A Power Law in Logarithm's Clothing: On the Scalability of Graph-Based Vector Search

Most vector databases rely on graph-based indexes, notably HNSW and Vamana, for approximate nearest neighbor search. With embedding models widely adopted, the datasets these databases store grow rapidly. At a fixed accuracy, how does search cost scale with dataset size? The prevailing answer is poly-logarithmic growth. Yet the claim is proven only under special conditions and asserted without proof for the indexes used in practice. It is also largely untested: standard benchmarks measure cost at one dataset size, not across sizes. We put the claim to the test. The answer depends on the scale itself. While the dataset size $N$ is small relative to the data's intrinsic dimensionality, search cost grows as $N^c$ for a constant $0<c<1$. We call this scaling the Sublinear Power Law. Once $N$ is large enough, growth slows to subpolynomial, consistent with the poly-logarithmic claim. The Sublinear Power Law appears on every dataset, mostly up to its full size, at every recall target, query hardness level, and index configuration we test. The transition to subpolynomial growth appears on the two datasets that grow large enough relative to their intrinsic dimensionality. One mechanism underlies both behaviors: a dataset's intrinsic dimensionality grows with its size until the data resolves its underlying distribution. Higher intrinsic dimensionality packs more vectors into the query neighborhood the search must examine. We present a unifying theory of beam-search cost that explains our observations. For exact and bounded-degree constructions, we prove the Sublinear Power Law and the eventual transition to poly-logarithmic scaling, and derive the scale at which it occurs. We also develop models that predict the power-law exponents for any recall target and index configuration. These models give a principled way to navigate trade-offs among search cost, insertion cost, and recall as data grows.

NeuRoute: Logit-Guided Neural Routing for Billion-Scale Vector Search with Sub-Hour Index Construction

Building approximate nearest neighbor (ANN) indexes at billion scale is often dominated by expensive global clustering or graph construction, making time-to-index a first-order systems concern. We present NeuRoute, a learned hashing index that turns short binary codes into an effective routing primitive for large-scale vector search. NeuRoute trains a lightweight neural network encoder with a selective similarity-preserving objective to produce well-balanced binary addresses. During construction, NeuRoute organizes vectors into buckets by their codes and performs bucket-local clustering in the encoder's low-dimensional space to form centroids. At query time, NeuRoute exploits the encoder logits as an uncertainty signal: it uses deviation-to-threshold scores to prioritize uncertain-bit perturbations for query-adaptive multi-bucket probing, scores bucket-local centroids by their distances to the query to form a compact candidate cluster set, and applies centroid-stage gating with heap-quality-driven early stopping to prune low-value clusters before exact refinement. On billion-scale benchmarks, NeuRoute achieves strong accuracy-throughput trade-offs with fast index construction: on BigANN-1B it reaches $90.3\%$ Recall@10 at 2,414 QPS and is $1.7\times$ faster than OPQ+IVF-PQ (refine) at comparable accuracy, while completing end-to-end training+construction in under an hour on both BigANN-1B and Deep1B-1B. These results show that logit-guided neural routing can make hashing competitive as a lightweight ANN indexing framework at billion scale. Source code and artifacts are available at https://github.com/XingqiaoWang/NeuRoute.

AkasicDB: Demonstrating Omni RAG with a Unified Vector-Graph-Relational DBMS

Recent Retrieval-Augmented Generation (RAG) systems increasingly combine vector retrieval with structured knowledge, such as Graph RAG and Filtered vector search. However, existing database architectures struggle to support such complex RAG workflows efficiently, as they rely on out-of-DB pipelines or in-DB non-native integration, leading to high overhead. This demo paper presents AkasicDB, a database system that natively supports such RAG workflows by jointly executing vector similarity search, graph traversal, and relational filtering within a single execution framework. AkasicDB extends our prior work, Chimera, with native vector support to enable such unified execution. Based on AkasicDB, we demonstrate the first native integration of Vector-Graph-Relational RAG, which we refer to as Omni RAG. Through an interactive chat-style demonstration, users execute and visualize Omni RAG queries, directly experiencing its superior retrieval and reasoning over vector-only approaches while observing the practical limitations of existing database architectures in supporting Omni RAG. A demonstration video is available at https://youtu.be/8d09_dtrEIM

QASP: Query-Adaptive Robust Vector Search Policy

A fundamental challenge of vector search is achieving consistently high recall while minimizing computational costs. Fixed search parameters cause significant performance variance across queries, and conventional evaluation on average recall masks these per-query disparities. We introduce QASP (Query-Adaptive robust vector Search Policy), which predicts the complete recall progression curve per query via a single upfront supervised regression, from which a search policy is derived for any recall target; this avoids iterative model invocations during search or separate predictors per target. By predicting normalized recall values with scale-invariant features and pre-search inference, QASP generalizes across recall targets, index configurations, and datasets. Its fine-grained progress predictions further enable a lightweight reactive complement that adjusts search depth based on predicted-versus-observed deviations without additional inference. We prove that QASP requires a finite training sample independent of dataset size and dimensionality, that its loss exceeds the irreducible lower bound of any fixed policy by a vanishing margin, and that its data access savings over fixed probing grow exponentially in intrinsic dimensionality. Experimentally, QASP achieves significantly lower recall variance and deviation from target, higher query satisfaction rate, and scales to large data and hierarchical indices without retraining, achieving 99% recall with 80% less data access.

