The paper introduces the Support Vector Graph (SVG), a graph index for vector search that uses kernel methods to guarantee navigability in both metric and non‑metric vector spaces, such as inner product similarity. It shows that popular indices like HNSW and DiskANN are special cases of SVG, and proposes SVG‑L0, which adds an ℓ₀ sparsity constraint to enforce bounded out‑degree while maintaining computational efficiency.
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
arXiv:2606. 10295v1 Announce Type: cross Abstract: The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry.
arXiv:2609.36359v1 Announce Type: new Abstract: Graph-based approximate nearest neighbor search (ANNS) is widely used for large-scale semantic search. Its indices are constructed primarily based on g...
arXiv:2606. 18520v1 Announce Type: cross Abstract: Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space.
arXiv:2603. 06660v2 Announce Type: replace-cross Abstract: Approximate Nearest Neighbor Search (ANNS) is fundamental to modern AI applications.
arXiv:2608.22980v1 Announce Type: cross Abstract: Dense vector retrieval has become the foundation of modern semantic search, yet existing approximate nearest neighbor (ANN) indexes treat an embeddin...
The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.
The paper introduces linear‑time randomized algorithms for unbiased approximation of general random walk kernels (RWKs) on sparse graphs, covering both labelled and unlabelled cases. By sampling dependent random walks and constructing novel graph embeddings in ρ^d, the method avoids building the direct product graph, enabling scaling to massive datasets that cannot fit on a single machine. The authors provide exponential concentration bounds for the estimator’s sharpness and demonstrate up to 27× speed‑ups and 128× larger graph handling compared to previous cubic‑time approaches.
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
arXiv:2607. 02338v2 Announce Type: replace-cross Abstract: Hierarchical Navigable Small World (HNSW) graphs serve as the industry standard due to their logarithmic complexity and strong empirical performance.
arXiv:2502. 17614v3 Announce Type: replace Abstract: The rapid growth of graph data creates significant scalability challenges as most graph algorithms scale quadratically with size.
arXiv:2505. 21285v5 Announce Type: replace Abstract: This work proposes a framework LGKDE that learns kernel density estimation for graphs.