Tensor Manifold-Based Graph-Vector Fusion for AI-Native Academic Literature Retrieval

TL;DR

This paper introduces a tensor manifold-based framework for AI-native academic literature retrieval, addressing existing limitations in graph-vector fusion methods with a theoretically grounded, scalable approach.

Contribution

It proposes a novel geometry-unified graph-vector fusion framework based on tensor manifold theory, enabling efficient, AI-native, and scalable literature retrieval.

Findings

The framework achieves linear time and space complexity.

It unifies graph topology and vector embedding through tensor manifold theory.

The approach effectively handles large-scale dynamic academic graphs.

Abstract

The rapid development of large language models and AI agents has triggered a paradigm shift in academic literature retrieval, putting forward new demands for fine-grained, time-aware, and programmable retrieval. Existing graph-vector fusion methods still face bottlenecks such as matrix dependence, storage explosion, semantic dilution, and lack of AI-native support. This paper proposes a geometry-unified graph-vector fusion framework based on tensor manifold theory, which formally proves that an academic literature graph is a discrete projection of a tensor manifold, realizing the native unification of graph topology and vector geometric embedding. Based on this theoretical conclusion, we design four core modules: matrix-independent temporal diffusion signature update, hierarchical temporal manifold encoding, temporal Riemannian manifold indexing, and AI-agent programmable retrieval. Theoretical analysis and complexity proof show that all core algorithms have linear time and space complexity, which can adapt to large-scale dynamic academic literature graphs. This research provides a new theoretical framework and engineering solution for AI-native academic literature retrieval, promoting the industrial application of graph-vector fusion technology in the academic field.