VecTree-RAG: An Agentic Retrieval-Augmented Generation Framework Combining Vector and Tree Retrieval for Efficiency and Accuracy

Scientific question answering requires a retrieval system to solve two distinct problems: identifying which papers are relevant and locating the supporting evidence within those papers. Conventional retrieval-augmented generation typically addresses both through similarity search over fixed-length passages, flattening document structure and separating scientific claims from their methodological and argumentative context. We present VecTree-RAG, an agentic framework that assigns these tasks to complementary retrieval mechanisms. Vector search ranks compact document and section representations across the corpus, whereas reasoning-guided traversal of source-verified section trees localizes evidence within shortlisted papers. Full text is retained in a page store and exposed progressively only after structural localization. We evaluate VecTree-RAG on 300 QASPER questions, an open-access subset of 54 LitQA2 questions, and 49 multi-document MOSAIC questions. Compared with Dense RAG, reranked Dense RAG, RAPTOR, and Search-o1, VecTree-RAG obtained the highest observed answer score on all three benchmarks, reaching 0.800 LLM-judge correctness on QASPER, 0.925 accuracy on LitQA2, and a 0.547 composite score on MOSAIC. On QASPER, its evidence-page precision was 0.274, compared with 0.046--0.071 for the baselines. LitQA2 ablations further showed that the complete vector--tree architecture required fewer inference tokens than variants without tree navigation or corpus-level vector routing. These results indicate that vector retrieval narrows the corpus-level search space and tree navigation concentrates reading on structurally relevant evidence. Although multi-turn inference remains more expensive than single-call retrieval, VecTree-RAG provides a structure-aware and traceable architecture for scientific literature question answering.

Cluster with Auctions for Vector Search

Large-scale approximate nearest neighbor search commonly relies on partitions for indexing: database vectors are partitioned into clusters, and for each query a probing function selects the clusters to be scanned. The query probing function and the database partition are rarely treated as separate entities: most techniques assign queries with the same assignment function as the database vectors, which is suboptimal especially when database and query distributions differ. This paper introduces CwA (Cluster with Auctions), which addresses this limitation by jointly learning a balanced database partition and a neural probing function. CwA optimizes search performance directly for the query distribution. It minimizes its objective by alternating two steps: (i) gradient descent on the neural network of the probing function, and (ii) a large-scale combinatorial optimization of the cluster assignment for the database vectors. We solve the latter with a parallelizable auction algorithm that balances the partition by design. To further scale CwA, we extend the method to a Cartesian product of clusters that increases the partition's granularity. When database and query distributions differ, CwA achieves up to 4.7$\times$ throughput over the state-of-the-art at equal recall. In the in-distribution (ID) setting, even a simple linear probing function trained with CwA outperforms competing deep neural methods.

When More Documents Hurt RAG: Mitigating Vector Search Dilution with Domain-Scoped, Model-Agnostic Retrieval

Retrieval-augmented generation degrades when scaled to large, heterogeneous document collections, where dense similarity loses discriminative power, and top-k retrieval increasingly returns semantically similar but contextually incorrect chunks. We refer to this failure mode as vector search dilution. Even when using hybrid dense+sparse retrieval, we observed this firsthand in a deployed Wyoming Department of Transportation corpus, where scaling from 54 to 1,128 documents (88,907 chunks) reduced accuracy from 75% to below 40%. To address this dilution, we propose MASDR-RAG ( Multi-Agent Scoped Domain Retrieval for RAG) and evaluate it on 200 expert-validated queries across five LLM backbones, six corpora, and two index stacks. Our results indicate that domain scoping using organizational metadata is the key fix, significantly improving P@10 from 0.77 to 0.86 ($p < 0.05$). Furthermore, our investigation of multi-agent orchestration revealed that a high degree of configuration dependence results --creating what we call the precision-faithfulness paradox. Based on these varied outcomes, our practical recommendation is simple: scope first, then perform a single synthesis call, reserving full multi-agent orchestration for genuinely multi-domain corpora paired with native-tool-call backbones. Code and Data will be made public upon acceptance.