bottom-right square, DiffSampling-minne applics trun- cation only among lokens with probability less than Pmin 0.1 times the highest probability.
0.9. In the

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grammatical structures and words (Fleisig et al. 2024 Reviriego et al. 2024 Although the temperature parameter may increase the likelihood of less frequent tokens, it also raises the chance of syntactically in- correct ones by flattening their probabilities, regardless of their actual ranking. An ideal solution should concentrate on where the critical mass of the probability distribution resides. More preciscly, with criti- cal mass, we refer here to the portion of the distribution that collectively accounts for the majority of the probability mass of the tokens. In this direction, a. common approach is nucleus sampling (Holtzman et al. 2020), which removes the tail of the distribution by focusing on the smallest subset of tokens whose global probability exceeds given threshold. However, a key issue remains: it either preserve incorrect tokens or exclude appropriate ones, depending on whether the critical mass is smaller or larger than the threshold, respectively. As suggested by Hewitt et al. (2022), the learned probability distribution can be viewed as a mixture of the true dist distribution, which assigns a non-zero probability only to appropriate tokens (the critical mass), and a smoothing distribution, which assigns a small but non-zero probability to incorrect tokens for learning purposes.
To address the subtle inconsistencies in existing truncation strategies, we introduce family of decoding strategies called DiffSampling, based on the analysis of the probability distribution of the tokens, and in particular, on the minimum discrete derivative (i.c., the largest difference between consecutive probabilities in a sorted distribution). We propase a method for excluding incorrect tokens introduced by the smoothing distribution, along with two relaxed variants designed to promote output diversity by correcting standard methods (see Figure D. We then provide a comprehensive evaluation of them under four different taske" namely mathematical problem-solving tasks, extreme summarization, the divergent association task" and story generation against the most common baselines, and discuss their advantages and limitations. We show that DiffSampling consistently performs at least par with the standard methods they aim to correct, while enhancing output diversily, especially in longer-form text generation.
2 Background
2.1 Language Modeling
An autoregressive language model (LM) is a probability distribution px(x) parameterized by 0 over a variable- length text sequence x = (x) ... ..)), where T is the sequence length and each token F2 is in a finite vocabulary V. The probability distribution is factorized as (x) = II [0( ... po(=:]21....2411 11, and the LM is usually trained to maximize the likelihood of the true distribution (x) for any x from a reference dataset (the training set). In other words, given as input 21 I4, the model learns to approximate the probability of each token from V being T++1- While this makes the model immediately capable of scoring the probability of a given text, it also allows for the generation of new sentences. Given commonly writtewritten prefix (also known a prompt)
xpp) of length P, we can decode a continuation & (#P+1... LM through its factorized representation introduced before. However, must remember that the model is trained to score and not to generate sentences. A given text might have zero probability for generation purposes (e.g., the text is syntactically incorrect), but non-zero probability for ranking purposes (Hewitt et al. 2022).
from the
2.2 Decoding Strategies
The decoding of tokens from the probability distribution learned by a neural language model can occur in several ways. The greedy strategy involves selecting the most probable token each time. However, this can lead to consistent lack of diversity and several repetitions. The standard approach involves sampling from the probability distribution, which can be transformed through a temperature parameter The temperature scales the dillerences among the various probabilities: temperature lower than 1 will increase the probability of the most probable tokens (a zero temperature degenerates to greedy strategy), while temperature higher than will increase the probability of the lcast-probable tokens, allowing for more diversity in generation
The code and results available at: htttp:///githu httpe///ggtabb.ccmggoorrroooooee wwt.o///wogooooooocccc////aaaaaa
2 A common task in creativity research that evaluates ability to generate semantically unrelated concepts OOson al.
2021
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PPeeperkrr et al. 2024p. However, this might lead to the selection of tokens that are not syntactically appropriate for the current input. Selective sampling (Troshin et al., 2025) dynamically switches between greedy and high-temperature sampling based on the likelihood of output errors estimated by a lightweight, ad-hoc classifier. Alternatively, top-k sampling (Fan et al., 2018) reduces the token space to the & most probable ones. To generate more natural and coherent solutions, contrastive search (Su et al. 2022) employs a greedy stratogy over the combination of a top-k truncation and a degeneration penalty. This promotes the selection of tokens that differ from those already generated, enhancing the diversity and quality of the output. Nevertheless, limiting the number of selected tokens a priort can lead to the exclusion of meaningful tokens or the inclusion of inappropriate ones. A possible solution is to set h dynamically, as in Mirostat [Basu et al. 2021]: to maintain the perplexity of generated text at a desired value, the k parameter is aclively tuned based on the current cross-entropy.
Alternatively, nucleus (or top-p) sampling (Holtzman et al. 2020 reduces the token space to the smallest subset of tokens with a total probability no less than p. To restrict the nucleus to tokens whose information content. is close to the expected one given prior context, locally typical sampling (Meister et al. 2023 focuses the tokens with negative log- probability within certain absolute range from the conditional entropy (and total probability no less than p). Finally, Hewitt et al. (2022) assert that a language model Icarns mixture of the true token distribution and a smoothing distribution to avoid infinite perplexity. For de-smoothing the distribution, they propose 6- and y-sampling, which truncate tokens with a probability smaller than a threshold set a priori or dynamically through the entropy of the distribution, respectively. This threshold can also be set according to the magnitude of the highest probability, as in min-p (Minh et al., 2025). or
based the logit rather than the probability distribution (Tang et al., 2025). However, such strategies do not guarantee the exclusion of the smoothing-indueeed tail. Contrastive decoding (Li ct al., 2023) leverages the difference in likelihood between a large language model and smaller, less capable one to prioritize tokens with sufficiently high probability under the expert model. However, it requires access to a smaller model with an identical vocabulary, which is not always available. While conceptually aligned, our method simplifies the threshold computation and provides more intuitive guarantees on the suitability of selected tokens.
3 DiffSampling
Given the probability distribution of the next token, let us imagine sorting it to have tokens in descending order based on their probability. Following Hewitt et al. (2022), only the first D) tokens have a positive probability under the true token distribution, while the remaining |V] tokens receive a non-zero final probability solely due to the smoothing distribution, which prevents infinite perplexity. To generate correct text, we need to limit our sampling among the first D tokens, thus, we need to identify a cutting point that is as close as possible to the D-th token. We propose to achieve this by truncating after the largest difference between probabilities: the token to its left should be the least probable token that our model considers correct.
From mathematical analysis perspective, this point is characterized simply and elegantly as the location where the derivative reaches its minimum. Tet us consider probability distribution p(wz) defined for a limited number of x!"' !!! with p() monotonically decreasing. According to the forward difference approximation, the discrete derivative of function f(a!")) is defined Af(x!")) (( -xx=)))) thus we have:
f(x(")),
Ap(a(")) (p(ottt)) (") if if -p((f())
(1)
if = N
which always non-positive. arg min min Ap(x("))) represents the index of the last token before the point characterized by the largest difference between consocutive probabilitics.
In particular, it seems plausible that arg min (ApnAA((""))) distribution ends and smoothing begins to take effect, or a point within the true distribution that separates tokens with significantly higher probabilities from the rest. Indeed, due to the inner nature of smoothing, it seems unreasonable that the maximum difference is between tokens with zero probability under the true
[']] - D, ie., it either marks the point where the true
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Algorithm 1 DillSampling
Input: probabilities probs [p!" ... M. lower bound p lb Pib. upper bound p min Pminn temper-
ature tau = T.
sorted probs, indices = (pobs)
fwd_probs = ported__robb[1
[0.0]
delta probs = fwd [wd__ross_________ - sorted probs
if p_min > 0.0 then
min
lim argmin(sorted probs p min sorted probs(O))
delta delta_probs[:: lim] 0.0
else
nucleus = cumsum (asssummmssttee (sorted probs) < p_lb delta prtta__probsnuucluu = 0.0
end if
cut _dx__dxx= aergmin(deltaa, probs)
sorted _acpl__robsssuuu__ idx 0.0
probs sort_ port_b__iie b_____dddxssotedddddde _ropid__pbs____ indices)
logits log( probss////mm (probs))/tau
probs = softmax(logits)
Output: probs.
distr distribution, and thus only because of the smoothing distribution (see Appendix for formal analysis on when arg min )))(((())))) is provably < D).
Building on this intuition, we propose DiffSampling, a family of three decoding strategies (the full algorithm is reported in Algorithm D The first onc, which we call DiffSampling-cut, leverages the aforementioned property and consists of cutting the distribution tail at the right side of the minimum discrete derivative, i.., sampling among the tokens z,, i < arg min( min(Ap(a)) (Ap(z!"))) Due to the guarantee of selecting a correct token, which prioritizes reliability over aggressiveness, this approach can be seen as an improved greedy strategy: when the model has high confidence single token, degenerates into the greedy stralegy; otherwise, it preserves other appropriate tokens, increasing diversity. The next section provides toy example to showcase this relation.
Since the minimum discrete derivative should guarantee the correctness of the truncation, any preserved token should come from the true distribution: we can sample at higher temperature to foster diversity without the usual trade-off with quality. Note that although temperature scaling is typically applied before truncation, doing so alters the probability distribution, potentially shifting the minimum of the discrete derivative forward possibly into the region of tokens that have zero probability under the true distribution. To preserve the mathematical propertics discussed above, we instcad apply temperature scaling after truncation.
However, previously discussed, this cutoff point can fall within the true distribution, thereby excluding tokens that are still correct; frequent scenario consists of the first token minimizing Ap(z!")), but still having quite low probability. To address this issue, we propose two relaxations right-move the truncation, The first one builds upon top-p sampling and introduces lower bound on the saved mass probability. DiffSampplin--ll considers Iruncating based on Ap(x)")) in such a way that the resulting tokens have total probability least equal to the lower bound pu- In other words, given cardinality of the smallest subset of tokens whose total probability is not lower than Pis. it computes the arg min min(AA(zx:") for n 2 (i.e., the cutting point is between tokens not included in the top-p nucleus). This approach can be seen as an improved top-p sampling: it corrects the p parameter via our derivative-basod approach to include appropriate tokens after the selected nucleus.
Alternatively, can build upon min-p sampling by introducing a dynamic upper bound the probability of truncated tokens. DiffSampling--iigg minp considers truncating based on Ap(=(")) in such a way that no discarded tokens have a probability greater than Pmin maxxrvvpt)). Tn other words, given j index of the
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Prompt:
Natural language generalion (NLG) is the subfield of artificial intelligence and compalational linguistics that is concerned with the co- struction of computer systems that can
Token
Prob
Top-p
Min-p
D-cut
D-lb
D-minp
generate
37.326
41.366
50.872
59.886
40.929
47.537
produce
25.002
27.709
34.076
40.114
27.416
31.842
understand
7.295
8,084
9.942
7.999
9.290
create
3.749
4.154
5.109
4.110
4.774
naturally
2.797
3.100
3.067
3.562
perform
2.352
2.606
2.579
2.995
reason
1.067
1.182
1.170
be
0.956
1.060
1.048
recognize
0.350
0.388
0.384
0.339
0.375
0.371
read
0.325
0.357
respond 0.321
0.352
interpret 0.318
0.348
interact
0.259
Table 1: Token probability comparison between top-p, min-p, and our methods, showing how they avoid treating tokens with very similar probabilities differently (reported in bold). The probabilities (in percent- age) are taken from SmolLM-135M Instruct (Ben Allal et al. 2024
lowest-probable token with a probability greater than Pmin max,ev p(v), computes the arg min min(Ap(a;") for n 2 This approach can seen as an improved min-p sampling: there are tokens after index j with probability very close to the threshold, it still preserves them.
Ap(a(")))
Overall, DifsSampling can be mass lower bound Pis and the truncated probability upper bound Pmin (where DiffSampling-cut just assumes value of 0.0 for the first and of 1.0 for the second), plus the additional temperature T.
sampling scheme governed by two parameters, i.e., the probability-
4 Illustrative Example
To make easier understand the advantages of our methods, Table presents an illustrative example comparing them with their most similar methods. For the sake of simplicity, top-p and DiffSampling-UU consider the same p Pw 0.9, while min-p and DiffSampling-ming consider the same p p= Pmin 0.1. As apparent, Dif[Sampling-cul improves upon the greedy stralegy by also considering the second-mosi probable token, while both DiffSampling-lt and DifSSampinng-iing improve upon top-p and min-p by not discarding tokens with very similar probability compared to preserved ones (for example, top-p would discard the 'read' token while having only a 0.014% probability less than ',". Although the differences between standard methods and ours are often minimal (typically involving low-probability tokens), even a slight correction in the right direction, the negligible computational cost of an arg min function, can lead to meaningful improvements.
5 Experiments
To evaluate whether Dis[Sumpling helps diversify outputs while maintaining a high accuracy, we lest. it on four case studies: math problem solving, text summarization, the divergent association task, and story generation. While slightly unconventional, these tasks are very different from each other, and provide meaningful ways evaluate diversity and quality together, as they have quantifiable goals which be reached in syntactically and semantically different ways.
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5.1 Models and Baselines
In all our experiments, we start from a state-of-the-art language model and test various decoding strategies. For the math problem-solving tasks, we use the Llama2-based MetaMath-7B-VV.0 model trained with self- supervised learning on MetaMathQA (Yu et al. 2024). For extreme text summarization and story generation, we utilize the 1lama-3.2-30 model (Grattaforri et al. 2024), with both original and -Instruct versions. Finally, for the divergent association task, we consider Meta-LLama-3-9B (Grattafiori et al. 2024), using both pre-trained and DPO-tuned - -Instruct versions. We study the performances of our three methods: DiffSampling-cutt DiffSampling-lb with pio 0.9; and DiffSampling-minng with Pnin = 0.1. While these values are somctimes sub-optimal (sec Appendix G for a full ablation study), we chose to standardize their values to match those used for the top-p and min-p baselines. Indeed, we compare them with a total of 5 decoding baased baselines: greedy strategy; 17sampling (with 17 = 0.0003); locally typical sampling (with p 0.9); top-p sampling (with p = 0.9); and min-p sampling (with p 0.1). While other methods, such as selective sampling (Troshin et al., 2025,, contrastive decoding (Li et al., 2023), and beam search [Roark] 2001), could also be considered, we restrict our analysis to sampling-basse methods to ensure fair comparison, selecting those with similar computational costs and operational principles to our approach.
5.2 Math Problem Solving
Experimental Setup. Solving math problems provides a useful case study for our decoding strategies, as it allows us to evaluate the correctness of solutions (as the percentage of correctly solved problems) and the
diversity of procedures to arrive at the result. In particular, we consider the GSM8K (Cobbe et al. 2021
and MATH (Hendrycks et al.) 2021) test sets; the relative prompts are reported in Appendix D To avoid resource wasting, we focus on entries with a problem and a solution of no more than 512 tokens.
We evaluate the quality of solutions through the ratio of correctly solved problems, i.e., with pass@1. Instead, the diversity is computed according to two methods: expectation-adjusted distinct N-grams (EAD) (Liu et al. 2022) and sentence embedding cosine diversity (SBERT) (Hong et al.] 2024), which should evaluate syntactic and semantic diversity, respectively (Kirk et al. 2024.. EAD counts the number of distinct N- grams tokens (averaging over N = 5). and removes the bias toward shorter inputs by scaling the number of distinct tokens based on their expectation The SBERT metric is 1 minus the cosine similarity between the embeddings of the sentences. While originally based on Sentence-BERT (Reimers & Gurevych] 2019), we employ the more recent all all-mpnet-base-v2 to obtain the embeddings, as suggested by their developers A Following Kirk et al. (2024), we compute cross-input EAD and SBERT, i..., by considering the set of all outputs produced for specific seed. In addition, we also compute against-greeds EAD and SBERT. Given each input, we compare the output with the greody one by calculating the average expectation-adlustee distinct N-grams not present in the greedy response, and 1 minus the cosine similarity between the two outputs, respectively. We refer the interested reader to Appendix C for a formal definition of all used metrics. Finally, for a more fine-grained analysis, Appendix HH reports a few examples of generated outputs.
Experimental Results. Table (left side) reports the results for the GSM8K test set. The greedy strategy achieves the highest average accuracy, closely followed by DiffSampping-cuu Among the other baselines, only locally typical sampling performs comparably, while DiffSampling-l6 and DifsSampling- substantially differ from top-p and min-p any metric (but different pib or Pmii values can significantly improve the accuracy at very small cost in diversity; see Appendix G
do not
Table 2 (right side) reports the results for the MATH test set. Here, the highest accuracy is reached by DiffSompling-cuu which also improves on the greedy strategy in terms of diversity. By contrast, our other two methods offer limited improvements over the sampling-basee baselines. Notably, all methods achieve the same cross-input SBERT score, i.e., the overall diversity between all outputs is always the same across
Note that EAD is not upper-bounded. Moreover, it counts for distinct N-grams across all outputs, including inside the same output: the EAD of set of equal, non-empty sentences is not as each sentence will contain least one distinct 1-gram. In general, an EAD score cannot be considered high or low per sc, but it must be compared with other EAD scores from experiments under similar conditions. htttp::/huuginggfcc.. co/sentence- tww.etooreere/eeerrtrrrr wawp://eer-t-ta-----------e---e- mean-
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Dataset:
GSM8K
MATH
Method
Accuracy
Cross-Inpus
Against-Creedy
Accuracy
Cross-lnput
Against-Grre
EAD
SBERT
EAD
SBERT
FAD
SBERT
EAD
SBERT
Greedy
66.4 66.44g.00
2.03_.00
0.644.00
20.62
5.65
0.80
Top-p
26.00=.18
2.08_.o1
0.64
0.23
0.03
20.02:
6.08 6.08
0.80
0.36
0.10+ 00
y-sampling
15.05
2.12=.00
0.64
0.25
0.04
19.67
6.36
0. 0.80 .0
0.39
0.11 00
Locally typical
66.29
2.09_.00
0.64
0.23 00
1.03
19.95 26
6.061.01 01
0.80
0.36
0.101.00
Min-p
65.761.44
2.09_.00
0.64
0.231.00
0.03
20.25 09
6.091.01
0.80
0.36
0.101
Diff
66.36_.23
2.04_.00 00
0.64
0.144.00 00
0.022.00
21.38 20
5.71
0.80
0.27
0.07
DiffS.-Ib
65.18_.05
2.09_.01
0.641g.00
0.23g 00
0.03g2.0
20.20 08
6.11
0. 0.80
0.37
0.10, 00
DiffS.-minp
65.48...0
2.09
0.641..o0
g.
0.03g.co
20.18 08
6.06
0.80
0.36
0.10g.o0
Table 2: Accuracy and diversity of results for the GSM8K and MATH test sets over 3 seeds. The mean and standard error of the final score for each run are reported for accuracy and cross-input diversity, whereas the mean and the 95% confidence interval for the full set of answers are reported for against-greedy diversity.
different methods, which might be due to the very similar levels of accuracy (and, therefore, due to the similar meaning of the proposed solutions).
5.3 Extreme Summarization
Experimental Sctup. Summarizing paragraphs represents another meaningful case study since the same text can be correctly outlined in different ways. To keep the resource consumption as low as possible, we consider the eXtreme Summarization (XSum) dataset (Narayan et al. 2018). which contains pairs of documents and ono-sentence summarics. In particular, we use the test partition (11334 entries) and exclude all entries with tokenized document. longer than 768, obtaining 9815 entries; then, we limit our experiment to 1000 random samples, and we use the prompt suggested by Chhabra et al. (2024) and reported in Appendíx D Again, we aim to verify whether the summaries generated with DiffSampling are both diverse and of high quality. For diversity, we consider the per-input EAD and SBERT metrics, computed over five outputs sampled from the same prompt (Kirk el al.] 2024), along with the against-greedy EAD and SBERT diversity scores introduced above. For quality assessment, we use ROUGE-1 (R-1) (Lin 2004], a standard metric for summarization that evaluates the ratio of I-grams present in both the target and generated summaries, as well as the sentence embedding cosine similarity (SIM) between the generated and target summaries. In this way, compute both syntactic and semantic quality metrics, as good summary might use entirely different words while still preserving the original meaning, In addition, following Sirtingguueee et al. 22022) compute the coherence (COH) between the generated outpul and the text to summarize through the cosine similarity between their SimCSE embeddings (aoo et al. 2021
Model:
RLHF instructed
Pre trained
Method
Quality
Per-Input
Against- Grondy
Quality
Per- Per-Inpus
AgninsttCreedy
R-1
SIM
COH
RAD SHRRT
EAD
SHERT
R-1
SIM
CDH
RAD
SHERT
RAD
SHERT
Gready
0:232.00
0.49g.01
0.66
0.18g.00
0.22g o0
0.51
0.74g
0:19
Tog-g
0.21
0.45g..1
0.30
0.362.00
0.47
0.66-2..
0.41
0.16g oc
0.34
0.48
0.72
0.662..0
0.77g.01
0.55g..0
pssmppling
0:20
0.45g.01
0.
0.38_
0.49
0.69
0.40 m
0.16g
0.34g
0.48
0.75g.1
0.67=00
0.80
0.56g
Locally typical
0:21g.00
0.45
g.
0.36 m
0.47g.m
m
0.66
0.
0.161 ne
0.341
0.481
0.72g
0.662.0
0.77g.0)
0.55...0
Min-p
0.222.00
0.46g.m1
g.61
0.36
0.43
0.64g
0.20g 0.38
0.44.
0.63
0.65
0.47
0.62
0.30g.m
Dut
0.48
0.63__o1
0.35 m
0.25_ m
0.45 m
0.23g m
0.21 nc
0.49
0.73 05
0.38 g.
0.19 20
0.32 ml
0.17
-il
0:21
0.45g.m
0.57 0.39
0.47
0.67
0.
0.16
0.34
0.48
0.72g.01
0.66
0.77..01
0.55g.m
minp
0.22
20
0.46g
0,00
0.35g
0.43
m.
0.38 oz
0.20 os
0.44g
0.62+
0.65
0.47
0.63
0.300
Table 3: Aggregate results over 5 outputs sampled for each of the 1000 prompts from the XSum dataset. for
the instructed model (Ieft) and the pro-trained model (right). The mean and 95% confidence interval are reported for all the metrics.
Experimental Results. With respect to the instructed model, as reported in Table 3 (left), all methods achieve similar quality scores, with the greedy strategy and Dif[Sampling-cul performing slightly better, followed closely by min-p and its relaxed variant, DiffSampling yield comparable scores, with the notable exception of --sampling, which achieves the highest against-groody diversity but the lowest similarity and coherence scores, thus confirming the well-known trade-off (Tppolito et al. 2019)
The remaining sampling methods
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On the other hand, shown in Table (right), the quality metrics exhibit greater variation for the non- instructed model: Dij[Sampling-cul out perforrsms all other sampling methods and performs par with the greedy strategy. While it does not reach the same diversity scores as the other sampling methods, it provides consistent deviations from groedy. Just below, DiffSamppiig--enn minp and min-p obtaín very similar scores across all metrics, while outperforming the other methods terms of accuracy as they deviate less from greody decoding. Finally, as expected, DiffSampling-li closely aligns with top-p, with negligible differences in diversity.
5.4 Divergent Association Task
Experimental Setup. The third considers the divergent association task (DAT) (Chen & Ding, 2023). Building the theory that creativity is related to the capability of generating more divergent ideas Beaty et al. 2014), it requires participants to name unrelated words. In particular, the task is the following:
Write 10 nouns in English that are irrelevant from each other possible, in all meanings and uses of the words. Please note that the words you write should have only single word, only nouns (e.g., things, objects, concepts), and no proper nouns (c.g., no specific people or places).
Then, their semantic distance can represent an objective measure of divergent thinking (Olson et al. 2021 DAT is a useful case study for docoding strategics as constrains the generation to different nouns (thus, assuming an optimal probability distribution, the tail due to smoothing should contain everything else) and requires generating terms that are as different as possible, which quite the opposite what typically happens in language modcling: optimal strategy should exclude non-appropriate tokens but also not limit too much the space of possible tokens. We strictly follow the setup proposed by Chen & Ding 2023 More concretely, given the embeddings of n words, the DAT score is the average cosine distance between each pair of embeddings (then scaled as a percentage). We use GloVe embeddings (Pennington et al. 2014 and ask the model to generate a list of 10 nouns. We discard outputs without at least 7 distinct nouns and compute the DAT score for all other outputs over their first 7 nouns. For completeness, Appendix G. reports results obtained when considering all 10 nouns. We repeat the experiment 100 times for non-greody strategies mitigate the sampling stochasticity.
90
92
80
90
DAT Score
88
70
60
50
40
Valid outputs
100
100
0
0
Top-p
n-sampling
Locally typical
Min-p
DiffS.-cut
DiffS.-Ib
DiffS.-minp
Figure DAT scores for our methods and the basclines over the instructed (left) and pre- trained (right) model. Below, the number of valid outputs produced by each sampling strategy. The dashed line reports the greedy score.

