SimpleStrat: Diversifying Language Model Generation with Stratification
Authors: Justin Wong
Yury Orlovskiy
Alexander Shypula
Michael Luo
Sanjit A. Seshia
Joseph E. Gonzalez
Venue: NeurIPS 2025 poster ()
Keywords: Coverage
Language Model Sampling
Stratified Sampling
Evaluation
Dataset
Primary area: probabilistic_methods
TL;DR: We propose SimpleStrat for diversifying LLM generations and introduce CoverageQA a benchmark of multi-answer questions for evaluating coverage.

Abstract: Generating diverse responses from large language models (LLMs) is crucial for applications such as adversarial testing, search, and synthetic data generation, where diversity provides distinct answers across generations. Previous approaches rely solely on increasing the temperature, sacrificing quality. Furthermore, the model's next-token probabilities may not be representative of the true answer distribution. To combat these challenges, we propose SimpleStrat, an alternative that uses the language model itself to partition the solution space into strata from which to sample. 
To measure resampling diversity, we introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible answers. We propose measuring resampling diversity as the KL Divergence between the response distribution and the uniform distribution over valid ground truth answers and use recall as an alternative when assessing proprietary models. On CoverageQA, SimpleStrat improves diversity across all temperatures, showing orthogonal benefits. Quantifiably, we achieve as much as 4X better recall when applied to GPT-4o, and an average reduction in KL divergence by 0.36 when applied to Llama 3. Furthermore, we show that SimpleStrat achieves more resampling diversity at temperature T=0 than scaling temperature to T=1 on creative writing, an open-ended domain. Implementation and dataset available at https://github.com/jwong8314/simplestrat.

SimpleStrat: Diversifying Language Model Generation with Stratification
Justin Wong UC Berkeley wong. justinbberkeley.ede edu
Yury Orlovskiy UC Berkeley yury. oww.oakiyyberreeeyyyooooo edu
Alexander Shypula University of Pennsylvania shypula@seas upenn. edu
Michael Luo
Sanjit A. Seshia UC Berkeley
Joseph E. Gonzalez
UC Berkeley
UC Berkeley jegonzal@berkeleyy edu
michael. aechael.luo@lle www.@berkeeey.cco. edu
sseshia@berkeley.com edu
Low Temp Sempling
High Temp Sampling
SimpleStrat Sampling
(CA)) of Maccedop Rier
INS5) Mussut
Coepptortis Line
Callfomii York
Califomia New
Callfornia
York
Washington
Washington
Texas
Virginia
Virginia
Georgia
Figure 1: SimpleStrat recovers diversity when temperature scaling fails. For the prompt "Name U.S. state," language models exhibit a strong bias toward "California." Our method, SimpleStrat, employs automatic stratification to uncover salient diversity dimensions (e.g.. whether state lies east west of the Mississippi River) and applies stratified sampling to achieve balanced and diverse coverage across responses.
Abstract
Generating diverse responses from large language models (LLMs) crucial for ap- plications such as adversarial testing, search, and synthetic data generation, where diversity provides distinct answers across generations. Previous approaches rely solely on increasing the temperature, sacrificing quality. Furthermore, the model's next-token probabilities may not be representative of the true answer distribution. To combat these challenges, propose SimpleStrat, alternative that uses the language model itself to partition the solution space into strata from which to sample. To measure resampling diversity, we introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible ans wers. We propose mea- suring resampling diversity as the KL Divergence between the response distribution and the uniform distribution over valid ground truth answers and use recall as an alternative when assessing proprietary models. On CoverageQA, SimpleStrat im- proves diversity across all temperatures, showing orthogonal benefits. Quantifiably, we achieve as much as 4X better recall when applied to GPT-4o, and an average re- duction in KI. divergence by 0.36 when applied to Llama 3. Furthermore, we show that SimpleStrat achieves more resampling diversity at temperature T=0 than seal- ing temperature to T=1 1 on creative writing, an open-ended domain. Implementation and dataset available at /httpss: :tattps://giii h/tg://hb...t/t/// com/jvong8311111 //pmm//estmaaaa.t...m.mmma
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Auto SalloSiiatificalin
Heuristic Estimation
Probabilstic Prompling
(E/) of Misseesppl River
West
East
Prompt Distribution
Name a US State
HLM
Sout Nom
0.34
Name US State, whore
Sample Sampler
LLM
0.18
0.54
E of M Misoissipo River
(1425) Missoon Compromise Line
+ of M Missouri Comp.
SimpleStrat workflow. SimpleStrat employs 3 phases: 1) auto-stratification to identify good dimensions of diversity that divide the solution space into equal partitions. 2) heuristic estimation to estimate the proportion of solutions in each stratum, and 3) probabilistic prompting where a concrete prompt randomly sampled from the prompt distribution specified by the previous two phases. Critically, diverse resampling comes from both the random choice of prompt as well as the temperature of the LLM decoding.
Figure 2:
1 Introduction.
Large language models (LLMs) are routinely resampled in order to get wide set of plausible generations. Three key settings where this important are: 1) improving exploration for planning and search (e.g. free-of-thoughh (Yao et al., 2024), AgentQ (Putta et al. 2024)). 2) generating inputs for integration tests, especially for L.LM systems Samvelyan et al. (2024), and 3) generating diverse
datasets for post-training (Dubey et al.) 2024) and fine-tuning (Dai et al. 2023). These use cases rely on resampling outputs to generate multiple plausible utterances in hopes of capturing multiple answers and candidate solutions.
Temperature scaling, which controllably flattens an LLM's s softmax distribution, is commonly used to increase response diversity. However, this approach assumes that next-token probabilities accurately represent the set of valid answers, which is not true under mode collapse. In such cases, increasing temperature does not lead to meaningful diversity. Moreover, temperature scaling introduces a second limitation: higher temperatures degrade generation quality. Recent evidence suggests that removing temperature scaling desirable for multi-step reasoning to reduce error compounding (Zhang et al., 2024). This is especially critical in syntax-sensitive settings such code generation, where low temperatures (5 0.15) are often used. We illustrate this severe mode collapse in Figure [ When asked to "Name US State," the model heavily skews towards answering "California" high temperature only marginally softens the skew while surfacing incorrect answers and hurting instruction following.
Our goal is improve response diversity when resampling LLMs, even in cases of severe mode collapse [Lanchnntin et al. (2025) in next-token probabilities without manual intervention. Our analysis reveals that GPT-4 assigns 87% of its logit weight to "California" when prompted to name a US state. This observed bias can be attributed to the worsening of calibration due to post-training as reported in the GPT-4 tech report (OpenAl et al. 2024). This stark bias mirrors human cognitive bias, exemplified by the blue-seven phenomenon- where individuals disproportionately select blue and seven when asked to choose a random color and number (Towse et al. 2014). To counteract similar biases in human populations, social scientists, particularly in political polling, employ stratified sampling techniques (Simpson [195 Howell 1992; Morris 2022). We propose adapting this method
to address mode collapse in LLMs.
We propose SimpleStrat, a training- free sampling approach to increase diversity of responses. Sim- pleStrat improves LLM generation diversity without compromising quality, yielding outputs that better align with the task's 's objective answer distribution. SimpleStrat consists of three stages: auto- stratification, heuristic estimation, and probabilistic prompting. Even if a language model cannot generate diverse solutions, we find that it can be prompted to identify useful partitions of the solution space based on the user request. We call this process auto-stratiiicttin. In Fig. [ SimpleStrat identifies two semantically significant strata from user request, "Name US State": "(East/West) of the Mississippi River" and "(North/South) of the Missouri Compromise Line."
Next, the heuristic estimation computes the joint probabilities across all strata. Returning to Fig. SimpleStrat estimates the proportion of solutions in each four possible regions of the US. Finally. SimpleStrat samples a stratum from the joint probability distribution and augments the original user prompt with constraints based on the selected stratum. This prompt can then be used to sample fully-formes answers to the user query. We note that this approach to repsonse diversity is orthogonal to increasing temperature which also introduces variance to the generation.

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Response diversity is notoriously difficult to measure as it requires a notion of quality specific to the application. Otherwise, random tokens present a trivial solution to achieving diverse yet meaningless responses. On the extreme of measuring quality, question answering benchmarks capture the quality of the responses but are carefully designed to only admit one valid solution. As such, a fitting setting to measure diversity is required to have underspecified questions for which more than one plausible answer exists. Distinct from ambiguous question answering where the goal is to measure the model's ability to ask clarifying questions, we seek questions where the quality of the response can be independently verified without additional context. Based on these requirements, we introduce CoverageQA, benchmark of underspecified questions with on average 28.7 equally plausible answers.
We adopt three measures of response diversity based on the setting: 1) In settings where the target answer distribution and logits are available, we measure distributional diversity by computing the Bellbackk-eibber (KL) Divergence from the response distribution to the target answer distribution over valid answers. By measuring diversity this way, we can both penalize models for producing nonsense responses and missing valid responses. 2) In settings where we have only black-box access to the model, the response distribution can be estimated by sampling. Since the tail of the distribution is inherently difficult to capture, recall and precision serve as a natural proxy for diversity and quality. We call this coverage diversity. 3) Finally, in settings where exhaustively enumerating valid solutions is infeasible, we cannot assess valid responses are missing. As such, we propose text embedding distance a proxy for diversity. We assess SimpleStrat across these three settings: measuring distributional diversity with Llama 3 and coverage diversity over Claude and GPT-4o with prompts from CoverageQA well as open-ended diversity with embedding distance on creative writing prompts from WritingPrompts Fan et al. (218)).
When assessing distributional diversity, we show SimpleStrat samples from a less biased distribu- tion by computing the response distribution of our method based next-token probabilities. On CoverageQA, SimpleStrat implemented on Llama 3 models demonstrate a substantial 0.36 average reduction in KL Divergence, signifying substantial decrease in dissimilarity between the model's response distribution and the target distribution. In the blackbox setting, we see as much as 4x increase in recall, especially evident at low temperatures. These gains lead to consistent increase in diversity on top of temperature scaling, leading to improved diversity at all temperatures. Finally, consider the open-ended setting of creative writing. We measure diversity by resampling pairs of creative writing story plots from WritingPrompte Fan et al. (2018) and see similar embedding distances temperature 0 sampling with SimpleStrat comparable temperature 1 with standard decoding. Crucially, these gains do not come at the expense of generation quality.
Concretely, our work contributes the following:
CoverageQA dataset of 155 underspecified questions automatically generated from Wiki- Data (Vrandečić & Krötzsch, 2014) automatically labeled with an average of 24.1 1 valid solutions per question.
We propose SimpleStrat training-free approach for improving diversity with auto- stratification and probabilistic prompting by introducing controlled randomness to the prompting process.
We demonstrate SimpleStrat improves diversity across several metrics and settings. On CoverageQA, we achieve an average of 0.36 reduction in KL Divergence on Llama 3 models and as much as 4x recall for GPT-4o. Further on WritingPrompts Fan et al. (2018). SimpleStrat shows similar pairwise embedding distance temperature 0 temperature 1 with standard sampling.
2 Related work.
Temperature Scaling. Going back as far Platt scaling (Plati 2000) and later applied to neural networks (Hinton) 2015 Guo et al.] (017),, temperature scaling controls the randomness of probability distribution For dataset generation with LLMs,, [Chung et al. (2023) extends temperature- -hase diversity by additionally downsampling previously sampled tokens. To address the decrease in quality, they advocate for human intervention manually filter out irrelevant diversity and manually fix wrong answers in QA tasks. We show in our work that temperature scaling leaves much to be desired.
Usee of temperature parameter goes back at least to Verhulst's 's development of logistic regression in response Malthus An Essay P Principle of Population (Malthus 1798 Verhulst 1838).
3

