Sub-Laplacian Spectral Hashing for Topological Proximity Indexing
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866902118172983296 |
|---|---|
| author | Pirolo, Andrés Sebastián |
| author_facet | Pirolo, Andrés Sebastián |
| contents | <p> </p> <p><strong>Description</strong></p> <p>Modern semantic search depends on <strong>expensive distance computations</strong> over massive embedding indices, where this single operation can dominate inference cost. This work poses a deliberately unconventional question: <strong>can such an index be queried using only its connectivity—its raw topology—after every coordinate vector has been permanently deleted?</strong></p> <p>We answer <strong>yes</strong>. Each node is assigned a <strong>compact binary identifier</strong> built by recursively bisecting the graph along its spectral structure. Nodes sharing a prefix naturally fall within the same region of the network. As a result, <strong>candidate retrieval reduces to a single bitwise (XOR) operation per node</strong>—no distances are computed during pruning, and <strong>no embeddings are stored</strong>.</p> <p>The central contribution is not only computational but <strong>predictive</strong>. Whether the method yields a strong signal—or none at all—is governed by a <strong>single classical graph statistic</strong> that can be computed in seconds. This:</p> <ul> <li><strong>Refutes the assumption</strong> that well-defined communities are required for the method to work.</li> <li><strong>Challenges the belief</strong> that high-dimensional embeddings inherently degrade performance.</li> <li>Provides a <strong>prior diagnostic rule</strong>: one number determines in advance whether a network is richly indexable or topologically silent.</li> </ul> <p>We trace this behavior from <strong>idealized lattice structures</strong>, through varying embedding dimensionalities, to a <strong>real-world collaboration network</strong> indexed in <strong>sub-second time on mobile hardware</strong>, without GPU acceleration.</p> <p>The result is a <strong>storage-free, constant-time routing layer for graph databases</strong>, together with a <strong>practical criterion to predict its effectiveness before deployment</strong>.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20370836 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Sub-Laplacian Spectral Hashing for Topological Proximity Indexing Pirolo, Andrés Sebastián Core Method: Sub-Laplacian Spectral Hashing Semantic proximity graphs Topological Memory Alignment Gnn Gcn L1 memory hash Hashing memory Vector Databases Spatial Indexing Dimensionality Reduction Topological Memory Alignment Semantic proximity graphs Llm graph neural network Watts-Strogatz GraphRAG <p> </p> <p><strong>Description</strong></p> <p>Modern semantic search depends on <strong>expensive distance computations</strong> over massive embedding indices, where this single operation can dominate inference cost. This work poses a deliberately unconventional question: <strong>can such an index be queried using only its connectivity—its raw topology—after every coordinate vector has been permanently deleted?</strong></p> <p>We answer <strong>yes</strong>. Each node is assigned a <strong>compact binary identifier</strong> built by recursively bisecting the graph along its spectral structure. Nodes sharing a prefix naturally fall within the same region of the network. As a result, <strong>candidate retrieval reduces to a single bitwise (XOR) operation per node</strong>—no distances are computed during pruning, and <strong>no embeddings are stored</strong>.</p> <p>The central contribution is not only computational but <strong>predictive</strong>. Whether the method yields a strong signal—or none at all—is governed by a <strong>single classical graph statistic</strong> that can be computed in seconds. This:</p> <ul> <li><strong>Refutes the assumption</strong> that well-defined communities are required for the method to work.</li> <li><strong>Challenges the belief</strong> that high-dimensional embeddings inherently degrade performance.</li> <li>Provides a <strong>prior diagnostic rule</strong>: one number determines in advance whether a network is richly indexable or topologically silent.</li> </ul> <p>We trace this behavior from <strong>idealized lattice structures</strong>, through varying embedding dimensionalities, to a <strong>real-world collaboration network</strong> indexed in <strong>sub-second time on mobile hardware</strong>, without GPU acceleration.</p> <p>The result is a <strong>storage-free, constant-time routing layer for graph databases</strong>, together with a <strong>practical criterion to predict its effectiveness before deployment</strong>.</p> <p> </p> |
| title | Sub-Laplacian Spectral Hashing for Topological Proximity Indexing |
| topic | Core Method: Sub-Laplacian Spectral Hashing Semantic proximity graphs Topological Memory Alignment Gnn Gcn L1 memory hash Hashing memory Vector Databases Spatial Indexing Dimensionality Reduction Topological Memory Alignment Semantic proximity graphs Llm graph neural network Watts-Strogatz GraphRAG |
| url | https://doi.org/10.5281/zenodo.20370836 |