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Published in Transactions on Machine Learning Research (12/2025)
Experimental Results. Figure 2 summarizes the DAT results, reporting both diversity (DAT score) and quality (count of valid outputs) measures. For Betta--laaaa--B--Inntre
the greedy strategy produces a strong set of nouns, achieving a DAT score higher than the average across all sampling methods. However, DiffSampling-cuu generates a better set in almost half of the generations, and always produces a valid set of nouns. Instead, the other sampling schemes can produce better scores only occasionally, while sometimes failing at providing a valid set of nouns, and both DiffSamplingIl) and PiffSamplinggmiing perform slightly better or almost identically to the top-p and min-p, respectively. The results for the pre-trained version Meta-Llama-3-88 are quite different, and the quality-diversity trade-off is more pronounced. DiffSampling cut is substantially better than the greedy strategy, and it produces only valid outputs. However, all other methods achieve higher DAT scores while producing significantly fewer valid outputs. Although very similar, both DiffSampling-ming and DiffSampling-li outperform their min-p and lop-p counterparts, yielding either slightly higher scores or a greater number of valid outputs.
5.5 WritingPrompts
Experimental Setup. The previous case studies focus on the generation of short or very short outputs. However, certain issues emerge only in longer-form tasks for example, the tendency of greedy decoding to repeat tokens, thereby degrading text quality (Fu et al., 2021). To address this limitation, the final case study involves gencrating storics of up to 1024 tokens using inputs from the WritingPrompts dataset (Fan eet al. 2018), which comprises a large collection of prompts sourced from Reddit's WritingPrompls forum. In particular, we sample 500 test prompts among those labeled as standard prompts (i.e., that start with [WP]), ) and we generate 5 outputs for each sampling scheme. Then, we evaluate their quality through their coherence (COH) with the prompt the cosine similarity between their SimCSE embeddings (Gao et al., 2021]; instead, diversity is computed through the per-input EAD and SBERT metrics, i.e., calculated among the outputs sampled given the same prompt (Kirk et al. 2024).
Model:
insttuentte
Pre-trained
Method
Quality
Per- Per-Input Diversity
Quality
Per-Input Diversity
COH
EAD
SBERT
COH
EAD
SBERT
Greedy
0.44..01
0.17
0.59 m
0.07
Top-p
0.42
0.73
0.25
0.42
0.64=.00
0.58
y-sampling
0.42
0.801.00
0.281.00
0.40
0.77
0.601.00
Locally typical
0.422
0.73..00
0.25.
0. 0.
0.642.00
0.582.00
Min-p
0.43
0.71
0.23
0.51 0.01
0.35
0.462.00
Dut
0.431.01
0.634.00
0. 0.191.00
0.60
0.15..00
0.31
DiffS.-Ib
0. 0.42
0.73+.00
0.25
0.41
0.67
0.58g.00
DiflS--miup
0.43
0.71
0.23
0.51
0.36
0.47
Table 4: Aggregate results for the WritingPrompte dataset for the instructed model (left) and the pre-trained model (right). The mean and the 95% confidence interval for the full set of answers are reported for all the metrics.
Experimental Results. Table reports the results for both instructed (left) and pre-trained (right) models. For the former, coherence remains largely consistent across all methods, while diversity metrics vary depending on the greediness of the approach: DiffSampllig--ot produces outputs that are significantly different from each other, though still less diverse than those generated by the other sampling-basee based baselines, among which 7-sampling achieves the best performance. In contrast, coherence varies more noticcably for the pre-trained model, where DifsSampling-euu achieves the highest score alongside the greedy strategy, but with substantial improvements in suggest tends to repeat the same tokens indefinitely. Instcad, DiffSampling--iing and DiffSampling-Ii match the coherence levels of min-p and top-p, respectively, while offering notable gains in EAD diversity for the non-instructed model, likely due to certain tokens being correctly preserved from truncation.
by near-zero scores for the greedy strategy, which
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GSMBK
XSUM (instructed)
DAT (instructed)
WP (instructed)
75
0.8
100
0.50
Accuracy
Coherance
Coherence
50-
Validity
25
0-
0.0
MATH
XSUM (pretrained)
DAT (pretrained)
WP (pretrained)
Accuracy
Coherence
Coherence
166
Valld
0.50
0.4
0-
0.0
0.00
0.6
1.0
1.5
2.0
10.
0.6
1.0
1.5
2.0
10.
0.6
1.0
1.5
2.0
10.
0.6
1.0
1.5
2.0
10.
Temperature
Temperature
Temperature
Temperature
Top-p Min-p
Diffs.-cut (Tt before)
DiffS minp (T before) DiffS -cut (T after)
DiffS.-lb (T after) Diffs.-minp (T after)
Diffs.-Ib (T before)
Figure 3: Average quality scores across different temperature values for top-p, min-p, and our methods when applying temperature before (dashed line) and after (full line) the truncation.
5.6 Temperature Scaling
Finally, experiment with different temperature values T, i.e. 0.6, 1, 1.5, 2, and 10. As detailed above, to preserve the mathematical guarantecs of our approach, we apply temperature after the DiffSampling truncation, while our baselines apply this before. Due to the different. nature of temperature scaling, this comparison is intended only to highlight the impact of temperature position, rather than to imply that our method is superior to the baseline. To allow for a fairer analysis, we also report quality scores for DiffSampling when applying temperature before truncation (see Appendix F.5 full comparison between temperature before and after truncation). As shown by Figure 3 DiffSampling teepompplling--ttemmtaaaaaa temperature preserves the output quality, and relevant differences only occur with our two relaxations and pre-trained models. Instead, the output quality rapidly drops with higher lemperatures for the min-p (by far the best of our baselines at T 1) and top-p baselines. In particular, the non-significant loss in quality for DiffSampling-coo confirms that our truncation strategy only preserves correct tokons. At the same time, temperature scaling has an (overall positive) impact on diversity; we refer to Appendix for a detailed analysis of how all our quality and diversity metrics change different T.
6 Discussion
Overall, DiffSampling-cru has demonstrated performance better than or equal the greedy strategy. Ad- ditionally, it offers the potential for greater diversity. By introducing lower bound the preserved total probability an upper bound the probability of truncated ones, the method can further relax selection constraints, enabling greater output diversity at the expense of a marginal reduction in prediction accuracy. Once truncation is applied, sampling at higher temperatures becomes viable, promoting greater variability without significantly compromising output quality.
However, selecting the most appropriate method and hyperparameters is not straightforward and requires a case-by-case analysis. If small validation set is available, the choice of which strategy and parameters can be made empirically. Otherwise, our experiments show that DiffSampling-ctt works best when the task requires precision: whenever user might otherwise rely enhances diversity without compromising accuracy. DiffSampling--i fosters output diversity by trading off some accuracy, especially at higher values of pts and, thus, appears most appropriate for divergent solutions. DiffSompling-miin more well-balanced. Both can be used place of top-p and min-p to "correct" them and potentially improve their diversity with no additional overhead. Increasing the temperature has proven highly effective for fine-tuned models across all methods, whenever it not strictly necessary to preserve the original distribution.
greedy decoding strategy very low temperature, it
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Our experiments were limited to relatively small LLMs, although preliminary results suggest that the same findings hold for larger models as well (see Appendix F. for a more detailed analysis), and based on quan- titative, automatic evaluation. Several of the adopted metrics exhibit significant limitations (e.g., [chluter 2017), often failing to align with human judgments (Tevet & Berant, 2021). Morcover, abstract concepts such as originality and creativity remain inherently difficult to deline with precision (Franceschelli & Mu- solesi p025p. We plan to experiment with human evaluators to verify whether the quality and diversity that DiffSampling aims to provide are also perceived by potential users.
7 Conclusion
In this paper, we have presented DiffSampling, a novel family of decoding strategies based on the analysis of the next-token distribution. In particular, given the distribution sorted in descending order, we compute the forward difference approximation of its discrete derivative and use it to remove tokens after its minimum value (possibly together with relaxations to allow for more diversity). In this way, we avoid incorrect tokens under the learned distribution. We have experimented with four different tasks, and our method has consistently performed at least well similar strategies in terms of accuracy, despite sampling from a larger set of tokens, which has positive impact diversity.
Our rescarch agenda includes investigating whether combining DiffSampling with complementary techniques, such as re-ranking or controllable generation, can lead to further improvements in output quality. We also plan to leverage additional properties of the underlying probability distribution (e.g., its entropy (Potraghloo et al. 2025)), ), beyond token likelihoods, to guide generation toward desired characteristics such as coherence, novelty, or uper-specific preferences. These directions open up promising opportunities for enhancing the adaptability of text generation systems in general-purpose and task-specific settings.
Broader Impact Statement
While our decoding scheme should, in theory, not increase the risk of generating tokens outside the true support, it may still produce unsafe content in certain contexts if the learned distribution itself is unsafe (e.g., containing learned biascs, inappropriate language, or mislcading information). Thus, it is important to continue using safely filters and domain constraints. Finally, we also perform a small check to ensure that DiffSampling does not increase unsafe content rates in the WritingPrompts use case, as it is the most open-ended generation task. Using Llama-Guard-3-9B (Inan et al. 2023), we found that the probability of unsafe outputs generated by our methods is identical to that of the corresponding methods at a temperature of 1.0 or lower. However, the application of temperature after the truncation dramatically reduces the rate of unsafe generated text, especially for DiffSampling-cot cut and DiffSampling-minpp We report our results in
Table 5
Method
Pre- Trained
Instructed
7 2.0
10.
2.0
10.
Baselines
Greedy
0.124.02
0.04
Top-p
0.12
0.09
0.62
0.70
0.69
0.04
0.05
0.57
0.60
0.71
p-sampling
0.11g
0.11
0.72
0.70
0.68 0.68
0.04
0.11g.m
0.62
0.69
0.69
Locally typical
0.12
0.09
0.66
0.60
0.68
0.04
0.05
0.58
0.69
0.70
Min-p
0.11
0.10
0.00
0.19
0.68
0.05
0.04
0.04
0.30
0.69
Ours (r before)
DLffS-cuu
0.13
0.12
0.12
0.12
0.58
0.04 on
0.04
0.0d
0.04.
0.47
DuISS-II
0.12
0.10
0.71
0.70
0.
0.04 on
0.05
0.64
0.69
0.69
mins
0.11
0.10
0.09
0.22
0.
0.04
0.04
0.05
0.30
0.69
Ouzs (r after)
DifSS-mm
0.12
0. 0.12
0.124.01
0.122.01
0.12
0.04
0.04
0.04g.01
0.04
0.054.m1
DitfS-Ib
0.11
0.10
0.44g.01
0.52
0.51
0.04
0.05
0.32
0.37
0.40
minp
0.11
0.10
0.09+
0.09
0.08
0.04 m
0.04+
0.04 oz
0.05
0.04
Table 5: Unsafe probability of Writing outputs for baselines and our methods at different tempera- tures according to are reported.
The mean and the 95% confidence interval for the full set of answers
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A Formal Analysis
In the following, we aim to formally define the conditions under which our truncation strategy is safe, i.e., the conditions under which all tokens up to arg min Ap(a!")) have positive probability under the true distribution.
According to Hewitt et al. 2022 we can define the true probability distribution as Pa((pee))
[1 :.... Px
[iAl|| with E. pt
1 and p-
p+
[++1] v i [1,11 1), and where exists a D < [V] such
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[ 0 D (with D |/ any truncation strategy is safe). Let define a smoothing distribution that pt Q(+(Z=))) (g .( . with q0) (tv MV Vi
ViE [1, and d constant between 0 and 1. Then, the learned distribution Po(-Irei)= = fpll,... .......llil) p with Σ pll = and p 2 p 2 Vie [1,]V] 1] can be defined the weighted sum between the true probability distribution and the smoothing distribution:
Po(-Iree)) = Xe, P. + (1 Ae:) Q(:))((()re)))
(2)
where Aci E (0, However, according to Hewitt et al. (002)) we can assume that dei 2 max (Tei X), Hes with He: entropy of P. (-(() and X constant close 1; for simplicity, we will follow Hewitt et al. (2022) and assume to have X 0.8. This has two implications. First, the contribution provided by the smoothing distribution is bounded by a exp- with E [0, 1] and generally very small, so the actual contribution depends on the entropy of the true distribution. Second, the weighting factor Aei has a lower bound equal to π 0.8.
where Tes M]a exp
1+8
In this article, we propose to truncate the learned probability distribution at an index K such that K arg min, (plitt) - p = arg max, (pli) plé+1l). The truncation is safe when K s D, i.,, if the truncation only preserves tokens with non-zero probability under the true distribution. Proposition 1. Given a learned probability distribution Po(-(xz2)) = "p"",....pplVi!! sorted in descending order, the truncation performed by means of arg max, (pl)) -plitll only preserves tokens from the support of the true distribulion Pa(-(xes)) is max:(pp) ps plittl) [V.
Proof. The truncation is safe whenever K D, i.e, whenever the maximum difference between a token from the true support and its next token is greater than the maximum difference between tokens from outside the true support. The maximun difference between tokens from outside the true support, iee, with [sl
p. p. [s+1] 0, is:
max -pbttll max((1 12D
Acr) (1 (xt)g
(3)
1 5
1- ) = (1 -dci)
28
-1 (1- -edee
-11-)c)) M
M
[V]
Instead, the maximum difference between a token from the true support and its next token given by:
max(p [1] D
-1 = max 15D
( (8] + (1 dee) Aciph 1esppt+1 - (1 -xxi)g
[1+1]
(4)
(i] -p :1ll + )e))( 1 (((11))).
iSD
This value is lower-bounded by maxx)DD(A<((2
[1l
pl
g dev max
pl pli+!l) + (1 - Acs) min - g [++ll). The second term is exactly the opposite of the maximum value
computed above: min;(g - g |+ = ao
14d
26
we define A = max - pz |+ we obtain
lower-bouded maximum given by A (1 dex)
28 M
To have K < D, we impose:
>ciA!1
28 )xo) D
> (1 - Xxx)
28
48
\ > (1 - >xe))
(5)
A
48 (1 \e1)
dei
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Since Agi is lower-bounded by X, the second term can be reduced to (1=A2, As suggested by Hewitt et al. 2022), we assumed X = 0.8; we obtain that our truncation strategy is safe if A. >
M4. Since 8 is M
46 1
upper-boundee to 1, we get lower bound of A > प that proves our proposition.
Proposition Given a learned probability distribution Po(-(xr2)) = (p")..... ..l.il...llll sorted in descending
order, the truncalion performed by means of arg max, (p 4 - plitil) preserves lokens only from the support with size D of the true distribution P. (-(x)e)) if D < 22VV.
2 (++1) is lower-bounded by D(D+1)) This bound holds when the Proof. The maximum difference (p. P+
differences between the first D+1 tokens (with the first D tokens having a positive probability and the D+L 1- th zero probability) are equal, i.c., when the first D + 1 tokens equidistant. According to Proposition
arg max;(pl)) -p -littl) v D if max; - !)+ > ক.. Thus, this is also true when DID+TJ > M ie.,
if D(D + 1) < 2/11, providing an upper bound for the true support size D of ze /2[V1, which proves our proposition.
In summary, our truncation strategy is safe whenever we have max(p! p. p To provide practical intuition of the meaning of these conditions, consider the case of an LLM, whose vocabulary size [V] is usually in the order of 50000. This sets the lower bound for the maximum difference at 0.00002 and the upper bound for the true support size at 316. If either of these conditions is satisfied, our truncation strategy is considered safe.
M. or D < V2M.
However, it is important to note that these two bounds represent only worst-case scenarios. First of all, we assumed that can be equal to 1 and dev = 0.8. In practice, 8 will be much smaller than 1, leading a proportionally smaller lower bound for max p ) Moreover, Aci will also assume the value of X which is likely to be higher than X when Hes is higher, i.c., for very homogencous distributions (unbalancod distributions most likely have max(p!) pl. + ) These two elements would make realistic bound
for max; (pl -p(t1) much looser. addition, the proof of Proposition 2 considers an extremoly conservative (and impossible to find in practice) lower bound for max - p FTl). Indeed, if all probabilities are equidistant, max pi+llly is not lower-bounded by Aei DD= (1 >xs) 26 but by Àçi D(D+1)- [o
While the latter does not provide valid lower bound for max4 <okk<<<ppll (pli) - -li+tl), the fact that the used lower bound cannot actually be attained, combined with the considcrations regarding 8 and des discussed above, makes the upper bound for D much looser in practice.
B Computational Infrastructure and Implementation Details
All experiments were carried out on a Linux-based local server equipped with 2 S0GB NVIDIA H100 GPUs running Python 3.11.9. All the trainings were repeated, varying the random seed among 1, 42, and 121 (sct through the set_seet mothod from the HuggingFace transformers library). The hyperparameters governing the sampling strategies adopted as baselines were selected according to the best results reported by their original paper for similar tasks and model sizes.
C Evaluation Metrics
In this section, we formally define the quantitative metrics used in our experiments.
Cross-Input Diversity: The diversity of outputs across inputs, i.e., the diversity of T (y): D(U π ())),;)), with D diversity metric (Kirk et al. 2024). In the case of cross-input EAD diversity, this is practically done by computing the EAD score for the entire set of outputs at the same time (i.c., the expected average distinct N-grams among all the sequences) for N E [1,5] 5] and returning their average. We refer to the original paper by Liu al. (2022) for the exact computation of EAD. On the contrary, in the case of cross-input. SBERT diversity, this is practically implemented
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by first encoding all outputs into latent vectors through given text encoder, then computing all the possible pair-wise cosine similarity between different vectors, and finally returning 1 minus the average cosine similarity.
Against-Greedy Diversity: The diversity between a given output sampled from π (2;) and the greedy output " D(yi, v!""). The against-greddy SBERT diversity requires computing the latent vectors of both outputs and returning 1 minus their cosine similarity. In the case of against-greed EAD diversity, however, we replace the classic ratio of distinct N-gram computation with the ratio of new, distinct N-gram from Y with respect to y," and then compute EAD for N E [1,5] starting from
Per-Input Diversity: The diversity of the output set over a specific input, ie., the diversity of Tylaa): D(( ..........0 ...M.......)))) (),,a)))
~ *(|[x;) (Kirk al., 2024). In the case of per-input EAD diversity, this is implemented by computing the EAD score for the set of outputs from the same input (i.e., the expected average distinct N-grams among all the sequences) for N E [1,5] and returning their average. In the case of the per-input SBERT diversity, this is obtained by first encoding the outputs into latent vectors through a given text encoder, then computing all the possible pair-wise cosine similarity between different vectors, and finally returning minus the average cosine similarity.
The percentage of correctly solved problems, i.c., given the count of solved problems Ccorrect and the count of total problems Crotel, accuracy is defined as 100 Cepcreat
Accuracy:
Clotas
Rouge-1 (R1): The ratio of 1-grams present in both the target of and the generated output yi [Lin 2004).
Sentence Embodding Cosine Similarity (SIM): The cosine similarity between the latent vector Vy, and the latent vector dy;; where yi is the target output and yi is the generated output. The latent vectors are obtained from pre-trained text encoder.
Coherence (COH):
The cosine similarity between the latent vector Us and the latent vector ug. where 8; represents target text (c.g., text to summarize) or the input passed to the model, and is the output from the model (e.g., the contimuation of 8; or its summary). The latent vectors are obtained from the SimCSE embedder (Gao et al. 2021).
The average cosine distance (i.e., 1 minus cosine similarity) multiplied by 100 between each pair of word emboddings from a given list of n distinct nouns. The word embeddings are obtained from GloVe (Pennington al. (004).. can be either or 10. If there not enough distinct nouns, the score is not computed at all.
DAT Score:
DAT Valid Outputs: The percentage of experiments in which the count of generated, distinct nouns is greater than or equal to n, i.e., the percentage of experiments where it is possible to compute the DAT score.
D Prompts
For the mathematical problem-solving tasks, we adopted the same prompt from Yu ct al. 2004 i..::
Below is an instruction that describes task. Write response that appropriately completes the request.
# ## Iuctron:
(question)
### # Response: Let's think step by step.
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For the extreme summarization task, the prompt adopted for Llama-3.2 1et.22---Inntttun Instruct is the same in Chhabra et al. (2024)
user
For the following article: (article]
Return summary comprising of sentence. Write the sentence in numbered list format. For example:
1. First sentence assistant
where user and assistant are special tokens used by the model to identify different roles the chat. Vice versa, for the non-instructed version, we used:
Generate 1 sentence summary for the given article.
Article: farticle)
Summary:
For the divergent association task, considered the following prompt for Keta-Llama-3-88 Instructs
user
Please write 10 nouns in English that are as irrelevant from each other as possible, in all meanings and uses the words. Please note that the words you write should have only single word, only nouns (e.g., things, objects, concepts), and no proper nouns (e.g., no specific people or places). assistant
Here the 10 nouns in English that as irrelevant from each other possible:
where user and assistant are keywords used by the model to identify different roles in the chat, while for Meta-Llama-3-88 we used the following:
Write 10 nouns in English that are irrelevant from each other possible, in all meanings and uses of the words. Please note that the words write should have only single word, only nouns (e.g., things, objects, concepts), and no proper nouns (e.g., no specific people or places).
Solution:
Here are the 10 nouns English that are as irrelevant from each other as possible:
Finally, for story generation, we used the same prompt adopted by Chung et al. 2025 in the case of -lama-3.2-3B-Ime Insttucc:
system
You write creative writing based on the user- eser-given writing prompt. user
[prompt}
assistant
where system, user, and assistant are keywords used by the model identify different roles in the chat.. Instead, for Llama-3. 2-3B used the following:
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Write a creative story based on the user-given prompt. Prompt: {prompt)
Story:
E
Scaling Model Size
Our main experiments focus only on models of limited size (i.e., 3B, 7B, and 8B models). To demonstrate that our sampling methods scale up with model size, we also conduct some preliminary tests with a larger model, i.e., with Meta-LJama-3-7088 (quantized to 4-bit precision), considering both its pre-trained and its instructed versions. In particular, we repeat all the experiments conducted in Section 5 at fixed temperature r 1.0.
Tables G and 7 report the results for the math problem-solving case study. As for the smaller model, DiffSampling-cuu performs on par or better than greedy in terms of accuracy, while achieving a higher diversity than groedy but lower than the other sampling methods. DiffSampling-Ii achieves slightly worse accuracy than top-p, but with increases in cross-input EAD. Finally, there between DifsSampling-miig and min-p apart from cross-input EAD, thus confirming that our relaxation allows for a little more diversity with no cost in terms of quality.
substantial differences
Dataset:
RLHF inntructet
Pre-trained
Method
Accuracy
Cross-Ingg Input
Against-Greedy
Accuracy
Cross-Input
Against- Greend
EAD
SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
Greedy
57 37.622.00
0.75_.00
0.65
10. 10.16..
0.97
0.56
Top-p
$3.855.20
0.88
0.65
0.56g.no .n
0.11
7. 7.83
2.00
0.50
0.63 000
0.31
y-sampling
48.37
0.92_.00
0.65
0.60
0.12
4.88 4.88_.11
2.22
0.60 .0
0.70
0.33
Locally typical
53.68
0.88 0.88_.00
0.65
0.56
0.11
7.43__.
2.00
0.59
0.63
0.32
Min-p
36.20=.ss
0.85_
0.65
0.54
0.10=.c0
9. 9.12__s
1.52+
0.56
0.51
0.28
DiffS.-cut
59 19.299..6
0.77=000
0.65
0.39
0.08
12.69
0.97
0.57
0.26
0.18;
DiftS.-lb
62.14
0.89
0.65
0.56
0.11
7.25
2.03
0.59
0.644..0
0.32
DiffS-mmin
56.00
0.85_.0 .0
0.65
0.54 no
0.10
9.93
1.564.01
0.56
0.51
0.28
Table 6: Accuracy and diversity of results for the GSM8K test set over 3 seeds for the instructed (left) and pre-trained (right) Meta-Llama-3-70p model. The mean and standard error of the final score for each run are reported for accuracy and cross-input diversity, whereas the mcan and the 95% confidence interval for the full set of answers are reported for against-greedy diversily.
Model:
Hinstrinst
Pre-trained
Method
Accuracy
Cross- Input
Against-Greedy
Accuracy
Cross- Cross-Input
Against-Greedy
EAD
SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
Greedy
22.56=.00
2.01=.00
0.80+.00
6. 6.70
2,18
0.78
Top-P
20.39 1.15
2.56_.01
0.791..0
0.55 no
0.171.00
4.04 15
5.12
0.79...0
1.57
0.34
y-sampling
19.02 13
2.
0.794.00
0.58 no
0.18
3.09
6.06
0.79
0.644.00 1.0
1.37..00
Locally typical
20.19
2.56
0.794..0
0.55
0.17
4. 4.122.18
5.154.02
0.79
0.57
0.34..o0
Min-p
20.58 04
2.41=.00
0.79
0.53 00
0.17
5. 5.46
3.73
0.78
0.45
0.30 o0
DiffS.-cut
21.27
2.08 2.08_.00
0.80
0.40
0.14g.00
7.50
2.29
0.78
0.251.00
0.22
DiffS.-Ib
19.79
2.58_.01
0.79
0.55 no
0.18
4. 4.15_.08
5.22+.00
0.79
0.57
0.34
DiftS DiffS-minp
20.75
2. 2.45=.00
0.79++.00
0.53 n0
0.17=.00
5.26
3.82+
0.78+.00
0.45+..0
0.30
Table 7: Accuracy and diversity of results for the MATH test set over seeds for the instructed (left) and
pro-trained (right) Keta-Llama-3-709 model. The mean and standard error of the final score for each run are reported for accuracy and cross-input diversity, whereas the mean and the 95% confidence interval for the full set of answers are reported for against-greedy diversity.
The findings from the XSum case study are similar. As reported in Table g DifsSampling-cud behaves on par with greedy in terms of quality, but increases scores in terms of per-input diversity. Instead, our two relaxations do not substantially differ from their corresponding basclines top-p and min-p. However, is remarkable that, contrary to what we found for smaller models, greediness does not provide qualitative advantages for the instructed version of Meta-Llama-3-700
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Model:
BLHF instructed
Pre tranned
Mothod
Quality
Per-Iopot
Agonnst-Grondy
Quality
Per-Ingus
Ageeinat-Creddy
R-1
SIM
COH
EAIE
SHERT
EAD
SHERT
R-1
SIM
CDH
RAD
SHERT
EAD
SHKRI
Greedy
0.29
0.63g.40
0.75
g.20
0.24g.00
0.
0.70g.00
0.20g.20
Top-p
0.29
0.62e..0
0.75
0.50=.00
0.10=.00
0.44g.m
0.062.00
0.222
0.48
0.63
0.72s.01
0:49=.co
0.71=.01
0.41s.01
#ssuppling
0:29
0.622.00
0.75
0.55g.00
0.11=.00
0.
0.09 o0
0.21 0
0.47..01
0.61
0.76g.01
0.52=.00
0.75g.01
0.502.01
Locally typical
2:20
0.622.00
u.75
0.50
0.10=.00
0.44
0.222 0.08
0.48
0.65+
0.72e.01
0:40=.c0
0.71=.01
0.422.01
Min-p
2.29
0.02
0.70
0.50
0:10=.00
0.44
0.08 o
0.23 00
0.50
0.67
0.65
0:422.00
0.60g.01
0.352.01
Dut
2.29
6.
0.75
0.33_
0.05_.m r
0.25g
0.06 o
0.24 o0
0.50
0.70 09
0
0.18_00
0,32
0.16
DifiS.-hh
1.29 1.00
4.63
1.70
0.51 a.
0.10
0.45 ot
0.08 mm
0.221 oc
1.48
0.63
0.73
0.50
0.72
1.42
DifSs.
2.29
0.63
g.75
0.50
0.10
0.44;
0.06
0.23
0.50
0.66
0.65
0.42-
0.60
0.35
Table 8: Aggregate results over outputs sampled for each of the 1000 prompts from the XSum dataset for the instructed (left) and the pre-trained (right) Meta-Llama-3-70B model. The mean and 95% confidence interval are reported for all the metrics.
The results are similar for the WritingPPrompts dataset. As shown in Table g the greedy strategy is not optimal for the instructed model; this impacts not only DiffSampling-cuk but also min-p and DiifSampling- minp. However, the other considerations still hold: DiffSampling-cul produces more diverse oulputs than the greedy strategy, while the two relaxations perform on par with their corresponding baselines. While greediness appears to guarantee higher quality for the pre-trained model, it should be noted that the per-input EAD becomes extremely low. This is due to extensive repetitions within the same output (but not shared across outputs, which causes the SBERT metric to increase) and may indicate that more greedy strategies perform worse with larger models, which may have learned more unbalanced probability distributions. In such scenarios, looser sampling strategics, such as 1-sampling DiffSampling-ty are likely to be better choices.
Model:
Pre-trained Per-Input Diversity
Method
Quality
Per-Input
Diversity
Quality
COH
EAD
SBERT
COH
EAD
SBERT
Greedy
0.27
0.06g.00
0.42
0.01
Top-p
0.29
0.53
0.58
0.26
0.18
0.72..00
g-sampling
0.299..1
0.58 00
0.57:.01
0.26
0.35
0.71
Locally typical
0.29
0.59
0.461.01
0.26
0.18g.00
0.722.00
Min-p
0.27
0.45g.01
0.55g.m1
0.34
0.03..00
0.60g.00
-itfS.-cut
0.27
0.231.01
0.241.01
0.41
0.01 1.00
0.32
DiffS.-Ib
0.291.01
1.53
0.57
0.25
0,191.01
0.72
DifTS,
0.27
0.44+.01
0.55+.m
0.34+.01
0.034.00
0.60+..0
Table 9: Aggregate results for the WritingPrompte dataset for the instructed (Ieft) and the pre-trained (right) Meta-Lie -at--a-ammm--000 model. The mean and the 95% confidence interval for the full set of answers are reported for all the metrics.
This consideration finds confirmation from the experiments on the divergent association task. As shown in Fig. 4 DiffSampling-crt always produces the greedy solution for the instructed model, while showing a little more variation for the pre-trained model. Again, both min-p and DiffSampling-ming are influenced by the poor performances of greedy for the pre-trained model, resulting in lower DAT score but higher valid output ratio compared with the other sampling strategies. On the contrary, top-p sampling, locally typical sampling, and DiffSampling-li seem to better trade off quality and diversity, having comparably high valid output ratio for the instructed model and especially a substantially higher DAT score for the pre-trained model.
In summary, our preliminary experiments on a larger model confirm the positive relation between our three methods and the corresponding basclines, while also demonstrating that models with different sizes may necessitate different degrees of greediness and thus suggesting a looser sampling strategy (e.g., DiffSampling- 1b) when dealing with sufficiently large language models.
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94
90
DAT Score
84
82
80
Valid outputs
100
100
50
50
0
Top-p
n-sampling
Locally typical
Min-p
Diffs.-cut
DiffS. -lb
Diffs.-minp
Figure 4: DAT scores for our methods and the baselines over the instructed (left) and pre-trained (right) Heta--Llma---- model. Below, the number of valid outputs produced by each sampling strategy. The dashed line reports the groedy scorc.
F Experiments on Temperature Scaling
In addition investigating performance temperature of T 1.0, we conduct experiments at lower temperature (0.6) and three higher temperatures (1.5, 2.0, and 10.0) to verify whether truncation strategy preserves only appropriate tokens, i.e., whether the quality of generated outputs remains competitive and diversity improves across different temperatures. Overall, we found that DiffSampling-cuu maintains the same level of quality even at very high temperature, and, thus, can be safely used even with > 1.0. On the other hand, DiffSampling-li tends to produce lower-quality outputs at higher temperaturcs. This effect particularly pronounced for non-instructed models, where performance for 1.0 decreases rapidly. However, fine-tuned models maintain competitive quality scores at higher temperatures while increasing diversity; the choice of t is matter of trading off quality and diversity. When accuracy not sine qua requirement, suggest adopting 2 2.0. Finally, DiffSampping-nin trend as Dif[Sampling-lt for pre-trained models, although the effect is less pronounced. For tuned models. however, it shows virtually no performance degradation at higher temperatures, enabling the use of larger values of F in most scenarios.
exhibits the same general
F.1 Math Problem Solving
Table 10 reports all the results with different temperatures for the GSMSK (left side) and MATH (right side) test sets. For the former, a lower temperature makes all the models (including the baselines) more line with the groody strategy, thus diminishing the diversity scores while usually increasing the accuracy. On the contrary, all the baselines lend to perform poorer at increasing temperatures in terms of output correctness, while diversity improves accordingly (especially for crntacticbbased metric such EAD; the qualitative examples reported below demonstrate why). Instead, our methods maintain the highest possible accuracy, with a slight improvement in diversity at higher T.
For the latter, a lower temperature makes all the baselines closer to our methods in terms accuracy, while diminishing their diversity scores. At incrcasing temperature, the baselines rapidly start failing to solve the problems, possibly due to more random selection of tokens that also causes syntactic diversity increase. By applying temperature after the truncation, our methods preserve their output quality regardless of the
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Dataset:
GSMSK
MATH
Method
Accuracy
Croes Input
Against-Grevdy
Accuracy
Cross Input
Against-Green SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
Temperatare = 0.0
Greedy
66.46
44.444.00
2.03
0.64
20.62,
5.65
0.80
Tomperature
I.0
Top-p
65.00
2.08
0.64_.00
0.23
0.03
20.02
6.08
0.80
0.36
0.10
p-sampling
65.05
2.12
0.64g.00
0.25
0.04
2.
6.36
0.80
0.39
0.11
Locally typical
66 26.299.55
2.09=
0.64_.00
0.23
0.03 .00
19.95
6.06g..0
0.80
0.36
0.10
Min-p
65.76+44 44
2.09
0.64_.00
0.23.200 .00
0.03 000
20. 20..55=2
6.09
0.80 oo
0.36-g.00
0.10,.00
DiffS.
66.36 23
2.04g.00
0.64_.00 00
0.14 00
0.02 00
38 a.
5.71...01
0.80 oo
0.27.2.00
0.07
DiffS.-Ib
65.18 o.
4.00
0.64_..o .o0
0.23
0.03 ...
20..00..0s
6.11
2.80
0.37
0.10
DiffS -miup
65.48 .0
2.09
0.64 on
0.23
0.03 oo
20. 300.88..05
6.064.00
0.80g.00
0.36+.00
0.10
Temperature 0.6
Top-p
66. 06.34::00
2.05+.00
0.64
0.17
0.02
21.58 2.
5.81
0.80
0.31+
0.09
p-sampling
66. 26
2.07
0.64=
0.19
0.03
20.36 332.111
5.944.00
0.80
0.33
0.09
Locally typical
06.34:
2.05g.0a
0.64
0.172.00
0.02
21.58
5.81
0.80
0.31
0.09
Min-p
06.52
2.06+.01
0.64 .00
0.17
0.02
21.31
5.81
0.80
0.31
0.09
DiffS.-cut
66. 66.74
2.05+.00
0.64
0.13
0.02
21. 1..22
5.72
0.80
0.25
0.07
DiffS -Ib
65. 73
2. 2.00
0.64 no
0. 0.19
0,03
20 65
5,89
0.80
0.32+
0.09
Dit'' -miup
67.05
2. 2.08
0.64
0.19+.00
0,03
20.56
5,88
0.80
0.32+
0.09
Temperature
1.5
Top-p
63.91
2.172.00
0.64_.00 00
0.28.2.0 .00
0.04
18.38 22
6.92+.02
0.80 oo
0.422..00
0.12
p-sampling
60.35
2.28
0.64_.00
0.32 000
0.05 00
15.63
7.774.01
0.80
0.45...0
0.14
Locally typical
64.39
2.17
0.64_.oo .00
0.28=.00
0.04 on
18.73
7.04
0.80
0.42
0.12
Min-p
64.29
2.15
0.64_.oo oo
0.28
0.04 on
18.944.25
6.54
0.80
0.40
0.122.00
DiffS -eut
66.72 s0
2.05#.00
0.64 on
0.15
0.02 on
11.366..15
5.73++.00
0.802.00
0.27=.00
0,07
DiffS.-Ib
65.20 25
2.11
0.64 on
0.255.00
0.04g oo
6,31
0.802.00
0.39
0,11
DitES -miu
65.55
2.11
0.64 oo
0.25
0.04g o0
20.04
6.19
0.80 oo
0.38
0.11
Temperatere
2.0
Top-p
25.40
10.13
0.66
0.70g.o1
0.36
2.49
48.71
0.52
0.92
0.68
1-sampling
35.51+.0
7.35
0.69
0.58
0.22
4.26
43.39
0.64
0.86
0.53
Locally typical
24.61+
10.65
0.65 000
0.71
0.37=
2.46+.08
51.042.07
0.50
0.93
0.69
Min-p
62.19..9
2.24+.0a
0.64
0.32
0.05
26.922
7.21
0.80
0.44+.00
0. 0,13
DiffS.
66. 10.44::1
2.05
0.64
0.15
0.02
21 21.66g
5.71
0,80
0.27
0,08
DiffS.-Ib
63.48
2.122.00
0.64
0.26
0.04
19.17
6.40
0.80 oo
0.40
0.12
DiffS.-ming
63.13
2.12
0.64_..o
0.26 .0
0.04
19.70
6.32
0.80 no
0.39
0.11
Temperature
10.0
Top-p
0.00...o
0.12..00 4.026
on
1.00
0.96 on
0.00
58.65
0.12
1.00
1.00
p-sampling
0.00g..o
17.434.04
0.12=.00 on
1.00g.00
0.96 oo
0.004..0
59.184.02
0.122.00
1.00
1.00
Locally typical
0.00...o
17.522.01
0.11=.0 o0
1.01
0.96 o0
0.004..0
59.692.01
0.11
1.01
1.00
Min-p
0.00...o
17.394.04
0.13 o0
1.00
0.95
0.00
59.162.02
0.13
1.00
1.00
DiffS.-utt
60.31,. 26
2.04
0.64
0.152.00
0.02
21. 21.22
5.74
0.80
0.28
0.08
DiffS.-Ih
64.11 13
2.15
0.64_.00 .00
0.29
0.04 .on
18. 18.20
6.72
0.80
0.42
0.12
DiffS -miup
63.58
2.17+.01
0.64-.00
0.29
0.04
18.64 20
6.54+.01
0.80=.oo
0.41+:00
0.12
Table 10: Accuracy and diversity of results for the GSM8K and MATH test sets over 3 seeds with different temperature values. The mean and standard error of the final score for each run are reported for accuracy and cross-inpul diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for against- greedy diversity.
temperature used, with small but relevant gains in diversity (for example, DifSampling-minng at T = =2. has an accuracy comparable with min-p at 7 = 1.0, but with higher diversity scores).
F.2 Extreme Summarization
Similar considerations can be Iraced for XSun, as reported in Table I1 For both RLHF-instructed and pre-trained models, the quality output produced by the baselines tends to dramatically decrease at higher temperatures (only min-p achieves good results at > 1.0), with the consequence of an increasing against- greedy diversity due the choice of random and meaningless tokens. Instead, the quality of the output generated by DiffSampling remains more stable, with small but consistent increases in diversity.
22

