Sub-Laplacian Spectral Hashing for Topological Proximity Indexing
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2026
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| _version_ | 1866902118214926336 |
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| author | Pirolo, Andrés Sebastián |
| author_facet | Pirolo, Andrés Sebastián |
| contents | <p>A vector database index built from millions of embeddings can be searched using only its edge structure-no coordinates required. Sub-Laplacian Spectral Hashing (SLSH) assigns compact binary identifiers to graph nodes by recursively decomposing local sub-Laplacians via their Fiedler eigenvectors, operating exclusively on topology after raw embedding vectors have been discarded. The scheme admits an O(1) candidate-pruning oracle at query time via a single XOR instruction over prefix bits. Three experimental regimes expose a sharp topological dichotomy: substantial accuracy gains as a positional encoding in community-structured graphs; complete signal collapse in scale-free networks, explained by the metric homogenization of preferential attachment; and sustained neighbor enrichment in simulated proximity manifolds. We further derive and empirically validate a Topological Stopping Criterion-the maximum hash depth beyond which spectral computation degrades to noise-expressed entirely in terms of graph degree statistics, and refine it into a deployment rule confirmed across four distinct graph configurations. </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20363911 |
| institution | Zenodo |
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| 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 <p>A vector database index built from millions of embeddings can be searched using only its edge structure-no coordinates required. Sub-Laplacian Spectral Hashing (SLSH) assigns compact binary identifiers to graph nodes by recursively decomposing local sub-Laplacians via their Fiedler eigenvectors, operating exclusively on topology after raw embedding vectors have been discarded. The scheme admits an O(1) candidate-pruning oracle at query time via a single XOR instruction over prefix bits. Three experimental regimes expose a sharp topological dichotomy: substantial accuracy gains as a positional encoding in community-structured graphs; complete signal collapse in scale-free networks, explained by the metric homogenization of preferential attachment; and sustained neighbor enrichment in simulated proximity manifolds. We further derive and empirically validate a Topological Stopping Criterion-the maximum hash depth beyond which spectral computation degrades to noise-expressed entirely in terms of graph degree statistics, and refine it into a deployment rule confirmed across four distinct graph configurations. </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 |
| url | https://doi.org/10.5281/zenodo.20363911 |