arxiv: 2604.02319 · v2 · submitted 2026-04-02 · 💻 cs.CL

Recognition: no theorem link

No Single Best Model for Diversity: Learning a Router for Sample Diversity

Yuhan Liu , Fangyuan Xu , Vishakh Padmakumar , Daphne Ippolito , Eunsol Choi

Authors on Pith no claims yet

Pith reviewed 2026-05-13 21:46 UTC · model grok-4.3

classification 💻 cs.CL

keywords diversity coveragemodel routerLLM diversityopen-ended promptsanswer generationmodel selectionensemble methods

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The pith

A router that predicts the best model for each query outperforms any fixed LLM at generating diverse answer sets to open-ended prompts.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that different large language models excel at producing diverse responses for different open-ended prompts, with no single model performing best across the board. For any given prompt, however, one model typically generates a significantly more comprehensive set of valid answers than the rest. The authors train a router to select the strongest model per query and demonstrate that this selection raises diversity coverage above the level achieved by always using the single strongest model. This approach matters because many user prompts admit multiple valid answers, and better coverage across a fixed number of generations can address a wider range of user needs. The router also maintains its advantage on new datasets and under changed prompting methods.

Core claim

Evaluating 18 LLMs on prompts that permit many valid answers reveals no single model dominates at generating diverse responses. However, for each prompt there exists a model that significantly outperforms the others in producing a comprehensive answer set, as measured by diversity coverage. This motivates training a router to select the best model per query, which improves performance from 23.8% to 26.3% on the NB-Wildchat dataset and generalizes to out-of-domain data and alternative generation strategies.

What carries the argument

A trained router that predicts the best LLM for maximizing diversity coverage on a given prompt.

Load-bearing premise

The router trained on observed model performances can reliably predict the optimal model for new prompts and that diversity coverage scores reflect meaningful differences in how comprehensively users experience the answer sets.

What would settle it

On a fresh collection of prompts, if the router-selected models produce lower average diversity coverage than the single best fixed model, the central claim of reliable improvement would be refuted.

Figures

Figures reproduced from arXiv: 2604.02319 by Daphne Ippolito, Eunsol Choi, Fangyuan Xu, Vishakh Padmakumar, Yuhan Liu.

**Figure 1.** Figure 1: Left: LLMs exhibit different diversity coverage. Right: There is no universal best model on NB-WildChat. A model is only considered to be the best model if its diversity scores are 5% higher than the second most best candidate. Queries without a model satisfying this margin are labeled as “No dominant single models”. On Simple Questions, all models perform similarly, resulting in 100% of “No dominant singl… view at source ↗

**Figure 2.** Figure 2: Scaling training data improves router performance on Infinity-Chat. Router trained to select single model can be used to ensemble outputs from two models which provides further gains. We observe consistent gains when using our trained router (Binary MLP(spec)) to select two models, as presented in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Efficiency analysis comparing the time (sec [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Div-Cov (%) results on NB-WildChat with various prompting strategies. Training the router under each prompting strategy ( in domain and out-of-domain evaluation). Large amount of work in diversity has focused on improving the prompt, while throughout this paper we used a fixed prompt template to sample answers and compute diversity coverage. In this last section, we explore two alternative prompt templates… view at source ↗

**Figure 5.** Figure 5: Generate-one prompt has higher answer quality. Under the generate-all prompts, as more answers are listed, the quality decreases with large variations if using generate-all prompt. Improving output diversity Concerns about the output diversity of LLMs (Padmakumar & He, 2023; Anderson et al., 2024; West & Potts, 2025) promoted two categories of solutions: methods that modify model weights (Lanchantin et a… view at source ↗

**Figure 6.** Figure 6: Frequency(%) of each LLM being the most diverse model.A model is only con [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: Prompt, generate one, simple questions Prompt for generate two, simple questions Output two different randomly selected days of the week. Output only the days between curly braces separated by a comma, like this: {answer_1,answer_2}. Don't output code [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 8.** Figure 8: Prompt, generate two, simple questions 14 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 9.** Figure 9: Prompt, generate all, simple questions Prompt for generate one, open-ended questions I am working on a memoir of a computer science PhD student who worked on machine translation in the 1990s. Suggest a single title and nothing else. Please use the following format: { { "answer-id": 1, "content": "Your answer here" }, } [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

**Figure 10.** Figure 10: Prompt, generate one, open-ended questions [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗

**Figure 11.** Figure 11: Prompt, generate two, open-ended questions [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗

**Figure 12.** Figure 12: Prompt, generate all, open-ended questions [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗