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Published in Transactions on Machine Learning Research (12/2025)
Model:
RLHF instructed
Pre-trained
Method
Qualitty
Per-inguut
Aguns--Grodl
Quality
Per-Inpuc
Agontsst-Grendy
R-1
SIM
COH
EAD
SBERT
EAD
SIBERT
R-1
SIM
COH
RAD
SBERT
RAD
SHKRI
Pemperttore = 0.0
Gredyy
0.40 oz
0.63..01
0.18
2000
0.222
0.51..0
0.P4g.co
0.10
0.00
Pemperatore = 1.0
Top-p
0,2
0.45 o
0.50_..
0.30
0.47
g.4.
0.16
0.34g. o
0,48g.1
0.72
0.66
0.77
0.56g o
esaappling
0,20
0.45 m
0.58
0.38
0:49
g.69
m.
0.16 oz
0.31g.m
0.48,441
0.75
0.67
0.56 0.
Localy typical
a.2
0.
0.50..01
0.36
0.47..01
0.08
0.41
0.16
0.34g.m
0.48
0.72
0.66
0.77
0.06
Min-p
0,22
0.46 m
0.01
0.36 o1
0.4
0.6
0.
0.20 m
0.44..0
0.63
0.6
0.47
0.62+ 01
0.30 o
DiffS
00
0.45 o
0.
0.35 o
0.45
0.23g
0.21 00
0.49g o
0.73g.co
0.191 0.
0.32
0.17
DHIS.
0,45 m
0.50 mi
0.37
0.47 2.00
0.67 4:4
0.41 o:
0.16]
0,48 0.30g.m
p.
0.66 m
0.55 a.
DiflS-min
0. po
0.46 o
0.600..01
0.36 01
D.64
0:38 o:
0:200
0.44g.m
0.622.c3
0 0.65
0.47+ o1
0.633
0.300
Temperaature
Top-p
0.45 0.
0.
0.35_
0,34
0.30
0.20
0.68
0.55g
0.37
0.50
0.30g
psampling
0.47 m
0.
0.38
0.38 1.01
0.59 u4
0.33 Lo:
0.20 oz
0.
0.68
0.42 g.59
0.333 p.
Locully typical
0.22
0.48
0.62..01
0.38
0.3
0.56
0.30
0:200 os
0:47a.0
0.68
0.53
0.37
0.50
0.500..m
Min-p
0,22
0.48
0.63...
0.38
0.34
0.55
0.30 m.
0:21 a:
0.47...
0.60g.01
0.50
0.33
0.46
0.282.o
-ut
00
0.49 o
0.60
0.35 o1
0.24
0.48_.1
0.22 m
0.21 m
0.49g. oo
0.73
0.37g.m1
0.18 00
0.30
0.16 on
Ditts lb
0.22
0.47 m
0.02
0.39 o
0.38
0.59
0.32
0.20
0.45
0.65
0.59
f.42
0.55
0.311
DUBS -iis
0.48g 0.
0.62g.o1
0.30 o1
g.07
g.58
0.322
0.20s oc
0.47g.m
0.67g.43
0.55
0.38 m1
0.52g.m:
0.31g.m m.
Temperature
1.5
Top-p
0.18g m
0.300..0
0.64 01
0.72g..0
0.88
0.77
0.033g
0.088.m
0.19g.co
0.79g..
0.772.00
0.97
0.56g.m
esampling
0.
0.25 m
0.38_.o
0.03
0.70
0.80
0.09
0.08
0.08
0.19
0.77 0.79
0.96
0.58
Locally lypiad
0.17 a.
0.30
0.60 01
0.70g.00
0.59
0.7F
0.02 oz
0.07g.m
0.19g.co
0.82g.c
0.72
0.90, o 0.97
Min-p
0:20
0.44
0.58-.01
0.
0.50
2.71
0.45
0.
0.38
0.53g.01
0.78
0.00..00
0.79
0.512.0
DiffS.-cut
0,23
0.48 m
0.
0.35 o1
0.25
0.46
2.
0.21 m
2.40 0o
0.73g.
0.38
0.19 00
0.33
0.18 on
Dufss lb
0. a0
0.43g
0.
0.40 o
0.52
0.71
0.45
0.11 on
0.20
0.34g
0.75g.m1
0.79,
0.70g 0.89
-min
0.
0.16 m
0.00
0.35 o1
0.45g.00
0.67 g.c
g.
0.19 oc
0.
0.60
0.70g.os
0.52, 00
0.70
0.41g.m m
Zemperature
2.0
Top-p
p.00
0.00 m
0.14g..o
0.60
0.60
0.92
0.00
0.01 oc
0.033.00
0.15g.co
0.81g.03
0.651 os
0.38
0.341.m
pssmpping
0.00 00
0.13__.o
0.655
0.67 2.07
0:92_
0.92
0.0L 00
0.08
0.14g.co
0.80
0.06]
01.88
0.90
Locally typical
0.08 m
0.14g.0
0.71
0.03
0.95
0. 0c
0.01 oz
0.03
0:15g.co
p.
0.63 os
p.
0.941.m
Min-p
0. 0,
0.42
0.56
0.41
0.56g.a1
0.76
0.50
0.132
0.30g.m
0.432.01
0.822.a1
0.724.00
0.89
0.622.o1
DiffS--et
m,23
0.48
0.60
0.35
0.25
0.46
0.24
0.21 w
0.40
0.79g.11
0.19 a.
0.33
0.182.o
DiRS.-Ib
09
0.43 o
0.
of
0.40 01
0.
0.48 o
0.06 o
0.19 on
0:29
0.
0.822 on
0.92 02
0.75, on
DunS minp
0.16 0.2
0.59
0.37 m0
0:47
0.69 .23
0.42
0.19;
0.42
0,58
0.72
[153
0.72
0.15 m
Zemperature 10.0
Top-p
0.02 m
0.12_..0
0.74g.m
0.64
0.32
0.001
0:03
0.13
0.78
1.60
1.07
1.86..00
p-sampling
0.02 m
0.112.00
0.742.01
0:642.00
0.90
0.93
0.00
0.02g.m
0.12g.co
0.75
0.63
0.97
0.96...m
Locally typical
0.02
0.12_.00
0.75g.m
0,63
0.95_.co
0
0.00
0.02..00
0.12
0.77
1.
0.
0.85
Min-p
0.00g.00
0.022.m
0.112.00
0.74g.01
0.642.00
0.93
m.
0.00
0.022.m0
0.12s.co
0.75g.0
0.633
0.
0.86..m
DiftS-cot
0:23+a00
0.48+
0.63_.01
0.35
0:25
0.47=.01
0.25
0.21 0
0.400..0
0.73+.01
0.30
0.19+
0.34
0.102
DidfS.-Ib
0.
0.40 m
0.52
0.48 01
0.
0:78=
0.54g
0.05 o
0.13
0.23g.41
0.77
0.83 09
0.50 0.95 o
DHSS minp
0.45 0.
0,58
0.38 m
0.49
0.72
0.45
0.18
0.50
0.55
0.76
0.57
0.79
0.50
Table 11: Aggregate results over 5 outputs sampled for each of the 1000 prompts from the XSum cattsstt for the instructed model (left) and the pro-trained model (right) when adopting different temperature values. The mean and 95% confidence interval are reported for all the metries.
F.3 Divergence Association Task
Figure 5 reports the DAT score and the percentage of output validity of the DPO-instructed and pre-trained models with different temperature values. Top-p sampling, locally typical sampling, and 7-sampling rapidly stop outputting valid lists of nouns when the temperature raises, even if the DAT score tends to be higher at 7 == 1.5; min-p returns a high percentage of valid outputs even at T = 2.0, but increase the DAT score only for the pre-trained model and cannot produce anything valid at 7 = 10.0. Instoad, the performance of our methods remains very similar across different temperatures in terms of both the DAT score and the percentage of valid outputs, except for DiffSampling-ll, whose scores increase at the cost of some validity.
On the other hand, the greedy decoding strategy is less effective for the pre-trained model, which results in higher lemperatures yielding better DAT scores across both the baselines and our methods. However, the number of valid outputs decreases faster, and top-p sampling, locally typical sampling, and 7-sampling produce very few correct lists at temperature of 1.5 (but with a higher DAT score). Again, min-p better manages temperatures around 1.5 and 2.0, with higher scores and still at least half of the outputs as valid, but cannot produce any correct output at temperature of 10.0.
23