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Improving Language Model Diversity with Search. In autoregressive generation, choices over early tokens tend to have more impact on the eventual completion. Beam search ameliorates this bias by allowing for multiple candidates in searching for the probability maximizing completion, Maximum a Posteriori (Lowerre & Reddy] 1976). At the end of the search, beam search will have multiple candidate solutions encountered during search. Diverse Beam Search (DBS) proposes introducing an auxiliary dissimilarity objective quantifying the diversity among candidates in the beam (Vijaykkumar et al. 2016). Especially on the task of image captioning. DBS shows improve- ment for discovering higher probability completions and discovering diverse continuations. Our improvements are orthogonal to beam search and in-context approach corrects for inaccuracies in the modeled likelihoods of candidate solutions.
Other approaches (Samvelyan et al., 2024 Bradley et al., 2023 Novikov et al.) 2025) based on
MAP-Elites (Mouret & Clune| 2015) require manual determined dimensions of relevant diversity and discretization of the solution space into equally-sized bins. Diversity is then achieved by mutations and evolutionary methods to cover adjacent bins. This search is potentially slow if the seed set of solutions does not already provide coverage over the solutions space. Our approach does not need seed solutions and avoids manually identifying dimensions of diversity. Instead, we rely solely on capabilities within the model.
In-context Methods Increase Diversity. When LLMs were first introduced, LMs were used to augment existing datasets with more diversity (Wei & Zou 2019 Ng et al. 2020, Dai et al. 2023). As natural language is difficult to guarantee correctness, the space of augmentations is conservatively limited to thesaurus-basee synonym replacement. More recently. Language Model Crossover proposes presenting a random subset of existing data points to an LLM and ask it to hallucinate more data points that likely came from the same distribution Meyerson et al. (2023). This limited to combining aspects of existing data points into new generations. Although these methods address the limitations of using the model's token probabilities by in-context learning, they ineffective at generating meaningful diversity. They are limited to either a human-identifcce domains of interest trivial variations sourced from synonyms random subsampling of the existing data.
Applications of Diversity. As shown by Raventós et al. (2024), dataset diversity is crucial for model generalization. Below sufficient coverage of the desired task, the model will resort to memorization, but when sufficient diversity is presented it will learn to generalize. As LLMs are increasingly used for generating synthetic data (Dubey et al., 2024), methods for diversity will be critical. This insight follows from extensive work demonstrating the benefits of data augmentation for bias mit- igation (Sharmanska et al. 2020) and domain adaptation (Huang et al. 2018 Dunlap et al., 2023
Trabucco et al. 2023)
In code and math applications, checking validity efficiently enables more aggressive augmentations. One such augmentation for diversifying the languages supported by the model, data translated to different natural or programming language (Chen et al.) [223] Cassano et al.) (023). In other domains such as images, text-to-image models have been used to diversify data into uncommon settings. In the setting of diversifying an accumulating dataset, these methods can take advantage of an existing source of variance (for translation) or a set of previously generated data points. Our primary focus is on settings where SimpleStrat is unaware of past data samples to support wider set of applications.
Ambiguous or Underspecified Datasets. ClariQ (Aliannejadi et al. 2020), CLAQUA (Xu et al. 2019), and AmbigQA (Min et al. 2020) focus on assessing LM's s ability formulate clarifying questions. These questions tend to have only two candidate solutions, as there exists a ground truth clarifying question whose answer fully specifies the question. Ambiguous Trivia QA (Kuhn et al.. 2022) also looks at under- specified questions but assumes user has contextual information that's hidden. For instance, "Where in England was she born?" or "Who was the first woman to make a solo flight across this ocean?". We distinguish our underspecified question setting in this paper as one where the user is indifferent. In this setting, given an answer it should be easy to verify the answer is correct without additional hidden context.
Coding datasets like Description2Code (Caballero et al. 2016). Wiki2SQL (Zhong et al. 2017 SPIDER (Yu al. 2019). code-contest (Li et al. 2022), Apps (Hendrycks et al. 2021). and Leetcode Hard Shinn et al. (2023) admit multiple valid answers. However, the space of valid implementations infinite, making diversity difficult to measure, and good coding practices enforce preferences among valid implementations. We additionally construct CoverageQA to have an exhaustive list of ground-truth answers in order to measure the impact of diversity on coverage.

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3 Method
3.1 Workflow overview
As illustrated in Figure 2 SimpleStrat consists of three stages, 1) auto-stratification, 2) heuristic estimation, and 3) probabilistic prompting. The outputs of the first two stages can cached per prompt to avoid recomputing partitions.
3.2 Auto-Stratification
For given user request, Yuser, we call S. the space of valid solutions. In many settings, the space of potential solutions, S may be naturally partitioned based geography, parity, or demographics. The partition function, P - I, assigns any solution from $ to partition label 1, in L the set of partition labels. Partition functions most useful if they're balanced possible. A balanced partition function minimizes
imbalance(P..) max (1( P(s) = 41) min (1(s P(s) = (31) IET.
Te
The goal of auto-stratiffiation is to search for set of partition functions P {PI, P2,.... Ps): that balanced. In settings where valid solutions are easy miss or the solution space is large (or even infinite), stratified sampling ensures that limited number of samples provides broad and even coverage.
Based on this insight, we prompt the language model to identify promising dimensions of diversity. Concretely, the language model proposes good clarifying questions that will potentially eliminate half of the potential solutions based on the user request. These clarifying questions tend align with semantically significant differences. In the running example, when asked, "Name a US State," the states be partitioned based on East West of the Mississippi River. See App. E for full prompt.
3.3 Heuristic estimation
As previously observed in Zou et al. (0022) Yan et al. 22033;; Halawi et al. (2024), LLMs can used in forecasting to estimate well-calibrated probabilities of events that have not yet occured. For forecasting, the model's 's success benefits substantially from having updated news through web search. Although unnecessary for the offline benchmarks we consider, this may helpful for accurate estimation depending from coarse-grate grain approximate proportions. We employ a similar reasoning template as Halawi et al.) (2024) to estimate the proportion of valid solutions that lies within each strata.
the application. However, as our goal is diversity, we stand to benefit even
In heuristic estimation, we look estimate the joint distribution for each stratum, /= [1, ...]. For- mally, we define the weighted-stee senedd--ttttfiittiooo 12.5, (s) = ...] for identified in strtsstratfiiaiinnn To improve scalability, we assume the parti- tion functions are independent and multiply the marginal probabilities to get the joint probabilities associated with each stratum.
W (P, p). where p(T) Pr.-s (P. I1jj Pa(s)
p(h la, bm)
II P.)))
We ask the LLM for each 4,, estimate the marginal proportion of solutions this holds for. As this may not add up to I, we normalize the estimates to form a proper probability distribution. For simplicity, focus in this work settings where all solutions in the solution space equally likely. As noted in Sec. 3.2 we encourage the LLM to propose balanced partitions. However, heuristic estimation allows us to support imbalanced partitions by reweighing the sampling to favor strata with more potential solutions. More details on prompting in App. I In Fig. 2 the LLM determines the joint probabilities across two strata, the Mississippi River and the Missouri Compromise Line.
3.4 Probabilistic Prompting.
Post heuristic estimation, set of strata are sampled from the joint probability distribution in Eqn. This implicitly forms probabilistic prompt, which specifies a distribution over concrete language model prompts. After prompt is sampled, the LLM is then used to sample from within the stratum. Back to Fig. [ East and South are sampled from the Mississippi and Missouri strata respectively, augmenting the final prompt with diverse specifications.
5

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Formally, call i' stratum defined by choices of 4. for each P. across all i. Call Prompl a function that maps the stratum, 1, to a concrete prompt, Prompt(I). The probabilities the prompt distribution are defined by Pr(Prompt(() (T) p(t). We then compute the probability of a solution as follows:
Pr[s]
Pr Proompt(() Pr(s| Prompt(i))
(2)
Σ pl) Pr[s Prompt(i).
The specific language model's next-token probabilities define Pr(s Prompt([).
As the probabilistic prompt in human readable form, the user can inspect the properties and the proportions and modify it to adjust for unwanted bias or remove unwanted factors. For instance, when proposing English baby names, we may want the model to propose male vs female names equally often, even though there are more female than male baby names [ This interpretability and controllability a major advantage of SimpleStrat practice.
CoverageQA Dataset
4.1 Overview
We wish to evaluate generation diversity in settings where 1) user requests have more than one distinct correct answer, 2) and answers are equally likely, and 3) answers do not require hidden or implicit context to verify. These three features allow us measure diversity quantitatively in terms of language model ability to represent the target distribution when resampled. The second condition makes the evaluation easier, reducing the problem to a measure of coverage over the solution space. Unfortunately, existing benchmarks discussed in Sec. dec.2ra do not suffice. As such, we introduce CoverageQA for assessing the language model generation diversity. The dataset consists of two splits: CoverageQA --Curatee, manually curated naturally underspecified questions, and CoverageQA-
an auto-generated dataset of underspecified questions.
4.2 CoverageQAA-Wkkipeaaai Approcc
To generate CoverageQA- we leverage the Wikidata knowledge base which contains all relational mappings between entities and properties in Wikipedia. Our generation process starts with an initial item-property pairing and constraint the number of correct answers. We then perform recursive search through Wikidata find all sets of item-property constraints and their corresponding answers that meet criteria. These constraints are subsequently transformed into natural language questions using GPT-4.
Consider an initial pairing of the Wikidata item "country" with the property "instance of".. We might specify that we want between 20 and 40 valid answers. Our search would then yield a set of all constraints from the knowledge base that fit the initial conditions, such as "instance country, located in Europe, uses Euro as currency". GPT-4 would convert this into natural language question like "Name a country located Europe that uses the Euro as currency." "
This approach has several advantages: 1) it allows to create diverse and extensive benchmark that can be easily updated with weekly updates to Wikidata, 2) it allows us to arbitrarily specify the size of the solution space as constraints can be added removed form; and 3) this process in principle can curate a large dataset with little manual effort or supervision. In the initial instantiation of -overageQA-iikipeddia dataset, we publish 145 questions across 6 domains, corresponding to a different initial seed item-property pair. To ensure quality, we employ both automatic filters (e.g., excluding certain generic properties) and manual curation to remove redundant or unsuitable questions. This dataset can be substantially expanded as we only used 4 domains, but we leave this for future work. For details on the dataset breakdown and details on the question generation process, see Appendix