**Figure 13.** Figure 13: Prompt verbalized all, simple questions Prompt verbalized all, open-ended questions I am working on a memoir of a computer science PhD student who worked on machine translation in the 1990s. List all the possible answers you can think of. For each answer, also provide a numeric probability of sampling that answer. Please use the following format: { { \"answer-id\": 1, \"content\": \"Your answer here\", \"… view at source ↗

**Figure 14.** Figure 14: Prompt verbalized all, open-ended questions 16 [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗

**Figure 15.** Figure 15: System vanilla, simple questions and open-ended questions System prompt for system verbalized all, simple questions and open-ended questions You are a helpful assistant. For each query, please generate all possible responses, each within a separate <response> tag. Responses should each include a <text> and a numeric <probability>. Please sample at random from the full distribution [PITH_FULL_IMAGE:figur… view at source ↗

**Figure 16.** Figure 16: System verbalized all, simple questions and open-ended questions C Diversity coverage calculation details on open-ended questions Here we discuss the details of how we evaluate the quality and diversity of answers to open-ended questions. We follow the exact procedure to partition the answer set and calculate. the quality scores in Zhang et al. (2025c). To determine semantic equivalence, we apply their eq… view at source ↗

**Figure 17.** Figure 17: Average answer quality for responses generated from different prompts on [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗

**Figure 18.** Figure 18: Comparing different prompts for generating diverse outputs. The number of [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗

**Figure 19.** Figure 19: The number of unique answers on NB-Curated. The X-axis is the log of the number of answers generated. Y-axis measures the diversity coverage of all the unique answers divided by the max possible score(generate 200 different good answers). K.1 Experiment settings Decoding settings For each prompting strategy and desired number of answers N, we repeatedly sample generations from the model until we collect N… view at source ↗

**Figure 20.** Figure 20: Smaller models generate more unique answers. As number of inferred answers [PITH_FULL_IMAGE:figures/full_fig_p026_20.png] view at source ↗

read the original abstract

When posed with prompts that permit a large number of valid answers, comprehensively generating them is the first step towards satisfying a wide range of users. In this paper, we study methods to elicit a comprehensive set of valid responses. To evaluate this, we introduce \textbf{diversity coverage}, a metric that measures the total quality scores assigned to each \textbf{unique} answer in the predicted answer set relative to the best possible answer set with the same number of answers. Using this metric, we evaluate 18 LLMs, finding no single model dominates at generating diverse responses to a wide range of open-ended prompts. Yet, per each prompt, there exists a model that outperforms all other models significantly at generating a diverse answer set. Motivated by this finding, we introduce a router that predicts the best model for each query. On NB-Wildchat, our trained router outperforms the single best model baseline (26.3% vs $23.8%). We further show generalization to an out-of-domain dataset (NB-Curated) as well as different answer-generation prompting strategies. Our work lays foundation for studying generating comprehensive answers when we have access to a suite of models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A router picking the best LLM per prompt beats the top fixed model on diversity coverage by 2.5 points and generalizes, but the metric's quality scoring needs scrutiny.

read the letter

The main takeaway is that no single LLM dominates at producing comprehensive sets of valid answers for open-ended prompts, yet a router trained to pick the right model per prompt delivers a small but consistent edge over the strongest fixed choice and holds up on new data and prompts. They evaluate 18 models, introduce a diversity coverage metric that sums quality scores of unique answers against an oracle top-k set, and show clear per-prompt variation in which model wins. The router then beats the best baseline at 26.3% versus 23.8% on NB-Wildchat, with similar gains on NB-Curated and under different generation prompts. This is a practical demonstration that model selection can address diversity without scaling any one model further. The empirical pattern is straightforward and the generalization results give the claim some grounding beyond the training distribution. The router itself is standard, but the application to this property and the concrete numbers are the useful part. The soft spot is the metric. Diversity coverage depends on how uniqueness is determined and how per-answer quality is scored, likely through embeddings or an LLM judge. If either step favors outputs from particular models or styles, the per-prompt labels used to train the router become noisy and the reported lift could partly reflect that bias rather than real coverage gains. The abstract gives no human validation of the metric, so the out-of-domain results rest on the same untested assumption. This paper is for people building multi-model serving systems who want better coverage on open-ended tasks. A reader focused on routing or evaluation metrics will find actionable details. It deserves a serious referee because the setup is testable and the core finding is narrow enough to discuss productively. I'd send it out for review with a request to clarify the uniqueness threshold and quality scorer plus any human correlation checks.

Referee Report

3 major / 2 minor

Summary. The paper claims that no single LLM among 18 evaluated models dominates at generating diverse responses to open-ended prompts, but that a per-prompt best model exists; it introduces a 'diversity coverage' metric (sum of quality scores of unique answers relative to an oracle top-k set of equal size) and trains a router that selects the best model per query, reporting 26.3% coverage versus 23.8% for the single-best baseline on NB-Wildchat with generalization to NB-Curated and varied prompting strategies.

