# ibUMAP: Coherent and Scalable Field Evaluation for UMAP Optimization

arXiv: https://arxiv.org/abs/2610.01445 · HTML: https://mlsanity.com/paper/2610.01445/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [ANN-Benchmarks: A Benchmarking Tool for Approximate Nearest Neighbor Algorithms](https://mlsanity.com/paper/1807.05614/) (2018)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
- [Bringing UMAP Closer to the Speed of Light with GPU Acceleration](https://mlsanity.com/paper/2008.00325/) (2020)
- [The Fast Kernel Transform](https://mlsanity.com/paper/2106.04487/) (2021)
- [Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution](https://mlsanity.com/paper/2303.03964/) (2023)
- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [t-SNE Exaggerates Clusters, Provably](https://mlsanity.com/paper/2510.07746/) (2025)
- [FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling](https://mlsanity.com/paper/2605.11428/) (2026)
- [SNAP-tFDP: Massively Scalable Graph Layouts via Sparse Negative Sampling](https://mlsanity.com/paper/2608.01907/) (2026)

## Abstract (arXiv)

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.