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Zre
Hurs
Kisignn
Orbrt
Supeto
GPT-40
SmpleStrat
434
6.6
4.31 4.6
Figure 3: Diversity scaled with temperature. We show 100 resamples of "Name one Great Lake in the United States." On the left, we show the result of resampling GPT-4o 100 times per temperature. In contrast to SimpleStrat the right, GPT-4o at temperature 1.5 still only samples Lake Huron once and never samples Lake Ontario. SimpleStrat improves the diversity across all temperatures.
Results
5.1 Measuring Diversity
We consider three measures of diversity. In the setting where we have access to all ground truth answers, we can measure distributional diversity when the model weights are available and coverage diversity when blackbox. Without a comprehensive list of valid solutions, we rely on embedding distance to measure open-ended diversity.
Distributional diversity. For models with accessible softmax next-token probabilities, we can compute the probability of each solution in the solution space. We then define distributional diversity the distributional distance between the response distribution implied by the sampling process and logits and the ground-truth distribution derived from these probabilities. For our baseline, we prompt the models and directly compute Pr[s Prompt(i)] for each solution, This is simply the product of the individual next-token probabilities. For SimpleStrat, the probability involves the next-token probability conditioned on the probability the prompt is selected. Formally, the probability an answer sampled by SimpleStrat can be computed based on Eqn The next-token probability based response distribution Pr[s] (romp[([) computed just the baseline, and do weighted by the joint probabilities assigned in heuristic estimation. We assign the remaining probability density to "Invalid" category form proper distribution. The probabilistic formulation allows to easily compute the response distribution of SimpleStrat. Note that by design the ground-truth distribution for CoverageQA is uniform valid solutions and zero elsewhere.
Coverage diversity. In setting where do not have access to the next-token distribution, evaluate diversity by resampling responses to CoverageQA 100 times per question. This allows us to empirically observe the diversity in the form of coverage. We call this coverage diversity. To measure coverage, we report the recall: unique valid solutions divided by total valid solutions on the reference solutions. This is not to be confused with notion of recall where might measure how many valid solutions classifier recognizes as valid. To ensure this does not come at the cost of quality, we also show precision is not reduced. We show an ablation of just asking the model to propose criterion without 20 questions formulation in Fig. We see little improvement from only allowing the model propose of criterion and then applying the uniform sampling like AtrPPrompt (Yu et al. (023)
Open-ended diversity. For many compelling applications of diversity, goal of diverse generation is to identify solutions not previously known to the user. In these open-ended settings, it's often the case that the space of valid solutions cannot be exhaustively enumerated. In this work, consider ask the model to provide plot outlines to
creative writing prompts as an example of this setting. make comparison easier to decouple high level creative choices from stylistic choices. We measure diversity by sampling a pair of story plots outline based on the same prompt and measuring the cosine distance of the plots' embeddings. Unlike CoverageQA, writing high quality plot is more challenging, longer context task. As such, we assess the model's 's quality by spell-checking
2 As reported in Wilson (0016). there are 18,993 unique names for girls and 13,959 for boys in 2015 report by Social Security Administration.

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05
GPT-4o with SimpleStrat
Tmo
Quality Format Adherence
Cluude 3.5
Average Recall
GPT-4o with AttrPrompt
T-1
02
01
GPT-4o GPT-4o with SimpleStrat
Temperature (T)
T=1.3
Figure 4: Diversity measured with recall scaled with temperature. SimpleStrat applied to GPT-4o shows the improved recall on CoverageQA compared to GPT-4o, AtrPrompt. Claude 3.5 Recall indicates the percent- age of ground truth questions observed after sampling times. benefit SimpleStrat is especially pro- nounced at low temperatures, but the benefit is evident across all temperatures. Prior work, AtrPPrompt, di- reetly asks for partitions instcad of our 20 questions style prompting, resulting in lower quality partitions.
0.1 0.2
0.3
0.4
0.5 0.6 0.7
0.8
Diversity Cosine Distance
Figure WritingPrompps Diversity. creative writing prompts, we generate pairs of plot outlines. We measure diversity with embedding cosine distance and quality checking for format adherence. Sim- pleStrat especially improves the diversity low peratures achieving T=0 same diversity as T=1 for base GPT-4o.
for non-standard English words and adherence to three act outline given in the prompt. These simple checks do not aspire to capture aspects quality but are sufficient to capture the quality degradation characteristic of high temperature. See App. H for more details.
5.2 Qualitative Example
Consider the question "Name one Great Lake in the United States." shown in Fig. 3 We see that temperature scaling with GPT-4o results in strong preference/bias for Lake Eric. This is certainly a correct continuation and under the language modeling objective should be incentivized. Increasing the temperature helps sample the next most likely candidate solutions more often. However, even when increasing the temperature past 1 there is still incomplete coverage over the solutions space. Specifically, Huron only seen once out of 100 samples at 1.5 temperature, and Lake Ontario is never observed. This is undesirable if the data is used propose candidate plans, generate test cases, generate training data. Further, the model has a strong persistent preference for Lake Erie potentially leading to undesired biases in downstream use cases.
In Fig- we observe much more uniform distribution over valid solutions when using SimpleStrat. Notably, we observe full coverage over all Great Lakes. lower temperatures, there is still preference for single lake over the others, in this case Lake Huron. However, this is less pronounced at higher temperature showing the orthogonal benefit of SimpleStrat.
5.3 Coverage Diversity on Proprietary Models
We first assess coverage diversity, specifically, the model's ability recall all the valid solutions upon resampling. This measure is clearly impacted by temperature temperature zero greedy decoding LLMs leads to a single deterministic result. We compare the coverage diversity (recall) of SimpleStrat, GPT-4o, and Claude 3.5 Sonnet as function of temperature. We sweep over temperatures from 0 to 1.5. SimpleStrat with GPT-4o leads to an improvement to recall across all temperatures shown in Fig Compared to prior work, AttrPrompt, SimpleStrat provides substantially more diversity when applied to the same underlying model (Yu et al. (2023). SimpleStrat scales well with temperature showing gains across all temperatures. The recall importantly does come at the expense of quality as measured by precision as App.
blations. We conduct two ablations to evaluate key design choices. First, we remove the 20 Questions framing (20Q Abl.) and directly ask the model for partitions. Second, test single-
Claude does not allow for temperatures above 1. GPT-5 was not studied because it does not allow for uset-controlled temperature.

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KL Divergence aota-Liama..77B.B 7----insttucct
Quelton: Name US des
Divergence (theeeiie)
Probability
XL Divergence (SimpleStrat)
Figure 6: KL divergence on individual question from CoverageQA Wikipedia. For cach question in CoverageQA, compare the KL divergence from ref- erence distribution of Llama-3 with and without Sim- pleStrat. Lower divergence indicates closer alignment with the desired uniform distribution, arrow indicates direction of maximum improvement from baseline
Figure 7: Distributional Diversity Comparison. We show the a posterior probability as defined by next- token probabilities for ground truth answers on Llama 3.1 70B. SimpleStrat provides meaningful improve- ment the sampling distribution both for values pre- viously overrepresented in distribution and those previously underrepresented.
Table I: Performance Different Prompting Strategies across Temperature Settings (GPT-40)
Temp.
GPT-4o (std)
SimpleStrat (std)
20Q Abl. (std)
Single Prompt Abl.(std)
0.0646 (0.0011) l)
0.2423 (0.0050)
0.1215 (0.0021)
0.0019 (0.0008)
0.25
0.0849 (0.0016)
0.2669 (0.0022)
0.1405 (0.0028)
0.5
0.1204 (0.0036)
0.3017 (0.0043)
0.1660 (0.0025)
0.75
0.1497 (0.0046)
0.3433 (0.0067)
0.1821 (0.0336)
1.0
0.1871 (0.0071)
0.3884 (0.0094)
0,2381 (0.0049)
0.0272 (0.0014)
1.25
0,2280 (0.0053)
0.4250 (0.0062)
0,2872 (0.0065)
0.2676 (0.0059)
0.4634 (0.0085)
0.3304 (0.0104)
stage version (Single Prompt AbL.) that combines all instructions into one prompt using the 20 Questions framing. Results in T that the single-prompt setup performs significantly worse than the baseline GPT-4o, suggesting that more tokens do not necessarily improve diversity and that our gains are not due to prompt complexity alone. This supports the intuition that probabilistic prompting- via "coin flips" introd--tro beneficial randomness. The 20 Questions ablation further confirms our 20 question framing provides better partitions.
5.4 Distributional diversity with Llama 3
We Llama 3 models measure distributional diversity by analyzing logits for all valid answers. This isn't feasible with GPT-4o or Claude 3.5 Sonnet, since estimating true probabilities would require heavy sampling. Although GPT models can output log probabilities, they report these only for the tokens in the observed generation trace, rather than for all possible continuations.
Across both 8B and 70B Llama models, SimpleStrat achieves an average reduction in KL divergence from uniform of 1.14 compared the baseline on the curated CoverageQA dataset. For the general CoverageQA dataset, the reduction is 0.36. These results indicate that SimpleStrat produces a response distribution closer to the ground truth distribution than the baseline method.
Additionally, analyze per-question KL divergence with the scatter plot in Fig 6 It shows KL divergence values for SimpleStrat (y-axis) versus the baseline (x-axis) for each question in the QoverageQA Wikipedia dataset. Points above the diagonal line represent questions where SimpleStrat outperforms the baseline by yielding a lower KL divergence. Points tend to fall near or above this line, indicating SimpleStrat produces more uniform samples CoverageQA.
As shown in Fig. 7 Llama 3.1 1's base distribution is heavily biased toward its preferred answer (e.g.. "California," as shown also Fig. []. Thus, it not surprising that we observed little diversity when simply increasing temperature. In contrast, SimpleStrat provides much more uniform distribution. The overrepresented solutions are adjusted to be lower and the underrepresented solutions are adjusted to be higher. For more examples, see App.

