Iterative Single-Keyword Refinement (ISKR)

• ISKR is an algorithmic framework that iteratively refines a seed query by adding or removing single keywords to precisely target result clusters.
• The method calculates benefit, cost, and value for each keyword modification, effectively balancing precision and recall while optimizing search output.
• By leveraging cluster-based feedback, ISKR enhances semantic disambiguation and improves the classification of ambiguous or exploratory queries.

Iterative Single-Keyword Refinement (ISKR) is an algorithmic framework for generating expanded keyword queries tailored to result clusters in information retrieval systems. ISKR iteratively modifies a seed query—by adding or removing keywords—to optimize retrieval performance for a specific result cluster, balancing precision and recall through a principled, greedy refinement procedure. ISKR is particularly relevant in contexts where user-issued queries are ambiguous or exploratory, and result clustering enables more precise semantic disambiguation of search intent.

1. Motivation and Conceptual Foundation

The motivation for ISKR emerges from the observation that conventional query expansion methods—primarily corpus-driven approaches that select popular words from retrieval results—often fail to capture the full semantic spectrum of a query, particularly in the presence of ambiguity or multifaceted intents. Typical expanded queries may miss relevant results or reflect only a subset of the possible meanings in the corpus (Liu et al., 2011).

ISKR directly addresses this by using the clustering of initial retrieval results as ground truth for query expansion. For each cluster, the aim is to generate an expanded query whose retrieval set closely matches—that is, maximizes both the inclusion and exclusion correspondences—the cluster content. This granular optimization contrasts with global, corpus-level approaches and enables a classification of results corresponding to distinct interpretations of the user’s query.

2. Core Algorithmic Procedure

ISKR operates in an iterative, greedy manner, refining the query through single-keyword addition or removal. The algorithm maintains a set of candidate keywords derived from the union of the target cluster $C$ and the complementary set $U$ (all other results).

At each iteration, for every keyword $k$ not currently in the query $q$ (or for removal candidates already present), ISKR computes three central quantities:

• Benefit $(\text{benefit}(k, q))$: Quantifies the improvement in precision when $k$ is added to $q$, i.e., the number (or ranking score) of results from $U$ (non-cluster) that are excluded by the addition of $k$.
• Cost $(\text{cost}(k, q))$: Quantifies the loss in recall, or exclusion of desired results from $C$, when $k$ is added.
• Value $(\text{value}(k, q))$: Defined as the ratio $\text{benefit}(k, q) / \text{cost}(k, q)$. If both benefit and cost are zero, value is set to zero.

In the case of removal, analogous computations are performed with benefit defined as increased recall and cost as increased inclusion of results from $U$.

At each step, the keyword (addition or removal) with the highest value is selected. If the top value exceeds 1, the query is modified accordingly and the computation proceeds. Values for only the affected keywords in candidate set $K$ are updated after each change, providing computational efficiency.

The process terminates when no keyword modification can further increase the F-measure (a harmonic mean of precision and recall), producing a query optimized for the current cluster.

Pseudocode Overview

The essential steps of ISKR can be condensed as follows:

def ISKR(user_query, cluster_C, noncluster_U): q = user_query K = keywords_in(C | U) T = priority_queue() # keyword candidates # Initialize keyword values for addition/removal for k in K: if k not in q: benefit = S(R(q) & (U - E(k))) cost = S(R(q) & (C - E(k))) value = benefit / cost if cost else 0 T.insert(k, value) else: # analogous computations for removal while T.not_empty(): k_star = T.top_value_keyword() if value(k_star, q) <= 1: break if k_star not in q: q.add(k_star) else: q.remove(k_star) T.update_affected_values() return q

Where $E(k)$ is the set of results not containing $k$, $S(\cdot)$ computes ranking scores or counts, and $R(q)$ denotes the set of results from the current query.

