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Welfarist Formulations for Diverse Similarity Search

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
Vector SearchApproximate Nearest Neighbor SearchNash Social Welfare
Abstract:

Nearest Neighbor Search (NNS) is a fundamental problem in data structures with wide-ranging applications, such as web search, recommendation systems, and, more recently, retrieval-augmented generations (RAG). In such recent applications, in addition to the relevance (similarity) of the returned neighbors, diversity among the neighbors is a central requirement. In this paper, we develop principled welfare-based formulations in NNS for realizing diversity across attributes. Our formulations are based on welfare functions---from mathematical economics---that satisfy central diversity (fairness) and relevance (economic efficiency) axioms. With a particular focus on Nash social welfare, we note that our welfare-based formulations provide objective functions that adaptively balance relevance and diversity in a query-dependent manner. Notably, such a balance was not present in the prior constraint-based approach, which forced a fixed level of diversity and optimized for relevance. In addition, our formulation provides a parametric way to control the trade-off between relevance and diversity, providing practitioners with flexibility to tailor search results to task-specific requirements. We develop efficient nearest neighbor algorithms with provable guarantees for the welfare-based objectives. Notably, our algorithm can be applied on top of any standard ANN method (i.e., use standard ANN method as a subroutine) to efficiently find neighbors that approximately maximize our welfare-based objectives. Experimental results demonstrate that our approach is practical and substantially improves diversity while maintaining high relevance of the retrieved neighbors.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces welfare-based formulations for diverse nearest neighbor search, grounding diversity-relevance trade-offs in mathematical economics. It resides in the 'Welfare Function Approaches' leaf, which contains only this paper within the broader 'Welfare-Based and Principled Formulations for Diverse Search' branch. This positioning reflects a sparse research direction: while the taxonomy includes 50 papers across diverse methods, the welfare-theoretic approach appears underexplored. The paper's focus on Nash social welfare and axiomatic foundations distinguishes it from the more populated heuristic and constraint-based branches, suggesting it occupies a relatively novel conceptual space within the field.

The taxonomy reveals neighboring work in 'Graph-Based Diverse Similarity Search' (one sibling paper using two-stage retrieval) and extensive activity in 'Heuristic and Constraint-Based Diversity Methods' (spanning spatial metrics, attribute-based approaches, and greedy constraints). The paper diverges from these by replacing fixed diversity constraints with adaptive welfare functions that balance relevance and diversity in a query-dependent manner. While graph-based methods prioritize indexing efficiency and constraint-based approaches enforce hard diversity thresholds, this work offers a parametric framework rooted in economic principles. The taxonomy's scope notes explicitly exclude welfare-theoretic foundations from heuristic branches, underscoring the conceptual gap this paper addresses.

Among 11 candidates examined across three contributions, no clearly refuting prior work was identified. The core welfare-based formulation examined zero candidates, suggesting limited direct precedent in the search scope. The algorithmic contribution examined one candidate without refutation, while the parametric trade-off mechanism examined ten candidates, none providing overlapping prior work. This limited search scale (11 papers, not hundreds) means the analysis captures top semantic matches and citations but cannot claim exhaustive coverage. The absence of refutations within this scope suggests the welfare-theoretic framing and parametric control represent relatively fresh angles, though broader literature may contain related ideas not surfaced here.

