PaperlayerView exact revision on arXiv

Source-linked AI summary

Gap Detection: Mitigating Homogenization through Demand and Defensibility

Xucheng Yu, Haibo Jin, Xiaoqi Wang, Runze Kong, Haohan Wang

arXiv:2610.20162v2cs.CLcs.LG

TL;DR

Open-ended answers often repeat semantically similar ideas, even when plausible alternatives exist, and useful alternatives must remain relevant while covering what prior responses miss. Gap Detection searches a shared embedding space for directions combining demand and separation, then maps and checks them as text. The reported experiments show lower Collision in open-ended generation, with ablations also showing that improved direction scores do not uniformly yield better output-level metrics.

  • Problem

    Open-ended answers often repeat familiar ideas, while sampling or reranking existing candidates does not explicitly search semantic space left uncovered by prior responses.

    Source: §1 · p. 1

  • Method

    Gap Detection combines query relevance and separation from occupied content in a GapScore, searches for directions, and uses language-model concept mapping and task-specific checks to realize them as text.

    Source: §1 · p. 2

  • Results

    12.8% and 10.8% are the reported mean relative Collision reductions on five curated topics and 90 INFINITY-CHAT queries, respectively, while the ablations show that better direction scores do not uniformly improve output-level metrics.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The results support explicit prior-content coverage as a practical mechanism for diversifying content, with task validity checked separately from geometric novelty.

    Source: §5 · p. 9, §6 · p. 10

    The evaluation depends on the encoder for Collision and Vendi, reports no independent human assessment of answer quality, and uses a manually selected query subset.

    Source: §5 · p. 9

Abstract

from arXiv · show

Language models often produce semantically similar answers to open-ended questions, even when many plausible alternatives exist. Generating useful alternatives requires identifying both what the query calls for and what existing responses already cover. We introduce Gap Detection, a framework that searches for relevant but unoccupied directions in a shared text embedding space. Its objective, GapScore, combines query relevance (Demand) with dissimilarity to the nearest existing item (Defensibility). The framework optimizes this product on the unit sphere, maps candidate directions to concept words with a language model, and uses task-specific filtering and constrained prompting to turn those concepts into text. On five curated topics and 90 INFINITY-CHAT queries, the reported mean relative reductions in output Collision are 12.8% and 10.8%, respectively. We also instantiate the framework for generative engine optimization over four product markets and for iterative synthetic-data augmentation. In the latter setting, with 100 training examples per method, Gap Detection reduces Collision from 0.324 to 0.298 relative to undirected accumulation and increases the Vendi Score from 27.16 to 29.20; the accuracy difference is one example on a 40-example test set. Component ablations expose the trade-off between semantic separation and relevance, while also showing that better direction scores do not uniformly yield better downstream metrics. These results support explicit gap search as a practical mechanism for diversifying content, with task validity checked separately from geometric novelty.

1 INTRODUCTION

Open-ended answers often repeat familiar ideas, so useful alternatives must differ in substance while remaining relevant to the query. Gap Detection searches for relevant unoccupied directions, realizes them as text, and is evaluated across answering, GEO, and synthetic-data settings.

1 INTRODUCTION

  • Sampling or reranking existing candidates does not search unoccupied semantic space, while maximizing distance alone can yield concepts irrelevant to the query.MMR balances relevance and redundancy when reranking a fixed candidate set.Source: §1 · pp. 1–2
  • Gap Detection combines query relevance and separation from the nearest occupied item in a multiplicative GapScore, then adds selected directions to the occupied set for later searches.The pipeline maps directions to concepts and uses task-specific validation before realizing them as text.Source: §1 · p. 2
  • The paper evaluates the framework across open-ended generation, GEO positioning, and synthetic-data augmentation, pairing spherical optimization with language-model mapping and task-specific validation.Its stated contributions also include geometric existence and conditional optimization results in Appendix A.Source: §1 · p. 2
  • 12.8% and 10.8% are the reported mean relative Collision reductions on five curated topics and 90 INFINITY-CHAT queries, respectively.The evaluation also includes GEO positioning and synthetic-data augmentation; ablations show that improved direction scores do not uniformly improve output-level metrics.Source: §1 · p. 2

2 RELATED WORK

The related work covers output diversity, relevance-aware diversification, and GEO and synthetic-data feedback. Gap Detection differs by using prior content during generation to search for new semantic directions rather than only evaluating or reranking existing content.