---

Table 2: We assess distributional diversity measured by KL Divergence. Smaller KL divergence is closer
uniform.
We see improvement to distributional diversity and 70B as well as Llama-3 and Llama-3.1.
EveerageQ-Curateer
Coverage
Model
Baseline
SimpleStrat
Baseline
SimpleStrat
Mlama-3-8BIImma
2.78
1.74
2.75
2.47
Llama-3.1 1e-ma-..--BB-nmsee 188--nrttutt
2.47
1.19
2.60
2.39
3.24
2.17
3.28
2.73
1lama-3.1-70-Imsse
2.70
1.54
2.78
2.38
5.5 Open-ended Diversity.
Fig. 5 shows SimpleStrat shifts the curve to the right, affording diversity while maintaining the same quality. We provide coarse grain measure of diversity by measuring the proportion of plots from the 100 random prompts taken from WritingPrompts that do not have formatting errors or more than 20% of words outside of the English dictionary. As we are asking for outline, format errors we check for include proper monotonic numbering and providing the number of requested chapters to the story. Notably, at temperature zero, we achieve the same diversity as temperature scaling to temperature 1. This suggests we get diversity for free without sacrificing quality.
Limitations and Future Work
While SimpleStrat demonstrates empirical gains, its effectiveness depends the model's ability to identify meaningful axes in citoostratificationn and estimate accurate joint probabilities. As LLMs improve in forecasting and external data integration, expect these estimates to become more reliable. Our prototype focuses on the model's intrinsic capabilities, but potential biases- such as those related to race or gender-man influence stratification and estimation. For critical applications, the probabilistic prompt distribution should therefore be carefully reviewed. Finally, because Cover- ageQA consists of short responses, evaluation is simplified; however, anticipate SimpleStrat will have the greatest impact low-temperature, multi-step reasoning tasks (Zhang et al.) 2024).
As research on learning beyond demonstrations and reinforcement learning accelerates, methods that promote diversity-such as SimpleStrat-are poised to become central to discovering novel solutions, strategies, and ideas. Wherever diversity currently achieved through temperature scaling, SimpleStrat provides more semantically grounded alternative. Task- pros--ropssing agents like InSTA and Explorer, for instance, could leverage SimpleStrat to explore websites more effectively and generate broader range of trajectories for web agent training (Trabucco et al. 2025 Pahuja et al. 2025). Similarly, AeciiyAAllphat AlphaEvolve employs evolutionary strategies to tackle optimization problems and references "stochastic formatting" as way introduce variance into prompts- likely early form of probabilistic prompting akin to the approach described this work (Novikov et al. 2025).
7 Conclusion
In this paper, we propose SimpleStrat which offers an innovative alternative by leveraging the LLM itself to partition the solution space into distinct strata. We call this process auto-stratificatio. Specifically, we reframe the stratification problem to the imperfect information game of 20 questions and show that this framing produces strata that are both balanced and orthogonal. At inference time, random stratum is selected, and sample is drawn from within that stratum. This method achieves greater diversity while maintaining quality, unlike simply increasing temperature.
To quantitatively measure diversity, we introduced the CoverageQA dataset, which consists of underspecified questions with multiple equally valid answers. We measure diversity with three metries: for soures models, we measure distributional difference with KL Divergence and for proprietary models, we measure coverage over the set of ground-truth solutions. In the open-ended setting without access to the ground truth distribution, we rely on distance in embedding space to measure diversity. Our rigorous evaluation on both proprietary and open-source LLMs demonstrated that SimpleStrat achieves significantly higher recall and produces answer distributions closer to uniform compared to traditional temperature- baseed sampling methods.
10

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Acknowledgement
We thank Anastasios Angelopoulos, Jacob Steinhardt, Brandon Trubucco, Kevin Yang, Alan Zhu, and Parth Asawa for their insightful discussion. This work was supported in part by DARPA Contract 118750-23-C-0088 (ANSR), by Nissan and Toyota under the iCyPhy center, and by Sky Computing Lab which is supported by gifts from Accenture, AMD, Anyscale, Broadcom, Cisco, Google, IBM, Intel, Intesa Sanpaolo, Lambda, Lightspeed, Mibura, Microsoft, NVIDIA, Samsung SDS, and SAP.
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A CoverageQA Dataset
Generation Procedure
To generate the questions, we manually came up with initial item and property pairings to run the recursive search. We constrain the recursive search yield between 20-40 possible answers keep the questions within common and relevant categories. We found that with fewer than 20 answers, the questions become obvious, while with more than 40, they tend to get too specific and stray from general knowledge. The recursive search first finds all items that satisfy the initial conditions, then iteratively adds properties in steps until either the maximum depth (number of constraints) is reached or the number of answers falls outside the desired range. We blacklist properties that are detrimental high-quality question generation, such as an item's presence in a specific database, numeric properties like population, and properties that introduce high ambiguity. We then manually evaluate the generated conditions and answers to ensure they meet our criteria. With an appropriate initial condition, one query can generate hundreds of valid constraints that can later be turned into questions. Finally, we use GPT-4 to convert these constraints into natural language.
B Results on Curated CoverageQA
We manually curate questions with known solutions sets such NFL teams and USA state capitals. This bank serve as split to validate results on less synthetic sources that are more common knowledge. We even stronger performance improvement on this set in Fig. 8
644
SveeSrp EPT4)
0.0
5.20
0.2
0.2
Tepeiaue
Figure see even stronger improvements on manually curated CoverageQA set.
C Experimental Setup
For our evaluation, we use proprietary models, gpt-4o-0024-88-06 and sonude-35-soonee-2222444 We use open-source models from the Llama 3 and 3.1 families. The inference of these models were run on A A100-80GB GPUs. CoverageQA Wikipedia is based on the snapshot from 07-03-2024. For text embeddings, we use 3rd generation embedding from OpenAI.
Table 3: CoverageQA Domains
Domain
Question Count
Average Number of Answers
General Knowledge (Curated)
10
64.1
US National Parks
11
Geography Questions
74
27.5
Periodic Table Flements
11
24.2
Physic Nobel Laureates
16.8
Famous Athletes
18
9
Musical Instruments
10
Total
155
24.1
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D Precision
We show precision in Fig. to emphasize that the precision does not change substantially as result of our method. Precision is calculated over the of 100 attempts how many are the ground truth. Recall as mentioned is calculated as how many unique ground truth solutions were observed in the 100 attempts. The reduced precision can be attributed to cases where the Heuristic Estimation is ineffective. This can lead to settings where stratum has no valid solution. Because the constraints are added as additional conditioning, the model now has competing objective to obey the constraints vs the original instruction. As such, infeasible requests lead to best effort solutions that are incorrect.
1.0
0.
0.6
0.4
02
GF7-4
Smppletrat GIT-4e
Chuude 3.5 Sonnet
0.0
Temporature
(a) CoverageQA-Curated
(b) CoverageQA-
Figure 9: Precision scaled with temperature. There is fixed minor reduction of 10% precision when using SimpleStrat, This indicates improved diversity does not come at significant cost to precision.
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E Auto-stratification Prompt
We provide the full prompt in Tbl. 4 To improve prompt adherence, we provide one in context example the form of one simulated round of multi-turn conversation, i.e. we provide an example set of reasoning following the template.
System Prompt:
You're helpful brainstorming assistant that careful consider all factors problem.
User:
am tasked with following request:
% User Request
Help me brainstorm how to respond to the user request by providing list of Truc/False properties the solution may may not have. Use the following step-by-step come up with good properties:
you were playing 20 questions, what's good first question ask that would split possibilities half? List least 5 questions and their corresponding propertics.
Question: <Description>
2. Rewrite each question True/False property that's true for one half and false for the other.
Question: <Description>
Truc/False Property: <Property Description>
3. For each property, come up with an example that would satisfy the property.
Property: <Description>
Example: <Description>
Is it valid answer to the user's request? <Yes/No>
For each property, come up with an example that would not satisfy the property.
Property: <Description>
Example: <Description>
Is it valid answer to the user's request? <Yes/No>
Does the property mention a candidate answer in it?
Property: <Description>>
Does the property mention a candidate answer in it? <Yes/No>
6. For each property, list whether should include not in the final list of properties. Do not include where an example from above is valid it mentions candidate answer
Property: <Description>
Include in final list? <Yes/No>
Final List of True/False Properties:
<Property Description 1>
2. <Property Description 2>
Ensure all properties are listed are sentences that are either True or False
Table 4: Full prompt for Auto-stratiffcation.
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System Prompt:
You are an expert superforecaster, familiar with the work of Tetlock and others. Your mission to generate accurate predictions for forecasting questions. Aggregate the information provided by the user. Make sure to give detailed reasoning.
User:
am tasked to estimate the probability that random solution to "User Request" has the following property "Partitioning Property"
Instructions:
Provide at least reasons why the answer might be no.
Insert your thoughts
2. Provide at least reasons why the answer might be yes.
Insert your thoughts
3. Rate the strength of each of the reasons given in the last two responses. Think like a superforecaster (e.g. Nate Silver).
{ Insert your rating the strength of each reason }
4. Aggregate your considerations.
Insert your aggregated considerations
5. Output your answer (a number between 0 and 1) with asterisk at the beginning and end of the decimal.
Insert your answer)
Table 5: Prompt for Partition-specific Heuristic Estimation.
Heuristic Estimation Prompt
We first take each partition function from auto stros-itttiiiiti and estimate a starting probability with the prompt in Table[5] This prompt is heavily inspired by Halawi et al. (2024). We then collect all the proportions and pass it through a final Hcuristic Estimation prompt to remove redundant propertics (negations for instance) and give the model chance to correct any incorrect probabilities. See Table for full prompt. Finally, we ask the model to select at most 3.
Note that for performance reasons, we estimate the marginal probabilities and make a simplifying assumption of independence. This is not strictly true if one partition function is the negation of the other. This leads potential stratum assigned positive probability but actually the stratum has no solutions. Otherwise, there would be 2 Parttion Funciios strata to estimate probabilities of. Further, LLMs seem less reliable when asked to estimate fine- fine-grained probabilities, whereas most marginal probabilities are by design close to 0.5.
Formally, if P = Q, the the stratum P A Q has zero probability, even though we assumed it to be Pr[P] Pr[Q]. We handle approximation error in estimating the true prompt distribution by allowing the model to reply "Invalid" to trigger a resample. With this adjustment, the probabilistic prompt distribution maintained for this extreme case. This correction however does ameliorate potential issues with
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KL Divergence Meta Lamma 3-08--88888 -8-instruct
KL Divergence Meta Liama- 1et.aa.-.-----mmmmme
(Bascline)
Inseovenaee
KL Divergence (Simplestrat)
Divergence (Siplestreat
(a) Llama 3.1 8B
(b) Llama 3.1 70B
KL divergence from uniform for Baseline vs SimpleStrat on CoverageQA Wikipedia. Lower divergence indicates closer alignment with the desired uniform distribution, arrow indicates direction of maximum improvement from baseline
Figure 10:
System Prompt:
You are an expert superforecaster, familiar with the work of Tetlock and others. Your mission generate accurate predictions for forecasting questions. Aggregate the information provided by the user. Make sure to give detailed reasoning.
User:
I'm playing game where my friend has been tasked to:
"User Request"
have the following Y/N statements can ask my friend. have probabilities that think it's true: % Insert numbered list of partitions and proportions. Instructions:
1. For each Y/N statement, is it redundant with another statement?
Y/N statement: <description>
redundant? <Y/N: Explanation
2. Are any of the probabilities in accurate? it's sufficiently accurate just report back the same value.
Y/N statement: <Description>
Is accurate? <Y/N: Explanation>
Probability: <Probability>
3. Pick at most three statements that are least redundant and pair well together. Prefer ones that are closest to 50% for most information.
Final List of True/False Properties:
1. <Y/N Properties> :: <Probability>
<Y/N Properties>: <Probability>
Table 6: Prompt for Final Heuristic Estimation.
G Additional Plots: Distributional Analysis with Llama
We provide additional examples in Fig 15 and scatter plots for Llama Fig 10a
Fig 10b
and
Fig IT
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KL Divergence Meta Llama 3-88 Instruct
KL Divergence Meta Llama 3-708 708-Instruct
improvemare
Divergencc (Bassllnn)
Divergence (Basselina)
2
Divergence (SimpleStrat)
Divergence (SimpleStrat)
(a) Llama 3 8B
(b) Llama 3 70B
Figure 11: KL divergence from uniform for Baseline vs SimpleStrat on Coverage Wikipedia. Additional plots for Llama 3 8B and 70B models
Question Name 1S sta0e
Question Name a state
Corpaation
Probabilty
Probabiity
Giound
(a) Llama 8B.
(b) Llama 3.1 70B.
Figure 12: Distributional Diversity Comparison. We show the response probability as defined by next-
proba--robasilltiess for the top 20 ground truth answers Llama 3.1. For both 8B and 70B, SimpleStrat provides meaningful improvement the response distribution both for values previously over-represented in the distribution and those previously underrepresented.
H Judging Plot Outlines
For this task, ask the model to generate outlines guided by the format shown in Table Notably, we ask for three acts to prevent the outlines from getting too long. To check for validity, we use pyspellcheck to assess there over 20% words are three acts and a THE END to finish the story. The last condition protects against the case where the model rambles alone, we can already see the degradation of the model due to temperature (Fig. 13). Finally, we see formatting is not affected by SimpleStrat and largely tracks the temperature used sample from the language model (Fig. 14
the English dictionary and ensure that there
incoherently and produces what is definitely not sensible outline. With spelling
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Trdeofff
Formatting Error us Temperature
1.00
Bacelte
000 Spdiratror Rand
Format ArTertece 06 with No Emoin
0.95
0.00
G77-4 Smoleitrat (OP7443)
0.70
0.8
2.4
0.5
3.2
Tenzerature
Figure 13: WritingPPrmppss Diversity. On creative Figure 14: Impact of temperature on formatting writing prompts, we generate pairs of plot outlines, measure diversity with emhedding cosine dis-
(including spelling). It's interesting to see that the tance and quality proxied by spelling. SimpleStrat impact of SimpleStrat is negligible compared tem- perature. We the SimpleStrat closely follows the especially improves the diversity at low temperatures expected quality degradation based on the temperature achieving T=0 the same diversity T=1 for base of the model generating the final outline. GPT-4o.
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System Prompt:
Format:
**iitcc*: <IITTLE>
"*Setting*": <ETTINN>>
*Characters <CHARACTERS>
** **At 1:00 <ACT I TITLE>
<Content>
2. <Content>
3. <Content>
**Act 2:34 <ACT TITLE>
1. <Content>
2. <Content>
3. <Content>
**Act 3:** <ACT 3 TITLES
1. <Content>
2. <Content>>
<Content>
THE END
User:
Write a part story outline based the following prompt:
"User Request"
Table Prompt for Plot Outlines.
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country caplal
country captb)
came 11:00
Probability
Probability
Ground Truth Answers
Ground Iruth Answers
(a) Llama 3.1 8B
(b) Llama 3.1 70B
Probabii 2A
Grrg Nart 1227
Question, Nome US pres dent.
Question: Nome US president
11.55
Probabiiity
Vir Cara
10-20 26
dernnn Maga""
Ground Truth Answers
Ground
(c) Llama 3.1 8B
(d) Llama 3.1 70B
Quastion: Name perlodic dlement.
poradic
Probabllitt
Teys hosality
Ground
Ground
(e) Llama 3.1 8B
(n) Llama 3.1 70B
Figure 15: Baseline SimpleStrat Probability Distributions This figure shows the answer distributions for 4 additional questions from CoverageQA curated. Each row represents a different question, showing distributions for Llama 3.1 8B and 70B.
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The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize other settings. is fine to include aspirational goals as motivation as long is clear that these goals are not attained by the paper.
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Justification: As discussed in the paper body, the dimensions of diversity identified by the model may be influenced by biases in the pretraining or post-training of the models. However, these biases would also exist in the models before the introduction of SimpleStrat. Our design in fact directly exposes biases via the dimensions of diversity. This may allow practitioners to combat these biases by adjusting the prompt distribution. These corrections are guaranteed apply once applied as the randomness associated with sampling constraints occurs outside of the model's control.
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If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
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8. Experiments compute resources
Question: For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Answer: [Yes]
Justification: We use a limited 8xA100 machine for inference of Llama models. Otherwise, API calls were made.
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30