Given the constrained search scope and sparse taxonomy positioning, the work appears to introduce a principled perspective underrepresented in the examined literature. The welfare-based formulation and adaptive balancing mechanism contrast with prevalent heuristic and constraint-driven methods. However, the analysis reflects top-30-scale semantic search, not comprehensive field coverage, leaving open the possibility of related welfare-theoretic or economic approaches in adjacent communities (e.g., fair ranking, social choice) not captured by this taxonomy.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
11
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Balancing diversity and relevance in nearest neighbor search. The field addresses the challenge of retrieving results that are both similar to a query and sufficiently varied to avoid redundancy. The taxonomy reveals a rich landscape spanning principled formulations, algorithmic techniques, and application domains. Welfare-Based and Principled Formulations (including works like Welfarist Diverse Search[0]) ground diversity objectives in formal frameworks, while Heuristic and Constraint-Based Diversity Methods offer practical trade-offs. Graph-Based Indexing (e.g., Graph Diverse Search[3], K-Diverse Neighbor Graph[28]) and Hashing approaches (Early Termination LSH[4]) tackle scalability through specialized data structures. Meanwhile, Exploration-Exploitation Trade-Off in Interactive and Adaptive Search (Exploratory Search Parameterization[13], Interactive Relevance Tradeoff[43]) and Recommendation Systems with Diversity-Accuracy Trade-Offs (Diversified Preference Network[14], BDARec[16]) emphasize user-centric adaptation. Approximate Diverse k-Nearest Neighbor Algorithms (Approximate Diverse KNN[36][40], Anytime Neighbor Diversity[15]) and Ensemble methods (ANN Ensemble Diversity[27]) focus on computational efficiency, while Feature Weighting and Distance Metric Learning refine similarity measures themselves. Several active lines of work highlight contrasting priorities. Graph-based indexing methods pursue efficient diverse neighbor retrieval at scale, often trading exact optimality for speed, whereas welfare-based formulations emphasize principled objective functions that capture user utility more rigorously. Interactive and recommendation-oriented branches explore dynamic adaptation to user feedback, balancing exploration of novel items against exploitation of known preferences. The original paper, Welfarist Diverse Search[0], sits squarely within the Welfare Function Approaches, offering a theoretically grounded perspective that contrasts with more heuristic strategies like Efficient Diversity Search[12] or constraint-driven methods. Compared to graph-centric works such as Graph Diverse Search[3] or Two-Stage Neighborhood Selection[1], Welfarist Diverse Search[0] prioritizes formal welfare criteria over indexing efficiency, positioning it as a principled foundation for understanding diversity-relevance trade-offs rather than an engineering-focused solution.

Claimed Contributions

Welfare-based formulations for diverse similarity search

The authors introduce novel formulations for nearest neighbor search that incorporate diversity using welfare functions from mathematical economics, specifically Nash social welfare and p-mean welfare. These formulations balance relevance and diversity in a query-dependent manner without requiring fixed diversity quotas.

0 retrieved papers
Efficient algorithms with provable guarantees for welfare-based objectives

The authors develop polynomial-time algorithms for optimizing their welfare-based objectives. For single-attribute settings, they provide an exact greedy algorithm that can leverage any ANN method as a subroutine. For multi-attribute settings, they provide a 0.63-approximation algorithm despite NP-hardness.

1 retrieved paper
Parametric control of relevance-diversity trade-off via p-mean welfare

The authors extend their framework to p-mean welfare functions that interpolate between pure relevance (p equals 1) and pure diversity (p approaches negative infinity), giving practitioners a tunable parameter to adjust the balance between these objectives based on application needs.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Welfare-based formulations for diverse similarity search

The authors introduce novel formulations for nearest neighbor search that incorporate diversity using welfare functions from mathematical economics, specifically Nash social welfare and p-mean welfare. These formulations balance relevance and diversity in a query-dependent manner without requiring fixed diversity quotas.

Contribution

Efficient algorithms with provable guarantees for welfare-based objectives

The authors develop polynomial-time algorithms for optimizing their welfare-based objectives. For single-attribute settings, they provide an exact greedy algorithm that can leverage any ANN method as a subroutine. For multi-attribute settings, they provide a 0.63-approximation algorithm despite NP-hardness.

Contribution

Parametric control of relevance-diversity trade-off via p-mean welfare

The authors extend their framework to p-mean welfare functions that interpolate between pure relevance (p equals 1) and pure diversity (p approaches negative infinity), giving practitioners a tunable parameter to adjust the balance between these objectives based on application needs.

Table of Contents