Output diversity and redundancy

  • Prior work documents semantically repetitive outputs across model families and decoding configurations, motivating complete-response similarity measures (Jiang et al., 2025).This paper uses mean pairwise embedding similarity, termed Collision, and the Vendi Score, a spectral diversity measure (Friedman & Dieng, 2023).Source: §2 · p. 2

Relevance-aware diversification

  • MMR balances query relevance and similarity when selecting documents, whereas Gap Detection searches continuous embedding directions and generates new text instead of reordering candidates.Its multiplicative objective avoids an additive trade-off coefficient, but the full pipeline still has optimization and filtering hyperparameters.Source: §2 · pp. 2–3

GEO and synthetic-data feedback

  • GEO research studies how source content affects visibility in generated answers [Aggarwal et al., 2024], while this paper asks which plausible position to express relative to existing claims.Its GEO experiment uses a controlled citation simulation; proposed claims require factual verification because target-product specifications are not provided.Source: §2 · p. 3
  • Prior studies examine recursive synthetic-data degradation and retention of real and synthetic data [Alemohammad et al., 2024; Gerstgrasser et al., 2024], while this augmentation experiment tests semantic-gap direction in a narrower setting.The procedure evaluates generated text with a downstream classifier and does not specify generative-model retraining.Source: §2 · p. 3

3 GAP DETECTION

Gap Detection represents demand and occupied content in a shared embedding space, searches for relevant yet separated directions, and passes them through concept mapping and task-specific text checks. Its adaptations use distinct inputs and validation procedures for GEO and synthetic-data augmentation.

3.1 OVERVIEW AND PROBLEM SETUP

  • The shared pipeline represents demand and occupied content, searches directions, maps directions to plausible concepts, and generates and checks text.The verifier checks coherence, task relevance, and novelty; rejected candidates feed back into another search, while accepted directions expand the occupied set.Source: §3.1 · p. 3, Figure 1 · p. 4

3.2 SCORING RELEVANT AND UNOCCUPIED DIRECTIONS

  • GapScore multiplies Demand, which measures weighted query–direction relevance, by Defensibility, which penalizes proximity to the nearest occupied item.The product rewards both factors when Demand is nonnegative, but is a preference rather than a hard lower bound; geometric separation does not establish factual validity.Source: §3.2 · pp. 3–4

3.3 SEARCHING FOR MULTIPLE DIRECTIONS

  • The search approximately maximizes GapScore on the unit sphere by moving toward demand and away from the nearest occupied direction, then projecting and normalizing the update.Adding each selected direction to the occupied set encourages later searches to cover different regions; multiple starts reduce reliance on one initialization but do not certify global optimality. A geometric lower bound does not guarantee a corresponding natural-language answer.Source: §3.3 · pp. 4–5

3.4 MAPPING DIRECTIONS TO PLAUSIBLE CONCEPTS

  • Candidate words near each direction are retrieved from a screened vocabulary, then language models select and check concepts for whether they plausibly answer the query.Geometric proximity is not a usefulness or correctness certificate: a nearby word may restate the query, and a separated word may be unrelated.Source: §3.4 · p. 5

3.5 GENERATING AND CHECKING TEXT

  • The generator uses accepted concept groups and instructions to avoid frequent occupied-content words and recurring sentence patterns; generated sentences then undergo novelty and repetition checks.The checks include maximum similarity below 0.7 to original responses and below 0.8 among new sentences; these semantic proxies do not establish creativity or factual accuracy.Source: §3.5 · p. 5

3.6 ADAPTING THE FRAMEWORK TO GEO AND SYNTHETIC DATA

  • For GEO, competitor claims and weighted search queries define the occupied set and demand, while synthetic augmentation uses the current sample pool and weighted task-class descriptions.GEO uses a controlled citation simulation and requires factual verification of proposed claims; sentiment augmentation adds VADER polarity filtering, and a classifier evaluates generated-data utility on a disjoint real test set.Source: §3.6 · pp. 5–6

4 EXPERIMENTS

The experiments test Gap Detection across open-ended generation, product-market positioning, and synthetic-data augmentation using separate task-specific evaluation protocols.