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Published in Transactions on Machine Learning Research (12/2025)
97.5
90
55.0
92.5
DAT Score
90.0
70
87.5
50
82.5
77.5
30
outs
Figure 5: DAT scores for our methods and the baselines for the instructed (left) and pre-trained (right) model with different temperature values, together with the number of valid outputs produced by each sampling strategy. The dashed line represents the score of the greedy strategy.
F.4 WritingPrompts
Finally, Table 12 reports the full results for the story generation task at different temperatures. As above, the quality of output produced by the baselines drops quickly at higher temperatures, and only min-p achieves competitive results at T = 2.0. On the contrary, the quality of the output generated by DiffSampling-crt and DiffSampling-miin minii remains more stable, with small but consistent increases in diversity; DiffSampling- behaves worse, but still better than its competitor top-p.
F.5 Temperature Before After Truncating
As thoroughly described in the article, we apply temperature after truncating based on the minimum discrete derivative to preserve the guarantees of correctness of selected tokens. However, the de facto standard is to apply temperature before any other truncation modification. In this section, examine the implications of the temperature position in lerms of quality and diversity.
Table 13 reports the results of our methods with temperature before (left side) and after (right side) the truncation for the GSMSK test set. As we can soe, applying the temperature before causes the accuracy to degrade at higher lemperatures, while ensuring a slightly higher diversity. Interestingly, at r 0.6, applying the temperature after leads better results in terms of both accuracy and diversity. This confirms that our choice preserves the quality as much possible, at the cost of some additional diversity.
Table 14 reports the results of our methods with temperature before (left side) and after (right side) the truncation for the MATH test set. Again, applying a higher temperature before causes the accuracy to drop quickly for the two relaxations, and smoothly for DiffSampling-cul, with benefits only in terms of syntactic diversity. Instead, applying the temperature after has a negligible impact on quality while fostering diversity.
The same considerations hold for XSum as well. For both the instructed (Table 15 and pro-trained (Table 16) models, the quality is not preserved with the temperature before, while it with the temperature after, although diversity does not increase in the same way. Again, for DiffSampling-I and DiffSampling the diversity at + = 0.6 is instead greater with the temperature after, even if the quality is, more or less, the same. However, in the case of DiffSampling-cul, we can observe the opposite behavior: moving the temperature before cutting leads to a higher diversity at the cost. of some quality.
Applying the temperature before does not seem to give benefits for the divergence association task as well. As shown by Figure G for both the instructed and pre-trained models, the DAT scores are very similar regardless of the temperature position, but almost valid solutions generated when a temperature of
24

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Published in Transactions on Machine Learning Research (12/2025)
Model:
RL.HF-intrrcted
Pre-trained
Method
Quality COH
Per-Input Diversity
Quality
Per-Input Diversity
EAD SBERT
COH
EAD SBERT
Temperature 0.0
Greedy
0.44 01
0.06
0.59 0.11
0.07 00
Temperature
1.0
Top-p
0.42
0.73
0.25+.00
0.42
0.64+.00
0.58
77-ampling
0.42
4.00
0.28
0.40
0.774.00
0.60..00
Locally typical
0.42 01
0.73
0.25+.00
0.42+.01
0.64+.00
0.58+.00
Min-p
0.43
0.71 +.00
0.23+.00
0.51
0.35+
0.46+.00
DiffS.-cut
0.43
0.63
0.19
0.60
0.15
0.31
DiffS.-Ib
0.42
0.73
0.25
0.41 0001
0.67
0.584.00 .00
DiffS.-minp
0.43
0.71 4.00
0.23
0.51 #.01
0.36 ..00
0.47 177.00
Temperalure 0.6
Top-p
0.43
0.67+.00
0.22+.00
0.55
0.21
0.42+.00
y-sampling
0.43 01
0.68
0.22+
0.53
0.28
0.45..00
Locally typical
0.43
0.67+.00
0.22
0.55
0.21
0.424.00
Min-p
0.43 01
0.66
0.22+.00
0.57
0.20 .00
0.404.00
DiffS.-cut
0.43
0.63
0.19+.00
0.60+.o1
0.16
0.31
Dif[S.-Ib
0.43 00
0.68 0.68
0.23
0.53
0.27 2.00
0.45..00
DiffS.-ming
0.43
0.68
0.22
0.54
0.24 ..00
0.43
Temperature
1.5
Top-p
0.18 .00
4.00
0. 0.14+.00
0.15
1.00
0.24
s-smmpling
0.21 .00
1.01
0.17
0.15
1.004.00
0.29
Locally typical
0.17 00
1.01
0.14+.00
0.14+.00
1.00=.00
0.25
Min-p
0.42
0.78 4.00
0.26
0.43
0.73
0.554.00
DiffS.-cut
0.43
0.63
0.194.00
0.60
0.16
0.31
Dif[S.-Ib
0.40 01
0.89 0.89
0.33+..0
0.31
0.92..00 ..00
0.63
DiffS.-minp
0.43
0.73+.00
0.24+.00
0.48+.o1
0.46.
0.49+.00
Temperature
2.0
Top-p
0.12 00
1.01
0.10+.00
0.12+.00
1.014.00
0.27
1-sampling
0.11 .00
1.02
0.12
0.11
1.00..00
0.32...0
Locally typical
0.12 0000
1.01
0.10+.00
0.11
1.01
0.294.00
Min-p
0.39
0.92+.00
0.33
0.35
0.85
0.62...00
-cftS.-cut
0.43 01
0.64+..0
0.19+.00
0.60
0.16 .00
0.314.00
DiffS.-Ib
0.38 01
0.93 1.00
0.33
0.26 #.01
0.97 4.00
0.524.00
-iffSpminpp
0.43
0. 0.74
0.24+
0.47+.01
0.53+ .00
0.50+.00
Temperature
10.0
Top-p
0.11 00
1.02+..0
0.13+.00
0.10
1.00...0
0.33
1-sampling
0.10
1.02
0.144.00
0.10+.00
1.00..om
0.36
Locally typical
0.10 00
1.02+.00
0.14+.00
0.10+.00
1.00...0
0.35+.00
Min-p
0.10
1.02
0.14
0.10
1.00
0.36...0
-effS.-cut
0.43
4.00
0.20.4.00
0.60
0.17
0.31
DiffS..Ib
0.32 m1
0.98+..0
0.294..0
0.19+.00
1.00 .00
0.37
DinpS
0.42
0.77
0.254.00
0.45
0.68 0.0
0.52..00
Aggregate results over 3 seeds for the WritingPrompls dataset for the instructed model (left) and the pre-trained model (right) with different temperature values. The mean and standard error of the final score for each run are reported for cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for the other metrics.
Table 12:
10.0 is applied before truncating (and the same happens for temperature of 2.0 in the case of DiffSampling- 1b). Finally, as above, for both the instructed (Table and pre-trained (Table 18 models, the quality of generated stories is not preserved with the temperature before, while it largely is with the temperature after.
25

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Published in Transactions on Machine Learning Research (12/2025)
Method
BEFORE
AFTER
Accuracy
Cross- -npss-
Accuracy
Cross- Input
Against- Creedy
EAD
SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
Temperature
0.6
Dit
66. 19
2.04
0.64 000
0.10..00
0.01
66.74
2.05
0.64_.00
0.13+.00
0.02
DiffS.-Ib -lb
66.59
2.06
0.644.00
0.18
0.022.00
65.T3
2.06
0.64g.00
0.19
0.03...00
-iffS--miup
66.14..15
2.05 on
0.64 on
0.17=.00
0.02..00
67.05
2.06
0.64g.00
0.19
0.03
Temperature
1.5
-iffS,-cut
66. 16
2.05
0.64+
0.17=.00
0.02=.00
66. 06.722.30
2.05=.00
0. 0.64=.co
0. 0.15
0.02+.00
DiftS--lb
63.841.a
2.18
0.641
0.28
0.04
65. 65.201.25
2.111.01
0.64_.00
0.251.00
0.04
DiffS.-minp
64.34
2.15
0.64 o0
0.28=.00
0.04
65.55
2. 2.11
0.64_.0o
0.25 on
0.04
Temperature
Dut
65.50 .00
2.06 01
0.64
0.19
0.03
16.44
2.05
0.64g..o
0.
0.02
DiIIS.-Il
18. 18.17
11.92+.04 2.25
0.61 o0
0.77..01
0.43
63.484.48
2. 2..00.00
0.64_.00
0.26 .00
0.04
DifiS -iffS-mimp
61.81
0.64
0.32
0.05
4..13
2.12
0.64 .00
0.26
0.04
Temperature
10.0
DiffS
61.31..1
2.22 01
0.64g oo
0.31
0.04=.00
66.31
2.042.00
0.64 o0
0.15 o0
0.022.00
DiffS.-Ib
0.00
17.38 02
0.13
1.00=.00
0.96
64.11
2.15
0.64g.00
0.29
0.04
DiffS.-iup
0.00
17.38 02
0.13
1.00g.00
0.96
63.58
2.17
0.64
0.291.00
0.04
Table 13: Accuracy and diversity of results for the GSM8K test set over 3 seeds. The mean and standard error of the final score for each run reported for accuracy and cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for against-greedy diversity.
Method
BEFORE
AF AFTER
Accuracy
Cross- Input
Against-Greet
Accuracy
Cross- Input
Against- Seninst-Greeds Greedy
EAD
SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
Temperature
DiffS.-cut
21.442.12
5.60
0.80
0.22=.00
0.06
21.52+.18
5.72
0.80
0.25 oo
0.07
DiffS.-Ih
21.22..14
1.83
0.80
1.31
0.091.00
20.65
5.891.01
0.80
0.32
0.091.00
DiffS DiffS-miup
21,20+
5.83
0.80+
0.31+.00
0.00
20.56+.21
5.884.00
0.80-.o0
0.322
0.09
Temperature
1.5
DiffS.
21.151.00
3.781.01
0.801.00 o0
0.30
0.08
21.361.11
5.73
0.80
0.274.00
0.07 1.00
DiftS.-Ib
18.28_.06 .05
7.05 o5
0.80 o0
0. 0.422.00
0.12=.00
19.55=.03
6.31
0,80
0.39
0.11+:00
minp
18.72 18.72..19
6.54
0.80 .00
0.41
0.12=.00
20.044.13
6. 6.19
0.80
0.38
0.11
Temperature = 2.0
DiftS.-cut
21.252.10
3.85:
0.80
0.32
0.09
21.66::20
5.71
0.80
0.27
0.08:..0
DiffS.-Ib
1.77#.06
51.00+.0
0.48 .00
0.94
0. 0.72
19.17
6.40
0.80_..o
0.40
0. 0.122.00
DiffS--minp
16.511.06
1.25
0.80 .0
0.45
0.13
19.70...9
6.32
0.80_.00 .o
0.39
0.111.00
Temperature
10.0
DiffS.-cut
16. 1..6
6.78 01
0.80
0.43
0.121.00
21.221.11
5.741.01
0.80__oo
0.28 1.00
0.08
DiffS.-Ih
0.001.00
59.151.00
0.131.00
1.00
1.00
18.20
6.72
0.80_.o0
0.42
0. 0.100.00
DifiS -minp
0.00+.on
59.15+.04
0,13+
1.00=.00
1.000.00
18.644.20
6.54+.03
0.80-..0
0.41+.00
0.12+.00
Table 14: Accuracy and diversity of results for the MATH test set over 3 seeds. The mean and standard error of the final score for each run are reported for accuracy and cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for against-greedy diversity.
While EAD does not increase in the same way, it is important to notice how SBERT is instead higher with the temperature after, highlighting how randomness does not correlate with semantic diversity.
F.6 Quality-Diversity Trade-Of Visualization
To simplify the comprehension of how temperature impacts the quality-diversity trade-off and how the temperature position changes the performance of different sampling methods, we present here the Parcto fronts for top-p, min-p, and our three DifsSampling methods (with temperature applied either before or after truncation) at five different. temperatures T. We omit the DAT plots for conciseness, as they convey the same message as Figures and
Figure 7 reports the plots for the math problem-solving datasets by considering both against-greedy EAD diversity and against-greedy SBERT diversity with respect to accuracy. As already discussed, applying the
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Published in Transactions on Machine Learning Research (12/2025)
Method
REFORE
AFTER
Quality SIM
Per-lppu
Againsi-Gredly
Quality
Pep-lapu-
Against-Greely
R-1
COH
EAD
SBERT
EAD
SBERT
R-1
SIM
COH
EAD
SBERT
EAD
SBERT
Tomgerateos
0.6
1illS.-eut
0.222..00
0.482.01
0.62
0.41 01
0.37
0.64..01 0.56
0.30g.01
0:23
0.402.00
0.683 01
0.36...0
0.24
0.482.00 01
0:222.01
DifSS-Ib
0.22..00
0/48..0
0.622.03
0.38 o
0.
0.30g.0
0.22
0.475.0
0.62; 01
0.39
0.38
0.50
0.52
DrffSs-miip
0,22
0.48 m
0.63
0.304 os
0.
0.
0.30
0.224..0
0.484.0 o
0.62+ 01
0.304
0.37
0.58+ 01
0.33
Temgeratore
1.5
0,231.00 n0
0.48_. on
0.
0.37. o
0.28
0.501.03
0.281.m
0:231..0
1.48
0.631 0n
0.36 m
0,25
0.461.m
0:231.
DstfS.-lb
0.06
0.16
0.84g 0.
0.73
0.89
0.79g.0
0,20
0.40g o1
0.57
0,40 oi
0.52
0.712
0.45g.0
0,20 ne
0.44_.m on
0.38 m
0.5
1.71
0.45 on
0.2
0.46.
0.60g o1
0.35 m
0.67).m
g.41
Tengerulory
2.0
-cllS.ccut
0.23
0.
0:45 on
0.
0.38 o
g. oo
0.54
0.29
0.23
0.48 m
0.63
0.35
0.25
0.46
0.24
Db
0.01
0.00=.00
0.85 0.13
0.66
0.92
0.92s.00
0.19
0.56 0.40a.m
0.403..0
0.54
0.73
0.48
DJESS, mming
0.19; 00
0:42 m
0.42 o
0.57 L.00
0.76
0.50 on
0.21 c.o
0.40
0.59, 0
0.37 mm
0.47
0.09 m
j:42
Temperattore
10.0
Iefis-ouut
0.17
0.38 m
0.57 0.51
0.53
0.74
0.501..01
0.23
0.48g.0 on
0.36g 0.832
0.20
0.47+
0:25g.01
DifiS--Ib
0.00
0.022.00
0.11
0.74
0.64
0.033.00
0.90
0.17
0.402.0
0.52+.0
0.484.01
0.59
0.78+.01
0.54
DiffS-mmii
0.00 00
0.02 0
0.01
0.74g 01
0.64
0.93
0.90 c0
0.21
0.45g on
0.58+ 01
0.08% 01
0.40+
0.72+
0.45
Table 15: The mean and 95% confidence interval of quality and diversity metries for the 5 samples generated by the instructed model with temperature before and after DiffSammling for each of the 1000 prompts from the XSum lest set.
Method
BEFORE
AFTER
Quality
Pre
Quality
Against-Grrodly
R-1
SIM
COH
EAD
SBERT
EAD
SBERT
R-1
SDM
COHI
EAD
SBERT
EAD
SBERT
0.6
Dills
0.00
0.48..o.
0.70g.01
0.50 or
0.29
0.47mm
0.27..01
0,21
0.40..00
0.73g n0
0.37g
0.18
0.300
0.16g.01
-iISS.Ib
0.20
0.46
0.68
0.54 on
0.
0.50
0.31p.01
0.20
0.45..0l
0.65 01
0.50
0.12+
0.56
0.31
DiflS-mmip
0,30..00
0.47....
0.69
0.50 oz
0.34
0.47
0.28
0,30
0.47..0.
0.67+
0.50
0.38+.c1
0.522+
0.31
Temperutare
1.5
Dut
0.21
0.40_m m
0.73
0.41g o
0.22
0.36
0.20
0.21g
0.49 00
0.73 01
0.36 oi
0.19
0.33
0.18g.m
DrffS.-lb
0.03
0.072.m0 0
0.18
0.79 on
0.75
0.97
0.80
0.11
0.23 o
0.34
0.75
0.80+ 0.
0.70g.0
DHESS minp
0.17
0.38_ m
0.52
0.77 oi
0.61
0,50
0.52
0.19
0.49 m
0.60
0.70 m
0.52 cco
0.70
0.44g.m
Temperulare
2.0
DatiS
0.21
0.49-.00
0.72
0.44 oz
0.24
0.39
0.22s.01
0.21
0.49..00
0.73 01
0.38..o
0.33 0.19
1.
-iISs-IIb
0.01
0.03
0.14g.00
0.80 m
0,98 0.
0.94g.00
0.09
0.19g.m
0.29,
0.76
0.82,.co
0.92 no
0.75
miin
0.
0.29
0.81 0.4
0.73
0.90
0.64
0.19
0.42a.m
0.58.
0.72
0.53+.co
0.72+
0.45
T Temgeratere
10.0
1elis-ceut
0007
0.17..0
0.53g 0.32
o
0.58
0.784.01
0.71
0:21+:00
0.402.00 m
0.73e.0
0.302
0.19
0.34
0.
-iI
0.00
0.02-
0,75 0.12
0.632.00
0,97
0.952.c0
0.05
0.13=
0.232
0.77
0.83+.co
0.86
0.83
minis-miin
0.00 20
0:02-.0 0
0.12
0.76 o
0.03
0.97
0.95 c0
0.18
0.40 m
0.65.
0.76 m
0.57
0.70+
0.50
Table 16: The mean and 95% confidence interval of quality and diversity metrics for the 5 samples generated
by the pre-trained model with temperature before and after DiffSampling for each of the 1000 prompts from the XSum test set.
temperature after preserves higher quality while reducing the increments in diversity. Vice versa, applying the temperature before has dramatic ellects accuracy, and only DiffSampling-cul achieves competitive results at very high т. In general, DiffSampling-miin with temperature applied after seems to provide the best balance between quality and diversity at different T.
The results for XSum are similar. As shown in Figure S the coherence of generated outputs degrades fast with 7 > 1 if temperature applicd before truncation. While min-p and DiffSampplin- have interesting performances at 7 5 2.0, for very high temperatures only DifsSampling-ent achieves comparable coherence. Overall, all sampling methods apart from DiffSampling-cuu have very similar quality-diversity trade-offs, but DiffSampling-minp with temperature applicd after seems to provide the best results considering the full range of temperature values.
Finally, Figure g shows the quality-diversse trade-offs in the case of the WritingPrompps dataset. Once more, DiffSampping-cut especially with temperature applied after, better preserves quality at different т, while HiffSamplinggmmnng with temperature applied after better balances quality and diversity for higher temperatures.
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Published in Transactions on Machine Learning Research (12/2025)
BEFORE
55.0
92.5
DAT Score
70
87.5
50
82.5
77.5
30
outs
Figure DAT scores and validity percentage of outputs with temperature scaling before and after the truncation for the instructed (left) and pre-trained (right) models. The dashed line represents the score of the greedy strategy.
Model:
BEFORE
AFTER
Method
Quality
Per-Iun Input Diversity
Quality
Per- Per-Input Diversity
COH
EAD
SBERT
COH
EAD
SBERT
Temperature
0.6
DiffS.ccut
0.43+.01 01
0.62+.00
0.18+.00
0.43 .01
0.63 00
0.19 00
DiffS.-lb
0.444.01
0.67
0.22+..0
4.43
0.68
0.23 .0
DiffS.-ming
0.43
0.674.00
0.21
0.43
0.68
0.22_.00
Temperature
1.5
DifTS.
0.44
0.64
0.20
0.43
0.63
0.19
DifiS.-Ib
0.174.00
1.01
0.154.00
0.40 .01
0.89 000
0.33 00
DiffS.
0.42+
0.79+.00
0.27+.00
0.43
0.73 00
0.24 .00
Temperature
2.0
DiffS. cut
0.44+.01
0.65
0.21+.00
0.43
0.64 00
0.19 00
DiffS.-Ib
0.11
1.024.00
0.12+.00
0.38
0.93
0.33_.00
DiffS.-mipp
0.39
0.924.00
0.34
0.43
0.74
0.24_.00
Temperature
10.0
DiftS.-cut
0.23
0.94
0.24
0.43
0.64
0.20=.00 .00
DiffS.
0.10+.00
1.024.00
0.14+.00
0.32
0.98
0.292.00
DiffS.-min
0.10+.00
1.02+.00
0.14+.00
0.42 001
0.77
0.25 .00
Table 17: Quality and diversity of results for story generation with the instructed model over 3 seeds. The mcan and standard error of the final score for cach mean and 95% confidence interval for the full set of answers are reported for the other metrics.
reported for cross-input diversity, whereas the
G Additional Experiments
G.1 Divergent Association Task over All Nouns
While the classic DAT implementation only considers outputs containing at least 7 distinct nouns (out of 10), and computes the score based on the first 7 nouns, it informative to examine performance when all 10 nouns are distinct and the score is computed over the full set. Indeed, the standard implementation may be overly conservative, allowing methods that fail to meet the full requirements to still reccive a final score. Figure I0 presents these scores for all baselines and our methods across the five temperatures considered. Although the DAT scores largely consistent with those in Figure the number of valid outputs changes.
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Published in Transactions on Machine Learning Research (12/2025)
Model:
BEFORE
AFTER
Method
Quality
Per-Input Diversity
Quality
Per-Inpe Per-Input Diversity
COH
EAD
SBERT
COH
FAI
SBERT
Temperature
0.6
-iffS.cutt
0.60
0.14
0.29
0.60
0.16
0.31=.01
DiffS.-lb
0.55+.01
0.22+.00
0.43+.00
0.53+.01 2.01
0.27=.00
0.45..00 00
DiffS. minp
0.57
0.20
0.41+.00
0.54 01
0.24 .00
0.43 .0
Temperature
1.5
DiffS.-cut
0.59
0.17
0.33+.00
0.60 01
0. 0.16
0.31=
DiffS.-lb
0.14
1.004.00
0.32
0.31 0.31 1.01
0.92
0.63_.00
DiffS.-minp
0.42
0.75
0.55
0.48 1.48
0.46
0.49...0
Temperature
2.0
DiffS.ccut
0.59
0.184.00
0.34
0.60
0.16
0.31
DiftS.-lb
0.11 0.11
1.00
0.32
0.26
0.97
0.52 .00
DiffS minp
0.34+.01
0.864.00
0.63+.00
0.47 #.01
0.53 00
0.50 00
Temperature
10.0
DiffS. ccut
0.19
0.69
0.43+.00
0.60
0.17
0.31=.01
DiffS.-Ib
0.10+.o0
1.004.00
0.36
0.19 00
1.00
0.37= .00
0.10
1.00
0.36
0.45
0.68
0.52_.00
Table 18: Quality and diversity of results for story generation with the pre-trained model over 3 seeds. The mean and standard error of the final score for each run are reported for cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for the other metrics.
Notably, the difference between DiffSampling methods and the baselines becomes even more pronounced, particularly at temperaturos 1.0 and 1.5. This further confirms that our strategy is more robust and better adheres to the task requirements.
G.2 Ablation Study the Lower Bound
Dataset:
GSM8K
MATH
Method
Aocuracy
Croes-Inpwe
Against-Creody
Accuracy
Cross-Input
Against-Creed
DittSamplig-Ib
EAD
SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
= 0.0
66.36
2.04
0.64
0.14g.00
0.02
21 18.38
5.71
0.80
0.271.00
0.07
0.1
66.46
2.05
0.64_
0. 0.14g.00
0.02
20.95
5.72
0.80
0.271.00
0.07
0.2
66. 06.46..32
2.05
0.64_.00
0. 0.14
0.02
20.95
5.72
0.80
0.274.00
0.07
0.3
66. 70.77-...
2.04+.00
0.64 .00
0.14
0.02
21. 30.0
5.73
0.80
0.27
0.07
Pib 0.4
66.57
2.06
0.64
0.14
0.02
21.05 00:
5.73
0.80 o0
0.27
0.07
PMb 0.5
67.17
2.04_..v
0.64_
0.15
0.02
21.18
5.74
0.80
0.28
0.08
PMo 0.6
66.67
2.05
0.64_.00
0.161.00
0.02
21.18 1.
5.79...0
0.80
0.30
0.09
P/o 0.7
65.58 =
2.06
0.64_.00 .00
0.18
0.03
21 21.14
5.861.01
0.80
0.32
0.09
F/o 0.8
66.92
2.07
0.64
0.20
0.03 .00
20.78
6.00
0.80
0.35
0.10
Pib 0.9
65.18
2.09
0.64 00
0.23 .00
0.03 00
20.20 08
6.114.02
0.80 oo
0.37
0.10
P% 0.95
64.82,
2.09
0.64 00
0.24
0.03 000
20.24
6.21
0.80
0.37
0.11
P6
64.87 20
2.12
0.64_.00 00
0.25
0.04
19.46
6.36
0.80
0.39
0.11
Table 19: Ablation study the Pts value over 3 seeds for the GSM8K (left) and MATH (right) test sets. The mean and standard error of the final score for each run are reported for accuracy and cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for against-greeds diversity.
We also conducted experiments on the four aforementioned case studies, varying the lower bound of the critical mass. Table reports the results for the math problem-solving tasks, considering the GSM8K (left side) and MATH (right side) test sets. As expected, the against-groode diversity scores and cross-input EAD increase together with Pu: instead, while accuracy tends to decrease with higher lower bounds, the differences not significant, and even quite high value (e.g., 0.8) achieves competitive results.
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Published in Transactions on Machine Learning Research (12/2025)
GSM8K
GSM8K
68
68
67-
67-
66
66
65-
65
Accuracy
Accuracy
64
64
63
63
0.85
60
60
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
Against-Greedy EAD Diversity
Against-Greedh SBERT Diversity
MATH
MATH
22
22
21
21
20
20
Accuracy
19-
Accuracy
19-
18
18
2.49
17
17:
124
1.24
16
16
0.0
15
15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.06
0.08
0.10
0.12
0.14
Against-Greedy EAD Diversity
SBERT Diversity
Method
Top-p
Diffs,-cut (t before)
Diffs.-mipp before)
Diffs.-Ib (T after)
Min-p
Diffs,-lb (t before)
DiffS.-cut (T after)
DiffS.-minp (T after)
Temperature
T= 0.6
x T= 1.0
1.5
+ T= 2.0
t= 10.
Figure 7: Quality-diversity trade-offs for GSM8K and MATH datasets at five different temperatures for two baselines (top-p and min-p) and our three DiffSampling methods, with temperature applied either before or after the truncation. Each point represents the mean score across the entire dataset and three different seeds.
Table 20 reports the results for the extreme summarization task for both instructed (left side) and pre-trained (right side) models. Again, diversity scores are directly correlated with the lower bound. Instead, qualitative metries do not vary much for the instructed model, while constantly decreasing for the pre-trained model
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Published in Transactions on Machine Learning Research (12/2025)
Instructed Model
Instructed Model
0.64
0.64
0.3
0.62
0.62
0.60
0.60
0.11
Coherence
0.63
0.69
0.74
Coherence
0.58
0.58
0.56
0.56
0.54
0.54
0.21
0.66
0.68
0.73
0.50
0.50
0.35
0.25
0.35
0.50
0.55
Per-Input EAD Diversity
Per-Input SBERT Diversity
Pretrained Model
Pretrained Model
0.7
0.7
Coherence
0.5
Coherence
0.5
0.4
0.4
0.3
0.1
0.1
0.4
0.5
0.6
0.7
0.8
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Per-input EAD Diversity
Per-Input SBERT Diversity
Method
Top-p Min-p
DiffS.-cut (T before)
DiffS.-minp (T before)
DiffS.-lb (T after)
DiffS.-Ib (t before)
Diffs.-cut after)
DiffS.-minp (T after)
Temperature
== ==
1.5
+ T 2.0
T
Figure 8: Quality-diversity trade-offs for the XSum dataset with the instructed and pre-trained models at five different temperatures for two baselines (top-p and min-p) and our three DiffSampling methods, with temperature applied either before or after the truncation. Each point represents the mean score across all the outputs generated from the same 1000 randomly sampled inputs.
with increasing Pis. this situation, the choice of Ptb is relevant and requires us to decide whether to trade off quality diversity.
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Published in Transactions on Machine Learning Research (12/2025)
Instructed Model
Instructed Model
0.445
0.445
0.440
0.440
0.435
0.435
Coherence
0.430
Coherence
0.430
0.4
0.0
0.25
0.25
1:00
0.1
0.22
0.410
0.410
0.600
0.625
0.650
0.675
0.700
0.725
0.750
0.775
0.800
0.18
0.20
0.22
0.24
0.26
0.28
Per-Input EAD Diversity
Per-Input SBERT Diversity
Pretrained Model
Pretrained Model
0.600
0.600
0.575
0.575
Coherence
0.525
Coherence
0.525
0.500
0.500-
0.475
0.475
0.450
0.450
42
0.1
0.1
0.85
1.02
0.24
0.44
0.400
0.400
0.1
0.2
0.3
0.4
0.5
0.6
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Per-Input EAD Diversity
Per-Input SBERT Diversity
Method
Top-p Min-p
DiffS -cut (T before) DiffS.-Ib before)
DiffS.-minp (T before) DiffS.-cut (T after)
DiffS.-lb (T after)
DiffS.-min minp (T after)
Temperature
1=100
1.5
2.0
10.
Figure 9: Quality- trade-offs for the WritingPrompts dataset with the instructed and pre-trained models five different temperatures for two baselines (top-p and min-p) and our three DiffSampling methods, with temperature applied either before after the truncation. Each point represents the mean score across all the outputs generated from the same 500 randomly sampled inputs.
Table 21 reports the results for the story gencration task for both instructed (left side) and pre-trained (right side) models. Coherence decreases higher Pis values, but this effect is significant only for the pre-trained model. However, both diversity scores are directly correlated with the lower bound, especially at high values.
32

