arXiv subjects

Ilias Azizi

Publications and source records attributed to Ilias Azizi.

3 recordsLinked to original sources

arXiv2026

From Embedding Geometry to Spectral Search: Energy Dispersion Networks For Vector Retrieval

High-dimensional vector spaces, particularly embedding spaces with dense semantic structure, are often interpreted primarily leveraging solely geometric relationships. In this work, we show that they can also be viewed as spectral energy networks induced by the topology of their underlying feature-space manifold with relevant improvements for downstream tasks. Building on this perspective, we introduce Graph Wiring, a general framework for exploiting feature-space spectral structure, together with Spectral Indexing, its task-specific instantiation for vector search. By coupling geometric similarity with spectral information, the proposed method improves Head-Tail coherence and semantic alignment relative to purely geometric retrieval methods. It further supports adaptive search behavior through tau-modulation, providing the flexibility increasingly required by modern Retrieval-Augmented Generation (RAG) pipelines. We present the complete algorithmic pipeline, establish its theoretical foundation through epiplexity, and evaluate the approach across benchmark and industrial settings using the open-source arrowspace library.

cs.IR↗

arXiv2025

Toward Efficient and Scalable Design of In-Memory Graph-Based Vector Search

Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus, increasing the complexity of their analysis. Vector search is the backbone of many critical analytical tasks, and graph-based methods have become the best choice for analytical tasks that do not require guarantees on the quality of the answers. Although several paradigms (seed selection, incremental insertion, neighborhood propagation, neighborhood diversification, and divide-and-conquer) have been employed to design in-memory graph-based vector search algorithms, a systematic comparison of the key algorithmic advances is still missing. We conduct an exhaustive experimental evaluation of twelve state-of-the-art methods on seven real data collections, with sizes up to 1 billion vectors. We share key insights about the strengths and limitations of these methods; e.g., the best approaches are typically based on incremental insertion and neighborhood diversification, and the choice of the base graph can hurt scalability. Finally, we discuss open research directions, such as the importance of devising more sophisticated data adaptive seed selection and diversification strategies.

cs.IR↗

arXiv2025

Graph-Based Vector Search: An Experimental Evaluation of the State-of-the-Art

Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus, increasing the complexity of their analysis. Vector search is the backbone of many critical analytical tasks, and graph-based methods have become the best choice for analytical tasks that do not require guarantees on the quality of the answers. We briefly survey in-memory graph-based vector search, outline the chronology of the different methods and classify them according to five main design paradigms: seed selection, incremental insertion, neighborhood propagation, neighborhood diversification, and divide-and-conquer. We conduct an exhaustive experimental evaluation of twelve state-of-the-art methods on seven real data collections, with sizes up to 1 billion vectors. We share key insights about the strengths and limitations of these methods; e.g., the best approaches are typically based on incremental insertion and neighborhood diversification, and the choice of the base graph can hurt scalability. Finally, we discuss open research directions, such as the importance of devising more sophisticated data-adaptive seed selection and diversification strategies.

cs.IR↗