4.1 EVALUATION PROTOCOL AND METRICS

  • Evaluations used five manually selected themes and 90 INFINITY-CHAT queries; Collision measures mean pairwise similarity, while novelty tests separation from the nearest original reference.The synthetic-data evaluation also reports Vendi Score and classification accuracy as distinct metrics from direction GapScore.Source: §4.2 · p. 6, §4.1 · p. 6

4.2 OPEN-ENDED GENERATION

  • 10.7%–17.9% Collision reductions across five topics accompanied lower Collision from 0.7766 to 0.6915 across 90 queries, with novelty threshold passed on 88 of 90 queries.The 90-query novelty pass rate was 97.8%.Source: Table 1 · p. 6, §4.2 · p. 7
  • GapScore scored 0.375 versus 0.298 for Demand-only and −0.228 for Defensibility-only, but Defensibility-only led Collision reduction and random directions led novelty passes.The full method’s novelty pass rate was 84% in this separate ablation.Source: §4.2 · p. 7, Table 2 · p. 7

4.3 TRANSFER ACROSS CONTENT SOURCES AND GENERATORS

  • Across occupied sources, mean Collision reduction was 10.4% with 96.7% novelty passes; with occupancy fixed, realization-model reductions ranged from 9.0% to 14.8%.A four-model mixed occupied set fell from 0.602 to 0.561, a reported reduction of 7.4%.Source: §4.3 · pp. 7–8

4.4 GEO MARKET POSITIONING

  • Selected GEO positions had a mean product score of 0.221; the ablation favored GapScore on product (0.149 versus 0.143), while Demand-only led PAWC (0.508 versus 0.482).Protein powder had Demand 0.383 and Defensibility 1.249, while yoga mats had Demand 0.763 and Defensibility 0.528.Source: Table 3 · p. 8, §4.4 · p. 8

4.5 ITERATIVE SYNTHETIC-DATA AUGMENTATION

  • Against Data Accumulation, GapScore reduced Collision from 0.324 to 0.298 and raised Vendi from 27.16 to 29.20; accuracy was 62.5% versus 60.0%, one test example.These are point estimates from 40 real test examples.Source: Table 4 · p. 9, §4.5 · p. 9
  • For K=3 direction coverage, GapScore scored 0.276 versus 0.199 for Demand-only, while Demand-only repeated a direction (cosine 1.000) and GapScore directions had similarities of 0.11–0.39.This is a direction-objective diagnostic, not an independent downstream quality metric.Source: §4.5 · p. 9

5 DISCUSSION AND LIMITATIONS

Gap Detection makes prior coverage, task fit, and realization separate questions; its ablations show that stronger geometric scores do not guarantee stronger downstream outcomes. The evaluation also has measurement, selection, and task-specific limits.

5 DISCUSSION AND LIMITATIONS

  • Better geometric scores can coexist with weaker novelty-check rates or lower citation share, so direction optimization alone does not explain all end-to-end gains.The method separates where the occupied set leaves room, whether a concept fits the task, and whether its realization is useful.Source: §5 · p. 9
  • Collision and Vendi depend on the search and evaluation encoder, no independent human answer-quality assessment is reported, and the query subset is manually selected.The record also lacks some aggregation details, raw outputs, and repeated-run uncertainty needed for complete replication.Source: §5 · p. 9
  • The sentiment study uses a small seed and test set, a lightweight classifier, and no documented generator-retraining procedure; it does not establish prevention of collapse in recursively retrained foundation models.VADER may favor simple polarity cues, and matched training-set sizes do not isolate its effect from direction selection.Source: §5 · p. 10

6 CONCLUSION

Gap Detection makes prior semantic coverage an explicit input to generation, with task-specific checks separating geometric novelty from useful text. The conclusion and accompanying statements delimit the evidence, reproducibility, and theoretical scope.