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Published in Transactions on Machine Learning Research (12/2025)
97.5
90
95.0
90
92.5
DAT Score
90.0
87.5
80
85.0
50-
82.5
77.5
30
outs
100
Figure 10: DAT scores over all nouns for our methods and the baselines for the instructed (left) and pre- trained (right) model with different temperature values, together with the number of valid outputs produced by each sampling strategy. The dashed line represents the score of the greedy strategy.
Model:
Ri.iF--merrcctel
Pro-trained
Methoo DiffSampling
Quality
Per-Ingul
Agpinss-Greedy
Quality
Per-Iapul
Ageinet-Greedly
COH
SBERT
SBERT
SBERT
EAD
SBERT
Fi = 0.0
0. 0.23
U.48g
0.632.01
0.35
0.25
0:45
0.233
0.21
0.49g.00
0.73g.co
0.38g.01
0.19
0.322
0.17..m
Pi
2:23
0.48 o
0.63_.01
0.35
0.25
0.45
0.23
0:21 =
2.49
0.78g.61
0.20 0.31
0.18..o 0.34
Pi 0.2
g0
0.48 o
0.60
0.35 o1
0.25g
0.45
0.23 m
0.21
0.48g.m o
0.71
0.43
0.27 m
0.40
0.24,
Pis
0.45 m
0.60_.01
0.37
0.26
0:47
0.24
0.21
0.46
0.68
0.35 0.48
0.18
0.30
Rie 0.4
0.
0.60g.o1
0.30 01
0.29g.03
0.50g.c1
0.27
0.20 oc
0.45g.m
0.68
0.54g.00
0.40 m
0.54g
0.34g m
Fit
0.22s.00
0.45
0.62=.ot
0.30
0.33
0.54
0.30
0.20
0.44a.m
0.63
0.58
0..62
0.59
0.36
An
0,22
0.47 on
0.622.01
0.40) 01
0.37
0.58
0.33 m.
0.19 m
0.12a.m
0.60g.c1
0:63
0.51 01
0.61g
0.122 m
0.461 0.22
0.61_.01
0.
0.41g.01
6.022
0.36
0.19
0.400..
0.57g.0
0.672..1
0.56
0.
0.46.
Pie 0.9
p.21
0.45
0.60
0.36
0.45
0.64
1 m:
0.18
0.38
0.53g
0.70
0.00
0.73
0.501.
0.21g
0.45 o
0.59
0.37
0.
0.67
0.41g
0.16
0.34g
0.48g
0.72
0.66
0.77
0.56
PiE 0.95
0,21
0.45 m
0.58
0.38
0.
0.68 .4
1.42 o:
0.15, oz
0.32
0.46
0.
0..6
0.58
1.0
0.20
U.44 m
0.58_.01
0.40
01
0.50
0.70
0.43
0.14g 0c
0.29..m
0/42..1
0.74
U.74 op
0.833
0.62
Table 20: Ablation study on the pis value over the 5 outputs sampled for each of the 1000 prompts from
the XSum dataset for the instructed model (left) and the pre-trained model (right). The mean and 95% confidence interval are reported for all the metrics.
Finally, Figure 11 reports the results for the divergent association task. As we would expect, the DAT score changes almost lincarly between that for a lower bound of O (that means DiffSampling-cut) and (that means slandard sampling). Interestingly, the number of correct answers by the non-instructed model drops constantly, while remains consistently higher in the case of the instructed model.
To sum up, when greediness is desirable, lower value of pa can load to high quality and diversity; otherwise, increasing pm, improves diversity, but the cost. in terms of validily is not negligible and requires careful consideration. We suggest practitioners select the most appropriate Pis value by rumning it on a validation set if available, and otherwise lie in the [0.8, 0.95) range, which has shown competitive results on both quality and diversity metrics.
G.3 Ablation Study the Dynamic Upper Bound
Finally, we conducted experiments on the four aforementioned case studies, varying the dynamic upper bound of the truncated tokens Pmin-
Table 22 reports the results for the math problem-solving tasks, considering the GSMSK (left side) and MATH (right side) test sets. As expected, the against-greedy diversity scores and cross-input EAD decrease
together with Puiin plateauing at Pmin 0.6 (from that on, results comparable with DifsSampling-cul);
33

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Published in Transactions on Machine Learning Research (12/2025)
Model:
RLHF-instructed
Pre-trained
Method
Quality
Diversity Per-Input
Quality
Per-Input
Diversity
DillSampling-l
COH
EAD
SBERT
COH
EAD
SBERT
Pte 0.0
0.43 01
0.63+.00
0.19+.00
0.60 01
0.15 00
0.31
ptb 0.1
0.43 01
0.63+.00
0.19+.00
0.60
0.162.00
0.32
Pte = 0.2
0.43
0.64
0.20
0.58
0.164.00
0.37
Pt 0.3
0.432.o1 01
0.00
0.20+.00
0.564.01
0.184.00
0.41
Pte = 0.4
0.43
0.65
0.21
0.54
0.19
0.434.00
Ptb = 0.5
0.43
0.66
0.22
0.52
0.23+.00
0.464..00
ptb 0.6
0,43 .11
0.67
0.22+.00
0.49
0.284.00
0.494.00
Ptt = 0.7
0.43
0.69
0.23+.00
0.47+.01
0.33 00
0.514.00
ptb 0.8
0.43
0.70 4.00
0.24
0.44
0.474.00
0.544.00
Pic = 0.9
0.42
0.73+.00
0.25++.00
0.41+.01
0.67
0.58+.00
Ptb 0.95
0.42 01
4.08
0.27+:00
0.39
0.76 .00
0.61
Pib 1.0
0.41
0.88 4.00
4.33
0.35
0.84
0.64
Table 21: Ablation study on the Pib value over 3 seeds for the WritingPrompts dataset for the instructed model (left) and the pre-trained model (right). The mean and standard error of the final score for each run are reported for cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for the other metrics.
94
DAT Score
86
60
50
40
Valid outputs
100
50
50
Pe 0.0
Rb 0.1
Pa 0.2
Rs 0.3
Ps 0.4
5
0.7
8
0.9
Pe 0.95
Rs 1.0
Rs 0.0
Ps 0,1
Re 0.2
Re 3.
Re 5
6
Pa 0.7
0.8
0,9
0.95
Rs 1.0
RS
Pe
Pe
Figure 11: DAT scores and output validity percentage for DiifSampling-li when varying the Pib parameter
for the instructed (left) and pre-trained (right) models. The dashed line represents the score of the greedy strategy.
specularly, accuracy is lower at smaller Pmin, but the instructed model reaches competitive score even at Pmin = 0.3.
The same holds for XSum as well. As shown in Table 23 diversity decreases when increasing Pmain and plateaus at 0.5, while quality rapidly increases for the pre-trained model and almost constant for the instructed model.
As reported in Table 24 in the case of story generation, diversity rapidly drops when increasing Pmánn and plateaus around 0.5, while quality increases for the pre-trained model and is almost constant for the instructed model.
The same considerations are even more apparent for the divergent association task with Figure 12 While behaving differently for the instructed and pro-trained models, the DAT score platcaus around Pmin 0.5. On the other hand, the percentage of valid outputs is close 100% for all Pmi values when considering the instructed model, and linearly increases when considering the pre-trained model.
34

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Published in Transactions on Machine Learning Research (12/2025)
Dataset:
GSM8K
MATH
Method
Accuracy
Cross-Inphe
Against-Groede
Accuracy
Cross-Input
Against- Greeid
DifiSenpling-minn
EAD
SBERT
EAD
SBERT
EAD
SBERT
EAD
SBERT
Prunn 0.0
64.87 20
2.12
0.64g.u0 00
0.25
0.04g.00
19.46..10
6.36 01
g.80
0.39
0.11,.00
Poiin 0.05
64.75
2.09
0.644.00
0.24
0.03
20.28
6.16+.00 000
0. 0.80 4.00
0.37 +.00
0.11+.00
Poii 0.1
65.48 60
2.09
0.64
0. 0.23+.00
0.03
20.18
6.06 0o
0. 0.80+.00
0.36
0.10+.c0
Pouin
65.48 41
2.07=200
0.644.00
0.21 0.21 #.00
0.03_..0
20.65
5.93 oz
0. 0.80 0.0
0.34
0.10+.00
Penin
66.442..5
2.05=.co
0.64
0.19
0.03
21. 21.13
5.874.01
0. 0.80
0.333g00
a.09
Penin
66.50
2.05
0.644.00
0.17
0.02=2.0
21.41 2.07
4.1
0. 0.80
0.31 +
0.09
Penin 0.5
66.67
2.04+.00
0.644.00
0.15
0.02=2.00
21. 21.23
5.75+.01 01
0. 0.80
0.28
0.08
Protn
66.64 29
2.04
0.64g.00
[..44..0
0.02g.00
21.67
6.722.01
0.80
0.27. 2.00
0.08
Penin
66.29
2.04
0.64g.00
0.144.00
0.022.00
21.25
5.722.00
0.80
2.07
0.07..00
Penin
66.21
2.04..00
0.64g.00
0.142.00
0.02=.00
21.16
5.704.01
0. 0.80
0.27
0.07..00
Prnin
66.21 52
2.044.00
0.644.00
0.142.00
0.02
21.25
5.70
0.80
1.277:000
0.07
Prean
66.36 23
2.04
0.64g.u0
0.144.00
0.02
21.38
5.71
0.80
1.07
0.07
Table 22: Ablation study on the Pmin value over 3 seeds for the GSM8K (left) and MATH (right) tost sets. The mean and standard error of the final score for each run are reported for accuracy and cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for against- greody diversity.
Model:
RLIP instrnctedd
Prestrained
Method
Quality SIM
Per-Inpott
Apoinat-Croodly
Quality
Por-Inpot
Againat-CCreotly
DiefSamping--nnn
R-1
COl
EAD
SBERT
EAD
SDERT
R-11
SIM
Con
EAD
SDERT
EAD
SIERT
Posio 0.D
0.44g 01
0.58g..
0.40
g.50g.m m
0.20g o:
0433g 43
0.14g.00
0.22% 01
0.42 m
0.74g 01
0.74g.00
0.83 m
0.62g oi
Proin 0.05
g.00
0:46
0.59g.0:
0.36
0.45
0 0.66g.0
0.00
0.19
0.433..01
0.60
0.60
0.52..00
0.68
0:42;
Pron 0.1
0.46 0
0:60
g.35
0.43g.m
0.6
0.38
0.20
0.44g.0
0.622.m
0.67
0.47g.00
0.63
0.30
Pron 0.2
0.22
0.47
0.622
2.37
0.40
0.61g
0.
0.20
0.46
0.06g
0.58_
0.41g.0)
0.56g
0.34
Prun
0.22
0. 01
0.62
0.38
0.300..0
0.58
0.33=.01
0.20
0.47
0:68
0.52=.01
0.30=..:
0.31 0.51gm
Prom 0.4
0.48 on
0.622
0.38
0.33g m
0.5kg.n:
0.30
0.21
0.472..1
0.70g m
0.49=
0.32g.a)
0.46
0.27
Poin 0.5
0.23
0.48 o
0.63g
0.38_.01
0.29 m
0.51g
0.
0.21
0.48_
0.71
0.45
0.27
0.41
0.24g
Puiin 11.6
gm
0:48 ot
0.63 0:
g.0
g.26
0.
0.25g.03
0.21
1.72
0.41 41
0.25g..:
0.57
0.21 o:
Puin 0.7
0:23
0.48g
0.633
0.36
0.25.
0 0.45
0:23
0.21
0.49:
0.73
0.
0.200..0
0.34
0. 0.19g.m
Puin
0:48 ot
0.63 01
0.3
g. m
0.45
0.28_.0
0.21
0.
p.73 m
0.38 41
0.19g.00
0.32 m
0,18 m
Priin 0.9
g.23
0:48 o1
0.63
0.35
0.25
0 0.45
0.23
0.21
0.492.00
0.73
0.58
0.19
0.52
0.17
Prom
0.23
0-48 oz
0.63
0.35
0.25
0.45
0.23-.03
0.21
0.40
0.73g m
0.3%
0.10
0.32
0.17
Table 23: Ablation study on the Pmin value over the 5 outputs sampled for each of the 1000 prompts from
the XSum dataset for the instructed model (left) and the pre-trained model (right). The mean and 95% confidence interval are reported for all the metrics.
Model:
RLHFF- Finstrustreeted
Pre-trained
Method
Quality
Per- rep-Input Diversity
Quality
Per- Input Diversity
DiffSampling- minp
COH
EAD
SBERT
COH
EAD
SBERT
Pmin 0.0
0.41
0.88 .00
0.33
0.35
0.84
0.644.00
Pmin 0.05
0.43
0.72 .0
0.244.00
0.48 01
0.462.00
0.49+.00
Pmáin 0.1
0.43
0.71 00
0.23
0.51
0.36
0.474.00
Poin 0.2
0.43
0.69 00
0.22
0.54 01
0.26
0.44+.00 .00
Punin 0.3
0.44 01
0,67 = 00
0.22.
0.56
0.22 00
0.42:+.00 .00
Ponin 0.4
0.43
0.66 0O
0.21+.00
0.57=
0.20
0.39+ .0
Punin 0.5
0.44 .1
0.65
0.21+.00
0.59
0.18 00
0.364.00
Pmin 0.6
0.44
0.64=.00 00
0. 0.20
0.59 01
0.16 000
0.34+
Pmin 0.7
0.43
0.64
0.204.00
0.60
0.16
0.32+.01
Pmán 0.8
0.43
0.63
0.194.00
0.60
0. 0.16
0.31 ..01
Pmin 0.9
0.43
0.63
0.19
0.60
0.15
0.31 .001
Pmán 1.0
0.43
0.63
0.19
0.60
0.15
0.31 1.11
Table 24: Ablation study on the Pmnn value over seeds for the WritingPrompts dataset for the instructed
model (left) and the pre-trained model (right). The mean and standard error of the final score for each run are reported for cross-input diversity, whereas the mean and 95% confidence interval for the full set of answers are reported for the other metrics.
To sum up, values above 0.5 are not different from DiffSampling-cuu while lower Pminn can help foster diversity with a small loss in accuracy, especially for instructed models. We suggest practitioners select the
35

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Published in Transactions on Machine Learning Research (12/2025)
94
DAT Score
86
60
50
40
outputs
100
50
50
Droa 0.0
Paio 0.05
0.3
0.4
0.5
m06
Pais 0.7
Poin 0.8
Pris 0.9
Pee m 05.05
Prie 0.1
Poin 0.2
f.,3
w
Prea w
Ani 0.8
Pai 0.3
Pre 1.0
Poie
Reie
Pais
Prou
Pros
Pess
Peis
Figure 12: DAT scores and output validity percentage for DiffSampling-miing when varying the pmin på-
rameter for the instructed (left) and pre-trained (right) models. The dashed line represents the score of the greedy strategy.
most appropriate Pmin value by rumning it validation set if available, and otherwise lie in the [0.05, 0.3] range, with a lower higher value depending on whether it is preferable to have more diversity or quality, respectively.
H Qualitative Analysis
In the following subsections, we present and qualitatively discuss some generated solutions from our met and the greedy, top-p, and min-p strategies at different temperatures.
H.1 Divergent Association Task
For the divergent association task, we analyze how the generated solutions differ from the groedy one from a qualitative perspective.
Instructed Model. In the case of the instructed version of Llama3-8B3 the greedy decoding produces a high-quality list of different nouns, with score comparable to more stochastic strategics. The best solution overall has been generated with y-sampling at temperature of 1.5; while it does not share any noun with the greedy solution, the first word starts with the same token. On the other hand, the best solution generated by one of our methods is made by DiffSampling- at a temperature of 0.6 and, predictably, shares more nouns with the greedy solutions; however, the different nouns lead to a significant increase in DAT score:
Greedy solution:
quark, fjord, salsa, heliotrope, gargoyle, kaleidoscope, ratchet.
Score: 89.786
Our Best solution (DiffSampling-lb, t=10.): quasar, fjord, oboc, quiche, heliotrope, ratchot, tornado
Score: 94.752
Best baseline solution (7-sampling, t=1.5): quasar, bungee, newsletter, virago, pertussis, node, pumpkinseed Score: 97.005
36