Reviews:
[{"review_id": "lGvFQJZIEi", "reviewer": "Reviewer_ruyA", "summary": "# Problem  \nGenerating meaningfully diverse outputs from large language models (LLMs) remains a challenge, especially when diversity must be semantically significant. Existing techniques like temperature scaling or context-based prompting have shown limited success in ensuring genuine response variety.\n\n# Contributions  \nThis paper makes three main contributions:\n\n- SimpleStrat - a training-free pipeline for controllable, interpretable diversification of LLM outputs that operates entirely at inference time.\n- CoverageQA - a dataset of underspecified questions designed to evaluate response diversity.\n- New diversity metrics - tailored for different evaluation settings (with or without access to model logits), aimed at capturing distinct types of diversity.\n\n# Method  \nThe SimpleStrat approach consists of three stages:\n\n- Automatic stratification - automatically identifies meaningful diversity dimensions within the solution space.\n- Heuristic estimation - estimates the relative proportions of identified strata.\n- Probabilistic prompting - samples prompts based on heuristic-driven distributions, balancing randomness with controlled diversity.\n\nSimpleStrat enhances diversity without the need for model fine-tuning and avoids the quality degradation often seen with naive sampling strategies like high-temperature generation.\n\n# Experimental Setup  \nRecognizing that existing datasets and metrics fall short for evaluating diversity, the authors created CoverageQA in two variants:\n\n- CoverageQA-Curated (manually curated set of underspecified questions)\n- CoverageQA-Wikipedia (derived from Wikidata)\n\nThey also introduce three diversity metrics:\n\n- Distributional Diversity — for models with access to token probabilities (KL-based).\n- Coverage Diversity — for black-box models, based on sampling over CoverageQA (Recall-based).\n- Open-Ended Diversity — for tasks with inherently unenumerable answer spaces (Embedding distance-based)\n\n# Results  \n\n- SimpleStrat outperforms GPT-4o and Claude 3.5 Sonnet on coverage diversity.\n- SimpleStrat achieves higher distributional diversity than LLaMA 3 (direct comparisons to GPT-4o and Claude were infeasible for this metric due to sampling costs).\n- SimpleStrat also surpasses GPT-4o in terms of open-ended diversity.", "questions": "# Major Questions and Comments  \n\nI strongly encourage the authors to address the points below. I will consider increasing the quality score and overall rating if the following issues are adequately addressed:  \n1. Statistical significance of the results: Regarding the experiments in Figure 4, only mean results are reported, with no indication of variance. A proper evaluation can be one of the following:  \n     (a) Resampling the set of 100 inputs multiple times, computing recall for each, and reporting standard error (or standard deviation) to demonstrate the robustness of the results with respect to sampling variability.  \n     (b) If resampling is computationally/monetary expensive for 100 inputs (as in (a)), this limitation should be explicitly stated. In that case, you could reduce the number of input questions (e.g., to 20–25) and increase the number of sampling runs (e.g., 4–5) to better estimate variability.  \n     (c) Additionally, bootstrapping (sampling with replacement) from the original inputs could be used to generate pseudo-samples and estimate variability. The computational/financial limitation should be explicitly stated as well in this case.\n\nI encourage the authors to explore which of these options are feasible within their available resources.  \n2. Figure 5: The same argument applies to the results in Figure 5. Assessing robustness is not possible when only mean values are reported. Please report standard error or standard deviation for these results as well.  \n3. Table 1:The same applies to the distributional diversity results in Table 1. Please report standard error or standard deviation to support your findings.  \n4. Use of open-source models: Are there any open-source models (at least one more) that you could include in the distributional diversity experiments to strengthen your evaluation?  \n5. Consistency with NeurIPS checklist (Q7): In light of points (1)–(4), I find your response to Question 7 of the NeurIPS checklist regarding statistical significance somewhat inconsistent with the reported results. Please verify consistency and adjust text/answer accordingly.\n6. Limitations of the work:  Unless I have overlooked it, I suggest explicitly stating the limitations of your work in the main text. This could be done in a dedicated paragraph or section, possibly incorporating your response to Question 2 of the NeurIPS checklist.  \n7. Code availability (Checklist Q4, Q5, Q13):  Could the authors clarify whether their responses to Checklist Questions 4, 5, and 13 refer to system prompts provided in the Appendix or the entire experimental pipeline (I have not found reference to the later one)?  \n\n\n# Minor Questions and Comments\n\nI will consider improving the quality score and overall rating if the following questions and comments are addressed. However, I strongly encourage the authors to prioritize the major comments first.\n\n1. Line 7: “Partition of space...” - Please clarify which space is being referenced (e.g., solution space).\n2. Lines 33 - 34: Please consider reformulating this sentence. While it is understood that increasing temperature leads to a less skewed distribution, the current phrasing is difficult to comprehend.\n3. Lines 41 - 42: Please consider citing relevant research from cognitive or social sciences that formally demonstrates the presence of the \"blue-seven\" phenomenon.\n4. Line 47: The phrase “aligned with true distribution of answers” appears overly strong, given that no experiments in the paper directly validate this claim. Moreover, for some experiments (such as open-ended questions), it may be impossible to compute this distribution.\n5. Lines 68 - 76: I suggest introducing all three diversity types here. For example, readers may not immediately associate the \"recall\" measure with \"coverage diversity,\" as introduced later. The same applies to \"text-embedding distance\" and \"open-ended diversity.\"\n6. Line 71: The phrase “recall being the most natural way” may come across as an overstatement. Consider avoiding superlative forms, though this is optional.\n7. Line 79: The value 0.36 is difficult to interpret, as KL divergence is only guaranteed to be non-negative and has no defined upper bound. Please consider providing additional reference values or context to help readers assess the significance of this figure. The same issue arises on line 96.\n8. Line 92: Consider adding “of output” or “of response” after the word “diversity” for clarity.\n9. Line 141: The sentence is somewhat difficult to read. Please clarify - the validity of what? Also, why are augmentations described as “more aggressive”?\n10. Line 198: Should this read “all **solutions** in the solution space”?\n11. Line 211: A closing parenthesis “)” appears to be missing.\n12. Lines 230 - 235: I recommend providing a clear example of how the method generates outputs. While I appreciate the authors’ efforts in the main text and Appendix A, the description remains somewhat abstract. A concrete example would be helpful (possible in the Appendix, but step-by-step).\n13. Figure 3 caption: I assume the left side shows GPT-4o results and the right side shows SimpleStrat. Please ensure the caption consistently reflects the figure’s layout.\n14. Figure 4 legend: Please clarify what is meant by “baseline.” Is it GPT-4o?\n15. Figure 4 legend: Please use “Claude 3.5 Sonnet” instead of “Anthropic” and “GPT-4o” instead of “baseline” for consistency.\n16. Figure 4 caption: Could you please elaborate on what exactly is meant by “SS Ablation Recall”?\n17. Figure 4 caption: I suggest adding a brief explanation for why the evaluation of Claude 3.5 Sonnet is limited to temperatures up to 1.0. The same clarification would be helpful for Figure 8 and Figure 9a.\n18. Figure 5: While this is a matter of presentation preference, since both plots are placed close together, I suggest using the same colors for curves representing the same model to avoid confusion. Currently, blue and orange denote different models in each plot.\n19. Line 286 - 287: The phrase “These simple checks are do not aspire” contains a grammatical error. Please revise.\n20. Line 297: Please correct “Furthre” to “Further.”\n21. Line 326: In Figure 6, the x-axis represents SimpleStrat and the y-axis represents the baseline. Please ensure that the text and figure labeling are consistent. 22. Plans for CoverQA release: Finally, are there any plans to release CoverQA? For example, as CoverQA-Curated is intended to remain unchanged, could it be published \"as is\"? Could CoverQA-Wiki be snapshotted and published (while being continuously updated online)? This is important, as it is one of the claimed contributions.", "limitations": "The authors provided clarification regarding the limitations of their work in the NeurIPS checklist; however, there is no dedicated section or paragraph explicitly discussing these limitations. In my comments, I recommended placing greater emphasis on this point within the \"Questions\" section.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strengths\n\n1. Originality: I found the core idea to be simple and straightforward, yet original. The proposed method enables increasing the diversity of LLM outputs in an interpretable and controllable manner (at the inference stage).\n\n2. Significance: Given the widespread use of LLMs and the large number of downstream applications where users require valid, faithful, yet semantically diverse generated content, I consider the significance of this work to be high.\n\n3. Clarity: The manuscript is well-structured and well-written. The problem statement and research gap are clearly articulated, and the subsequent ideas are logically developed and easy to follow (apart from a few points which I have listed in the \"Questions\" section.)\n\n\n# Weaknesses\n\n1. Quality: While I found the paper to be of reasonable quality overall, I have significant concerns regarding the lack of statistical significance in the results and the limited scope of the evaluation. Additionally, there are several minor issues scattered throughout the manuscript that I encourage the authors to address (please see the \"Questions\" section).", "was_revised": true, "final_justification": "The authors have adequately addressed my concerns; consequently, I have increased the quality score and overall ranking to reflect the improvements made during the rebuttal phase.", "rebuttal": "We appreciate the detailed review and the constructive feedback! We hope the following clarifications and experiments address your questions.\n\n## Major Questions\nWe designate answer to major questions with **(Q#)**\n\n### On code availability and dataset availability **(Q7)**:\nAs part of the submission, we included a zip supplemental file including the experiment pipeline as well as plotting scripts. We include the prompts in the appendix of the manuscript for easier access and legibility. Additionally, we provided the CoverageQA datasets and raw inference outputs from the language models in this zip file. In particular, we want to highlight that the CoverageQA evaluation pipeline requires careful handling of redundant ways of expressing the same answer – for instance countries (e.g. \"United Arab Emirates\",\"UAE\", and \"Emirates\") as well as for names (e.g. \"J. Robert Oppenheimer\", \"Robert Oppenheimer\", \"Oppenheimer\", and \"J. R. Oppenheimer\"). Our inclusion of the experiment pipeline in the supplemental is important for replicability given the need for handling these duplicates. \n\nIn summary, CoverageQA has already been made available in the submission. As noted by the reviewer, CoverageQA is procedurally generated and thus will be periodically updated with future versions based on changes to WikiData.\n\n## Experiment robustness (**Q1-Q3**), \nAs recommended, we reran the results in figure 4 and 5 to obtain statistical confidence. In the original experiment, we focused our compute/cost budget on running a wider variety of temperature and large number of resampling to provide confidence that the results are not due to randomness of samples. As requested, below are the results of replicating the figure 4 CoverageQA experiment on a smaller subset of temperatures (to reduce cost) repeated 5 times. They confirm the results are robust to sampling:\n\n### CoverageQA Results with std and additional Ablations -- Original Figure 4 **(Q1)**\n\n| Temperature | Baseline GPT-4o (std) | SimpleStrat with GPT-4o (std) | AttrPrompt with GPT-4o (std) | SimpleStrat w/o 20-questions|\n|-------------|-----------------------|-------------------------------|---------------------------------------|--|\n|0 | 0.0646 (0.0011) | 0.2423 (0.0050) | 0.1244 (0.0006) | 0.1215 (0.0021)|\n|0.25 | 0.0849 (0.0016) | 0.2669 (0.0022) | 0.1389 (0.0021) | 0.1405 (0.0028)|\n|0.5 | 0.1204 (0.0036) | 0.3017 (0.0043) | 0.1619 (0.0027) | 0.1660 (0.0025)|\n|0.75 | 0.1497 (0.0046) | 0.3433 (0.0067) | 0.1925 (0.0061) | 0.1821 (0.0336)|\n|1 | 0.1871 (0.0071) | 0.3884 (0.0094) | 0.2265 (0.0035) | 0.2381 (0.0049)|\n|1.25 | 0.2280 (0.0053) | 0.4250 (0.0062) | 0.2824 (0.0043) | 0.2872 (0.0065)|\n|1.5 | 0.2676 (0.0059) | 0.4634 (0.0085) | 0.3360 (0.0042) | 0.3304 (0.0104)|\n\nWe rename SS Ablated from the manuscript to AttrPrompt to emphasize the similarity of the ablation to AttrPrompt and the role it serves as a baseline approach. We add two additional ablation requested by other reviewers: \n- SimpleStrat w/o 20-Questions ablates the 20 questions approach keeping everything else the same\n- SimpleStrat Single Prompt ablates the need for multiple stages\n\nThe ablations further support the claim that 20-Questions formulation leads to far better partitions and is crucial to the observed improvements. The single prompt ablation supports the importance having multiple stages. In particular, the single prompt is missing probabilistic prompting severely limiting the diversity. The standard deviation gives us confidence that the gains of full SimpleStrat are not the result of sampling variance.