6 CONCLUSION

  • Gap Detection combines Demand and Defensibility to search directions, maps them to concepts, and uses task-specific checks to realize them as text.Reported experiments show lower Collision in open-ended generation, diversity gains in a small augmentation task, and differentiated position discovery in a GEO study.Source: §6 · p. 10

AI USE STATEMENT

  • The authors used generative AI for experimental pipeline tasks, related-work discovery, drafting and polishing, and checking derivations, while stating that AI did not design the core method or select reported results.They report reviewing AI-assisted work and taking responsibility for the final content.Source: AI USE STATEMENT · p. 11

ETHICS STATEMENT

  • The GEO citation simulation does not verify that proposed claims are true of target products, so deployment requires factual verification; semantic novelty alone does not establish safety, correctness, or usefulness.The sentiment experiment trains a small downstream classifier, not a deployed model.Source: ETHICS STATEMENT · p. 11

REPRODUCIBILITY STATEMENT

  • The materials provide aggregate results but not executable experiment code, raw outputs, or a complete run manifest.Implementation settings, available prompts, supplementary results, and theoretical proofs are documented in appendices.Source: REPRODUCIBILITY STATEMENT · p. 11

A THEORETICAL ANALYSIS

  • The appendix’s formal geometric results concern embedding-space vectors and do not establish that every vector can be realized as valid text.Results borrowed from smooth optimization and submodular maximization retain their additional assumptions.Source: A THEORETICAL ANALYSIS · p. 14

A.1 EXISTENCE OF A GEOMETRIC GAP

  • For a finite, nonempty occupied set, GapScore attains a maximum on the unit sphere; when the occupied span has dimension below d, its orthogonal complement has dimension d − r and unit vectors there have Defensibility one.Positive-demand existence additionally requires a nonzero projected demand component, and linguistic realizability remains separate.Source: §A.1 · p. 14

A.2 A ONE-SIDED PERTURBATION OF THE ORTHOGONAL DIRECTION

The appendix gives a one-sided condition for improving an orthogonal reference direction, then distinguishes conditional properties of related objectives from guarantees for the implemented search. It also records the pipeline’s vocabulary, avoidance, and diagnostic choices.

A.2 A ONE-SIDED PERTURBATION OF THE ORTHOGONAL DIRECTION

  • When b > am, a positive perturbation of the orthogonal direction locally improves GapScore; the condition is one-sided and does not establish global tightness or optimality.Observed search values exceed the geometric lower bounds by approximately 0.25–10.2%, but these are comparisons to returned solutions, not approximation ratios to unknown optima.Source: §A.2 · p. 15, Table 5 · p. 15

A.3 WHAT THE PRODUCT OBJECTIVE IMPLIES

  • The product objective has a conditional Nash-bargaining interpretation only if the achievable utility pairs meet the stated convexity conditions; the paper does not establish that condition for unit-vector directions.Ambient log-concavity also does not establish geodesic concavity or initialization-independent optimization on the sphere.Source: §A.3 · pp. 15–16

A.4 OPTIMIZATION: SMOOTH GUARANTEES AND THE IMPLEMENTED OBJECTIVE

  • The smooth-objective theorem gives an O(ε^-2) stationarity rate only under its assumptions; the implemented fixed-step search is a multistart heuristic for a nonsmooth objective with no asserted convergence rate.The theorem does not directly cover the exact nearest-neighbor maximum in GapScore.Source: §A.4 · p. 16

A.5 COVERAGE AS A SEPARATE SET OBJECTIVE

  • Exact greedy maximization of auxiliary F achieves F(S_K) ≥ (1 − 1/e)F(S*), but this guarantee does not apply to sequential GapScore search or SetGapScore.Multiplying coverage by average Defensibility need not preserve monotonicity or submodularity.Source: §A.5 · pp. 16–17