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Published in Transactions on Machine Learning Research (12/2025)
hep-p==0a
0.55
0.96
0.3
0.29
0.06
0.2
0.51
-1.
n:
ITt=0.6
0.53
0.96
0.3
0.29
0.96
0.2
0.31
Min t-06
0.55
0.98
0.38
0.35
0.07
0.27
0:39
pifss.cut
0.57
DMSS ib t-0.6
0.53
0.92
0.24
0.16
0.061
0.24
0.22
DiTS ming. t=0.6
0.34
0.95
0.31
0.22
0. 0P0
0.19
0.28
n-S. t=10
0.36
0:99
0.03
0.01
0.071
0.24
0.001
0.03
Min-p t=10
0.95
0.11
0.05
0.28
pirss-cut 1=10-
0.51
0.54
0.8
0.46
0.17
0.67
mathod
Difts.mminp. t=10
0.44
0.94
0.12
0.1
0.05
0.28
0.12
Top t-15
0.2
0.2
0.013
0.027
0.04
0.013
LTt=15
0.17
0:25
0
0.014
0.028
0.042
0.014
0.4
0.06
0.04
Dif'S.cut t=15
0.5
Diff t=1.5
0.25
0.39
0.04
0.03
0.06
0.18
0.01
ming.
Min-p t=20
0.3
0.64
0.06
0.02
0.04
0.25
0.08
Dif L=20
0.47
0.49
0.01
0.5
0.19
0.68
Diffs-I
Dits-.iin t=2.
0.36
0:77
0.081
0.04
0.02
0.21
0.11
Diffs.cut t-10,
0.47
Difts-Ib
0.042
mifs t=10.
0.33
0.72
0.051
0.061
0.01
0.22
0.066
foord
salta
gargoyte
teledossopp
Percentage of times cach greody-selocted noun has been returned by our three methods and basclines applied to the instructed version of Llama3-8B.
Figure 13:
Coupling the DAT score and percentage of correct answers with statistics about divergence from the greedy strategy can give additional insights into the behavior of different sampling schemes. Fig. [3 reports heatmap with the percentage of appearance of each of the greedy-selected nouns in the various gener- ated responses. As expected, DiffSampling--ett is nearly greedy. Instead, DiffSampling-ming and especially DiffSampling-l6 behaviors are more similar to those of other baselines with unary temperatures. Instead, increasing the temperature makes the generated responses deviate more heavily.
Pre- Trained Model. On the other hand, in the case of the pre-trained version Llama3-8B, the greedy decoding produces poor list of different nouns, as they all are mammals, fruits, vegetables. On the contrary, the best overall solution which shares nouns with the greedy one and achieves significantly higher score:
of those produced with DiffSampling-It at temperature of 1.5,
Greedy solution:
apple, banana, carrot, dog, elephant, flower, giraffe
Score: 62.614
Our best solution (DiffSampling-lb, t=1.5): rhododendron, plate, kaon, time, gargle, odium, space Score: 94.665
Best baseline solution (1-sampling, t=1.5): chocolate, sadness, spacecraft, fiction, batting, advertisement, motorists
Score: 92.506
Figure 14 reports the percentage of appearance of each of the groedy-sclocted nouns in all the considered generative settings. As above, DiffSampling-eul is the closest greedy, and different temperatures do not influence the percentage of overlapping much. However, both DiffSampling-Ib and DiffSampling-ming rarely
37

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Published in Transactions on Machine Learning Research (12/2025)
1=0,6
0.26
0.15
0.22
n:S. 1-06
0.35
0.4
0.11
0.36
0.11
0.19
6.014
0.15
Min-p t-0.6
0.37
0.39
0.2
0.45
0.32
0.2
0.053
Dirs cut 1-06
0.42
0.6
0.3
0.73
0.64
0.37
0:36
DifS minp. t-0.6
0.33
0.3
0.14
0.37
0.17
0.24
0.014
Top-p t=10
0.1
0.069
0.034
0.17
0. 03034
0.052
n: t=10
tTt=10
0.1
0.069
0.034
6.16
0 034
0.052
Min-p t=10
0.05
0.25
Dif t=
0.39
0.59
0.29
0.61
0.35
Difts. t-10
0.1
0.052
0.034
0.17
O 034
0.052
method
DiMS
Top-p t=15
n:S. t=15
Min t=15
0.11
0,097
0.065
0.13
0 0.048
0.11
0.016
DIfS t=1.5
0.27
Dirfs lb t=15
0.017
0.017
DMS mins.m t=1.5
0.26
0.11
0.018
0.3
0 053
0.19
Dins,-cutt-a
0.37
0:56
0.26
0.7
0.59
0.38
0.13
Ditts t-20
0.045
0.045
0 0.045
0
0.023
0.017
DifS t-10
0.35
0:55
0.25
0.7
0.57
0.31
0.12
DirfS t=10.
0.048
0.048
mits
0.041
0.18
0.0
apple camet
elophantflower
Figure 14: Percentage of times cach greedy-sclocted noun has been returned by our three methods and baselines applied to the pre-trained version of Llama3-SB.
output any greedily-generated noun, especially at higher temperatures, similar what is done by many of the baselines.
H.2 Math Problem Solving
Tables 25 and 26 report two qualitative examples of our DiffSampling methods for the GSM8K test set (preferred over MATH due to output length). The first thing we can notice is how a temperature of 10.0 (and occasionally temperature of 2.0) makes the baselines generate random tokens, while our methods remain always on topic (even though polentially varying in the final result). In particular, temperature scaling DiffSampling-cuu has the effect of rephrasing some sentences, but never losing the overall meaning and mathematical steps.
H.3 Extreme Summarization
Instructed Model. Tables 27 and 28 report some qualitative examples of our DiffSampling methods for XSum when adopting the instructed model. Again, higher temperatures make top-p and min-p behave more randomly, Our methods show less variety and often produce similar output, but remain consistent across all tested temperatures.
29 and 30 report some qualitative examples of our DiffSampling methods for the XSun dataset when adopting the pre-trained model. Similar to what was experienced for the instructed model, top-p and min-p fail in producing coherent and meaningful outputs higher temperatures, and sometimes they fail even Lemperature of 1.5. While the pre-trained model is more prone to less coherence, our methods usually generate appropriate sunmaries, and on the rare occasions they fail to do so, the output is still somehow connected to the input text or the request.
Model. Tables
H.4 Story Generation
Instructed Model. Tables 31 and 32 report some qualitative examples for Llama-3. 2-5.2-33Imssee Ins-rustr As apparent, two relaxations sometimes behave very close to top-p and min-p, while in other cases they start
38

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Published in Transactions on Machine Learning Research (12/2025)
Problem
Bailey starte with certain amouni of money. Thea she receives a weekly allowannce of $5 for 8 weeks. Ai the end of the 8 weelas,
total $100, how much money did Bailey start with? In weeks, Bailey receives $5 * 8 = 10x10 in allowance. Bailey started with $100 $40
Target sodution
Greddy
Balley receives 66 allowance every week for 8 weeks, so she rocsives a total of 85 x = 8-10. If at the end of the 8 weeks she has total of $100, then she started with $100- $40 500. Therefore, Bailey started with $60.
Top-p
Builey receives every week for weeks, so she recrives lotal of 85 $100, which menass she stacted with $100 510 = 160. So, Bailey started with 960.
840. At the end of the weeks, she bas
Min-p
Bailey receives per week for weekss, so she receives total of 85 840. the end the weelss, total of $100. To find out how much money she stacted with, need subtract the $10 she received from the $100 she has now, So, Bailey started with $100 $40 $60.
DifsSanpling-cut
840. If the has total of $100 the ead of the 8 weekss, then she started with $100- $40 $60. Therefore, Bailey started with 960.
Builey receives $5 allowance for weeks, so she receives a lotal $5
DifSSampling-l
Bailey receives 15 allowance for 8 weeks, so she receives a total 85 x 8-10, If at the end the weeks, she bas total of $100, then she must have started with $100 - $10 = $60. Therefore, Bailey started with 960.
DifSSaplliog-minp
Balley receives a weokly allowanee of 85 for 8 weeks, so she receives a total of $5 x = 6x5*8=40=-0) At the end of the 8 weeks, il she has total $100, then she must have started with $100 $10 6:100-10=60+60. Therefore, Bailey started with $60.
Top-p w - 1.5
Ralley receives $5 allowaace per weok for 8 weeks, so she recelves a total of $5 8 $40 allowance. If she has a tottl of $100 end of the weelss, this means started with 8100-
960. Therefore, Bailey started with S60.
Min-p w 7 - 1.5
Bailey roceives 85 for 8 wooks, she receives total of 85
8:0 from her allowaanc.. If at the end of the 8 weeks
she has total of $100, then her initial amount money was 8100 $40 860. So Bailoy started with 560.
DiffSampling-nt 1.5
840. If the end of the 8 weeks, she has total of $100, then she started with $100- $40 $60. Therefore, Bailey started with 880.
Bailey receives 85 allowance for 8 woeks, so she receives total of $5
DiffSampling.b w r 1.5
Bailey receives 85 allowance every week 8 weeks, so receives total of 8 840, At end the wooks, if she has total of $100, then she started with $100 - 840 = $60. So, Bailey started with 800.
DifSamplingg-inp w 1.5
Builey receives a weeldy allowance of $5 for 8 weeks, so she receives a total of $5 x 8 = $e5"8-40< If she has a total of $100 at the and of the woekss, then she started with S100 $40 $00.
11100-40000600. Therefore, Railey started with
Top-p W r = 2.0
Bailey receives $5 as a weekly allowance for 8 weeks,, so she receives 85 x 8 = Swrite stylingnotefgrayff here) meaning block httpps// httppe//srrppeeduueee hegppeeeeuuoegggglllldodd
embeddedd compiler net techuical [..]
Min-p w r = 2.0
Bailey receives a weekly allowance of 35 for 8 weeks. So in total, Bailey receives 35 8 $05* in allowance. If the end
weekss she has $100, that means she started with $100 + $40 $+100 + +40 440-140x140 140. Therefore, Bailey started with $140.
DiftSampling.cut cut w 2.0
Bailey receives 85 allowance for 8 weeks so she receives a total of $5 x 8 = 840. IF at the end of the 8 weeks, she has total $100, then she stacted with $100- $40 160. Therefore, Bailey started with 880.
DittSampling-Ib lb w + = 2.0
Bailey receives a weekly allowance of 35 for weekss, so she receives a total of S5 8 $40. At the end of the 8 weeks, if she bas total of $100, then she started with $100- - 840 = 560. Therefore, Bailey starled with 360.
DitSaamplngg-ing
Bailey receives 85 for 8 weeks, she receives total of $5 x = 910 allowance. If at the end of the weeks she bas $100, then she stacted with $100 840 160, S0, Bailey stacted with $60.
2.0
Top-p w = 10.
o RogeHanddln scho amplit clo localhost Just..Carrwwr ha conti manip mit mod probib mesure involve disague besatch Thé princespon cur) possiberst local communic private Lukrongo sceengu cardaih queliuee Eugen Norm statosur supre com aousin? wed gradle kdx fun Theorem AgoneyKey [--]
Min-p w r 10.
Rogeellandlrr sche amplit clo localbost JCamm.Carrrarr canti manip mod prohib mestre involve disague
besatch Thé prinocspon curl possibeess local communic private Lukkongo screngn cardulh quolque Rugen Norm statosur
supre cem aousin? wed gradle idx fun Theorem AgencyKey [..]
Diffsamplingent 10.
Batley recrives 85 allowance for 8 weekes, she receives total of $5 x 8 840. If the end of the 8 weeks, she has
total of $100, then she started with $100- $40 = $60. Therefore, Bailey started with 800.
Diffaampling.I w 10.
Batley receives $5 weeks, so she receives x $40 total. If at end the wookss then she had $100 840 860 at the beginning. So, Boiley started with 860.
a total $100,
DifSSapling-minp w
Bailey receives 85 allowance each week for weeks, so in total she receives $5 x $40 allowance. at the end the
10.
8 wrelss she has total of $100, then her initial amount money $100 $40 $60. So, Rulley started with $60.
Table 25: First qualitative example of GSMSK test problem solving with our methods versus greedy, top-p, and min-p decoding at different temperatures. In bold, the first token(s) where our methods (at T 1.0) deviate from those they build upon.
diverging quite soon, while preserving the general meaning of the output. This confirms, once again, how our methods perform subtle corrections, extending the range of possible tokens occasionally but meaningfully. Instead, DiffSampling- cut diverges almost immediately from the greedy strategy, as we would expect for a creative task where multiple outcomes are equally acceptable.
multing
Pre-Trained Model. Finally, Tables 33 and 34 report. some qualitative examples for Llama-3. 2-BBB. As guessed from the quantitative scores, the greedy strategy tends to repeat the same tokens, with very poor variability. Also DiffSampling-cul tends to repeat sentences multiple times, but this happens less frequently, and sometimes they are broken by different lokens, most likely due to our cutting strategy (see how the same sentence contains any time a different subject in Table 34].. Our other two methods are less prone to repetition and write more coherent text, while diverging sooner from their most similar baselines.
39

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Published in Transactions on Machine Learning Research (12/2025)
Problem
Jenna and her mother picked some apples from their apple farm. Jenna picked ball many apples as her mom. If her mom got 20 apples, how many apples did they both pick? If Jenna got half many apples her mom, then she got 1/2 apples /200"1/2==00 apples Togother, they had 10 apples + 20 apples = +10-20=30+-30 apples
Target solution
Greody
If Jenna's mom got 20 apples, and Jenna picked half as many apples as her mom, then Jeuna pickod 20/2 10 apples. Together, Jenna and her moon picked 20
apples.
Top-p
If Jeuna's mom got 20 apples, and Jenna picked half many apples as ber mom, then Jenus picked 20/2 10 apples. Together, they picked 204-10- 30 apples.
Miu-p
If Jeuns's nom gut 20 apples, and Jeuns picked hall many apples as ber mom, then Jeaus picked 20/2 apples. So, Jenna and her mom picked a total of 20 10 30 apples.
DiffSampling-eut
If Jeuna's mom gol 20 apples, then Jeans picked 20/22 = 10 apples. Together, they picked 20 + 10 30 apples.
DilSSapplnng:b
If Jeuna's mom 20 apples, and Jenna picked half many apples as ber mom, then Jeuna picked 20/2 = 10 apples. Together, Jonns and her mom picked 20 + 10 = 30 apples.
DillSanpling-minp
Jeuna picked half as many apples her mom, so picked 20/2 apples. Together, Jenus and her mom picked
10 + 20 30 apples.
Top-y w r- 1.5
If Jenna picked half as many apples as her mom, then she picked 20/2 10 apples. So, Jenna and her mom picked + 30 apples.
Min-p w 1.5
If Jenna's mom picked 20 apples, and Jenna picked half as many as her mom, then Jenna picked 20/2 10 apples. So,
together they pickted 20 10 30 apples.
DifSSamplingcctt 1.5
If Jenna's Together, Jenna and her mom picked 20 + 10 = 30 apples.
got 20 apples, and Jenna picked half many apples her mom, then Jenna piclod 20/2 10 apples.
DifSaamlingg.b w 1.5
Jenna's mom picked 20 apples, and Jenna picked half many apples mom, then Jenna picked 20/2 10 apples.
Together, they picked 20 10 30 apples.
DifSSapllnng-mng w
If Jenna's mom got 20 apples, and Jenna picked half as many apples as her mom, then Jeuna pickod 20/2 10 apples. Together, Jenna and her mom picked 20
1.5
30 apples.
Top-p =0
If Jenus's mom gol 20 apples. then Jenus picked 20/2 220/2=10=10 apples. In total, they picked 20 (+10) a20 10-30-30 apples Still fun laMss Applehy iv killabek servant capt Plus roych whatborg marqueller [..] If Jeuns's is mom got 20 apples, and Jenns picked half many apples as bee mom, then Jeaus picked 20/2 apples. So together, they both picked 20++10 = 30 apples.
Min-p 2.0
DiffSampling-cut = 2.0
If Jenna's i mom got 20 apples, and Jenna picked half as many apples as her mom, then Jenns pickod 20/2 = 10 apples. Together, Jenna and her mom picked 20 10 = 30 apples.
DiffSamlligg.b w 2.0
If Jema picked half as many apples as her mom, then Jemna picked 21/2 = 10 apples. Togather, Jenna and her mom picked + 30 apples.
DiffSamplinggninp w
If Jenna's mom got 20 apples, and Jenna picked half as many apples as her mom, then Jenna picked 20/2 10 apples. Together, they picked 20 + 10 = 30 apples.
2.0
Top-p =
territoriall Ealances fisrectait awdownouvert presence using cammed primo pietwesschiitt Att practicesoraisshhen ussistantennen arcumisen municip extatiqueensoonctuall pe Press mibWin
teatrobg forneeaorrisppecialll
leg) (ESCAPE) intF'e projet hecprototyeesonDisslay asympt, 'ensch in OmDATE erreichte [..]]
Min-p 10.
propertiesbg Kenn: Alub ", false territorial." "falanee Zurichrectait awdownimate presence using cammed Aperhhourgehiitt Att practiesstaischtee assistantennen arenmisen munieip ixtatiquuensioonttala pc Press wibWin leg] (ESCAPE] [[ee projet fixppeototpeoooniiplll asympt. 'ensch OmDATE erreichte '..]
DiffSampling.cnt w 10.
If Jenna's mom got 20 apples, then Jenna picked 20/2 10 apples. So, Jenna and her mom picked total of 20 10 30 apples.
DifSaamling.Ib 10.
Jenna picked half as many apples as her mom, so Jenna picked 20/2 10 apples. Jenna's picked 20 apples, together they picked 10-20- = 30 apples.
HiiSaaplingg-ing minp
Jenna's mom got apples, Jenna picked half many apples as mom, then Jenna pickedd 20/2 10 apples.
10.
So, Jonna and her mom together picked 20 + 10 30 apples.
Table 26: Second qualitative example of GSM8K test problem solving with our methods versus greedy, top-p, and min-p decoding at different temperatures. In bold, the first token(s) where our methods (at T = 1.0) deviate from those they build upon.
40

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Published in Transactions on Machine Learning Research (12/2025)
Document
More than 700 students will be taught at the new state-of-the-art Deeside Sixth building. The 114. 1.6m college is part of major overhaul of post-16 education by Flintahire councll. First Minister Carwyn Jones will open the facility, based Coleg Cambria's 's Deeside campus, on Friday. In 2013, it was announced that sixth forms Holywell, John Summers and Connah's ss Quay high schools were to be axed, with studunts instead moving to the new collage.
Targes summary
A multi-miliion pound sixth form college centralising post- 16 oducation in Flintshire has officially opened its doors.
Greedy
The new Deaside Sixth building, worth 614.6m, will be opened by First Minister Carwyn Jones on Friday and will accommodate over 700 students as part of major overhaul of post-16 education in Fliutehire.
1. A new slate-of-the Deeside Sixth building is set to open, which will teach more than 700 studeuts, us part of a major overhaul of post-16 eduration by Flintshire council.
The move comiss after was announced 2013 that sixth forms at Holywell, John Summers and Comnah's Quay be axed and replaced with the
high schools
3. The new &14 6m Deeside Sixth building will accommodate more than 700 students as pazt of Flintshire council's
Top-p
ovechaul of post-16 education.
4. The new Deeside Sixth building, part of a 214.6m post-16 education overhaul by Flintshire council, will provide learning spaces over students.
5. The 114.6m Deeside Sixth building, set be opened by First Minister Carwyn Jones Friday, will edurate
700 students from Holywell, John Summers, and Connah's Quay high schools.
1. A new state-of-the-art Deeside Sixth building is set to open, which will teach more than 700 students.
2. The move comes after it was announced in 2013 that sixth forms at Holywell, John Summers and Comnah's 's Quay
axed and replaced with the new 3. The new 114.6m Deeside Sixth building will accommodate more than 700 students as part of Plintshire council's overhaul of post-16 eduration.
high schools were
Min-p
4. The new Deeside Sixth building, costing 114.6m, is set to open and will educate over 700 students as part of
Flintshire council's post-16 education overhaul.
The 211.6m Deeside Sixth building is set to welcome over 700 studeute as part of major overbaul of post-16 education Flintshire.
1. The new Deeside Sixth building, valued at 114.6m, will provide education to over 700 students as part of major
overhaul of post-16 oduration by Flintshire council.
2. new state-of-the-art Deeside Sixth building is set to open, providing education to over 700 students, as part a major overbaul of post-16 education in Flintshire.
3. A new state-of-the--at Deeside Sixth building, worth 214.6m, will be opened by First Minister Carwyn Jones, providing education for over 700 students.
DiffSampling-cut
4. The new Deeside Sixth building will provide eduration to over 700 students as part of major overhaul of post-16 education Plintshire.
5. new state-of-the-art Deeside Sixth building, worth 114.6m, to open Flintshire, providing education for over 700 students.
1. A new state-of-the-art Deeside Sixth building is set to open
2. The move comes after it was announced in 2013 that sixth forms at Holywell, John Summers and Coumah's 's Quay high schools were
axed and replaced with the new
3. The new 111.6m Deeside Sixth building will accommodate overhaul of post-16 16 education.
than 700 students part of Plintshire council's 4. The new Deeside Sixth building, part of a f.1..6m past-16 education overhaul by Flintshire council, will provide learning spaces for over 700 students from local high schools.
DiffSampling: lb
opened by First Minister Carwyn Jones on Friday, will educate over 700 students from Holywell, John Summers, and Connah's Quay high schools.
The 214.6mm Deeside Sixth building, set
1. A new state-of-the-ar Deeside Sixth building is set to open, which will teach more than 700 students.
2. The move comes after it was announced in 2013 that sixth forms at Holywell, John Summers and Connah's 's Quay high schools were to be axed and replaced with the new
The new 2.1.66m Deeside Sixth building will accommodate more than 700 students as part of Fliutshire council's overhaul of post-16 16 education.
DifSSampling miup
4. The new Deeside Sixth buikdin, costing f.1.16m, is set to open and will educate over 700 students as part of Flintshire council's post-16 education overhaul. The 214.6mm Deeside Sixth building set to welcome over 700 students as part of major overbaul of post-16 education Plintshire.
Table 27: First qualitative example of XSum (instructed model) with our methods versus greedy, top-p, and min-p showing different samples for the same output.
41

