# e-means

e-means replaces the k-means centroid update with a mini-batch exponential moving average and uses fitted scaling laws to set batch size and decay directly from the problem configuration, so no hyperparameter sweep is needed. Across embedding datasets it reaches the loss Lloyd k-means attains at 25 epochs in 1.4 to 2.6 epochs, translating to 9.5 to 45.5 times wall-clock speedups over Flash-KMeans while converging to a lower loss. On DINO10B, the exact-assignment version partitions 10 billion vectors into 16 million clusters in 2.5 epochs at a loss below Lloyd at 25 epochs.

e-means replaces the k-means centroid update with a mini-batch exponential moving average and uses fitted scaling laws to set batch size and decay directly from the problem configuration, so no hyperparameter sweep is needed. Across embedding datasets it reaches the loss Lloyd k-means attains at 25 epochs in 1.4 to 2.6 epochs, translating to 9.5 to 45.5 times wall-clock speedups over Flash-KMeans while converging to a lower loss. On DINO10B, the exact-assignment version partitions 10 billion vectors into 16 million clusters in 2.5 epochs at a loss below Lloyd at 25 epochs.