A.6 A CONDITIONAL CONNECTION TO SOURCE SELECTION

  • A fixed marginal-relevance score increases with Defensibility under the stated assumptions, but the citation simulation is not shown to satisfy them, so higher GapScore is not shown to cause higher PAWC.The GEO ablation measures GapScore and PAWC separately.Source: §A.6 · p. 17

B.1 SHARED SEARCH AND VOCABULARY

  • The shared vocabulary is screened from tokenizer entries to alphabetic English words of length 3–15, then reduced to the top 10,000; these fixed heuristic weights screen domain vocabulary, while novelty is imposed later.The 13,409 retained words are embedded once, using a dictionary whitelist of 234,454 entries.Source: §B.1 · pp. 17–18

B.2 AVOIDANCE INSTRUCTIONS AND OUTPUT DIAGNOSTICS

  • The generator receives frequent-word and sentence-pattern avoidance instructions as prompts, not enforced decoding constraints; CrossCollision measures mean similarity rather than distance.The diagnostics remain embedding-distance proxies rather than judged novelty scores.Source: §B.2 · p. 18

B.3 GEO SCORING AND SYNTHETIC-DATA FILTERING

This section specifies how the GEO scorer assigns credit and how synthetic-data concepts and examples are filtered. It also notes that matched sample counts do not isolate direction choice from filtering or generation cost.

B.3 GEO SCORING AND SYNTHETIC-DATA FILTERING

  • Equation (9) credits all words in a sentence to source position five when it cites [5], without dividing by the sentence’s citation count or normalizing source scores.The scorer uses the first four supplied competitor claims and appends the candidate at position five; it does not retrieve pages from a deployed engine.Source: §B.3 · p. 18
  • Eight candidate words are reranked by absolute VADER compound score to retain five, and directed methods receive a polarity check that Data Accumulation does not share.The generator receives the target label separately, and the final polarity check uses the sign and thresholds described in Section 3.6.Source: §B.3 · p. 18
  • Equal final sample counts control training-set size but do not isolate direction choice from filtering or equalize generation cost.The earlier self-evaluation returned 100% fidelity for all six methods, while a seed-trained classifier produced unstable rankings; VADER avoids that small-seed classifier but can misread irony or mixed polarity.Source: §B.3 · p. 18

C.1 QUERY GROUPS AND TOPIC DIAGNOSTICS

The diagnostics report query-group coverage and diversity measures, while supplementary studies vary occupied content and realization models. Qualitative excerpts illustrate concept realization but are not human evaluations of originality.

C.1 QUERY GROUPS AND TOPIC DIAGNOSTICS

  • Table 7 breaks down the 90 open-ended queries by question type.The passage identifies the grouping scope but supplies no group counts.Source: §C.1 · p. 19, Table 7 · p. 19
  • Mean final Collision is 0.6915, mean GapScore is 0.2012, and the mean best-direction/competitor statistic is 0.5137; its aggregation is unspecified.The Vendi diagnostic reports mean effective diversity of 2.63 across 20 responses per topic under the chosen cosine kernel.Source: §C.1 · p. 19

C.2 VARYING CONTENT SOURCES AND GENERATION MODELS

  • The mixed-source study pools four models, while separate-source and realization-model studies vary different dependencies and should not be pooled.The supplied tables cover pooled before/after Collision, between-model similarity, separate-source novelty pass, and realization-model comparisons.Source: §C.2 · p. 19, Table 10 · p. 20, Table 11 · p. 20

C.3 QUALITATIVE EXAMPLES

  • The excerpts show concept words realized in generated text, but they are not human originality evaluations and some words remain close to query semantics.The examples are truncated, and lexical substitution is narrower than style-transfer approaches that alter surface form while holding content fixed.Source: §C.3 · p. 21, Table 13 · p. 21

D ADDITIONAL GEO RESULTS

The additional GEO results present candidate positions and direction factors, while the separate multi-generator study reports comparisons that must remain distinct from the main-text experiment. The GEO simulation and market coverage impose important scope limits.

