Research Papers in Vector Search & AI Systems

Field of application: Vector Databases, Spectral Methods, and Agentic AI

A curated collection of foundational and emerging papers that inform the design and implementation of arrowspace, optical compression, and next-generation retrieval systems.

Graph Signal Processing & Spectral Methods

The Emerging Field of Signal Processing on Graphs

Authors: David I Shuman, Sunil K. Narang, Pascal Frossard, Antonio Ortega, Pierre Vandergheynst
arXiv: 1211.0053 (2012)

Foundational work extending classical signal processing operations to graph-structured data. This paper establishes the theoretical framework for spectral graph analysis used in arrowspace’s energy-distance metrics and Laplacian-based search.

Key contributions: Graph Fourier Transform, spectral filtering, and multi-resolution analysis on irregular graph domains.

What Is Positive Geometry?

Authors: Kristian Ranestad, Bernd Sturmfels, Simon Telen
arXiv: 2502.12815 (2025)

Foundational introduction to positive geometry—an interdisciplinary field bridging particle physics, cosmology, and algebraic geometry. Positive geometries are tuples \((X, X_{\geq 0}, \Omega(X_{\geq 0}))\) consisting of a complex algebraic variety, a semi-algebraic positive region, and a canonical differential form satisfying recursive axioms. The framework represents physical observables (scattering amplitudes, cosmological correlators) as geometric structures like amplituhedra and cosmological polytopes.

Relevance to arrowspace: The canonical form construction—recovering volume integrals from positive regions via \(\Omega(P) = \text{vol}(P-x)^\circ dx\)—directly parallels arrowspace’s energy map pipeline. Just as positive geometry “linearizes” high-dimensional semi-algebraic varieties into canonical differential forms, arrowspace’s energymaps.rs constructs a graph Laplacian over the data manifold and projects it onto a 1-dimensional taumode spectrum (Rayleigh quotients). Both frameworks encode complex geometric structures (amplituhedra / energy graphs) as scalar fields that preserve topological invariants while enabling efficient computation.

Key contributions:

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Agentic Systems & Planning

RPG: A Repository Planning Graph for Unified and Scalable Codebase Generation

Authors: ZeroRepo Team
arXiv: 2509.16198 (2025)

Introduces the Repository Planning Graph (RPG), a graph-driven framework for generating complete software repositories. Relevant to formal agent protocols and structured generation workflows.

Key contributions: Persistent graph representations unifying proposal- and implementation-level planning for autonomous code generation.

Retrieval Fundamentals & Limitations

On the Theoretical Limitations of Embedding-Based Retrieval

Authors: Orion Weller et al. (Google DeepMind)
arXiv: 2508.21038 (2025)

Theoretical analysis proving fundamental limitations of single-vector embeddings for complex retrieval tasks. Introduces the LIMIT benchmark to expose failure modes in cosine-similarity-based retrieval.

Key contributions: Sign-rank bounds on embedding expressiveness, motivating energy-distance and spectral approaches beyond cosine similarity.

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Document Reranking

jina-reranker-v3: Last but Not Late Interaction for Document Reranking

Authors: Feng Wang, Yuqing Li, Han Xiao
arXiv: 2509.25085v2 (2025)

State-of-the-art 0.6B parameter multilingual document reranker achieving 61.94 nDCG@10 on BEIR. Demonstrates lightweight alternatives to generative listwise reranking.

Key contributions: Late-interaction architecture for efficient cross-encoder reranking with strong BEIR performance.

Context Compression & Recursive Models

Recursive Language Models

Authors: Alex Zhang, Omar Khattab (MIT CSAIL)
Paper: alexzhang13.github.io/blog/2025/rlm

Proposes Recursive Language Models (RLMs), where models recursively call themselves to decompose and interact with unbounded context. RLM with GPT-4-mini outperforms full GPT-4 by 87% on long-context benchmarks.

Key contributions: Divide-and-conquer strategy for handling 10M+ token contexts without performance degradation, mitigating “context rot.”

Quantum Computing & Hybrid Systems

Mind the Gaps: The Fraught Road to Quantum Advantage

Authors: Jens Eisert, John Preskill
arXiv: 2510.19928 (2025)

Perspectives on the transition from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant application-scale quantum computing. Identifies four key hurdles including error mitigation, scalable fault tolerance, and verifiable algorithms.

Relevance: Explores hybrid classical-quantum systems for optimization and simulation tasks relevant to graph algorithms and energy minimization.

Computational Methods in Software Engineering

Vulnerability2Vec: A Graph-Embedding Approach for Enhancing Vulnerability Classification

Source: Tech Science Press - CMES 2025

Vulnerability2Vec converts Common Vulnerabilities and Exposures (CVE) text explanations to semantic graphs.

Key contributions: Security vulnerability; graph representation; graph-embedding; deep learning; node classification.

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Implementation Resources

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