Significance. If the diversity coverage metric is shown to be reliable, the work provides empirical evidence against a universal best model for diversity and demonstrates that lightweight routing can yield measurable gains in comprehensive answer generation, which is a practical contribution for multi-model serving systems. The absence of a single dominant model and the router's reported lift are the core findings.

major comments (3)

[Abstract] Abstract: the diversity coverage metric is defined only at a high level as summing quality scores of unique answers relative to an oracle top-k set; the manuscript must specify (1) the exact criterion for uniqueness (embedding cosine threshold, exact string match, etc.) and (2) the procedure for obtaining per-answer quality scores (LLM judge prompt, reference-free scoring, etc.). These details are load-bearing for the 26.3% vs 23.8% headline result and all generalization claims.
[Abstract] Abstract and evaluation sections: no human validation or correlation study is reported for the automated diversity coverage metric against human judgments of answer-set comprehensiveness. Without such validation, the router's training labels and the reported out-of-domain gains rest on an untested assumption.
[Abstract] Abstract: the router is said to be 'trained' on per-prompt performance, yet no details are given on training data construction, input features, model architecture, or held-out evaluation protocol. This information is required to assess whether the 2.5-point improvement is statistically reliable and whether the generalization results are robust.

minor comments (2)

The paper should cite prior work on model routing (e.g., mixture-of-experts routing, LLM routing papers) and existing diversity metrics to clarify the novelty of the proposed coverage measure.
Notation for the diversity coverage formula should be introduced formally with an equation rather than only in prose.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below and will revise the manuscript to incorporate clarifications and additional details where needed.

read point-by-point responses

Referee: [Abstract] Abstract: the diversity coverage metric is defined only at a high level as summing quality scores of unique answers relative to an oracle top-k set of equal size; the manuscript must specify (1) the exact criterion for uniqueness (embedding cosine threshold, exact string match, etc.) and (2) the procedure for obtaining per-answer quality scores (LLM judge prompt, reference-free scoring, etc.). These details are load-bearing for the 26.3% vs 23.8% headline result and all generalization claims.

Authors: We agree that the abstract provides only a high-level overview and that precise specifications are essential for reproducibility. The full manuscript describes these components in the evaluation section, but we will revise the abstract to explicitly state the uniqueness criterion (cosine similarity threshold on sentence embeddings) and the quality scoring procedure (reference-free LLM judge). We will also move the full implementation details, including the exact prompt and threshold, to the main text and appendix in the revised version. revision: yes
Referee: [Abstract] Abstract and evaluation sections: no human validation or correlation study is reported for the automated diversity coverage metric against human judgments of answer-set comprehensiveness. Without such validation, the router's training labels and the reported out-of-domain gains rest on an untested assumption.

Authors: We acknowledge the importance of validating the automated metric against human judgments. No such study was included in the original submission. We will add a small-scale human evaluation on a subset of prompts in the revised manuscript, reporting correlation between diversity coverage scores and human ratings of answer-set comprehensiveness. This will be placed in the evaluation section to support the metric's reliability. revision: yes
Referee: [Abstract] Abstract: the router is said to be 'trained' on per-prompt performance, yet no details are given on training data construction, input features, model architecture, or held-out evaluation protocol. This information is required to assess whether the 2.5-point improvement is statistically reliable and whether the generalization results are robust.

Authors: We agree that additional details on the router are required to assess reliability. We will add a dedicated methods subsection describing the training data construction (labels derived from per-prompt diversity coverage across the 18 models on the training split), input features (prompt embeddings), model architecture (lightweight classifier), and held-out evaluation protocol (cross-validation with significance testing). These additions will directly address concerns about the reported improvement and generalization. revision: yes

Circularity Check

0 steps flagged

No circularity: router is a standard supervised predictor trained on held-out labels

full rationale

The paper first computes diversity coverage on a training split to label the per-prompt best model, then trains a router (presumably a classifier or regressor over prompt features) to predict that label, and finally reports router performance on a held-out test split (NB-Wildchat) plus out-of-domain sets. This is ordinary supervised learning; the test-set lift (26.3 % vs 23.8 %) is not forced by construction because the router never sees the test labels during training. No equations reduce a claimed prediction to a fitted parameter, no self-citation supplies a uniqueness theorem, and the diversity-coverage definition is used only to generate training labels, not to tautologically reproduce the test metric. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are described. The router is presented as a trained predictor but its architecture, loss, and features are not specified.

pith-pipeline@v0.9.0 · 5519 in / 1158 out tokens · 39787 ms · 2026-05-13T21:46:04.219900+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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No Single Best Model for Diversity: Learning a Router for Sample Diversity

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