D ADDITIONAL GEO RESULTS

  • The GEO tables present selected candidate positions and direction factors, not verified product specifications or real-world market claims.The simulation does not verify real-world market claims.Source: Table 14 · p. 21, D ADDITIONAL GEO RESULTS · p. 21
  • For the water-filter directions, the highest PAWC and highest GS × PAWC select different candidates.The table reports values directly rather than recomputing products from rounded Demand and Defensibility figures.Source: Table 15 · p. 21, D ADDITIONAL GEO RESULTS · p. 21
  • The GEO simulation lacks a held-out citation check, source-order randomization, and repeated-run intervals; its yoga-mat occupied set covers only three brands and twelve claims.Source: D ADDITIONAL GEO RESULTS · p. 21

E.1 SEPARATE MULTI-GENERATOR RUNS

  • The separate four-generator runs use a different sampling procedure from the main-text budget-matched comparison, so their GPT-4o-mini values should not be pooled.For Qwen, the reported accumulation Vendi is 29.78, making the deficit roughly 2.5%; without repeated runs or intervals, it cannot be dismissed as noise or attributed to model size.Source: §E.1 · p. 22, Table 16 · p. 22

E.2 DIRECTION-SET DIAGNOSTICS AND FIDELITY

The direction-set diagnostics distinguish set-level and mean-direction aggregation from downstream output quality. A qualitative comparison also shows that using three directions can trade diversity against Collision and accuracy relative to one direction.

E.2 DIRECTION-SET DIAGNOSTICS AND FIDELITY

  • GapScore’s set score is approximately 44% higher than its mean-direction score because the two use different aggregations, not because generated-data quality improved.The diagnostics distinguish these direction scores from downstream metrics.Source: §E.2 · p. 22, Table 17 · p. 22
  • Defensibility-only yields Collision 0.259 and Vendi 32.10 despite a negative direction score, so direction diagnostics cannot replace downstream evaluation.Source: §E.2 · p. 22
  • For Gemini-2.0-Flash, K = 3 improved Vendi relative to accumulation but worsened Collision and accuracy, whereas K = 1 improved all three.A full K-sensitivity curve is not reported.Source: §E.2 · p. 22

F AVAILABLE PROMPT TEMPLATES

Appendix F provides verbatim selection and filtering prompts, while describing final answer and synthetic-sample generation prompts qualitatively.

F AVAILABLE PROMPT TEMPLATES

  • Appendix F presents selection and filtering prompts verbatim, but describes final answer and synthetic-sample generation prompts only qualitatively.Source: F AVAILABLE PROMPT TEMPLATES · p. 23

F.1 QWEN CONCEPT SELECTION

  • For concept selection, Qwen receives the query and candidate words, selects up to top_n concrete, creative, unexpected answers while avoiding query-concept synonyms, and uses temperature 0.0 with max_tokens=40.The numerical direction retrieves candidate words; it is not passed directly to the model.Source: §F.1 · p. 23

F.2 ANSWER PLAUSIBILITY FILTER

  • The answer-plausibility filter asks which candidate words could answer the query, excludes synonyms of key query concepts, and returns at most top_n words.Source: §F.2 · p. 23

F.3 GEO PLAUSIBILITY FILTER

  • The GEO plausibility filter applies the same answer-word and synonym criteria while supplying a market description alongside the market query.Source: §F.3 · p. 23

F.4 CITATION SIMULATION

  • Citation simulation requests concise answers grounded only in summarized search results, with inline citations; sentences containing [5] receive position-weighted word-count scores.The scorer uses zero-based sentence indices; the source text lists four competitor claims followed by the candidate claim.Source: §F.4 · p. 23

F.5 TASK-LABEL PLAUSIBILITY FILTER

  • The task-label filter retains words corresponding to valid instances of the classification task, excluding off-topic words and words outside the label space.Source: §F.5 · p. 23

F.6 TEXT-GENERATION INSTRUCTIONS

  • Generation prompts condition on the query or task, three concepts, forbidden words, and recurring sentence patterns; synthetic examples are followed by a polarity check.GEO requests product-claim sentences that avoid competitor-claim duplication, while synthetic-data prompts request labeled examples; exact prompts, decoding settings, and raw completions are not provided.Source: §F.6 · pp. 23–24
Loading 2610.20162v2…