Self-balancing, Memory Efficient, Dynamic Metric Space Data Maintenance, For Rapid Multi-kernel Estimation

Abstract

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, parti

Stats

• citations0
• S2 citations—
• github stars0
• HF likes0
• heat score0.00
• arxiv keyellendula2025self

Related papers

• Dynamic Metric Learning From Pairwise Comparisons (2016)3.58
• Dynamic Sampling For Deep Metric Learning (2020)5.84
• Variance & Greediness: A Comparative Study Of Metric-learning Losses (2026)0.00
• Accurate And Fast Retrieval For Complex Non-metric Data Via Neighborhood Graphs (2019)0.00
• Metric Learning For Dynamic Text Classification (2019)6.34
• Efficient Autotuning Of Hyperparameters In Approximate Nearest Neighbor Search (2018)6.77
• On Simplifying Large-scale Spatial Vectors: Fast, Memory-efficient, And Cost-predictable K-means (2024)5.24
• A Practical Index Structure Supporting Fr\'echet Proximity Queries Among Trajectories (2020)6.34