发表机构
University of Konstanz; Renmin University of China（康斯坦茨大学; 中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
ibUMAP通过同步场评估和FFT加速，解决了UMAP随机负采样导致的嵌入不稳定问题，在CPU和GPU上实现数倍加速并保持质量。
AI 中文摘要
UMAP通过随机负采样实现可扩展的布局优化。然而，这种随机性可能导致跨重运行和下游重用时的嵌入不稳定，因为估计的排斥力依赖于采样事件的顺序。我们提出了ibUMAP，一种连贯的基于场的替代方案，它从共享的嵌入快照中评估吸引力和排斥力，并同步应用它们。其度加权排斥场由固定嵌入下负采样的条件期望所激发，并由三个标量矩表示，这些矩通过基于插值的FFT方案在CPU和GPU上高效评估。该公式避免了显式的全对计算，同时引入了与标准在线UMAP不同的优化动态。受控实验表明，同步和核截断改变了局部-全局保真度权衡，而FFT评估在最终质量上产生较小的平均变化。端到端基准测试显示，在CPU上，未播种和播种情况下，相对于umap-learn的中位加速分别为3.29倍和5.79倍；在GPU未播种执行下，相对于cuML在百万规模数据集上的加速为1.44倍。这些增益伴随着更大的运行间稳定性和可测量的保真度权衡。
英文摘要
UMAP achieves scalable layout optimization through stochastic negative sampling. However, this stochasticity can lead to unstable embeddings across reruns and downstream reuse, as the estimated repulsive forces depend on the ordering of sampling events. We present ibUMAP, a coherent field-based alternative that evaluates attraction and repulsion from a shared embedding snapshot and applies them synchronously. Its degree-weighted repulsive field is motivated by the conditional expectation of negative sampling for a fixed embedding and represented by three scalar moments, which are evaluated efficiently on CPUs and GPUs using an interpolation-based FFT scheme. This formulation avoids explicit all-pairs computations while inducing optimization dynamics that differ from those of standard online UMAP. Controlled experiments show that synchrony and kernel capping alter the local-global fidelity trade-off, whereas FFT evaluation produces small average changes in final quality. End-to-end benchmarks show median speedups of 3.29x unseeded and 5.79x seeded over umap-learn on CPU, and 1.44x over cuML on million-scale datasets under unseeded GPU execution. These gains accompany greater run-to-run stability and measurable fidelity trade-offs.
Comments35 pages, 11 figures, 18 tables. Under review at ICLR 2027. Code: https://github.com/Bachery/ibUMAP