3. Theoretical Formulation and Optimization Objective

ISKR formalizes per-cluster query expansion as an APX-hard problem, with the goal of maximizing the F-measure between the refined query’s results and the ground-truth cluster. Each cluster corresponds to an interpretation, and the locally optimal query identifies documents associated with that meaning while excluding others. The greedy strategy for benefit/cost ratio selection is effective in practice, though it does not guarantee global optimality (Liu et al., 2011).

Through dynamic updates of keyword statistics after each addition/removal, ISKR avoids full recomputation of scores at every iteration, resulting in computationally tractable execution even for large result sets.

4. Practical Implications and System Integration

Within cluster-driven query expansion frameworks, ISKR supports result classification and improves user search experience. By generating a distinct refined query for each cluster, it enables granular disambiguation, particularly when user queries are underspecified or polysemic.

ISKR’s output queries function as classifiers for clusters, providing near-ideal separation between relevant and irrelevant results. Empirical evaluation in (Liu et al., 2011) shows high F-measure for the expanded queries compared to baseline methods and demonstrates superior relevance and interpretability in user studies.

The computational overhead from iterative refinement is moderate, mainly attributable to scores maintenance and candidate filtering, but justifiable given the improvement in classification quality for ambiguous queries.

Expansion Method	Interpretability	Precision/Recall Balance	Computational Burden
Popular keywords	Low	Poor	Low
TF-IDF ranking	Medium	Variable	Low-Medium
ISKR	High	High	Medium

5. Relationship to Iterative Refinement Paradigms and Reward Hacking

Iterative refinement, where an output is successively optimized using internal feedback, is a key paradigm in modern information retrieval and generative LLMing. ISKR represents an instantiation where feedback is restricted to individual keyword impacts.

Recent research on iterative self-refinement in LLMs (Pan et al., 5 Jul 2024) identifies risks associated with reward hacking, wherein the iterative process optimizes a proxy metric (evaluator ratings) at the expense of true quality. ISKR’s more constrained feedback channel—operating primarily on single keywords—may make it less susceptible to such vulnerabilities; however, careful design is still needed to avoid gaming or spurious refinement.

A plausible implication is that limiting feedback scope, as in ISKR, can mitigate collusion between optimization and evaluation modules, reducing divergence between proxy and true objectives. Insights from reward hacking studies suggest further robustness can be achieved by decoupling context between evaluator and refiner and occasionally using external validation.

6. Comparative Perspectives and Related Approaches

ISKR contrasts with dense retrieval and RAG frameworks, such as IterKey (Hayashi et al., 13 May 2025), which also employ iterative keyword refinement but use LLMs to generate, validate, and regenerate keywords for enhanced RAG performance. IterKey’s three-stage loop (generation, answer, validation) operationalizes LLM-driven refinement with sparse retrieval (BM25), achieving both accuracy and interpretability.

While IterKey leverages LLMs to “think aloud” and revalidate outputs for answer quality, ISKR focuses on per-keyword benefit/cost for optimizing document classification within clusters. There is convergence in the emphasis on iterative self-feedback and human-readable query evolution; ISKR remains more strictly formalized in the explicit measurement of retrieval metrics per iteration, providing deterministic guarantees of precision–recall improvement.

7. Limitations and Future Directions

ISKR’s greedy optimization may at times yield locally but not globally optimal queries. Its performance is tightly coupled to the quality of initial result clustering; poor clusters limit the algorithm’s capacity for effective separation.

Future work may investigate hybrid approaches combining the interpretability of ISKR and the contextual sophistication of LLM-driven iterative refinement (as embodied by IterKey), especially in domains where user intent is complex or multimodal. Integrating external forms of validation and further minimizing shared context between refinement steps could provide additional safeguards against optimization artifacts analogous to reward hacking.

In sum, ISKR embodies a principled, efficient, and interpretable mechanism for query expansion and result classification in information retrieval, contributing significantly to the advancement of search quality for ambiguous and exploratory queries in clustered result environments (Liu et al., 2011).