\n\n### WritingPrompts Results with std -- Original Figure 5 **(Q2)**\n\nAs recommended, we report the standard deviation of the metrics over the 100 samples for each temperature setting. The generations require producing full outlines of stories based on creative writing prompts from reddit, WritingPrompt. This reported variance ensures against sampling variance over the set of prompts taken from the full writing prompts dataset.\n\n**Baseline GPT-4o**\n| Temperature | Diversity – cosine distance (std) | Quality – Format Adherence (std) \n|-------------|-----------------------|------------| \n | 0.0 | 0.0007 (0.0043) |  1.0000 (0.0000) | \n | 0.25 | 0.3897 (0.1320) |  0.9700 (0.1706) | \n | 0.5 | 0.4537 (0.1281) |  1.0000 (0.0000) | \n | 0.75 | 0.5171 (0.1050) |  0.9500 (0.2179) | \n | 1.0 | 0.5511 (0.1057) |  0.9500 (0.2179) | \n | 1.25 | 0.7097 (0.1815) |  0.3400 (0.4737) | \n\n\n**SimpleStrat with GPT-4o**\n| Temperature | Diversity – cosine distance (std) | Quality – Format Adherence (std) \n|-------------|-----------------------|------------|\n | 0.0 | 0.5444 (0.1664) |  0.9900 (0.0995) | \n | 0.25 | 0.5627 (0.1723) |  1.0000 (0.0000) | \n | 0.5 | 0.5979 (0.1434) |  0.9900 (0.0995) | \n | 0.75 | 0.6176 (0.1211) |  0.9700 (0.1706) | \n | 1.0 | 0.6420 (0.1142) |  0.9300 (0.2551) | \n | 1.25 | 0.7535 (0.1465) |  0.3100 (0.4625) | \n\nWe emphasize that SimpleStrat is able to randomize in the prompt space even for temperature zero. As seen the diversity as measured by cosine distance in the embedding space is significantly larger than without SimpleStrat and is comparable to much higher temperatures. It’s interesting to note that even with temperature = 0 on longer generation tasks the generated outlines have small deviations. \n\n**(Q3)**: For results on distributional diversity, the constraints are generated with temperature 0 and the next token probabilities are computed deterministically from the model weights. As such, there's no natural notion of sample variance. **(Q5)** We will update the checklist in the appendix to clarify which experiments we provide standard deviations for.\n\n### On open source models **(Q4)**: \nAt the time of selection, we chose Llama 3.1 as it was the state-of-the-art open-weight model. We believe the learnings are general as the observation of existing mode collapse and improvements by SimpleStrat are consistent with analysis on proprietary models. We will include Qwen-3 as well in the final revision as it has grown in popularity and capability. We do not anticipate significant differences in results as new open-source models get released since the proprietary models also show the same limitation. Particularly, we anticipate mode-collapse in instruction-tuned models may become even more severe in reasoning models where models have been trained on objective single-answer math problems. We leave analysis of reasoning focused models as future work.\n\n### On limitations **(Q6)**,\nIn section 3.4, We acknowledge the risk that SimpleStrat identifies “unwanted bias or unwanted factors” when proposing strata and proportions. Specifically, we mention that even in the case that the LLM correctly follows the 20 questions-inspired instruction to divide the space of unique solutions into equal proportions, this may have unintended consequences. For instance, there are more female baby names than male baby names as reported by the census. In that case, SimpleStrat would exhibit a preference for female baby names. We will include a dedicated section to emphasize the potential limitation of relying on model produced stratification in the main text.\n\nTo further elaborate, although SimpleStrat shows improvement empirically, it is sensitive to the model selecting good meaningful axes in auto-stratification and correct joint probabilities in heuristic estimation. As work on LLMs for forecasting improves, we expect LLMs to produce better estimates especially when given access to external data and data analysis tools. For our prototype, we restricted ourselves to studying the model’s intrinsic capabilities and tendencies. Further, the model may have biases concerning race and gender that may be reflected also in the auto-stratification and heuristic estimation. As such, it is recommended the probabilistic prompt distribution of SimpleStrat is carefully inspected for critical applications. Finally, CoverageQA is a dataset of short responses. Although this makes evaluation more practical, we believe SimpleStrat will be especially impactful in settings that require low temperature, especially multi-step reasoning as identified by Zhang et al. (2024).\n\n----------------------------------------------\n## Other questions:\n### SimpleStrat Ablation (SS Ablation): \nTo clarify, the abbreviation SS Ablation refers to the ablation described in section 5.1 under coverage diversity. The ablation asks the language model directly to propose criterion instead of the 20-questions approach in AutoStratification and the ablation applies uniform sampling akin to AttrPrompt (Yu et al 2023) instead of using heuristic estimation. We will make this explicit in the caption as recommended.\n\n### Abbreviated Legend in Figure 4: \nIndeed Baseline indicates using GPT-4o without SimpleStrat, Anthropic stands for Claude-3.5 sonnet, SS stands for SimpleStrat, SS Ablation stand for the Ablation described above where we replace the 20-questions approach to AutoStratification with a direct prompt asking for partitions. We will make the recommended changes to the manuscript make sure the legend is clear and precise.\n\n### Anthropic Model Temperatures: \nFootnote 3 for figure 4 explains that Claude models are only allowed temperatures between 0 and 1; the footnote unfortunately rendered on page 9. This is possibly because alignment of models is more difficult to guarantee for high temperatures.\n\n### Blue-Seven Phenomena:\nWe will include a citation for blue-seven and raise a caveat that the effects may vary across cultures: Simon, William E. \"Number and color responses of some college students: Preliminary evidence for a “blue seven phenomenon”.\" Perceptual and motor skills 33.2 (1971): 373-374."}, {"review_id": "J6U1ZNyI1m", "reviewer": "Reviewer_VKJt", "summary": "This work aims to improve the sampling diversity of LLMs for tasks that are open-ended or have multiple valid solutions. To this end, the authors introduce CoverageQA, a dataset of underspecified questions with multiple equally plausible answers. A multi-stage prompting method, SimpleStrat, is also proposed to improve the sampling diversity. The empirical experiments demonstrate the effectiveness of the proposed prompting method across multiple settings.", "questions": "1. What is “Anthropic Recall” in Figure 4? It does not appear to be mentioned anywhere in the main text.\n\n2. How exactly is “SS Ablation” different from “SS”? The description is somewhat vague.", "limitations": "Yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. The studied problem, improving the sampling diversity of LLMs, is important and has practical value.\n\n2. The introduced dataset, CoverageQA, could be a useful resource for studying the diversity and coverage of LLM generations.\n\n3. The proposed prompting method, SimpleStrat, outperforms baselines across various evaluation settings.\n\nWeaknesses:\n\n1. Stronger baselines from prior work should be included to better validate the advantages of the proposed method, such as [1][2][3]. In particular, no baselines aimed at increasing sampling diversity appear to be compared.\n\n2. More thorough ablation studies should be conducted to better understand the role of each component in the proposed method, SimpleStrat, which would help clarify the impact of each stage. For example, a single-stage prompting variant can be compared to the original multi-stage version.\n\nReferences\n\n[1] Zhu, Wenhong, et al. \"Improving Open-Ended Text Generation via Adaptive Decoding.\" ICML 2024.\n\n[2] Adaptive Contrastive Search: Uncertainty-Guided Decoding for Open-Ended Text Generation (Garces Arias et al., EMNLP Findings 2024)\n\n[3] Meyerson, Elliot, et al. \"Language model crossover: Variation through few-shot prompting.\" ACM Transactions on Evolutionary Learning 4.4 (2024): 1-40.", "was_revised": true, "final_justification": "As discussed in my response to the authors' rebuttal, I believe that more thorough empirical comparisons with related methods/baselines for improving sampling diversity should be considered to better demonstrate the significance of the proposed approach. Therefore, I maintain my original assessment.", "rebuttal": "We appreciate the thoughtful review and the constructive feedback! We hope the following clarifications and experiments address your questions.\n\n### Figure 4 Legend: \n`Anthropic` stands for Claude-3.5 sonnet. This is in contrast to the `Baseline` which stands for GPT-4o which is a more direct comparison since the instantiation of SimpleStrat we implement uses GPT-4o. SS stands for SimpleStrat, SS Ablation stands for the Ablation described above where we replace the 20-questions approach to AutoStratification with a direct prompt asking for partitions. Thanks for raising bringing this confusion to our attention; we will rename the manuscript's legend to be clear and consistent with the main text's names.\n\n### Ablation:\nThe existing ablation coined `SS Ablation` in the main result in Figure 4 constitutes replacing both using a direct prompt instead of the 20-questions inspired prompting in AutoStratification and heuristic estimation is replaced with uniform sampling instead of heuristic estimation. \n\nIn addition to the ablations provided in the original manuscript, we add two additional ablations: as suggested, we consider the setting where we provide all the instructions to the model asking it to generate both the partitions and the sampling probabilities in one step. Second, to analyze the importance of the 20-questions approach to AS, we substitute only that prompt with a simple direct prompt asking for partitions.\n\n| Temperature | Baseline GPT-4o (std) | SimpleStrat with GPT-4o (std) | AttrPrompt with GPT-4o (std) | SimpleStrat w/o 20-questions| SimpleStrat Single Prompt with GPT-4o (std)| \n|-------------|-----------------------|-------------------------------|---------------------------------------|--|-|\n|0 | 0.0646 (0.0011) | 0.2423 (0.0050) | 0.1244 (0.0006) | 0.1215 (0.0021)| 0.0019 (0.0008) |\n|0.25 | 0.0849 (0.0016) | 0.2669 (0.0022) | 0.1389 (0.0021) | 0.1405 (0.0028)| - |\n|0.5 | 0.1204 (0.0036) | 0.3017 (0.0043) | 0.1619 (0.0027) | 0.1660 (0.0025)| - |\n|0.75 | 0.1497 (0.0046) | 0.3433 (0.0067) | 0.1925 (0.0061) | 0.1821 (0.0336)| - |\n|1 | 0.1871 (0.0071) | 0.3884 (0.0094) | 0.2265 (0.0035) | 0.2381 (0.0049)| 0.0272 (0.0014)|\n|1.25 | 0.2280 (0.0053) | 0.4250 (0.0062) | 0.2824 (0.0043) | 0.2872 (0.0065)| - |\n|1.5 | 0.2676 (0.0059) | 0.4634 (0.0085) | 0.3360 (0.0042) | 0.3304 (0.0104)| - |\n\nWe rename SS Ablated from the manuscript to AttrPrompt to emphasize the similarity of the ablation to AttrPrompt and the role it serves as a baseline approach. We add two additional ablation requested by other reviewers: \n- SimpleStrat w/o 20-Questions ablates the 20 questions approach keeping everything else the same\n- SimpleStrat Single Prompt ablates the need for multiple stages. We append the prompts for the three stages into a single stage and give the model a 1000 token prompt and a budget of 1000 tokens to follow the instructions. We chose to only sample temperature 0 and temperature 1 as the results show substantially worse performance than directly prompting gpt-4o.\n\nThe ablations further support the claim that 20-Questions formulation leads to far better partitions and is crucial to the observed improvements. The single prompt ablation supports the importance of having multiple stages. In particular, the single prompt is missing probabilistic prompting severely limiting the diversity. The standard deviation gives us confidence that the gains of full SimpleStrat are not the result of sampling variance.