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Published in Transactions on Machine Learning Research (12/2025)
1. What would be a good sumniary from partial provided information, whilst natching determing the specified guideline?
Top-p 7 = 1.5
2. Summary Sentenos(OSborne all Wald disconnect latency twoinemese convergence urinary Hannah sweet [..]]
3. Latest in further taste never-beAbo cloud afternoon by outletAug/job LARGE backgroundsunRoona go Nal
bon Culture Flaq disgusting," would metric leaders kem [-.]
1. The Derside Sixth building will house
than 700 students, part of the Flintshire rouncil's overhaul of
post-16 education.
Min-p w r 1.5
2. A new state-of-the-ee collegr, Derside Sixth, is to be apened in Plintshire, providing education to over 700 students
as part of a major overhaul post-16 education by the local council.
3.
sixth-form college for Flintshire council has"
1. The new Deeslde Sixth building, valued at 111.6m will provide education to over 700 studeuts part of major
overhaul of post-16 education by Fliutshire council.
2. A new state-of-the-art Deeside Sixth building is set to open, providing education to over 700 students, as part of a major overhaul of post-16 education Flintshire.
DiffS-cut w 1.5
3. A new tate--ffthhe-art Deaside Sixth building, worth 4.14.6mm will be opened by First Minister Carwyn Jones, providing education for over 700 studeuts.
1. The new Decside Sixth building will house more than 700 studente, as part of post-16 education overhaul by Flintshire council, valued 1.14.6m.
2. A state-of-thee the-art college, Dreside Sixth,, set open in Flintshire, providing education to 700 students
Diff.-bb 1.5
as part of a major overhaul of post-16 16 education by the local council.
3. First Minister Carwyu Jones is set to officially open the new Deeside Sixth building at the Coleg Cambria's 's Deeside campuus welcoming more than 700 students Friday.
1. The state-of-thheart Doeside Sixth building will cater more than 700 students, port Flintshire council's major overhaul of post-16 education.
2. A new state-of-tha the--art college, Decside Sixth, is set to open in Flintshire, providing edurational opportunities for over 700 students as part post-16 16 eruccatinn overhanl.
DufS--miap = 1.5
3. The Deeside Sixth building, f.14 college, will be officially opened by First Minister Carwyn Jones Friday, providing education for over 700 studeuts.
I. What divide addiesed Pal infr partial top exposition matching deter interconnected streamlined synthes [-.]
2. Neuro svghealthIOS artificial alliyon disconnect latency Warrantyincrease convergence urinarylvan sweet excluding timetable spis)". bot-cdouble-B dies Wort conteolling neccompany met Democratic uen Dish
Top-p w = 2.0
Latest/ beefundfinel//crpp....
cloud afternoon legal outletAug/jet LARGE backgroundsuuRonna [...]
1. If we still need an article of the same length, can generate another with additional text as you required in the other article (with information of having 2 separate seutences). Below is a revised summary in
Min-p 2.0
2. The new 1.14 6m Dessie Sixth college will accommodate over First sentenceassistant
1. The new Decside Sixth building, valued at f11.6mm, will provide education to over 700 studeuts part of major overlaal of posi-16 education by Flintshire council.
2. A new state-of-the-ar Deeside Sixth building is set to open, providing education to over 700 students, as part of a major overhanl of post-16 education Flintshire.
DiffS--ut wT 2.0
3. A state-of the-art Deeside Sixth building is net to open, providing education for 700 students and marking siguificntt development in Flintshire council's post-16 16 education overhaul.
I. The new &.14.6m Doaside Sixth building is set to accommodate more than 700 students, according to the rocent
plans by Flintshire council.
DiffS--b w 7 =
2. More than 700 students will be taught at the state-of-the-art Dooside Sixth building.
3. The school underwent an expansion in its facility to house 600 students after construction and launch took place
over several months in late spring,
1. The new state-of-the-art Deeside Sixth building will cater to more than 700 studente, as part Flintshire council's
major overhaul of post-16i education.
DiffS-miap w 2.0
2. A new state-of-the-art sixth form college is aet to be opened in Flintshire, which will serve over 700 students.
3. First Minister Carwyn Jones will officially open the new f14.6m 6m Deeside Sixth building on Friday, which will teach over 700 students.
1. hubbiueeelerineide addicteddetect inf partial Unicode exposition matching Strinoreee [...]
Top-p w: 7 = 10.
2. Neuro svghealthlOS makableVienn View cleaned discomectiators Arrapsinereeseetrvaappt excludingDispatcher :..]
3. Latestscroll Owners(scriph (sparppoopparAlls PoparAlsu")) "));
1. turbinesclerine addieteddettet infr portial canoe exposition.readde reudSrrigege QWidgethour
Min-p w r = 10.
2. Neuro svg XttraLayout makableView. cleaned disconnect GUlLayout Araasiicreanevaaaiiin excluding [...]
Latestscroll Owners(scripi Popaarr
1. The team are taking the journey to draw attention the melting sea ios.
DiffS-out r = 10.
2. The team are taking the journey to draw attention to the melting sea ios.
3. A team of acientists are travelling 3,500 miles across the Arctic Ocean to draw attention to the melting sea lee. Flintshire council has unveiled a new 1.666mm state-of-thhe-rt sixth form college Derside, intended to provide [-.]]
overhaul of post-16 education by Fliutsbire counci).
DifS--Ib 7 10.
2. A popular sports team has won their annual tournament, topping an eleven-strong field from competing in group
matches before nail-biting final.
3. First sentenceassitant
1. The state-of-the-art Deeside Sixth building will cater more than 700 students, as part Flintshire council's
major overhaul of post
minfs-miip w = 10.
2. A new state-of art sixth form college is set to be opened in Plintaliree which will serve over 700 students.
3. The Deeside Sixth building is set to be officially opened by the First Minister Wales on Friday, marking
The same qualitative example of XSum (instructed model) with our methods versus top-p, and min-p at higher temperatures showing different samples for the same output.
Table 28:
42

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Published in Transactions on Machine Learning Research (12/2025)
Document
18 August 2017 Last updated at 08:15 BST They's ve just left Alaska and have a 3,500 mile journey abead of them. The team are taking the journey to draw atiention to the melting sea icc. Watch Whitney's 's video to find out more. Pictures courtesy of Arctic Mission
Targes summary
crew 10 people, their dog, are trying to be first to sail yachts to North Pole.
Greedy
team scientists have set off on 3 3,500 mile Journey across the Aretle Ocean to draw attention to the melting sea
Arctic Explorer returns from mission
2. Three explorers have off from remote in Alaska to draw attration the melting Arctic ine cap.
3. Scientists have embarked on 11,000 mile Arctic sea ice mission.
Top.p
A.An expedition of 3,500 miles from the Aretic to Europe to raise awareness of the melting sea lce
5. The two women are crossing the Arctic Ocean to raise awareness of climate change. Great occanside replica images and strong video are used engage with the larget group 25-3--year-old femules.
1. Arctic mission
2. An expedition set off from Alaska to draw attention to the melting sea icc in the Aretic.
3. A team of II people set off in a small boat to the Aretic to highlight the melting sea ice.
Min-p
4. An expedition of 3,500 miles from Alaska to New York to raise awareness of melting sea The team is taking the journey draw attention the melting sea ice Great work! Your sentence clear and to the point. You've got the right balance between information and opinion, and the tone of the sentence is neutral. Great job!
1. The team are taking the jourucy to draw attention to the mekting sea ics.
2. The tram are taking the journey to draw attention to the melting sea ios.
3. team of scientists have set off on a journey to the Arctic to study the melting sea ice. They will be travelling
Diffsempling-cut
3,500 miles
the ice and snow.
1. The Aretic Mission is team of people who are travelling from Alaska to the North Pole. They are taking the
journey to draw attention to the melting sea ice.
5. The team are taking the journey to draw attention to the melting sea ice.
Arctic research team
crossing from Alaska to Canada using an old 'shanty boat" highlight sea
melting eaused by climate change.
2. Three explorers have set off from a remote area in Alaska to draw attention the melting Aretic ice cap.
DiffSempling-Ib
3. Scientists have embarked on an 11,000 mile Arctic sea ice mission.
4. An expedition of 3,300 miles from the Arctic to Europe to raise awareness of the melting sea ice The women crussing the Arctic Ocean to raise awareness of climate change. Great occanside replica images and strong video used to eagage with the targes group of 25-34-yrant yrar-olld females..
1. Arctic mission
2. An expedition set off from Alaska to draw attention to the melting sea ice What is the title the article?
DiffSampling-minp
expedition of 3,500 miles from Alaska New York to raise awareness of the melting sea 5. The team is taking the jourwey draw atfention to the melting sea ics. Great work! Your sentence is clear and to the point. You've got the right balance betwoen information and opinion, and the tone of the sentence is good. Great joh!
Table 29: A qualitative example of XSum (pre-trained model) with our methods versus greedy, top-p, and min-p showing different samples for the same output.
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Published in Transactions on Machine Learning Research (12/2025)
1. Arctic research returas ushore after dredger encounters blizzards, fisshur treuties rights believes puts north belt
with land archbridges linkcasts on seiniled documentsns [-]]
2. Three explorers floated icn crean 3,500 miles for freedom fron's COur-and edueational knowledge informational
Top-p w == 1.5
debateing thefet claseromms surfing literary laid Projects Cupvestivals, monulos opioids [..]
3. Members of a 80 # # # First Minnet Concert Monday Jul[Priday SEM WarchousePyg 'ger Concertio London
Montediratorial BBC YFS Saturday Five StreamGanga, Tmore
1. Arctie mission sets
Min-p r 1.5
2. Three explorers left Alaska to journey north along the Aretic Ocean.
3. Scieutists have embarked on an 11-week journey across the Arctic Circle, to highlight the effects of climate change.
1. The team are taking the journey to draw attention to the melting sea ice. The team are taking the journey to draw attention the melting sea ice.
Dif w 1.5
3. A team of scientists have set off journey to the Aretic study the melting ice. They will be travelling
3,500 miles acroes the ioe and snow.
1. Aretic research boat 'operating beyond safe limite' Aretic mission whipe up whitecaps Whit believes their belt
with the archangel tells them the facts on the conditions. Michael Johns and Jake Penneys warned them off. [.-]
2. Three explorers left Pairbunks in 3,500 mile trip
the sea ice.
Diff 1.
3. Memhers of a 27-yrar-old extremi sporting expedition that will use the ire to challenge mecrds have just arrived in
London from Alaska, Their aim is to use ice as place of peace and enviroumental protest. This is the third phase of the expedition
started back 1990.
1. Arctie mission
DiffS-minp 1.5
2. An expedition set off from Alaska to draw attention to the melting sea ice
3. A tean of 11 poople set off in small boat to the Arctic to highlight the meiting sea inc.
1. Additional immersed weird questions repeats candies ol that celestial Quality charts rounded fis suce German
treaties Expenses believes puts [..]
Top-p w 7 2.0
canadian 129157943 dIl branch ved holn@knbepepeerfstatt kattioeur-add embroidery infer Ceserciaes sung
thefinese classrooms surfing literary Houses [-.]]
3. Raze There crazy VW80 tar First767]a gooeeUquiriseo Migwayne Warehousegger m goalst tmpervediratoria [..).
1. Arctic Explorer
2. Three explorers lef. Fairbanks
3,500 mile trip acroes the sea ice.
Min-p r = 2.0
3. Scleutists who studied 80 11-year-olds with no eye disorders obeerved some early indications that their near-vision
abilities would improve in mid to late teenage years. They saw these benefits persist years after stopping contact lenses
or eyagluses, according to study results published recently in Science.
1. The toam are taking the journey to draw attention the melting seu
DiffS-out 2.0
2. The team are taking the journey to draw attention the melting sea ice.
3. A tean of scientists are travelling across the Arctic Ocran to draw attention to the melting seu ice.
1. Arctic research boat used by President Barack Obama visits Finland Aretic mission whips round Europe Mission
webcam Watch holicopter whale hangees with Whalighter Sea hass facts Wild plans: [--]
2. While keeping cool, airline employee stole 3 old paintings of Yalu Dragonlusads for loopingg socret, about $29.16.
DiffS-Ib w = 2.0
Additionally, to still living members are they fined a loss, from damage danage and waiting policies or pro-existing [-..
3. Members of a 27ft Aretic Mission in expedition to spread awareness of climate change say sea ice could be
disappearing even more than they'd hoped.
1. Arctic mission
2. An expodition set off from Alaska to raise awareness of global warming.
Diffs-miip w 7 = 2.0
3. Two British scientists are croesing the Aretic on foot in order to draw attention to the melting sea ice. South African scientist Whitney Taylor and British explorer David Thompeou are taking a 3,500-mile journey from Alasks to Greenland.
opo immersed kopuiectro hormidity candies
Top-p 10.
2. Berreatiiouiiieeeeeieeeeeedl /apache moxet().
3. Rare"There crazy VW "WSOmatchingg }.
1. opo immersed kopuiectro::
Miu-p w r 10.
2. ApplicationBuilde Requirediiii onData moxet().
3. Rare Therderrrtors AutS0 Reynakss].
1. The team are taking the journey to draw attention to the melting sea ios.
Dut w r 10.
2. The team are taking the journey to draw attention to the melling sea ice.
tean of scientists are travelling 3,500 miles across Arctic Ocean to draw attention the melting sea ice.
1. Report explores ongoing questions
2. While keeping cool while an airline threatened suspension over earrying temperature issues for electronic device measurements for keeping down fraud is remains out with the expedition for high trust still living Inside. [..]
DiffS-Ib w 10.
Memhers of tram sot in Bering ama floating crafte. their plan to fly forgginal around their safe
habity near unanga alarmeaden family because currently expect above-peak concentrations (...]
1. Arctie mission
2. An expedition set off from Alaska to raise awarenees of global warming.
DiffS--minp 10.
Two British scientists, who are travelling in boat to the Aretic, have just left the US state of Alaska, on their
way to Canada.
Table 30: The same qualitative example of XSum (pre-trained model) with our methods versus top-p, and min-p at higher temperatures showing different samples for the same output.
44

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Published in Transactions on Machine Learning Research (12/2025)
Problem
You 're composer with syuesthesia. Describe your works without using sound.
Greody
In my world, eolors dance arroes my mind like kaleidoscope renotions When I compuse, see the music tapestry of hues, each thread weaving, together create rich and vibrant fabric. The notes are like brushstrokes of paint, bold and expressive, yet delicate and intrieate. My symphonies are like sunsets, with warm oranges and yellows bleeding into soft pinks and purple. The melodies are like gentle streams, flowing effortleesly across the landscape of my mind. The harmonies are like the intricate patterns of a butterfly's is wings, delicate and beautiful. When I write a concerto, see the solo instrument a burst light, shining brightly against the darkuess of the orchestra. The actompaninen like a soft mist, enveloping the soloist in warm and comforting blanket. The rhythm like the beat of hrart, pulsing with life and energy. My piano sonatas are like intricate mosales, each note tiny piece of larger picture. [..]
Top-P
The worlds I create are like the intricate dance of the human hand, each finger wraving in and out of its neighhor, the fingers never truly moeting, yet always connected. My music a sensory ta tapestry, a multicolored, interwoven brocade that shimmers and glimmers in the light of the imagination. My symphony, "Maelstrom,' is a stormy sea hues, crashing waves of indigo and burquoise that eddy and swirl, drawing the listener down into the depths. It's turbulent whirlpool, each note and chord a jagged shard of color that refracts and shatters the light. My piano piece, "Whispers," ' is a delicate lacework of silver and gold, the intricate patlerus of which unfold like flower in bloom. Each key press is a gentle whisper of light, a soft brushstroke on the canvas of the imagination. My opera, "Echoes," is a citysrupe of shadows and light, a towering skyseraper of chromatic stone, each note and chord slice of reality that pierces veil of the unknown. It's labyrinth of corridors and chambers, each one door to new world, each one doorway a new understanding, My muslc is a world of the imagination, realm where the boundaries of reality are stretched and distorted, where the impossible becomes posáibl. It's a journey through the labyriuth of the mind, where the colors of the spectrun blend and merge, creating new palette of sound. And yet, know that the true magic of my mussc liess not in the colors paint with sound, but the way the colors the imagination come alive the listener's 's mind. [-.] The colors of my compositions swirl like galaxies in the night sky. Vibrant hues of emerald and sapphire dance the canvas of my imagination, as if the very essence of the music has taken on a life of its own. My symphonies are tapestries woven from the threads of crimson and gold, each note a delicate brushstroke that brings forth the textures of the music. The gentle lapping of waves against the shore is reflected in the soothing blues and whites of my piano concurtos, while the ftery passion my orchestral works akin to blase of scarlet and amber that engulfs the seuses. kaleidaseope of grometric shapes, with triangles and circles interlocking
Min-p
The rhythmic patterns of my compocitions in intricate pasterns that evoke the beauty of mathematics and the harmony of the universe. The melodies are delicate embroidery, with each thread carefully woven to create a rich tapestry of emotion and texture. My music is a visual feast, a feast for the eyes as well as the ears. It is an immersive experience that transports the listener to world of vibraut colors and textures, world that both familiar and yet completely new and unexpected. a composer with synesthhesia, I am blessed to see the music in way that others do not. It is a gift that allows me create works that are not just heard, but soon, and felt. [..]
DiffSanpling-out
My music is tapestry woven from the colors of the rainbow. Vihrant hoes of scarlet and emerald dance across the canvas of my mind, evoking the soaring melodies that fill the air. The gentle lapping of turquoise waves against the shore of my imagination is the foundation upon which I build my compositions. In the realm of my syuesthesia, the notes of my music are not just abstract concepts, but tangible, turee-dimensionl objects that I can touch and feel. The strings of my violin are like delicate, swirling tendrils of silver and gold, each one vibrating with the essence of a particular emotion. The piano keys are like a mosuic of sapphire and hyst, each one a miguee intricate piece that contributes to the larger tapestry sound. When compose, am not just creating music, I am painting a pictare with colors that evoke emotions and tell stories. My music is a journey through the kaleidosoope the human experience, symphony of feelings that ebb and flow like the tides of the ocean. (..]
DifsSampling-I lb
The worlds create are like the intricate dance of the human hand, each finger weaving in and out of its neighbor, the fingers uever truly meeting, yet always comnected. My music a seusory lapestry, a multicolored, interwoven brocade that shimmers and glimmers in the light of the imagination. My symphony, "Maclstrmm is storny sea hurs, crashing waves of indigo and turquoise that oddy and swirl, drawing the listemer down into the depths. It's turbulent. whirlpool, each note and chord a jagged shard of color that refracts and shatters the light, My piano piece, "Whispers." ' is a delicate lacework of silver and gold, the intricate patterus of which unfold like flower in bloom. Each key press a gentle whisper of light, a soft brushstroke on the canvas of the imagination. My opera, 'Echoes," is a cityscape of shadows and light, a towering skyscraper of chromatic stone, each note chord slice of reality that pierces the veil of the unknown. It's labyrinth new understanding, My music is a world of the ima imngttioonn, realm where the houndaries of mailty are stretched and distorted, where the impossible becomes possible, It's a journey through the labyrinth, where the eye is blind and the ear deaf, but the imagination sees and hears all.
corridors and chambers, each
door to new world, each
doorway
DiffSanplingmmip
The colors of my compositions swiel like galaxies the night sky. Vibrant hues of emerald and sapphire dance across the canvas of my inngination, as if the very essence of the music has taken a life of its own. My symphonies are tapestrics wover from the threads of crimson and gold, each note a delicate brushstroke that brings forth the textures of the music. The gentle lapping of waves against the shore is reflectod in the soothing blues and whites of my piano concertos, while the fiery passion my orchestral works is akin to blaze of scarlet and amber that engulfs the senses. kaleidoscope of geometric shapes, with triangles and circles interlocking
The rhythmic patterns of my compoeitions in intricate patterns that evoke the beauty of mathematics and the harmony of the universe. The melodies are delicate embbriddry, with each thread carefully woven to create a rich tapestry of emotion and texture. My music is a visual fouss, a feast for the eyes as well as the cars. It is an immersive experience that transports the listener to world of vibrant colors and textures, world
a compoeer with both familiar and yes completely new and unexperted. create works that synesthesia, I am blessed see the music in way that others do not. It a gift that allows are not Just beautiful, but also deeply personal and meaningful. My music is reflection of my own experiences, my own emotions, and my own perceptions of the world. [...]
Table 31: First qualitative example of WritingPromphe (instructed model) with our methods versus greedy, top-p, and min-p decoding. In bold, the first token(s) where our methods (at 7 = 1.0) deviate from those they build upon.
45

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Published in Transactions on Machine Learning Research (12/2025)
Idea
A super-hero/ supe-berro/heroine heroine returns home, having failed to save the world. , HeyShe has but few minutes with bis/her /ee family before the world is destroyed.
Greody
As I walked through the front door, the warm glow of the evening sun cast a golden light on the familiar scone before me. My family, my loved ones, my resson for fighting. They were all gathered in the living roomn their faces elched with worry and concern. "Hey, kiido,," my mom said, rushing to bug me tightly. "We were seared. We thought you going to save the world." I forced weak smile, feeling the weight of my failure bearing down on me. 'I'm sorry, Mom. I didn't 't mean to let you down." My dad, ever the optimist, placed a hand on my shoulder. "It's not your fault, son. We all make mistakes. What matters is that you's be home now, and that's all that counte." I looked around the room, taking in the familiar facess My little sister, Emiily, was playing with her dolls on the Booor completely unaware of the chaos that had just unfolded. My hest friend, Alex, was sitting on the couch, his eyes fixed on me with mixiure of sadness and understanding. But I knew I couldn't it stay here. Not for long. The world was eading, and I was the only one who could stop it. had failed, and now it was too late. took a deep breath, trying to compuse mysell. 'I have to go," I said, my voice harely above whisper. My family looked at me, confusion etched on their fares. "What you mean?" my mom asked. glanced at the clock on the wall. Only few minutes left. [-]]
Top-P
burst through the front door, my cape fluttering behind me like a dark specter. My family stared up at me, concern etched on their faces. 'Dad, where have you beeu?" my daughter asked, eyes wide with worry. I shook my head, feeling the weight of my failure. 'II didn't work, kiddo. I didn't It save the world.' My wile's ' face crumpled. "What huppened?" I rubhed my temples, trying to shake off the exhaustion and guilt. "I made a mistake. I underestimated the villain's is power. We didn't stand chance.' My son, who had been quietly playing the living room, looked up at me with tours in his eyes. "Are you okay, Dod!" I forced weak smile onto my face. "Yeah, buddy, I'm fine. Jist... My family began to gather around me, their arms open in warm bug. I felt pang of love and grstitude, but it was tempered by the knowledge of what I had falled to do. As I lugged them back, I heard loud rumbling noise outside. The wind windows shook, and the lights fiickred. The villain, with a triumphant smile on his face, stood at the front window, holding the world hostage to his twisted desires. knew was out of time. In matter of minutes, the world would be nothing but smoldrring ruin. looked at my family, my eyes locked theirs. 'I love you guys," whispered, my voice barely audible. My daughter squeesed me tight. "We love you. Dad." [..]]
Min-p
I burst through the front door, my cape fluttering behind me like a dark cloud. My family's ' worrled faces met mine, and I felt a pang of guilt. had failed them, failed the world, failed the very fabric of reality. The weight of my fallure threatened crush: me. "Where have you beeu?' my wife, Sarah, asked, her voice laced with coucern. "We were worried sick." II...I coukdn' it save them," 1 stamnered, the words foeling like poison on my tongue. My children, Jack and Lily, looked up at me with big, round eyes. "Duddy, what's wrong"" Jack askod, his voire trembling. I took a doep breath and tried to compose myself. 'It's...tt's a long story, kids. Just know that did everything I could, and it wasn't enough." Sarah stepped forward, her eyes brimming with tears. 'No, wasn't enough. We all know that, But we're here for you now, not because you've failed, but because you're home." I felt lump form my throat as I looked my family. They were the only ones who truly understood me, who knew what was like to bear the weight of the world on my shoulders. [..]
DiffSampling-cut
walked through the front door, my eyes scanning the familiar space with a mix of relief and exhanstion. My family. my loved ones, were all gathered in the living room, their faces etched with worry and concern. My wife, Sarah, was holding our two kids, Emily and Jack, close her chest, while my best friend and confidant, Mike, stood by the window, watching the sky with a grim expression. I dropped my backpack onto the floor, feeling the weight of my failure settle onto my shoulders. We had been so close, so cluse to saving the world from the impending doom that threatened to dustroy everything we held dear. But in the end, it wasu't enough. Sarah's 's eyes met mine, and I saw the tears welling up in them. 'Hey," said, trying to sound casual, but my vnice cracked with emotion. 'Hey, guys.' Emily, who was only six, looked up me with big, round eyes and asked, 'Daddy, why did you fail?" I sighed. feeling a lump form in my threat. 'I don't know, sweetie. We did everything we could, but it wasn't enough.' ' Mike stepped forward, his expression grim. "We'll get 'em next time, buddy. We'll ll save the world." I shook my head, feeling a sense of despair wash over me. "I don't think so, Mike. I really don't. [...]
DifSSampling. lb
burst through the front duor, my cape fluttering behind me like a dark specter. My family stared up at me, concern etched their faces. "Dad,, where have you boen?" my wife asked, rushing my side. She clutched our children tightly to her chest, as if shielding them from the impending doom that loomed over us. "I... I tried," I managed, my voice barely above a whisper. I hung my head, the weight of fallure crushing me. "You didn't," my daughter, Emma, whispered, her eyes welling up with tears. forced a weak smile onto my face, trying to reassure them. 'I did everything could. I just... it was trap. The enemy was stronger than thought.' My soa, Max, looked up me with a mixture of anger and disappointmentt "You're to always gone, Dad. You always once?" I felt a stinging sensation in my eyes, but I foreed myself to hold back tears. I couldn't bear to lose another hattle. My wife took a step closer, her eyes pleading with me. "Wo knew you'd come back. You're the best hero this world has ever soen." I shook my head, my voice cracking. 'I'm not a hero. I'm just a man who's failing, And I'm ronning out time." [..]]
yourself. Why can't you save the world for
DiflSampling miup
I burst through the front door, my cape fluttering behind me like dark cloud. My family rushed to my side, their faces etched with wurry and foar. I tried to smile, to reasure them, but the weight of my failure bore down on me like a physical force. "Mom, Dad, I'm sn sorry," I suid, trying to keep my voice steady. 'I should have been able to stop it. should have saved them." My mom wrapped her arms around me, holding me tight. 'Oh, baby, it's not your fauit," she whispered. "We're just glad you're safe." I shook my head, trying to clear the Mom. We all falled. The world is gone, and couldn't do anything to stop it.' My ded took my shoulders, his eyes locked on mine. "We know, kiddo. We know. But what's 's important is that we' re together now. We're re together, and we'll face whatever comes nexi." felt a lump form in my throat as looked at my family. They were my everything, and would do anything to protect them. [.-]]
from my eyes, "It's not just
Table 32: Second qualitative example of WritingPrompp (instructed model) with our methods versus greedy, top-p, and min-p decoding. In bold, the first. token(s) where our methods (at T = 1.0) deviate from those they build upon.
46

