Self-Balancing, Memory Efficient, Dynamic Metric Space Data Maintenance, for Rapid Multi-Kernel Estimation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909593723994112 |
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| author | Ellendula, Aditya S Bajaj, Chandrajit |
| author_facet | Ellendula, Aditya S Bajaj, Chandrajit |
| contents | We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as dynamical systems whose representations evolve during training, requiring fast, adaptive spatial organization. Our two-parameter octree supports logarithmic-time updates and queries, eliminating the need for costly full rebuilds as data distributions shift. We demonstrate its effectiveness in four areas: (1) accelerating Stein variational gradient descent by supporting more particles with lower overhead; (2) enabling real-time, incremental KNN classification with logarithmic complexity; (3) facilitating efficient, dynamic indexing and retrieval for retrieval-augmented generation; and (4) improving sample efficiency by jointly optimizing input and latent spaces. Across all applications, our approach yields exponential speedups while preserving accuracy, particularly in high-dimensional spaces where maintaining adaptive spatial structure is critical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-Balancing, Memory Efficient, Dynamic Metric Space Data Maintenance, for Rapid Multi-Kernel Estimation Ellendula, Aditya S Bajaj, Chandrajit Machine Learning We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as dynamical systems whose representations evolve during training, requiring fast, adaptive spatial organization. Our two-parameter octree supports logarithmic-time updates and queries, eliminating the need for costly full rebuilds as data distributions shift. We demonstrate its effectiveness in four areas: (1) accelerating Stein variational gradient descent by supporting more particles with lower overhead; (2) enabling real-time, incremental KNN classification with logarithmic complexity; (3) facilitating efficient, dynamic indexing and retrieval for retrieval-augmented generation; and (4) improving sample efficiency by jointly optimizing input and latent spaces. Across all applications, our approach yields exponential speedups while preserving accuracy, particularly in high-dimensional spaces where maintaining adaptive spatial structure is critical. |
| title | Self-Balancing, Memory Efficient, Dynamic Metric Space Data Maintenance, for Rapid Multi-Kernel Estimation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2504.18003 |