\n\n### Baseline to increase sample diversity: \nWe disagree that no baselines aimed at sample diversity were included. We argue temperature scaling is the most common and widely accepted baseline to `increasing sample diversity`. We show just applying SimpleStrat to temperature zero gives as much benefits to diversity as increasing the temperature to 1.2 in CoverageQA and 1 in WritingPrompts. We not only show absolute improvement over temperature scaling but orthogonal gains that show even at temperature 1.5 we can improve the recall on CoverageQA from 0.35 to 0.45. We further compare to AttrPrompt (Yu et al 2023) labeled SS Ablation which we believe to be the most comparable baseline also introducing variance by sampling from a family of prompts.\n\nZhu et al. [1] and Garces Arias et al.,[2] will naturally shine in settings with longer generations as it selectively chooses where to spend “temperature” based on model confidence. In the short answer setting of CoverageQA, these approaches are similar to just temperature scaling as there are few (5-10) tokens in the generation. Moreover, as illustrated in Figure 1 and Figure 7, the instruction-tuned models tend to be poorly calibrated in terms of next-token probability. In the context of the WritingPrompts experiment, the goal is to highlight the degradation of quality at higher temperatures. Thus, SimpleStrat accesses a different kind of variance than accessible using model confidence. \n\nWe discuss LMX[3] in line 127 of the related works. This approach relies on carefully choosing a few-shot examples from a seed set of diverse examples to extract variance. Our approach does not rely on external guidance by providing few-shot examples. A natural extension of SimpleStrat to consider is “sampling without replacement” where past samples can be leveraged to generate new unique samples. In the “without replacement” setting, SimpleStrat can be extended in 3 key ways: \n1. AutoStratification can be used to introduce partitions that distinguish already seen solutions from not yet seen solutions, \n2. AutoStratification can repartition the remaining unobserved solution space,\n3. Probabilistic Prompting can upweighting partitions that have produced less than expected samples. \nIn this setting LMX and SimpleStrat can be viewed as complementary mutators for discovering new solutions. In summary, LMX cannot be directly compared to SimpleStrat as it relies on a strong seed bank of solutions."}, {"review_id": "16RQcdk0Rv", "reviewer": "Reviewer_ucfG", "summary": "The paper proposes an approach called SimpleStrat using the language model itself to partition the answer/solution space into plausible regions from where sampling is performed. The authors develop a dataset of underspecified questions called  CoverageQA with multiple equally plausible answers. The paper also proposes to use KL divergence for measuring the resampling diversity between the output and true distributions. The paper reports better recall and average reduction in KL divergence when compared with widely used LLMs.", "questions": "1. The authors should mention why they chose certain LLMs over others for their experiments.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "SimpleStrat is a training-free approach to improve diversity with auto-stratification, heuristic estimation,  and probabilistic prompting by controlling the randomness in prompts. The workflow of the approach is very intuitive with focus on tackling the pain points. All the steps are clearly defined with examples. The comparison with temperature as a factor is insightful.\n\nIt is not clear why only Llama 3.1 models are considered for the experiments with KL divergence. The authors should mention the selection criteria for the chosen LLMs.", "was_revised": true, "final_justification": "I have already reviewed the author rebuttal and I am satisfied by the response to the issues addressed by the authors.", "rebuttal": "We appreciate the thoughtful and enthusiastic review. \n\n### Temperature comparison: \n\nWe also found the temperature scaling comparisons “insightful” and emphasize the importance of finding general purpose approaches to improving output variability orthogonal to temperature scaling which trades off prompt adherence and diversity.\n\n### Choice of Language Models: \n\n*Open-source models.* At the time of selection, we chose Llama 3.1 as it was the state-of-the-art open-weight model. We will include Qwen-3 as well in the final revision as it has grown in popularity and capability. We do not anticipate significant differences in results as new open-source models get released since the proprietary models also show the same limitation. Particularly, we anticipate mode-collapse in instruction-tuned models may become even more severe in reasoning models where models have been trained on objective single-answer math problems. We leave analysis of reasoning focused models as future work. \n\n*Proprietary models.* We chose OpenAI’s 4o models as and claude-3.5-sonnet as they demonstrate the key general domain capabilities characteristic of large language models, while remaining affordable for extensive resampling experiments. As models are becoming cheaper to experiment with, we are happy to include more models in the evaluation if desired.\n\n### Intuitive presentation\n\nWe are glad the reviewer finds the approach intuitive with the carefully chosen examples we used to illustrate the approach. We believe the intuitive simplicity of SimpleStrat makes it easy to incorporate in other settings."}, {"review_id": "ISAYWLyx4d", "reviewer": "Reviewer_UC4f", "summary": "The authors introduce SimpleStrat, a new method designed to enhance diversity in LLMs. SimpleStrat uses stratified sampling guided by auto-generated criteria (auto-stratification) from the LLM itself. To evaluate the quality of the sampling method the authors introduce CoverageQA, a benchmark to evaluate response diversity. SimpleStrat performs well on the introduced benchmarks.", "questions": "Do you think it is possible to do something similar but without the need for computing stratification prompts?", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths: \n- The paper addresses an important and promising area—improving sampling methods in LLMs—which remains relatively underexplored compared to, e.g., diffusion models where this is a very active area of research. \n- The methodology is intuitive and well-explained, featuring detailed examples that illustrate how SimpleStrat operates. The newly introduced benchmark CoverageQA seems like a step into the right direction for assessing the quality of such methods.\n- The empirical evaluation, while mostly limited to CoverageQA shows promising results across the considered measures of diversity (KL divergence, recall, embedding distances).\n\nWeaknesses:\n- The effectiveness of SimpleStrat heavily relies on the LLM's ability to propose meaningful stratification criteria through self-prompting. Poor initial stratification could reduce potential benefits significantly. Relying exclusively on self-prompting for stratification might miss opportunities for more sophisticated stratification methods—perhaps leveraging neuron activations or intermediate representations could yield more effective stratifications.\n- Computational overhead may be substantial due to multiple stages (auto-stratification and heuristic estimation), possibly limiting applicability in resource-constrained or latency-sensitive scenarios.\n- While useful, the CoverageQA dataset’s heavy reliance on automatically generated constraints from Wikidata could lead to overly synthetic or unintuitive scenarios, potentially limiting real-world applicability. It would be nice to validate the dataset via labelling a small set with human annotators. The same would be nice to assess the quality of the sampling method. Does sampling with this method improve the scores on something like LMArena?", "was_revised": true, "final_justification": "I have read the rebuttal and my concerns remain largely unchanged. Also upon revisiting the work I have some concerns about whether it meets the high bar of NeurIPS. I will leave my score unchanged.", "rebuttal": "We appreciate the thoughtful review and the constructive feedback! We hope the following clarifications and experiments address your questions.\n\n### Limitations of Self Prompting: \nIt’s indeed the case that the approach is sensitive to the quality of the stratification. In fact, our ablation in Figure 4 indicates the 20-questions prompting-approach is crucial to the quality of the stratification and subsequently the resulting diversity. \n\nIt’s certainly true that stratification can be discovered with other techniques. We are familiar with (Hu et al): https://arxiv.org/pdf/2505.05145 which analyzes the contribution of the attention heads to the final prediction, but the semantic analysis is limited to simple tasks. It’s not immediately obvious if the head-wise distinction would always lead to semantically interpretable strata (possibly better with SAE). Is this what you mean by leveraging activations? We would be curious to understand better how neuron activation and intermediate representations can be used to identify semantic strata as future work.\n\nWe added an additional ablation to emphasize the importance of quality partitions by only changing the 20 questions: \n\n##### CoverageQA Results with std and additional Ablations -- Original Figure 4\n\n| Temperature | Baseline GPT-4o (std) | SimpleStrat with GPT-4o (std) | AttrPrompt with GPT-4o (std) | SimpleStrat w/o 20-questions| SimpleStrat Single Prompt with GPT-4o (std)| \n|-------------|-----------------------|-------------------------------|---------------------------------------|--|-|\n|0 | 0.0646 (0.0011) | 0.2423 (0.0050) | 0.1244 (0.0006) | 0.1215 (0.0021)| 0.0019 (0.0008) |\n|0.25 | 0.0849 (0.0016) | 0.2669 (0.0022) | 0.1389 (0.0021) | 0.1405 (0.0028)| - |\n|0.5 | 0.1204 (0.0036) | 0.3017 (0.0043) | 0.1619 (0.0027) | 0.1660 (0.0025)| - |\n|0.75 | 0.1497 (0.0046) | 0.3433 (0.0067) | 0.1925 (0.0061) | 0.1821 (0.0336)| - |\n|1 | 0.1871 (0.0071) | 0.3884 (0.0094) | 0.2265 (0.0035) | 0.2381 (0.0049)| 0.0272 (0.0014)|\n|1.25 | 0.2280 (0.0053) | 0.4250 (0.0062) | 0.2824 (0.0043) | 0.2872 (0.0065)| - |\n|1.5 | 0.2676 (0.0059) | 0.4634 (0.0085) | 0.3360 (0.0042) | 0.3304 (0.0104)| - |\n\nWe note that in addition to relying on quality partitions. The inclusion of external variance introduced by sampling constraints is also critical. We see SinglePrompt approach where we append the prompts together and allow the model in prompt space to select the positive or negative constraint lead to signification regression even compared to baseline GPT-4o. Noting that the language model has been trained to ignore random irrelevant tokens. The key to self-stratification is producing token efficient constraints with outsized impact on model's diversity. Critically, these small number of constraints allowing the system to inject external randomness to token space giving $2^n$ candidate prompts.\n\n### Computational overhead: \n\nAs articulated in section 3.1, we advocate for caching of AutoStratification and Heuristic Estimation per prompt. Effectively, once the stratification has been discovered, it can be reused and the excess token overhead viewed as amortized cost across many rounds of resampling. For a cached prompt, only a small overhead of ~20 tokens per constraint (3-5 constraints per problem on average) is needed for each query in Probabilistic Prompting. \n\nUnder extreme latency conditions, the model can be assumed to be small (1B-8B) with latency below 10ms to the first token. This should render the minimal per query overhead to be negligible. In highly-resource constrained and latency-sensitive settings, we can go further to optimize latency by precomputing stratification for common prompts.\n\n### CoverageQA realism: \nWe agree there is some risk of a sim-to-real gap between the Wikipedia CoverageQA questions/answers and more natural human generated questions/answers. We have taken several measures to address this: \n\n1. As discussed in line 247, we manually curate the answer set to ensure the answers are reasonable. Although the heavy-lifting has been done by the WikiData community. This manual check was crucial in both removing poorly phrased or ambiguous questions but more importantly identifying missing answers. For instance, certain noble gasses were missing from the WikiData queries. We are also careful to not over punish the model by enumerating possible ways of expressing the same answer – for instance countries (e.g. \"United Arab Emirates\",\"UAE\", and \"Emirates\") as well as for names (e.g. \"J. Robert Oppenheimer\", \"Robert Oppenheimer\", \"Oppenheimer\", and \"J. R. Oppenheimer\"). \n\n2. We separately show evaluation on CoverageQA-curated in Appendix B. This set represents a small set of 15 questions generated by the authors: e.g. give me a NFC East team. Although at a smaller scale, this evaluation gives us some confidence the wiki generated questions are representative of real questions. SimpleStrat shows similar improvement in that setting.\n\n3. WritingPrompts experiments show diversity improvement on prompts purely human generated on Reddit. Although diversity is measured differently given the open-endedness of the prompts, this gives us confidence that SimpleStrat discovers productive stratification. \n\nAlthough these measures have been taken, we agree human annotation and pair-wise comparison like LMArena can be added to further improve the quality of the CoverageQA dataset and potentially broaden the scope of questions to more subjective domains."}]

