e-means Matches K-Means Loss 10x Faster

e-means meaningfully improves the speed–quality frontier for large, static embedding datasets, though its headline gains are workload-specific rather than a universal k-means replacement.

• –EMA centroid updates, cosine scheduling, dead-cluster revival, and fitted scaling laws reduce both optimization cost and hyperparameter tuning.
• –Tests reach Flash-KMeans’ 25-iteration loss in 1.4–2.6 epochs, with 9.5–35.9x GPU speedups across 1M–100M-vector datasets.
• –The DINO10B experiment clusters 10 billion embeddings into 16 million centroids; IVF assignment cuts the reported runtime from 779 to 22.8 GPU-hours.
• –The strongest fit is for high-dimensional, static embeddings used in retrieval, quantization, and data curation; small or low-dimensional datasets remain less certain.
• –The results are empirical, and the largest-scale speedup depends on approximate assignment, so production users should validate loss and recall tradeoffs.