In recent years, the widespreadavailability of large-scale, high-dimensionaldatasets has driven significant interest in clustering algorithms that are both computationally efficient and robust to distributional shifts and outliers. The classical clustering method, K-means, can be seen as an application of the Lloyd-Max quantization algorithm, in which the distribution being quantized is the empirical distribution of the points to be clustered. This empirical distribution generally differs from the true underlying distribution, especially when the number of points to be clustered is small. This induces a distributional shift, which can also arise in many real-world settings, such as image segmentation, biological data analysis, and sensor networks, due to noise variations, sensor inaccuracies, or environmental changes. Distributional shifts can severely impact the performance of clustering algorithms, leading to degraded cluster assignments and unreliable downstream analysis. The field of clustering has a rich history. One of the most popular algorithms in this field is theK-means (KM) algorithm, introduced by [1], which computes centroids by iteratively updating the conditional mean of the data in the Voronoi regions induced by the centroids. However, standardK-means is sensitive to initialization and, in general, converges only to a local minimum.

Weight-sharing quantization has emerged as a technique to reduce energy expenditure during inference in large neural networks by constraining their weights to a limited set of values.

As a result, our method significantly accelerates ViTs for dense prediction tasks.