Author rebuttal:

Meta-review: This work introduces the method SimpleStrat which is designed to increase diversity from LLM output. The approach uses stratified sampling from auto-generated strata produced by the LLM. The method is evaluated on CoverageQA, a benchmark that is introduced by the authors to measure response diversity. The approach performs well on the benchmarks.

Strengths:
* The paper addresses an important underexplored research area, sampling diverse responses from LLMs.
* The method is easy to understand explained well.
* The work introduces a new benchmark CoverageQA to assess response diversity.
* Several metrics are measured including KL divergence, recall and embedding distance.

Weaknesses:
* The approach relies on the ability of the LLM to generate good strata through prompting. This may not be effective for certain applications such as generating answers to math questions which may have multiple valid answers.
* There is a significant amount of computational overhead involved in generating strata and heuristic estimation. The authors state this can be cached but that is still going to be costly if only generating a few samples for a given user request and requires the user to explicitly use this method for generation.
* The evaluation relies on automatic constraints from Wikidata so doesn't represent a comprehensive evaluation of diversity. Measurements by humans would help.

Due to the novelty of approach, the benchmark contribution and the likely significant impact on work that explores sampling diversity, I recommend that this work be accepted.

During the discussion, reviewers asked for more careful ablations, including whether the 3 stages are needed and whether the 20 questions approaching to stratification were needed. The authors successfully addressed these questions by adding additional ablations. This was helpful for the final decision.
Decision: Accept (poster)