$k$-means has historically been positioned primarily as an offline processing primitive, typically used for dataset organization or embedding preprocessing rather than as a first-class component in online systems. In this work, we revisit this classical algorithm under the lens of modern AI system design and enable $k$-means as an online primitive. We point out that existing GPU implementations of $k$-means remain fundamentally bottlenecked by low-level system constraints rather than theoretical algorithmic complexity. Specifically, the assignment stage suffers from a severe IO bottleneck due to the massive explicit materialization of the $N \times K$ distance matrix in High Bandwidth Memory (HBM). Simultaneously, the centroid update stage is heavily penalized by hardware-level atomic write contention caused by irregular, scatter-style token aggregations. To bridge this performance gap, we propose flash-kmeans, an IO-aware and contention-free $k$-means implementation for modern GPU workloads. Flash-kmeans introduces two core kernel-level innovations: (1) FlashAssign, which fuses distance computation with an online argmin to completely bypass intermediate memory materialization; (2) sort-inverse update, which explicitly constructs an inverse mapping to transform high-contention atomic scatters into high-bandwidth, segment-level localized reductions. Furthermore, we integrate algorithm-system co-designs, including chunked-stream overlap and cache-aware compile heuristics, to ensure practical deployability. Extensive evaluations on NVIDIA H200 GPUs demonstrate that flash-kmeans achieves up to 17.9$\times$ end-to-end speedup over best baselines, while outperforming industry-standard libraries like cuML and FAISS by 33$\times$ and over 200$\times$, respectively.

翻译：传统上，$k$-means主要被视为一种离线处理原语，通常用于数据集组织或嵌入预处理，而非作为在线系统中的一等组件。在本工作中，我们从现代人工智能系统设计的视角重新审视这一经典算法，并将其实现为在线原语。我们指出，现有的GPU版$k$-means实现从根本上仍受限于底层系统约束，而非理论算法复杂度。具体而言，分配阶段因在高速带宽内存中显式物化庞大的$N \times K$距离矩阵而遭受严重的IO瓶颈；同时，质心更新阶段因不规则、分散式令牌聚合引发的硬件级原子写竞争而严重受限。为弥合此性能差距，我们提出flash-kmeans——一种面向现代GPU工作负载的IO感知且无竞争的$k$-means实现。Flash-kmeans引入两项核心内核级创新：(1) FlashAssign：将距离计算与在线argmin融合，完全绕过中间内存物化；(2) 排序逆映射更新：显式构建逆映射，将高竞争性的原子分散操作转化为高带宽、分段级的局部归约。此外，我们整合了算法-系统协同设计，包括分块流重叠与缓存感知编译启发式策略，以确保实际可部署性。在NVIDIA H200 GPU上的大量实验表明，flash-kmeans相比最佳基线实现了高达17.9$\times$的端到端加速，并分别以33$\times$和超过200$\times$的性能优势超越行业标准库cuML与FAISS。