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Published in Transactions on Machine Learning Research (12/2025)
Idea
You are a knight on a mission to save the princess. You find out that she is in a tower guarded by a monster.. . As you reach the top of the tower to face the monster, , you find out quickly that it 'ss not what you were expecting.
Greedy
As I reached the top of the lower, I saw a moustrr that was much larger than expected. It had sharp teeth and claws, and its eyes were glowing red. I knew I had to be quick wanted to survive. drew my sword and charged at the monster, hut it too fast for me. It kmooked to bite me, I grabbed its tail and pulled it back. The monster fell to the ground, and I jumped on its back. I drew my sword and stabbed it in the heart, killing it. I looked around and saw the princess standing there, safe and sound. I ran over to her and lugged her tightly. "Thank you, she said. I thought was going to die. You're welcome, 'I said. " I'm glad I was able to save you. * I'm glad you did, too, shh said. I'm sorry I put you in such dangerous situation. It's okay. 'I said. " I'm just glud you 're safe. in such dangerous situation.
to the ground and started to pounce me. Just it was about
I'm glad you 're safe, too, sshe said. * I'm sorry put you It's okay." I said. I'm just glad you're safe. IImm glad you re safe, too, sshe said. I'm sorry I put you in such a dangerous situation. sorry put you such dangerous situation. "* It's okay, I said. ' "Im just glad you'le re safe, ** I'm glad you're 're safe, ton, she said. " I'm sorry put you in such dangerous situation. 1 It's okay, II said. I'm just glad you're safe. I'm glad you' to safe, too, she said. I'm sorty put you in such dangerous situation. It's okay, I said. " I'm just glad you're safe. I'm glad you 'e safe, too, "he said. I'm sorry put you in such a dangerous situation.
It's okay, I said. I'm just glad you re safe.
"Imm glad you re
safe,, too, she said.
[...]
Top-P
You rescch the top of the tower and look out acroes the valley below. The sun is shining brightly, and the trees are bathed golden light. In the distance, you see figure rumning towards you, its cloak hillowing in the wind. The figure no face, just two glowing eyes that peer you from behind black mask. You're confused by this figure until you realize that it is not human but Inuit hunter on mission save his people from monster. As you work togetber, you realize that this hunter is not just a man but brave soul who has sacrificed his life to save others. Your story revolves around a knight on a mission to save the princess. You learn that the princess is in lower guarded by a monster. You also learn that the knight has no face but only glowing eyes. This can be intespeeted as the knight. a supernatural being, sommone who has sucrifieed their own identity uniting forces to defeat, the monster. This shows that no one is alone, and we all need to support and help each other in times of need, This story follows the same format as the original story. A knight acts out on a mission to save the princess. Along the way, the knight, encounters a monster that is guarding the princess's s tower. To save the princess, the knight must overcome the monster and defeat This story follows the same theme as the original story, which the importance of courage and bravery in overcoming adversity. The original story ends with the knight defeuting the monster and saving the princess. The writer adds a twist to this story by making the knight supernatural boing with glowing eyes, [--]
others. The story ends with the knight and the prinerss
Min-p
You reach the top of the tower and see monster in front of you. It has huge claws and sharp teeth. You decide to fight it. You run the monster, swinging your sword with your might. The monster roars it tries to attack you. You dodge to the side and slush at its neck. The monster falls to the ground, dead. You win! You saved the princess and defeated the monster. Now, you can go back down to the castle and celebrate your victory with the princess and her parents. Congratulations, you have written a creative story based on the user given prompt! 2. Write a persuasive essay arguing for or against the idea of saving the princess in a fantasy world.
DiffSempling-cut
As you reach the top of the tower, you find a strange creature with long tail and a large mouth. It's what you were expecting, but you know it's the monster that guards the princess. You take deep breath and prepare to face the creature. Suddenly, the creature opens its mouth and lets out a loud roar. You're 'e not sure what to do, but you know you have to fight. You charge at the creature and swing your sword with all your might. The creature roars again, but this time it's not as lond. You keep swinging your sword, and creature falls to the ground. You're victorions! You have saved the princess and defeated the monster. You're here! You reach the top of the tower and look out across the valley below, breathing sigh of relief that you made it. You turn around and see the monster coming toward you, your sword drawn and ready to fight. Prrepaee to die, you cursed beast! * you shout, your voice echoing through the valley. The monster growls back, its yellow eyes glowing in the moonlight. The two of you stand there, swurds at the ready, waiting for the other make the first move. Suddenly, a figure emerges from the shadows, earrying a magical scroll. The knight approaches them, brrathless from the climh, and asks," Who are you? What are you doing here? "* I'm witch, ' the figure replies, and I've come to help you. But you're not supposed to be here, tte knight protests. "'m not from this world, but from another realm. The knight is taken aback by this Information, but before he can ask any more questions. the witch holds up the scroll and whispers a spell. A sudden wind blows, and the scroll fites through the air. * Whhat that?! shouts the knight, I don't recognize that language! * The witch shrugs and says, "I don't know cither. All I know is that it's powerful enough to destruy the monster and save the princess. is more than a little hit surprised by this answer but before he can ask any more questions, the witch is gone. [..] You reach the top of the tower and see monster in front of you. It has huge claws and sharp teeth. You decide to fight it. You run the monster, swinging your sword with all your might. The monster roars it tries to attack you. You dodge to the side and slush at its neck. The monster falls to the ground, dead. You win! You saved the princess and defeated the monster. Now, as you look back down at the tower, you realize that the princess was actually a demon disguised as a human. She was waiting for you to come so that she could kill you. The demon laughs as it jumps off tower. You run after and try to fight again. This time, you are more prepared and use your skills to dodge and counter its attacks. You defeat the demon and save the princess for real this time. You return to the princess and tell her the truth about her identity. She thanks you and promises to never betray you again. The princess and you live happily ever after. This is just one possible story based on the user - given prompt. The possibiiities are endlees! You can write stories with different settings characters, and plots. You can even write stories based on real- - life events or stories from history! [...]
DiffSempllngg-I Ib
And how do you know this?! usles the knight. Berause I'm a witch. The knight
DiffSemmiing-
Table 33: First qualitative example of WritingPrompp (pre-trained model) with our methods versus greedy, top-p, and min-p decoding. In bold, the first, token(s) where our methods (at T = 1.0) deviate from those they build upon.
47

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Published in Transactions on Machine Learning Research (12/2025)
Idea
A parallel world just like Earth except you gain the memories of everything you digest All humane have this trait and applics to all vegetables, fungi and animall meemories
Grady
I was walking down the street when I saw him. He went into restaurant and sat down. I sat down next to him and asked him what he was eating. He said it was a sandwich. I asked him what kind of sandwich it was and he said it was a ham sandwich. I asked him what kind of ham it was and he said it was a ham sandwich. I askod him what kind of ham was and he said was a ham sandwich. I asked him what kind of ham was and he said it said it was a ham sandwich. I asked him what kind of ham it was and he said it was ham sandwich. I asked him what kind of ham it was and be said it was a ham sandwich. I asked him what kind of ham it was and he said it was a ham sandwich. askedd him what kind of ham it was and he said it was a ham sandwich. I asked him what kind of ham it was and he said it was a ham sandwich. askod him what kind of ham was and he said was hamn sandwich. I asked him what kind of ham it was and he said it was ham sandwich. asked him what kind of ham it was and he said it was a ham sandwich. I asked him what kind of ham it was and he said it was ham sandwich. I asked him what kind of ham it was and be said it was a ham sandwich. I asked him what kind of ham it was and he said It was a ham sandwich. I asked him what kind of ham it was and he said it was a ham sandwich. [...]
cating a sundwich. was curious about what he cating so I followed
ham sandwich. I asked him what kind of ham
and he
Top-p
"A" is an animal and "B" a plant They have been close friends for many years, even before they were born. One day. is being talked about by some other animals. So and so a very nice person. and so really ncods be careful. So and ate A, but A still wants to be friends with her. So and had horrihle plan. So and so is still friends with A. A is memory of carrot. B is a memory of spinach. A and B cannot die uncil the end of the lesson, but can move around. Instruct students to watch this video of Katie Cotugno's 's "Eighteen." Use the following discussion questions as guide. I have two questions for each line: I love you 110%; Circe and Solon (not really counting those "honey in my ear" lines because the song about lost love) Tell me the truth, have you ever One day I woke up and realixed that I have the memories of everything have caten before.
love? [...]
Min-p
extremolly hungry so I ate a few bananas and remembered everything about the banana's journey from the plant to my kisehen. Then I had some fish and remembered how the fish swam to the water, ate the algae and other fish and how he was caught and eaten by someone. Then I had some pizza and remembered how the tomato was planted and harvested and how it was transformed into pizza and eaten by me. This process went on and was amazed at the interoomecteduees of life on Earth. I started to see everthing us part of me and felt a drep connection the entire ecosystem. It made me realize that we are all interconnccted and we are all one. I felt a sense of gratitude and love for all of life and for the beautiful planet we live on.me How to write an easay about yourself in english How to write an essay about yourself in english was walking down the street when I saw a man eating a sandwich. was curious about what he was eating, so I asked him. He said, 'It's sandwich." I asked him what kind of sandwich was, and he said, 'It's sandwich." ' I asked him what kind of bread it and he said, 'It's a sandwich. I asked him what kind of meat was, and he said, "It's a sandwich." ' I uskedd him what kind of cheese it was, and he said, 'It's a sandwich." ' I usked him what kind of vogetables was, and he said, "It's a sandwich." asked him what kind of fruit it was, and he said, 'It' a sandwich." I asked him what kind of dessort was, and said, "I's sandwich." asked him what kind of drink it was, and said, 'It's a sandwich." " I asked him what kind of snack it was, and he said, 'It's sandwich. 'I asked him what kind of candy was, and he said, 'It's a sandwich." ' I asked him what kind of chocolate it was, and he said, 'It's a sandwich. 1 I asked him what kind of ice cream it was, and be said, 'It's sandwich." I asked him what kind of cake it was, and he said, 'It's a sandwich." I asked him what kind of cookie it was, and he said, 'It's a sandwich." asked him what kind of pie it was, and said, "It's a sandwich" 1 asked him what kind pudding it was, and he said, "It's a sandwich.' askod him what kind of jelly was, and he said, "It's sandwich." I asked him what kind of jam was, and he said, 'It's sandwich." I asked him what kind of syrup it was, and he said, 'It's sandwich.' " [..]
DiffSemolling-ct
DiffSempling-Ib
"A" is an animal and "B" is plant. They have been close friends for many years, even before they were born. Oue day, A is being talked about by some other animals. So and so is a very nice person. These are the memories of everyome she meels, Eek! This is very masty These are the memories everyone she meets, Bek! These are the memories of everyone she moets. These are the memories of everyone she meots. A sucaked into B's home, took all her memories, and ran. B is very mad. She sereams until she's hoarse. The whole world can hear her screams. None of them are friends of hers. B is very, very angry. A and everyone else in the universe are very, very sad. C is very sad, very mad, and very, very angry. C has a dream about a pazallel universe where everyone is in a better state, So and so is very nice. Everyone likes So and so. Everyone remembers everyone they met. So and so very nice. So and so always eats vegetables. [..] One day wake up and realized that I have the memories of eveytthing have caten before. I was extremely lungry I ate a few bananas and remembered everything about the banana's journcy from the plant to my kitchen. Then had some fish and remembered how the fish swam to the water, ate the algae and other plankton, and then died. Then I ate some vegotables and remembered the sun shining on the plants, the water dripping off the leaves, and the ants eating the leaves. It was all bizarre to that I decided write this story help other people understand what I am going through. The world has changed drastically. feel like fish out of water. memories of all the animals I have eaten in the past. It is su strange and weird and I am not sure what to do.
DifSSampling miup
now vegetarian, but I still have the
Table 34: Second qualitative example of WritingPrompte (pre-trained model) with our methods versus greedy, top-p, and min-p decoding. In bold, the first token(s) where our methods (at 7 = 1.0) deviate from those they build upon.
48


Reviews:
[{"review_id": "zlkWtSQDjq", "reviewer": "Reviewer_zQ1r", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes DiffSampling, a new decoding strategy for large language models that aims to balance diversity and accuracy. Instead of truncating token probabilities by absolute thresholds as in top-p or min-p sampling, DiffSampling determines the cutoff by analyzing the discrete derivative of the token probability distribution. The point of minimum derivative is used as the truncation boundary, and two relaxed versions, DiffSampling-lb and DiffSampling-minp, are introduced to further control diversity.\n\nThe method is motivated by the intuition that abrupt probability drops correspond to transitions from likely to unlikely tokens. The authors demonstrate through experiments on GSM8K, MATH, XSum, divergent association, and WritingPrompts that DiffSampling produces more diverse outputs while maintaining accuracy.\n\n**Strengths:**\n\n1. The algorithm is simple, fast, and compatible with existing decoding pipelines.\n2. Experiments cover several types of tasks, including reasoning, summarization, and creative writing.\n3. The evaluation includes both accuracy and diversity metrics, showing consistent improvement over baselines.\n\n**Weaknesses:**\n\n1. The proposed solutions, particularly in Section 3, are highly intuitive and lack deeper theoretical grounding. The transition from the derivative-based observation to the final algorithm is more heuristic than principled.\n2. The novelty is moderate given the extensive literature on decoding heuristics; the proposed approach can be viewed as a straightforward modification of existing truncation methods.\n3. Evaluation is limited to relatively small models without human judgment, so the generality and perceptual value of the claimed diversity improvements remain unclear.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The experiments are comprehensive and systematically presented. Comparisons against established baselines are fair, and results on both quality and diversity support the authors’ claims. The implementation details are transparent and reproducible. However, the evidence primarily confirms empirical consistency, not theoretical validity. The central intuition in Section 3 is reasonable but lacks formal justification or analysis of when and why the derivative-based cutoff should be optimal.", "audience_yn": "Yes", "audience_explanation": "The study addresses an important practical aspect of LLM generation—decoding control—which is of interest to TMLR readers working on natural language generation, efficiency, and interpretability.", "requested_changes": "1. Strengthen the theoretical explanation of why the minimum derivative consistently marks a meaningful boundary in token distributions (critical).\n\n3. Expand experiments to larger model scales to confirm whether the approach generalizes beyond small LLMs (critical).\n\n1. Add a human evaluation or qualitative comparison to verify whether the increased diversity leads to perceptually better results (recommended).\n\n1. Discuss connections and differences with prior gradient- or derivative-based truncation methods, if any, to better position the contribution (minor).\n\n1. Clarify in Section 3 how the derivative-based intuition transitions into the implemented algorithm, possibly with a visualization or toy example (minor).", "broader_impact_concerns": "The proposed method does not introduce new ethical risks.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "vGuAaDYiBA", "reviewer": "Reviewer_Y2Qd", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper propose a new heuristic to choose the subset of plausible next tokens (cropping of vocabulary given a model output distribution), complementic the existent techniques like top-p/min-p sampling. The idea is based on the difference of the next token probabilities in the sorted list of the token probabilities (discrete derivative), motivated by the intuition that a sudden drop in probability should happen at the boundary between plausible and noisy next tokens. \n\nI have a list of concerns about experimental methodology in the Requested Changes, and I would like to see these resolved. \n\nI would like to applaud the comprehensive and deep literature review and extensive experiments on multiple diverse tasks. Experimental results confirm that the proposed method is not worse than the alternatives in terms of quality/diversity. I appreciate a broad appendix with lots of interesting experiments and supporting tables/plots.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The authors are quite cautious with the claims and I appreciate that, however, the results are quite inconclusive: \"We have experimented with four different tasks, and our method has consistently performed at least as well as similar strategies in terms of accuracy, while potentially improving diversity\". I would like to see more conclusive analysis, even if method does not always ourperform the baselines, what are the cases when you expect your method to be better?", "audience_yn": "Yes", "audience_explanation": "Improving diversity-quality trade-off is an active research topic, and this work will definetely be interesting for language modelling comunity. One of the main weaknesses of the work is that the results seem to be not strictly better compared to the baselines.\n\nI am overall quite skeptical about using the model distribution *alone*, as a source of features to decide which tokens to keep, and which tokens to crop, as many approaches have tried that over the years (min-p, top-p, eta sampling etc.). Even more, I would expect these methods to work quite similar for modern language models (e.g. see \"Min-p, Max Exaggeration: A Critical Analysis of Min-p Sampling in Language Models\" by Schaeffer et al., or \"Control the Temperature: Selective Sampling for Diverse and High-Quality LLM Outputs\" by Troshin et al.) Said that, any new such approach would be useful, if there is significant evidence that it can improve diversity-quality trade-off.", "requested_changes": "I would like to understand the results better, as some numbers are quite confusing. While I appreciate that the authors use EAD metric (I was not aware of it before) instead of more classic diversity metrics like distinct n-grams, could the authors clarify the range of the values of this metric? E.g 2.03±.00 for *greedy* -- is it high/low, does greedy result in exactly the same outputs or not (I would be surprised if not)? For SBERT score in table 2, why are all the scores the same?\n\n\"The hyperparameters governing the sampling strategies adopted as baselines were selected according to the best results reported\nby their original paper for similar tasks and model sizes.\" - for such comparisons, choosing the best hyperparameters on a validation set is quite important and should not be overlooked! These can be quite task and model specific.\n\nFigure 3:  \"As detailed above, to preserve the mathematical guarantees of our approach, we apply temperature after the DiffSampling\ntruncation, while our baselines apply this before (see Appendix D.2 for a comparison between temperature before and after truncation).\" -- this is not a fair comparison, I think, and results in very different behaviour, I would like to see the same experimental setup for baselines and your method: please, use the same way to scale the temperature.\n\nFigure 3: demonstrating *temperature* vs quality can be very confusing, and you cannot draw any conclusions about the cross-method difference, as temperature is only a parameter of the model and not a metric. I would either keep this comparison for reference with a remark that you should not use it to compare methods using these results, or keep only diversity-quality comparisons instead.\n\nFor DAT task, do you promt a model to output several words in sequence? Then I would explain it in the text, and also explain why in this case greedy also can produce diverse outputs.\n\nHave you considered visualising quality-diversity pareto plots for the methods (by changing the temperature parameter)? How do you choose the temperature for main tables with results for a given method?\n\nMinor: don't use math character for method names, if those are just word letters.", "broader_impact_concerns": "no concerns", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "fVDhmX5zZR", "reviewer": "Reviewer_DCZp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces DiffSampling, a new decoding family that truncates the next-token probability distribution at the point of minimum discrete derivative, preserving only tokens most likely to belong to the “true” distribution. After truncation, temperature sampling is optionally applied to enhance diversity without major quality loss. Two relaxations are proposed: DiffSampling-lb, which enforces a lower bound on cumulative probability mass, and DiffSampling-minp, which imposes an upper bound relative to the top probability.\n\nExperiments across diverse tasks—including math problem solving (GSM8K, MATH), summarization (XSum), creativity (DAT), and story generation (WritingPrompts)—show that DiffSampling-cut performs comparably or better than strong baselines in quality while increasing diversity. The paper also demonstrates that applying temperature after truncation maintains quality better than applying it before truncation.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The empirical case is strong and well organized across multiple task families that stress different quality–diversity trade-offs. For math problem solving (GSM8K, MATH), the paper reports accuracy and shows that DiffSampling-cut matches or exceeds strong baselines while avoiding the diversity collapse of greedy decoding. For summarization (XSum), the evaluation includes both syntactic and semantic quality proxies (for example ROUGE and embedding similarity), together with per-input and against-greedy diversity measures that make it easier to see whether outputs are both varied and faithful. For the creativity task (DAT) and for open-ended story generation (WritingPrompts), the authors track coherence and multiple diversity indicators, not just n-gram overlap, which helps avoid the common pitfall of mistaking randomness for meaningful diversity.\n\nThe methodological choices are adequately motivated and tested. The paper isolates a single design decision that often gets muddled in practice, namely where to apply temperature. By running temperature-before versus temperature-after truncation in parallel, it shows consistent quality retention when temperature is applied after truncation, with diversity improvements that are commensurate with the added randomness. Ablations on the lower bound and minimum-probability relaxations offer further evidence that the method degrades gracefully as one dials in more diversity.\n\nThe main caveats are that the central intuition about cutting at the minimum discrete derivative is presented heuristically rather than with formal guarantees, that guidance for choosing the lower-bound and minimum-probability parameters is still light for practitioners, and that human judgments for open-ended generation are limited. These do not undermine the empirical headline results, but they do leave room for sharpening the theoretical and practical story.", "audience_yn": "Yes", "audience_explanation": "Balancing quality and diversity at decoding time is a core issue for the TMLR community, spanning controllable generation, evaluation methodology, and deployment practice. DiffSampling is a drop-in modification that clarifies how to combine truncation with temperature, and it connects cleanly to widely used strategies such as top-p and min-p. This means the work is relevant to both theory-minded readers who think about the geometry of token distributions and practitioners who maintain inference stacks or build user-facing products. The framing is practical and easy to adopt, so even readers who do not switch wholesale to DiffSampling can benefit from the guidance about temperature placement and from the diagnostic metrics proposed.", "requested_changes": "Critical for acceptance:\n1. Provide a formal statement with sufficient conditions under which $\\arg\\min_i \\Delta p_i$ lies at or before the boundary of the true support. Plausible assumptions include unimodality or log-concavity of the sorted next-token probabilities, mild smoothness on the discrete forward differences, and bounded tail curvature. If a full proof is out of scope, add a systematic synthetic study that sweeps families of distributions which emulate common next-token shapes: Zipf-like heavy tails, mixtures with secondary bumps, flattened plateaus induced by label smoothing, and over-smoothed regions. For each family, quantify false positives and false negatives for inclusion relative to an oracle support and report where the heuristic fails. \n\n2. Add a practitioner appendix with default ranges for $ p_{\\mathrm{lb}} $ and $p_{\\min}$ by task family, together with sensitivity curves that show quality and diversity as functions of these parameters. Propose a simple auto-tuning rule: choose $p_{\\mathrm{lb}}$to target a desired entropy band or a validation-set diversity threshold, and set $p_{\\min} = \\alpha \\cdot p_{\\max}$ with $\\alpha$ selected by cross-validation on a small held-out set.\n\n3.  Provide one figure per task family comparing temperature-before vs temperature-after across several $\\tau$ values, with truncation and parameters fixed. Match prompts and seeds to isolate the temperature effect. Use McNemar or stratified bootstrap for accuracy, paired bootstrap for ROUGE and embedding similarity, and paired nonparametric tests for diversity. Report confidence intervals and standardized effect sizes, plus invalid-output rates and any metric saturation at high $\\tau$. Conclude with clear recommended $\\tau$ ranges for each decoding variant.\n\nGood to have:\n\n1. add a small human evaluation for open-ended generation. Run a paired-comparison study on WritingPrompts with 3 to 5 raters per item, 100 to 200 prompts, and criteria such as coherence, specificity, creativity, and overall preference.\n\n2. Include a scaling analysis. Add at least one larger model and one smaller model, both instructed and pre-trained, to test whether the quality–diversity benefits persist with scale.", "broader_impact_concerns": "Decoding changes can shift diversity and novelty. While the method aims to exclude implausible tokens, relaxing the cut or coupling with higher temperature might increase the chance of unusual or unsafe generations in some contexts. I recommend adding a short Broader Impact paragraph that \n- states the intended use as a quality-diversity tradeoff mechanism\n- notes that safety filters and domain constraints should remain in place  \n- reports a small check that DiffSampling does not increase unsafe content rates versus top-p or min-p under a standard filter pipeline.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)